a systems analysis of sustainable groundwater management

A Systems Analysis of Sustainable Groundwater Management in California:

Homology and Isomorphology with Monetary Policy

by

Guy Wallace Bates Jr., B.S., M.S., P.E.

A Dissertation

In

Systems and Engineering Management

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

Doctor of Philosophy

Approved

Mario G. Beruvides, Ph.D., P.E.

Chair of Committee

Milton Smith, Ph.D., P.E.

Jennifer Cross, Ph.D.

Clifford Fedler, Ph.D.

Mark Sheridan, Ph.D.

Dean of the Graduate School

Texas Tech University, Guy Wallace Bates Jr., May 2017

ii

ACKNOWLEDGEMENTS

I would like to express my gratitude to my entire committee for their help in

this process. Without the help, advice and encouragement of Dr. Beruvides, Dr.

Fedler, Dr. Smith and Dr. Cross, this dissertation would not have been possible. I

would also like to thank Steve Phillips, Scott Boyce and Randy Hansen of the USGS

for granting me access to their groundwater data and providing insight into the

complexities of groundwater systems.


iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .................................................................................. ii

TABLE OF CONTENTS ..................................................................................... iii

LIST OF TABLES ............................................................................................. viii

LIST OF FIGURES ............................................................................................. ix

CHAPTER I - INTRODUCTION TO RESEARCH ......................................... 1

1.1 History and Background ............................................................................. 1

1.2 Problem Statement ...................................................................................... 4

1.3 Research Questions ..................................................................................... 5

1.3.1 Research Question for Research 1 ..................................................... 5

1.3.2 Research Question for Research 2 ..................................................... 6

1.4 General Hypotheses .................................................................................... 7

1.4.1 Research 1 Hypotheses ...................................................................... 8 1.4.2 Research 2 Hypotheses ...................................................................... 9

1.5 Research Format........................................................................................ 10

1.6 Research Purpose ...................................................................................... 11

1.6.1 Theoretical Purpose .......................................................................... 11 1.6.2 Practical Purpose .............................................................................. 12

1.7 Research Objective.................................................................................... 12

1.7.1 Theoretical Objectives ..................................................................... 12 1.7.2 Practical Objectives .......................................................................... 12

1.8 Delimitations ............................................................................................. 13

1.8.1 Limitations ....................................................................................... 13 1.8.2 Assumptions ..................................................................................... 14

1.9 Relevance of this study ............................................................................. 15

1.10 Need for this Research ............................................................................ 16

1.11 Benefits of this Research ......................................................................... 16

1.11.1 Theoretical Benefits ....................................................................... 16 1.11.2 Practical Benefits ........................................................................... 17

1.12 Research Outputs and Outcomes ............................................................ 17

1.12.1 Theoretical Outcomes .................................................................... 17 1.12.2 Practical Outcomes......................................................................... 17


iv

CHAPTER II - LITERATURE REVIEW ........................................................ 18

2.1 Introduction ............................................................................................... 18

2.2 The Nature of Water.................................................................................. 19

2.2.1 The Value of Water .......................................................................... 20

2.2.2 Water as an economic good ............................................................. 21 2.2.3 Marginal Cost ................................................................................... 22 2.2.4 Subtractable Good – Competing Uses ............................................. 23

2.3 Water Resource Sustainability .................................................................. 23

2.3.1 Sustainability Defined ...................................................................... 24

2.3.2 Externalities...................................................................................... 25

2.3.3 Stewardship ...................................................................................... 27

2.3.4 Recycled Water ................................................................................ 27 2.3.5 Recycled Water in California ........................................................... 29 2.3.6 Is water recycling a sustainable practice? ........................................ 34

2.4 System Archetypes in Water ..................................................................... 36

2.4.1 Fixes that Fail ................................................................................... 37 2.4.2 Limits to Growth .............................................................................. 39

2.4.3 Tragedy of the Commons ................................................................. 40

2.5 Groundwater Management ........................................................................ 44

2.5.1 Groundwater in the United States .................................................... 45

2.5.2 Groundwater in California ............................................................... 48

2.5.3 Groundwater as Savings ................................................................... 51 2.5.4 Groundwater as Credit ..................................................................... 53 2.5.5 Groundwater Management Tools ..................................................... 56

2.5.6 Aggregate Groundwater Demand .................................................... 58 2.5.7 Contractionary Groundwater Policy in California ........................... 59

2.6 Economic Theory ...................................................................................... 62

2.6.1 General Equilibrium Theory ............................................................ 62

2.6.2 Loanable Funds Theory ................................................................... 63 2.6.3 Endogenous Credit Theory .............................................................. 63

2.7 Monetary Theory ....................................................................................... 64

2.7.1 Keynesian Theory ............................................................................ 64 2.7.2 Post-Keynesian Theory .................................................................... 65 2.7.3 Monetarist Theory ............................................................................ 66 2.7.4 New Classical Theory ...................................................................... 66

2.8 Monetary Policy ........................................................................................ 66

2.8.1 Monetary Policy Tools ..................................................................... 67 2.8.2 Credit ................................................................................................ 69 2.8.3 Aggregate Demand........................................................................... 70


v

2.8.4 Contractionary Monetary Policy ...................................................... 71

2.9 Systems Analysis ...................................................................................... 71

2.9.1 General Systems Theory .................................................................. 72 2.9.2 Open and Closed Systems ................................................................ 73

2.9.3 Stock and Flow ................................................................................. 73 2.9.4 Feedback and Delay ......................................................................... 74 2.9.5 Systemic Overshoot ......................................................................... 75 2.9.6 Dynamic Equilibrium ....................................................................... 75 2.9.7 Confidence Testing and Validation .................................................. 76

2.9.8 Statistical Validation Methods ......................................................... 84

2.10 Analogy, Homology and Isomorphology ................................................ 87

2.10.1 Analogy .......................................................................................... 88 2.10.2 Homology ....................................................................................... 88 2.10.3 Isomorphology ............................................................................... 89

CHAPTER III - RESEARCH 1: SYSTEM DYNAMIC MODEL FOR

SUSTAINABLE GROUNDWATER MANAGEMENT ................................. 91

3.1 Abstract ..................................................................................................... 91

3.2 Introduction ............................................................................................... 91

3.3 Research Methodology.............................................................................. 92

3.3.1 System Dynamics Modeling ............................................................ 92

3.3.2 Statistical Analysis ........................................................................... 93

3.4 Hypotheses ................................................................................................ 94

3.5 General Procedures ................................................................................. 100

3.5.1 Year-over-year Simulation ............................................................. 100

3.5.2 Successive 5-year simulations........................................................ 101 3.5.3 Successive 10-year simulations...................................................... 101

3.6 Data ......................................................................................................... 102

3.6.1 Water Data ..................................................................................... 102

3.7 Model Development and Parameters ...................................................... 106

3.7.1 Model Development ....................................................................... 106

3.7.2 General Water System Parameters ................................................. 108 3.7.3 Cuyama System Parameters ........................................................... 109 3.7.4 Pajaro System Parameters .............................................................. 112 3.7.5 Modesto System Parameters .......................................................... 116

3.8 Model Validation Procedures .................................................................. 119

3.8.1 Expert Review ................................................................................ 119 3.8.2 Structural Validation Tests ............................................................. 120


vi

3.8.3 Behavioral Validation Tests ........................................................... 129

3.8.4 Policy Implication Tests ................................................................. 140

3.9 Analysis Procedures ................................................................................ 144

3.9.1 Statistical Analysis ......................................................................... 144

3.9.2 Goodness of Fit .............................................................................. 144 3.9.3 Cumulative Error ............................................................................ 146 3.9.4 Error Decomposition ...................................................................... 146 3.9.5 Regression Analysis ....................................................................... 148

3.10 Results and Discussion .......................................................................... 149

3.10.1 Cuyama Models ........................................................................... 149 3.10.2 Pajaro Models .............................................................................. 152

3.10.3 Modesto Models ........................................................................... 154

3.11 Hypothesis Test Results ........................................................................ 156

3.12 Methodological Concerns ..................................................................... 159

3.13.1 Reliability ..................................................................................... 159

3.13.2 Validity ......................................................................................... 159 3.13.3 Bias ............................................................................................... 159

3.13.4 Replicability ................................................................................. 160

3.13 Discussion and Conclusions .................................................................. 160

3.14.1 Discussion of Results ................................................................... 161

3.14.2 Conclusions .................................................................................. 164

3.14 References ............................................................................................. 166

CHAPTER IV – RESEARCH 2: EXPLORATORY STUDY - POTENTIAL

ISOMORPHOLOGY BETWEEN GROUNDWATER AND MONETARY

SYSTEMS .......................................................................................................... 169

4.1 Abstract ................................................................................................... 169

4.2 Introduction ............................................................................................. 170

4.3 Research Methodology............................................................................ 170

4.3.1 Structural Homology ...................................................................... 171 4.3.2 Behavioral Comparison .................................................................. 172

4.4 Hypotheses .............................................................................................. 172

4.5 Procedures ............................................................................................... 175

4.5.1 Systems Analysis and Structural Homology .................................. 175 4.5.2 Behavioral Comparison Procedures ............................................... 175

4.6 Parameters and Variables ........................................................................ 176

4.6.1 Economic Parameters ..................................................................... 176


vii

4.7 Data ......................................................................................................... 177

4.7.1 Economic Data ............................................................................... 177

4.8 Structural Homology Analysis.......................................................... 178

4.9 Behavioral Comparison ........................................................................... 187

4.10 Hypothesis Test Results ........................................................................ 197

4.11 Methodological Concerns ..................................................................... 199

4.11.1 Bias ............................................................................................... 199 4.11.2 Replicability ................................................................................. 200

4.12 Discussion and Conclusions .................................................................. 200

4.13 References ............................................................................................. 201

CHAPTER V – GENERAL CONCLUSIONS AND RECOMMENDATIONS

FOR FUTURE RESEARCH ............................................................................ 203

5.1 General Conclusions ............................................................................... 203

5.2 Recommendations for Future Research .................................................. 206

REFERENCES .................................................................................................. 208

BIBLIOGRAPHY ............................................................................................. 225

APPENDIX ........................................................................................................ 248

Appendix A - Definitions .............................................................................. 248

Appendix B- Groundwater Data for the Modesto Region (Philips, Rewis, &

Traum, 2015) ................................................................................................. 250

Appendix C - Groundwater Data for the Pajaro Valley (Hanson, Lear, &

Lockwood, 2014) .......................................................................................... 253

Appendix D - Groundwater Data for the Cuyama Valley (Hanson, Flint, Faunt,

Gibbs, & Schmid, 2015) ............................................................................... 256

Appendix E - Economic Data for the United States ..................................... 261

Appendix F – Economic Analysis................................................................. 264

Appendix G – Simulation Results ................................................................. 271

Appendix H – Expert Review Questions ...................................................... 282

Appendix I – Research Log........................................................................... 283


viii

LIST OF TABLES

Table 2.1 Tests of Model Structure (Forrester & Senge, 1979). ........................... 82

Table 2.2 Tests of Model Behavior (Forrester & Senge, 1979). ........................... 83

Table 2.3 Tests of Policy Implications (Forrester & Senge, 1979). ...................... 84

Table 2.4 Summary of Statistical Metrics in the Literature. ................................. 87

Table 3.1 Null and Alternative Hypotheses. ......................................................... 94

Table 3.1 Null and Alternative Hypotheses, Continued. ...................................... 95

Table 3.2 Null and Alternative Sub-hypotheses for Hypothesis 1. ....................... 95

Table 3.2 Null and Alternative Sub-hypotheses for Hypothesis 1,

Continued. ..................................................................................... 96

Table 3.3 Null and Alternative Sub-hypotheses for Hypothesis 2. ....................... 96

Table 3.4 Sub-hypotheses test for Hypothesis 1 in Mathematical Form. ............. 97

Table 3.5 Sub-hypotheses test for Hypothesis 2 in Mathematical Form. ............. 98

Table 3.6 Test / Hypothesis Matrix. ...................................................................... 99

Table 3.7 Cuyama System Parameters. ............................................................... 110

Table 3.8 Pajaro System Parameters. .................................................................. 112

Table 3.8 Pajaro System Parameters, Continued. ............................................... 113

Table 3.9 Modesto System Parameters. .............................................................. 116

Table 3.9 Modesto System Parameters, Continued. ........................................... 117

Table 3.10 Selected Structural Validity Tests. .................................................... 120

Table 3.11 Selected Behavioral Validity Tests. .................................................. 129

Table 3.12 Cuyama 1-year Simulation. .............................................................. 150

Table 3.13 Cuyama 5-year Simulation. .............................................................. 151

Table 3.14 Cuyama 10-year Simulation.............................................................. 151

Table 3.15 Pajaro 1-year Simulation. .................................................................. 152

Table 3.16 Pajaro 5-year Simulation. .................................................................. 153

Table 3.17 Pajaro 10-year Simulation. ................................................................ 154

Table 3.18 Modesto 1-year Simulation. .............................................................. 155

Table 3.19 Modesto 5-year Simulation. .............................................................. 155

Table 3.20 Modesto 10-year Simulation. ............................................................ 156

Table 3.21 Sub-hypotheses Results for Hypothesis 1. ........................................ 157

Table 3.22 Sub-hypotheses Results for Hypothesis 2. ........................................ 158


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Table 4.1 Null and Alternative Hypotheses. ....................................................... 174

Table 4.2 End Dates of Monetary Tightening Periods (Adrian &

Estrella, 2008). ............................................................................ 176

Table 4.3 Structural Elements. ............................................................................ 180

Table 4.4 Policy Levers....................................................................................... 181

Table 4.5 Aggregate Demand Response to Interest Rate Increase. .................... 188

Table 4.6 Aggregate Demand Response to Reserve Requirement

Increase (Adapted from (Board of Governors of the

Federal Reserve System, n.d.). .................................................... 192

Table 4.7 Results for Sub-hypothesis 1............................................................... 197

Table 4.8 Results for Sub-hypothesis 3............................................................... 199

LIST OF FIGURES

Figure 2.1. EPA Suggestions for Recycled Water Treatment and Use ................ 31

Figure 2.2 Fixes that Fail Generic Archetype (Braun, 2002). ............................... 38

Figure 2.3 Inter-Basin Transfers (Gohari, et. al, 2013). ........................................ 38

Figure 2.4 Limits to Growth Archetype (Braun, 2002). ....................................... 39

Figure 2.5 Tragedy of the Commons Generic Archetype (Braun, 2002).............. 40

Figure 2.6. Groundwater depletion rates from 1900 to 2000. (Konikow

L. F., 2015). ................................................................................... 46

Figure 2.7. Groundwater depletion rates from 2000 to 2008. ............................... 47

Figure 2.8. California Water use by Hydrologic Region (Water

Education Foundation, 2015) (Values in thousand acre-

feet). .............................................................................................. 50

Figure 2.9. Central Valley Aquifer system in predevelopment condition ............ 52

Figure 2.10. Central Valley Aquifer system in post-development

condition ....................................................................................... 52

Figure 2.11. Credit and Savings in an Aquifer. Adapted from

(California Department of Water Resources, 2003). .................... 55

Figure 2.12. Monetary Policy Tools (O'Brien, 2007). .......................................... 68

79

Figure 2.13. Simplified Modeling Process (Qudrat-Ullah & Seong,

2010). ............................................................................................ 79

Figure 2.14. Major Aspects of Model Validation (Barlas, 1989). ........................ 81


x

Figure 3.1 Groundwater Data for the Modesto Region, California

(Philips, Rewis, & Traum, 2015). ............................................... 103

Figure 3.2 Groundwater Data for the Pajaro Valley, California

(Hanson, et. al., 2014). ................................................................ 104

Figure 3.3 Groundwater Data for the Cuyama Valley, California

(Hanson, et. al., 2015). ................................................................ 105

Figure 3.4 Cuyama Hydrologic System. ............................................................. 111

Figure 3.5 Pajaro Hydrologic System. ................................................................ 115

Figure 3.6 Modesto Hydrologic System. ............................................................ 118

Figure 3.7 Cuyama Annual Structure Test. ......................................................... 121

Figure 3.8 Cuyama Cumulative Structure Test. .................................................. 122

Figure 3.9 Pajaro Annual Structure Test. ............................................................ 123

Figure 3.10 Pajaro Cumulative Structure Test. ................................................... 124

Figure 3.11 Modesto Annual Structure Test. ...................................................... 124

Figure 3.12 Modesto Cumulative Structure Test. ............................................... 125

Figure 3.13 Cuyama Low Precipitation Test. ..................................................... 127

Figure 3.14 Pajaro Low Precipitation Test. ........................................................ 127

Figure 3.15 Modesto Low Precipitation Test. ..................................................... 128

Figure 3.16 Cuyama Annual Behavior Test. ....................................................... 130

Figure 3.17 Cuyama Cumulative Behavior Test. ................................................ 131

Figure 3.18 Pajaro Annual Behavior Test. .......................................................... 132

Figure 3.19 Pajaro Cumulative Behavior Test. ................................................... 133

Figure 3.20 Modesto Annual Behavior Test. ...................................................... 134

Figure 3.21 Modesto Cumulative Behavior Test. ............................................... 135

Figure 3.22 Cuyama Zero Pumpage Test. ........................................................... 137

Figure 3.23 Pajaro Zero Ag Pumpage Test. ........................................................ 138

Figure 3.24 Modesto Low Pumpage Test. .......................................................... 139

Figure 3.25 Cuyama Policy Implications Test. ................................................... 141

Figure 3.26 Pajaro Policy Implications Test. ...................................................... 142

Figure 3.27 Modesto Policy Implications Test. .................................................. 143

Figure 3.28 Cuyama 5-year Cumulative Change in Storage............................... 162

Figure 3.29 Modesto 5-year Cumulative Change in Storage. ............................. 164

Figure 4.1 Groundwater System Diagram. ......................................................... 183


xi

Figure 4.2 Monetary Policy Diagram.................................................................. 184

Figure 4.3 Cuyama Pump Tax Test. ................................................................... 190

Figure 4.4 Modesto Pump Tax Test. ................................................................... 191

Figure 4.5 Cuyama Reserve Requirement Test................................................... 194

Figure 4.6 Modesto Reserve Requirement Test. ................................................. 195


1

CHAPTER I

INTRODUCTION TO RESEARCH

1.1 History and Background

Fresh water is unlike any other economic good. It is a natural resource with

multiple benefits, which are vital to all life on earth. It is ubiquitous, yet often scarce.

It is part of a complex, dynamic system in which use, waste and reuse impact other

uses. In water-scarce areas like California, overexploitation of water resources can

stress the entire system. It can reduce water quality, damage aquifer structure, and

harm the natural environment.

On a global scale, water is a plentiful resource existing in various states of

stock and flow. The prospect of exhausting the global fresh water supply is of little

concern to the general population (Gleick & Palaniappan, 2010). The total stock of

fresh water on earth is approximately 35 million km3 (Sivakumar, 2011). Humans

only consume around 0.01% of that supply annually, and much of that is replenished

through the natural hydrologic cycle. Unfortunately, the majority of the existing

supply is located far from major agricultural and population centers (Sivakumar,

2011).

Groundwater is an important resource for modern society and an important part

of the overall water resource portfolio. In the United States groundwater makes up

approximately 22% of the fresh water consumed (Water in the West, 2013). It

represents up to 40% in the arid western states like California (Carle, 2009).

Unfortunately, consumption of groundwater has become unsustainable in many

groundwater basins.

The overexploitation of groundwater is commonly considered an example of a

system archetype called the Tragedy of the Commons (Meadows, Meadows, Randers,

& Behrens, 1972). Solutions to the problem of aquifer overexploitation, like many

commons dilemmas, lie in management rather than technology. Recently, the

California legislature enacted three bills collectively known as the Sustainable


2

Groundwater Management Act of 2014. This act mandates the creation of

groundwater management agencies (GMAs) (California Association of Water

Agencies, 2014). These GMAs are charged with developing and implementing

groundwater management plans to reduce overconsumption and create sustainable

groundwater basins. The GMAs will be allowed to monitor pumping rates, assess fees

and regulate groundwater withdrawals as necessary to bring consumption to

sustainable levels.

This new groundwater policy appears to be analogous to “tightening”

monetary policy in which the Federal Reserve (Fed) curtails credit growth to maintain

sustainable economic growth. Groundwater is an important source of natural credit

(Hudson & Donovan, 2014). It can help us through periods of drought just as

financial credit can help us manage fluctuations in cash flow. However, unrestricted

access to groundwater credit can push demand to unsustainable levels. In this way, the

role of groundwater credit in the groundwater system is similar to the role or credit in

our monetary system. In either system, credit is a way of supporting current levels of

consumption at the expense of future consumption.

History shows that the Fed has been successful in past attempts to curtail

growth. However, there have been times when monetary policy has constrained credit

growth too quickly resulting in a “credit crunch” or “credit crisis.” A credit crunch

can result in a reinforcing cycle in which investment, employment, asset values and

aggregate demand spiral downward. The goal of tightening monetary policy is to

facilitate a controlled contraction rather than a systemic shock with drastic negative

consequences.

If groundwater policy makers intend to curtail the growth of groundwater

consumption or contract demand to sustainable levels, they risk creating a

“groundwater credit crunch”. The goal should be to control the rate of contraction to

achieve sustainable levels without the crippling consequences of a credit crunch. To

accomplish this goal, regulators will need to understand the impact of reducing water

consumption so that contraction can occur at a manageable rate. Knowledge about

how to accomplish this goal may be found in finance and monetary policy.


3

There are many similarities between the fields of water policy and finance.

Terms like budget, overdraft, and banking are used in both fields. While these terms

have different meanings for the different fields, the similarities are sufficient to enable

a general conceptual understanding across both fields. A financial budget is analogous

to a water budget. In many ways, they are more similar than different.

Analogies are helpful because they relate well-understood concepts to

confusing concepts in a way that permits greater understanding. However, the

similarities between analogous concepts are usually weak. Extrapolating analogous

concepts too far can lead to incorrect understanding and action. Water banking may

be considered analogous to financial banking. Both involve storage, but the policies

and procedures used by a commercial bank will probably not help with banking

groundwater. Extrapolating analogous concepts too far can lead to incorrect

understanding and action (Bertalanffy, 1969).

Similarities between disparate fields can be truly useful if they are structural.

When the components and structure of a concept can be mapped directly to a different

concept the relationship is said to be homological. Identifying a homological

relationship is valuable because knowledge about one concept can increase the

understanding of the homologous concept in the system of the same general class or

structure.

When components interact with each other, they are said to have a systemic

structure. This structure dictates how system components interact, and the resulting

patterns of behavior. When two systems have similar components and systemic

structure, they will produce similar patterns of behavior. If the similarity is sufficient,

the relationship between the two concepts or systems can be said to be

isomorphological.

Identifying a homological and isomorphological relationship between two

systems is valuable because knowledge about how actions in one system affect

patterns of behavior can provide insight into how similar actions will affect patterns of

behavior in the other system. However, identifying isomorphism can be difficult. It


4

involves a combination of systems analysis, structural comparison and behavioral

comparison. Currently, there is no universally accepted methodology for identifying

isomorphisms.

Developing a system dynamics model for use in groundwater management can

provide a useful tool for testing groundwater management policies and strategies. If

this model can be used to show that groundwater systems and monetary systems are

isomorphic, then it may be possible to use knowledge about monetary policy to inform

groundwater management. Specifically, knowledge gained about how monetary

policy can be used to contract aggregate demand in the economy can assist managers

tasked with reducing groundwater consumption. Ideally, this model, combined with

knowledge about monetary policy will help facilitate a contraction to sustainable

groundwater use without creating a “groundwater credit crunch”.

1.2 Problem Statement

Groundwater is a unique and critical resource. This is particularly true in

California, where groundwater consumption has become unsustainable in many

groundwater basins. This reliance on groundwater to support population growth and

agricultural consumption is similar to a reliance on credit to support economic growth.

Credit, in financial terms, is the use of someone else’s money to raise one’s standard

of living in the present with the promise of future repayment. The use of groundwater

can be seen as credit because users borrow groundwater to support current water use

with the expectation that it will be repaid with future recharge. Pumping at

unsustainable rates is a form of deficit spending. The resulting groundwater overdraft

is similar to financial debt. As groundwater stocks become depleted, policy makers

have realized the need to reduce consumption to sustainable levels. Contracting

groundwater consumption to sustainable levels can potentially create a downward

spiral in output similar to a credit crunch that occurs when monetary policy is used to

contract economic growth. The problem is that contracting groundwater consumption


5

can create a downward spiral in output similar to a credit crunch that occurs when

monetary policy is used to contract economic growth.

It will be important to minimize the systemic shock that could be associated

with the contraction of groundwater consumption. Doing so will require an in-depth

understanding of the system. Information about systems that are homologous and

isomorphic to the groundwater system may help policy makers and managers make

better decisions about how to address the problems associated with contraction to

sustainability. If a model of a groundwater system that is based on the structure of

monetary systems can predict groundwater behavior, it may strengthen the argument

that the two systems are isomorphic.

1.3 Research Questions

The primary goal of this research is to develop and test a system dynamics

model of groundwater systems in California. The structure of the proposed model is

based on the structure of monetary systems. The secondary goal of this research is to

explore the potential for isomorphisms between groundwater systems and monetary

systems. The primary research questions and related sub questions for this study are

provided below

1.3.1 Research Question for Research 1

The primary research questions for research 1 are: What aspects of

groundwater systems can be modeled with a system dynamics model based on the

structure of monetary policy systems? What are the implications for groundwater

management? This research will involve the creation of a system dynamics model and

comparison to historical groundwater data. It will include model validation testing

appropriate for system dynamics models as identified by Forrester and Senge (1979)

and Barlas (1989 & 1996).

Research 1 includes several sub-questions.


6

Sub-question 1: How closely does output from the system dynamics model fit

historical groundwater data?

Sub-question 2: What system parameters are the most sensitive for model calibration.

Sub-question 3: What policy actions (parameter changes), or combination of policy

actions in the groundwater management model, if any, reduce aggregate groundwater

demand?

Sub-question 4: What policy actions (parameter changes), or combination of policy

actions in the groundwater management model, if any, increase groundwater storage

and avoid a groundwater credit crunch?

1.3.2 Research Question for Research 2

Research 2 is an exploratory study to evaluate the potential isomorphic relationship

between groundwater systems and monetary systems. The primary research question

for research 2 is: What structural and behavioral similarities, if any, support the

assertion of an isomorphology between groundwater systems and monetary systems

when considered in a contractionary environment?

The following sub-questions are also addressed in research 2.

Sub-question 1: What systemic structures (feedback loops and/or causal links)

in groundwater systems, if any, are similar to systemic structures in monetary systems

when considered in a contractionary environment?

Sub-question 2: What structural elements (stocks, flows, and/or policy levers)

of the groundwater system, if any, can be mapped to structural elements of the

monetary system on a one-to-one basis? Mapping structural elements is the process of

identifying structural elements of a system, and there position in the system, then

comparing them to corresponding elements in the other system. Elements that can be

mapped between two systems demonstrate a structural relationship beyond ordinary

analogy.


7

Sub-question 3: What policy levers in groundwater systems, if any, are

logically equivalent to monetary policy levers? Policy levers are structural elements

with parameters that can be changed by policy in order to change system output and/or

dynamic equilibrium. Logical equivalence is defined as two policy levers performing

the same function within their respective system. This equivalence is identified

through logical argument and observed changes in system behavior due to similar

changes in equivalent parameters.

Sub-question 4: What policy levers in the groundwater system, if any, can be

mapped to the policy levers the monetary system on a one-to-one basis? Policy levers

that can be mapped between two systems must occupy the same position in the system

and perform a logically equivalent function.

Sub-question 5: What systemic behaviors in groundwater systems, if any, are

similar to systemic behaviors in monetary systems when considered in a

contractionary environment?

Sub-question 6: What policy levers in groundwater systems, if any, create

changes in behavior-over-time that are similar to those produced by the operation of

logically equivalent policy levers in monetary systems?

Sub-question 7: What policy (parameter) changes in groundwater management

systems, if any, create changes in behavior-over-time that are in the same direction as

those observed in the United States monetary system during periods of monetary

tightening?

Sub-question 8: Are groundwater and monetary systems governed by

mathematical equations of similar form?

1.4 General Hypotheses

The general hypotheses for this proposed research are provided below:


8

1.4.1 Research 1 Hypotheses

The primary hypotheses for research 1 are:

Hypothesis 1: A system dynamics that is based on the structure of monetary

policy systems is a valid model of a groundwater system.

Hypothesis 2: A system dynamics groundwater model based on the structure of

monetary policy systems can produce behavior-over-time that matches historical

groundwater data with accuracy that is sufficient for the purposes of testing

groundwater policy.

There is no single, accepted test for the validity of a system dynamics model.

Instead, several tests are used to build confidence in the model. Hypothesis 1 will be

accepted or rejected based on a preponderance of evidence derived from several

relevant verification tests identified by Forrester and Senge (1979) and Barlas (1989 &

1996). These tests pertain to model structure, behavior and policy implications. The

relevant verification tests are identified below as sub-hypotheses for hypothesis 1.

Sub-hypothesis 1.1: The proposed model will pass structure verification tests.

Sub-hypothesis 1.2: The proposed model will pass parameter verification tests.

Sub-hypothesis 1.3: The proposed model will pass extreme conditions tests.

Sub-hypothesis 1.4: The proposed model will pass boundary adequacy tests

related to structure.

Sub-hypothesis 1.5: The proposed model will pass dimensional consistency

tests.

Sub-hypothesis 1.6: The proposed model will pass behavior reproduction tests

through calibration and comparison.

Sub-hypothesis 1.7: The proposed model will pass behavior anomaly tests.


related to behavior.


9

Sub-hypothesis 1.9: The proposed model will pass extreme policy tests related

to behavior.


related to policy.

Sub-hypothesis 1.11: The proposed model will pass policy sensitivity tests.

Sub-hypothesis 1.12: The proposed model will pass review from experts in the

field of groundwater resources.

Hypothesis 2 will require comparison of model output to observed system

behavior. Hypothesis 2 will be accepted or rejected based on a preponderance of

evidence derived from several statistical tests identified by Sterman (1984).

Regression analysis is used to provide a basis for comparison with traditional

statistical methods. The relevant statistical tests are identified below as sub-hypotheses

for hypothesis 2.

Sub-hypothesis 2.1: The proposed model will demonstrate a Percent Root

Mean Square Error (RMSPE) of less than 5%.

Sub-hypothesis 2.2: The fraction of total error attributed to systemic bias in the

model will be less than 10% of the total error.

Sub-hypothesis 2.3: Regression analysis comparing model output to observed

behavior will result in a coefficient of determination (R2) of 0.90 or higher.

1.4.2 Research 2 Hypotheses

Research 2 is an exploratory study intended to evaluate the potential for

isomorphology between groundwater systems and monetary systems. However, there

is no single accepted test for isomorphology. As such, this research is only intended to

compare the structure and behavior of these two systems to evaluate the potential for

isomorphology.

Hypothesis 3: Groundwater systems and monetary systems exhibit sufficient

structural and behavioral similarities to support the assertion that they are isomorphic.


10

The three sub-hypotheses below are interim hypotheses intended to support the

primary hypothesis.

Sub-hypothesis 3.1: Groundwater systems and the monetary systems

demonstrate structural similarity sufficient to support the assertion of structural

homology. This hypothesis is necessary to relate the structure of groundwater systems

to the structure of monetary systems, which is the first step in demonstrating the

potential for system isomorphology.

Sub-hypothesis 3.2: A system dynamics model of a groundwater system that is

based on the structure of a monetary system will produce behavior representative of

behavior in groundwater systems. This is a dynamic hypothesis linking structure and

behavior through the use of system dynamics modeling. The dynamic groundwater

model to be developed with this research connects monetary system structure with

groundwater system behavior. This is a critical second step for demonstrating the

potential for system isomorphology.

Sub-hypothesis 3.3: Policy actions (parameter changes) in the groundwater

system will result in changes in aggregate groundwater demand that are in the same

direction as changes in aggregate economic demand when similar policy changes are

made in the monetary system. This hypothesis links behavior of groundwater systems

to behavior of monetary systems and is the final step in demonstrating potential

system isomorphology.

Sub-hypothesis 3.4: Groundwater and monetary systems are governed by

mathematical equations of similar form.

1.5 Research Format

This dissertation is in a two-paper format. The research is both qualitative and

quantitative. Research 1 incudes model development, verification and validation.

Research 2 provides a qualitative approach to evaluate the potential for systemic

isomorphology.


11

In Research 1, a system dynamics model of the groundwater system is

developed based on the monetary system. Quantitative methods and statistical

analysis techniques are used to compare the behavior of the system dynamics model to

data from calibrated physical models developed by the United States Geological

Survey (USGS). This model is used to analyze the behavior of the groundwater

system during a policy driven contraction.

In Research 2, a qualitative comparison of model structure and modeled

system behavior is used to evaluate the potential systemic isomorphology. Systems

analysis techniques are used to evaluate the potential structural homology between

groundwater management and monetary policy based on logical, mathematical and

theoretical mapping of structural elements (policy levers, parameters, stocks, flows

and causal loops) in each system to corresponding elements in the other system.

Finally, systemic behavior from the groundwater system model is compared to

observed behavior in the United States monetary system.

1.6 Research Purpose

The primary purpose of this research is to increase the body of knowledge

about system isomorphology and sustainable groundwater management. This purpose,

like most research, has theoretical and practical aspects.

1.6.1 Theoretical Purpose

The theoretical purpose of this research is to explore the systemic similarities

between groundwater management and monetary policy in order to evaluate the

potential systemic isomorphology. Knowledge about monetary systems is much more

developed than knowledge about groundwater management. Identifying an

isomorphological relationship between two systems is valuable because knowledge

about how actions in one system affect patterns of behavior can provide insight into

how similar actions will affect patterns of behavior in the other system. This research

may allow for the application of policies that are effective in monetary systems to be


12

applied to groundwater management. The exploratory study performed in Research 2

will help guide future research regarding the potential isomorphology between these

two systems.

1.6.2 Practical Purpose

The practical purpose of this research is to develop a systems dynamics model

of the groundwater management system based on the monetary system. This model

may provide insight into the complex groundwater system that is difficult to see in

traditional groundwater models. Such a model may be used to evaluate the

implications of various groundwater management strategies and policies. System

dynamics modeling may be a less expensive process than the traditional physical

modeling used by the USGS.

1.7 Research Objective

This research has several objectives including a thorough review of

groundwater management and monetary policy from a systems perspective. The

general objective is to use systems analysis and systems modeling to help understand

groundwater management. There are also specific theoretical and practical research

objectives.

1.7.1 Theoretical Objectives

The primary theoretical objective is to evaluate the potential for structural

homology and systemic isomorphology between monetary and groundwater systems.

If this research can show sufficient potential for isomorphology, it may provide the

basis for future research.

1.7.2 Practical Objectives

There are two practical objectives for this research. The first practical

objective is to develop a system dynamics model of the groundwater system based on

the monetary system. The development of a system dynamics model can help


13

groundwater managers to better understand the complexities of groundwater systems.

Any specific groundwater system will require a unique model. The process of model

development will help managers identify the information and key parameters

necessary to develop their own unique model. It will also identify the most sensitive

parameters.

The second practical objective is to use the systems dynamics model to

illustrate the potential implications of various policy actions on groundwater

consumption. This may also help managers make better policy decisions and

communicate the rational for groundwater policies to the people that are effected by

the transition to sustainable groundwater management.

1.8 Delimitations

This research, like most research is subject to limitations and assumptions that

serve to confine the scope and protect against misapplication of the results. The

following sections identify the limitations and assumptions associated with this

research project.

1.8.1 Limitations

The research is limited to groundwater management and monetary policy in a

contractionary environment. Due to the nature of groundwater, it is not necessary to

consider policies designed to facilitate expansion of groundwater use. As such,

monetary policies aimed at economic expansion are not considered.

This research examines the structure and behavior of the system in the context

of United States monetary policy. The structure of monetary systems vary. Although

this research may be applicable to other monetary systems, they are not considered

herein.

Groundwater systems also vary. This research is limited to groundwater basins

in California. The specific regions under consideration are the Modesto groundwater

region in the Central Valley, the Cuyama Valley Groundwater Basin in Santa Barbara


14

County, and the Pajaro Valley Groundwater Basin in Santa Cruz and Monterey

Counties. The research regarding groundwater management is generally limited to

California where the government is attempting to transition to sustainable groundwater

management.

1.8.2 Assumptions

Several assumptions were made regarding this research. The primary

assumption is that a transition to sustainable groundwater management will require a

reduction or contraction in groundwater consumption. Furthermore, it is assumed that

knowledge about contractionary monetary policy will be valuable for contractionary

groundwater management policy. It should be noted that there may be other ways to

achieve sustainable groundwater systems that are beyond the scope of this research.

This project proceeds under the assumption that groundwater management and

monetary policy can be modeled as a system of interrelated elements. It is also

assumed that a dynamic model of groundwater systems can be based on a model of

monetary systems and that such a model will provide meaningful information to

support decision-making. Implicit in this assumption is the idea that groundwater can

be conceived as a form of natural or environmental credit.

Groundwater data, and the associated inflows and outflows from groundwater

systems is limited. This research will use data derived from groundwater models

developed by the USGS. These models are based on physical characteristics of the

specific groundwater systems in question. They are calibrated to available physical

measurements and provide simulated inflow, outflow and storage volumes on an

annual basis. Due to the paucity of observed data, the simulated results are used to

calibrate and verify the proposed system dynamics model. It is assumed that the

simulated data is the best available data. It is also assumed that the USGS models are

the best available representation of the physical groundwater systems in question.


15

1.9 Relevance of this study

This study is relevant because it concerns sustainable groundwater

management. Fresh water is a scarce natural resource that is vital to our survival.

Water shortages affect nearly 40% of the global population (Hamdy, Ragab, &

Scarascia-Mugnozza, 2003, p. 3). As surface sources of fresh water supply have

become scarce, the reliance on groundwater has also increased. This is particularly

true in California and other western states where demand exceeds the renewable

supply of fresh water and many groundwater basins are overexploited. The transition

to sustainable groundwater management may have significant social, environmental

and economic impacts.

Current events in California indicate that this research is both timely and

relevant. Recently the California legislature passed a suite of three bills requiring

sustainable groundwater management throughout the state (California Legislative

Information, 2014). The State Water Resources Control Board has set a target of

nearly quadrupling the current use of recycled water by 2030 (California State Water

Resources Control Board, 2013). California voters recently passed the Water Quality,

Supply, and Infrastructure Improvement Act of 2014, which allocates funds for

projects associated with water conservation, supply and recycling (Legislative

Analyst's Office, 2014).

The agricultural sector in California uses the majority of the current supply of

groundwater in the state. Historically, agricultural water uses has accounted for nearly

90% of human fresh water consumption (Khan & Hanjra, 2009). Although

agricultural needs vary depending on location and crop type, sustainable groundwater

management will likely have a significant impact on this sector.

Restricting the use of groundwater, by policy or physical constraint, can have

significant social, environmental and economic impacts. Despite the potential

impacts, it may be necessary to restrict consumption in many areas to prevent the

permanent destruction of the resource. Knowledge about systems that are isomorphic

to groundwater can lead to new insights about how to transition to sustainable


16

groundwater management. The development of a system dynamics model based on

the monetary policy system may allow managers to test various policies and strategies

and evaluate the potential impacts prior to implementation. Therefore, this research is

very relevant to the transition to sustainable groundwater management.

1.10 Need for this Research

In the face of growing demand and increased reliance on groundwater, it will

be important to use this resource in a sustainable manner. To do so it is necessary to

understand the structure of the groundwater system and its behavior with respect to

various policies and strategies. There are several policy tools available to facilitate a

reduction in groundwater consumption. However, the impacts of these policies within

complex systems are not well understood. The development of a system dynamics

model may help managers and policy makers to better understand the groundwater

system.

With the passage of the Sustainable Groundwater Management Act in 2014,

groundwater management agencies will be required to develop conceptual

hydrogeologic models by the end of 2017 in order to understand the systems they

manage (California Department of Water Resources, 2016). This research may help

managers develop the required conceptual models.

1.11 Benefits of this Research

The benefits of this research project are listed below:

1.11.1 Theoretical Benefits

1. An understanding of groundwater management and monetary policy from

the systems perspective.

2. An understanding of the systemic, structural similarities between

groundwater management and monetary policy systems.


17

1.11.2 Practical Benefits

1. A review of the current state of groundwater management in California.

2. An understanding of the various policy levers available to manage

groundwater.

3. A general systems dynamics model of groundwater management systems

to evaluate the effects of various groundwater management strategies.

4. Specific system dynamics models for three separate groundwater basins.

1.12 Research Outputs and Outcomes

The anticipated outcomes for this research are:

1.12.1 Theoretical Outcomes

1. A systems analysis of the groundwater management system to identify the

structural elements and causal links in the system.

2. A systems analysis of the monetary system to identify the structural

elements and causal links in the system.

3. A homological comparison between the groundwater management and

monetary policy systems based on system structure, underlying theory and

mathematics.

4. An isomorphological comparison between the groundwater management

and monetary policy systems based on systemic behavior-over-time.

5. A conceptual model of groundwater systems to improve understanding a

decision making.

1.12.2 Practical Outcomes

1. A thorough review of the literature regarding groundwater management.

2. A thorough review of the literature regarding monetary policy.

3. A system dynamics model of the groundwater management system based

on the monetary system.

4. An understanding to the parameters required to calibrate a system

dynamics model for groundwater.

5. A model-based assessment tool for testing various policy measures related

to sustainable groundwater management and an understanding of their

implications for aggregate groundwater demand.


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CHAPTER II

LITERATURE REVIEW

2.1 Introduction

Groundwater is a complex system. It involves the interaction of physical,

social and economic elements. The complex, systemic interaction between these

elements make it difficult to model any one element in isolation. As such, it is

difficult to predict the results of changes to any element within the system.

A monetary system is also a complex system of interrelated elements.

Changes in monetary policy result in changes to the economic system as a whole.

Predicting these changes is also difficult. The field of economics is, in many ways, a

divided science. It is full of competing paradigms and conflicting economic theories

that can obscure the true nature of the system. However, some of these theories

support a model of the monetary system that is structurally similar to the groundwater

system.

There are many similarities between groundwater systems and monetary

systems. Improving our understanding of these complex systems may improve our

ability to predict their behavior. As W. Edwards Deming once said, management is

prediction” (1993, p. 104). If this is true, then perhaps improving our understanding of

the groundwater system (from this monetary approach) could improve our ability to

manage it.

One way to improve our understanding of complex systems is to identify

isomorphological similarities in two separate systems through systems analysis. If,

under certain conditions, groundwater management is isomorphic to monetary policy,

then knowledge about either system is transferable to the other system. Identification

of isomorphic systems will increase our understanding of both systems while avoiding

the “vague analogies” (Bertalanffy, 1969, p. 34) that can lead to misunderstanding and

incorrect action. Systems analysis can help demonstrate that the similarities between


19

these systems are strong enough to consider them isomorphic. This will require a

thorough understanding of both systems.

This review presents an in-depth review of the literature relevant to

groundwater and monetary policy. It is divided into three major topics. It begins with

a discussion of water and groundwater before moving to economics and monetary

theory. Finally, it presents a discussion of systems and systems analysis.

This review starts with a discussion of water and the underlying concepts of

value, sustainability, externality and stewardship. A discussion of system archetypes

in water is presented to help understand the complexities of the system. The discussion

then moves to groundwater and groundwater management. This includes a discussion

of the concept of groundwater as credit and the role that this credit plays in aggregate

groundwater demand.

The discussion then turns to economics and monetary policy. It presents a

review of the literature on economic theories relevant to credit including General

Equilibrium Theory, Loanable Funds Theory, Credit Theory of Money and

Endogenous Credit Theory. The discussion then moves to monetary theory from the

perspective of various competing schools of economic thought. The economic

discussion concludes with a discussion of monetary policy, credit and the role of credit

in aggregate economic demand.

Finally, the discussion moves to systems analysis of similar systems. A review

of the literature about systems theory, components and characteristics is presented.

This is followed by a discussion of analogy, homology and isomorphology in order to

illustrate the value and strength of similarities between systems.

2.2 The Nature of Water

This section describes the unique characteristics of water. It describes the

importance of water in our society to illustrate the need for this research. It also

discusses the concept of water as an economic good and identifies economic issues

that make water a unique resource. An understanding of these issues, including


20

marginal cost and subtractability, help illustrate the difficulties associated with water

management and the need for management solutions.

2.2.1 The Value of Water

The true value of water is difficult to place in economic terms. Fresh water has

many competing uses. It is vital for agricultural production, human consumption, and

industry. Its role in our natural ecosystems helps support life in all its forms.

Organizations including the United Nations Department of Economic and Social

Affairs (2014), and the African National Congress (2011) consider clean water a basic

human right because it is fundamental to our right to life (Donovan & Hudson, 2011).

Despite its importance, most people pay very little for the water they use (Carle,

2009). As such, people do not appreciate the value of water (Glennon, 2009)

One of the keys to making good funding decisions is the appropriate valuation

of water. From the perspective of global water resource management, it is important

to account for all the valuable uses of water (Batten, 2007). Competing uses for fresh

water include environmental, domestic (municipal) consumption, sanitation,

agricultural and industrial. These sectors compete for the same supply, but may assign

a significantly different value per unit of water consumed.

Regulations are often used to allocate water and mandate conservation.

However, current research indicates that a market-based approach may be more

effective at conserving and allocating water resources when the true value of water is

considered (Batten, 2007). Mansur (2012) found that adjusting the price of water to

reflect reductions in supply could be a more effective tool to reduce consumption than

rationing. However, this can only be accomplished if the value of water can be

defined.

The value of groundwater can also be defined by the stabilizing role it plays in

arid and semi-arid environments (Tsur, 1990). This role is similar to the role of credit

in economic systems. Groundwater can provide a stable and reliable alternative to

surface water. When surface water is unavailable, groundwater can be used to bridge

the gap in the same way that credit can be used to provide continuity when income is


21

uncertain. Tsur (1990) argues that the value of groundwater as an economic stabilizer

may exceed the value of groundwater used to augment irrigated agriculture.

2.2.2 Water as an economic good

“Water is not a commercial product like any other but, rather, a heritage which

must be protected, defended and treated as such” (EU, 2002). Tsagarkis (2005)

considers water an ‘eco-social asset”. It is generally considered a public good because

it is difficult (and often undesirable) to exclude users. In most cases, it is non-

substitutable, finite, and therefore highly subtractable.

In some instances, water can be considered a “factor input” with little intrinsic

value (Kindler, 1999). Value is added through the agricultural or manufacturing

process. It can be economically similar to electricity (Tsagarkis, 2005). This situation

is quite different from other examples of resource extraction, like gold mining, where

the cost of the resource is closely linked to the value of the resource. Because water

functions as a factor input, many people call for governments to subsidize water to

encourage production (Macdonald et al, 2005).

Water’s role as a productive input does not adequately explain its value. It

provides vital environmental and social benefits that often do not command the same

monetary value. However, these benefits are arguably just as important as the pure

economic value of water in agriculture or industry.

According to Rogers et al. (2002), most water users do not pay the full cost of

the water they use. Instead, they pay for the cost of acquiring and delivering the

water. The resource itself is free. The constitution of California requires that water

prices be derived from the cost of service rather than the value of the resource

(Hildebrand et al, 2009). According to Hildebrand et al, this type of price structure

makes it difficult to legally implement pricing structures designed to incentivize

conservation. This may lead to a Tragedy of the Commons because the benefit

derived from the use of water is not adequately reflected in the price.


22

There are no substitutes for fresh water. The two primary sources of fresh

water in California are groundwater and surface water. However, after some

processing, recycled water and desalinated water can contribute to the total fresh water

supply. The cost of the required processing represents the marginal cost of increasing

the available supply. It is possible to increase supply through technology, but the

increase comes at a high marginal cost.

2.2.3 Marginal Cost

Many areas of the western United States may have passed the point of peak

water (Gleick & Palaniappan, 2010) through the overexploitation of groundwater

stocks and surface water flows. Peak water is the point at which increasing fresh

water consumption becomes infeasible (Gleick & Palaniappan, 2010) due to the

increasing marginal cost of new supplies.

The marginal cost, of water is the value of obtaining one additional unit of

water, or losing a unit of water. The value of water at the margin will vary from sector

to sector in the same way that the overall value of water varies from sector to sector.

In agriculture, “the shadow price is an estimate of the economic value to agricultural

production of one additional acre-foot of water supply” (Sunding, et. al, 2008, p. 25).

This value will be different for industrial or municipal water use. The value will also

vary within the agricultural sector depending on the value of the crop.

The fact that shadow prices for water vary from sector to sector, and within

each sector, is one of the reasons that it is so difficult to value water. Consumers who

can use water to create economic value will prefer to divert water from users that do

not, rather than invest in marginal supply increases that are more expensive. In a free

market situation, where competing users value water differently, the resource will tend

to be allocated to the sector that places the highest value on it. As demand and

marginal cost increase, demand management will become more important. Competing

uses make demand management a challenge.


23

2.2.4 Subtractable Good – Competing Uses

Water is a subtractable good. The renewable supply of fresh water is finite for

all practical purposes. Alternative sources, like recycled water or desalinated water,

can only augment the supply. Water that is consumed by one user cannot be used by a

rival consumer (Tsagarkis, 2005) unless it is recycled and returned to the system. It is

therefore considered rival or subtractable.

In rival goods, property rights can result in inefficient allocation (Romer P. ,

2002). In the absence of social or regulatory influence, water use in a competitive

rivalry will tend to concentrate in the sectors that place the highest value on water and

have the ability to pay the highest cost. Typically agricultural and landscape users

place a lower value on water than industrial and municipal users. Industrial and

municipal consumers often pay a higher price for water.

Traditionally, the management of water has focused on increasing supply and

moving water from locations of abundance to locations of scarcity (Diamandis &

Kolter, 2012). Increasing water supply is a technical solution that is limited by

increasing marginal cost. Different sectors place different value on water. As these

sectors compete for this limited, subtractable resource, it will become increasingly

important to manage for long-term sustainability.

2.3 Water Resource Sustainability

There is mounting evidence that water use in the semi-arid areas of the United

States is unsustainable (Gleick, 2010). In California, the historic management

approach has been to increase supply by capturing and storing water where it is

abundant and transferring it to areas of high demand (Diamandis & Kolter, 2012).

This approach has been detrimental to wetland ecosystems and the services that they

naturally provide (Custodio, 2002). Despite these supply-based solution, water

demand has outpaced supply resulting in an increased reliance in groundwater

pumping. Many believe that continued reliance on groundwater and inter-basin water

transfers is unsustainable (Gleick, 2010).


24

This section presents a review of the literature of sustainability as it relates to

water and groundwater management. The concept of sustainability is defined. A

discussion of the related concepts of externality and stewardship is also presented.

2.3.1 Sustainability Defined

In 1987, the World Commission on Environment and Development (Bruntland

Commission) defined sustainable development as “development that meets the needs

of the present without compromising the ability of future generations to meet their

own needs” (World Commission on Environment and Development, 1987, p. 41).

This definition implies the need to limit present resource consumption for future use.

Improving efficiency and productivity are important, but they will not lead to

sustainability unless the unused resources are preserved for future use.

According to Jeremy Caradonna (2014) the term sustainability was first used

with respect to forest management in the book “Sylva, or A Discourse of Forest-Trees

and the Propagation of Timber in His Majesty's Dominions” by John Evelyn in 1664.

The term “Sustainable Agriculture” gained popularity through the work of authors

like Gordon McClymont (1984) and Wes Jackson (Harwood, 1990). Sustainable

agriculture has since developed in response to the rapid increase in agricultural

intensification known as the “Green Revolution” (Matson, et al. 1997). McClymont

was a proponent of agricultural systems that could sustain agricultural productivity in

perpetuity rather than systems that create short-term gain. He argued that sustainable

agricultural systems would result in greater productivity in the long run, because they

do not require the use of non-renewable inputs or result in harmful waste products.

In groundwater systems, the concept of sustainability is often confused with

the concept of “safe yield”. The concept of safe yield was developed in the 1920s

(Custodio, 2002). The consumption of groundwater “is considered to be safe if the

pumping rate does not exceed the rate of natural recharge” (Zhou, 2009, p. 207). Most

groundwater users would consider groundwater use sustainable if the withdrawals

from the basin are below the safe yield of the basin. However, pumping at safe yield

would actually result in continued drawdown and eventual overdraft.


25

Many researchers consider safe yield to be unsustainable (Custodio, 2002 and

Sophocleous, 2000) because it does not consider the natural aquifer discharge that is

required for a healthy hydrologic system. At safe yield, the majority of water

discharged from the groundwater basin is allocated for human use. Water that would

have created a natural discharge is instead used to recharge depleted storage in the

aquifer. This has a significant impact on surface water flows, resulting in reduced

ecosystem services and general degradation.

Because of the problems identified above, sustainable yield is gradually

replacing safe yield in the lexicon of groundwater management (Zhou, 2009).

Sustainable yield is a level of groundwater withdrawal that seeks to balance the

hydrologic, social, economic and ecological uses (Ponce, 2007) in a way that

preserves the resource, and the systems it supports, for future generations.

Maintaining pumping rates below the sustainable yield can preserve the groundwater

resource and protect the other systems that rely on water. However, it is difficult to

quantify the sustainable yield of a groundwater basin.

Meadows, Meadows and Randers (2004), view sustainability as the primary

tools for mitigating the negative impacts associated with systemic overshoot. In

systems terms, overshoot occurs when the system exceeds its natural limits and

quickly declines (see section 2.9.5 for more information). Systems that overshoot

their natural limits often show a rapid, dramatic crash. Sustainable water use may

prevent the system from reaching its limits or slow the eventual decline. Others like

Diamandis and Kolter (2012) view sustainability as a stopgap measure, necessary to

buy time until technology can provide solutions to our resource constraints. In either

case, sustainability and efficiency will play an important role in the future.

2.3.2 Externalities

The concept of externality is important to welfare economics (Cooper &

Dobson, 2007) because of the potential for suboptimal results for society. The Oxford

English Dictionary defines externality as “a side effect or consequence of an industrial

or commercial activity that affects other parties without this being reflected in the cost


26

of the goods or services involved” (Oxford University Press, 2014). In a common

pool water resource system, externalities occur when water use benefits a subset of

water users and harms other users. This is the case when water users increase

pumping in order to maximize their private economic benefit. If water is scarce, other

users will be deprived of access to the resource, and/or a negative environmental

impact will result.

Externalities are the result of “market failure” (Brown & Hagen, 2010) in

which the private optimum diverges from the social optimum in market economies

(Scitovsky, 1954). A “market failure” occurs when market processes drive conditions

toward an optimum for private parties, but do not lead to optimal conditions for

society as a whole (Brown & Hagen, 2010). According to Stavins (2011), there are

two types of externalities present in open access, common pool systems. They are

contemporaneous externalities and intertemporal externalities.

Contemporaneous externalities occur when there is an overabundance of

resources dedicated to resource extraction (Stavins, 2011). In a water resource system,

this type of externality results from population increase and the proliferation of private

water users (farmers, cities, etc.). In agriculture, improvements in pumping

technologies have increased the number of pumps in operation.

Intertemporal externalities occur when overconsumption of a resource reduces

the existing stock (Stavins, 2011). This type of externality is evident in groundwater

resource systems when an aquifer is overdrawn. The loss of supply means that users

must put more effort into groundwater extraction. Wells must be made deeper and the

cost of extraction increases. If left unchecked, this type of externality will result in a

“race to the bottom” of the aquifer that is typical in the Tragedy of the Commons.

Both types of externality are found in groundwater systems. The competition

for subtractable goods results in a situation where market processes can drive

consumption to unsustainable levels. A management system with a focus on

sustainability and stewardship is one possible solution.


27

2.3.3 Stewardship

The concept of stewardship is central to groundwater management. According

to Davis et. al. (1997), “stewardship theory defines situations in which managers are

not motivated by individual goals, but rather are stewards whose motives are aligned

with the objectives of their principals”. It contrasts agency theory in which managers

are motivated by personal goals or incentives.

In California, “water is owned by the state on behalf of the people” (Carle,

2009). The state acts as a steward to ensure the wise use of water for current and

future generations. The state constitution requires that water be put to the highest

beneficial use and prohibits waste and unreasonable use (Carle, 2009). The complex

system of laws and property rights that govern surface water help to ensure that water

is used in accordance with the state constitution. However, the lack of regulation over

groundwater may contribute to unsustainable management practices.

Sustainable management of lakes, oceans and rivers requires a stewardship

approach (Lubchenco & Sutley, 2010). This may also be true of sustainable

groundwater management. Managers who are stewards must focus on what is best for

the resource and the consumers over the long-term. This type of stewardship may

require that groundwater management districts restrict consumption in order to

preserve the resource for future generations (Job, 2010).

Ideally, other sources of freshwater would offset the necessary reduction in

groundwater consumption. However, the marginal cost of additional supply currently

limits access to alternative sources. The following review of system archetypes in

water will show that demand management with a focus on stewardship and

sustainability may be a more effective option.

2.3.4 Recycled Water

In many areas the demand for water is increasing, but the supply is limited. In

this situation, recycled water has become an appealing option. Recycled water, also

called reclaimed water, is “wastewater treated to a quality suitable for beneficial use”


28

(Newton, et al., 2009, p. 3). The source of this water is usually (though not always)

municipal wastewater from sewer treatment operations. This urban sewage effluent

has historically been considered a waste product to be disposed of in the most cost

effective manner possible while maintaining public health and safety. Disposal is

distinct from recycling because no direct beneficial reuse occurs. Recycling is a way

to turn this waste product from one part of the system into a resource for other parts of

the system.

Using recycled water is one way to reduce the stress on the system by

converting municipal wastewater into a useable water resource. Since agriculture

consumes more water than any other sector of human water use, it would seem like a

natural place to use recycled water. However, there are many barriers to

implementing recycled water projects for agriculture. Issues like salinity, nutrient

management, timing, cost and general psychological aversion to recycled water have

limited the use of recycled water.

Agricultural use of recycled water can offset existing use and make more fresh

water available for other uses. These include groundwater protection, environmental

services, domestic use and industrial use. It can also provide economic benefit by

increasing the amount of water available for agricultural production. Too often,

recycling projects fail to incorporate agricultural reuse because the municipality must

recover the cost to produce recycled water, and the farmers refuse to pay more than

the cost of their current supply. The difference between these figures is often very

large. The positions of the municipality and the farmers both fail to account for the

systemic value of recycled water use.

Under sustainable groundwater management, the value of water may change.

Consumers who were opposed to paying the higher marginal cost for water may be

more willing to do so if the alternative is a forced reduction in consumption by

restricting the use of groundwater to sustainable levels. Determining the value of

recycled water in an environment where groundwater consumption is contracting may

help facilitate widespread implementation of water recycling and sustainable

groundwater management.


29

2.3.5 Recycled Water in California

Due to the systemic nature of water, use in one sector can affect other uses, and

waste generated by one use can affect the supply for other users. In water scarce

areas, wastewater generated by urban sanitation is of particular interest because of the

potential for reuse. This is particularly true in California, where the State Government

is actively encouraging the use of recycled municipal wastewater.

The operational definition of recycled water is treated wastewater that is reused

for beneficial purposes (Newton, et al., 2009). According to Newton et al, (2009)

municipal wastewater has been used for irrigation since the late 1800s. However, the

treatment of wastewater did not become common until public health concerns sparked

legislation in 1918. By 1953 there were 107 communities using recycled water for

irrigation in California (California State Water Resources Control Board, 2012). This

number slowly increased until the early 1970s, when treatment technologies and

resource constraints made the practice appealing (Ongerth & Jopling, 1977). The use

of recycled water in California has grown from 175,000 Acre-feet per Year (AFY) in

1970 to 669,000 AFY in 2009 (California State Water Resources Control Board,

2012).

As water becomes increasingly scarce in California, the concept of recycled

wastewater becomes more attractive. In 2013, the California State Water Resources

Control Board issues resolution 2013-0003 regarding the use of recycled water. It

states:

“The State Water Board and Regional Water Boards will exercise the authority

granted to them by the Legislature to the fullest extent possible to encourage

the use of recycled water, consistent with state and federal water quality laws”

(California State Water Resources Control Board, 2013, p. 3).

The goal of this resolution is to encourage “the substitution of as much recycled water

for potable water as possible by 2030” (California State Water Resources Control

Board, 2013). According to the California Department of Water Resources (DWR,

2003), California produces approximately 5,000,000 acre-feet of treated municipal


30

wastewater annually. The CSRWCB specifically indicates a target of 2,525,000 acre-

feet of recycled water be used per year by 2030 (California State Water Resources

Control Board, 2012). This represents an increase of 2,000,000 acre-feet per year over

2002 levels, and 50% of the total treated municipal waste for 2003 (the most recent

available data). However, California uses approximately 14,800,000 acre-feet of

groundwater per year (Water Education Foundation, 2015). If California reaches its

goal of 2,525,000 AFY of recycled water by 2030, it will account for approximately

17% of the 2015 groundwater consumption.

Titles 22 and 17 of the California Code of Regulations dictate the required

treatment of recycled water for various uses (California Department of Public Health,

2009). Levels of treatment include primary treatment, secondary treatment,

disinfected secondary treatment and tertiary treatment. The California Department of

Public Health (2009) requires secondary treatment for all recycled water used for

irrigation and disinfected secondary treatment for irrigation of food crops. Tertiary

treatment is required for recycled water that may come in contact with the edible

portion of food crops. Figure 2.1 below show the United States Environmental

Protection Agency suggestions for recycled water treatment and use.


31

Suggested Water Recycling Treatment and Uses

Increasing Levels of Treatment:

Increasing Levels of Human Exposure

Primary Treatment:

Sedimentation

Secondary Treatment:

Biological Oxidation,

Disinfection

Tertiary / Advanced

Treatment:

Chemical Coagulation,

Filtration, Disinfection

- No Use Recommended

at this level

- Surface irrigation of

orchards and vineyards

- Non-food crop

irrigation

- Restricted Landscape

Impoundments

- Groundwater Recharge

of non-potable aquifer

- Wetlands, wildlife

habitat, stream

augmentation

- Industrial cooling

processes

- Landscape and golf

course irrigation

- Toilet flushing

- Vehicle washing

- Food crop irrigation

- Unrestricted

recreational

impoundment

- Indirect potable reuse:

Groundwater recharge

of potable aquifer and

surface water reservoir

augmentation

Figure 2.1. EPA Suggestions for Recycled Water Treatment and Use (United States Environmental Protection Agency, 2013).


32

On July 1, 2014, the Drinking Water Program transferred from California

Department of Public Health to the State Water Resources Control Board (California

Department of Public Health, 2014).According to the California State Water

Resources Control Board (2012), recycled water can be used for any of the following

purposes:

Golf Course Irrigation and Landscape Irrigation

Agricultural Irrigation

Industrial and Manufacturing

Energy Production

Seawater Intrusion Barrier

Groundwater Recharge

Recreational Storage (lakes) and

Natural Systems/Restoration

Technology has advanced to the point where recycled water can be made safe and

clean enough for direct human consumption. Indirect potable use is the blending of

treated water with traditional sources via groundwater recharge or reservoirs. As of

2009, indirect potable water use accounts for approximately 130,000 AFY (California

State Water Resources Control Board, 2012). Direct potable use is very rare. These

so-called “toilet-to-tap” projects have met with significant resistance due to

psychological aversion to consuming water associated with human waste (Menegak, et

al. 2009). However, the City of San Diego California has recently voted to proceed

with a project that will provide approximately 83 million gallons per day of recycled

water for direct human consumption. This project was supported by 71% of the city’s

residents (Allshouse, 2014) signaling a shift towards acceptance of recycled water.

This aversion to treated water extends to agriculture as well. Many farmers

view recycled water as inferior to traditional sources of fresh water. This is due, in

part, to reluctance of consumers to pay for products irrigated with recycled water

(Bakopoulou, et al. 2010). Farmers appear to be less willing to use recycled water on

crops because they fear that the end consumer will be reluctant to purchase the

product.


33

Despite this perceived reluctance to accept recycled water, California has seen

some successfully agricultural recycled water use projects. The Monterey Regional

Water Pollution Control Agency (MRWPCA) operates the largest water recycling

facility for raw food crop irrigation (Monterey Regional Water Pollution Control

Agency, 2012). In 1987, the MRWPCA commissioned the Monterey Wastewater

Reclamation Study for Agriculture. This study showed that irrigation with recycled

water is safe and effective (Engineering-Science, 1987). Today the MRWPCA

delivers approximately 4,000 AFY for irrigation of vegetable crops in the Pajaro

Valley (Monterey Regional Water Pollution Control Agency, 2012). This recycled

water offsets groundwater withdrawals and protects the aquifer from seawater

intrusion from the Pacific Ocean.

In 1991, California passed the Water Recycling Act. Today, the success of

projects like MRWPCA Pajaro project, along with the need to reduce reliance on

groundwater, has lead the state to modify regulations pertaining to recycled water use.

“It is State policy to promote the use of recycled water to the maximum extent in order

to supplement existing surface and ground water supplies to help meet water needs”

(California State Water Resources Control Board , 2006).

Although the State is actively encouraging the use of recycled water, many

municipalities are struggling to find willing users. This is in part due to the high cost

of production relative to existing sources and in part due to complexities associated

with recycled water use including salt and nutrient management, irrigation scheduling

and storage.

Since the agricultural sector uses the majority of the water allocated to human

consumption, selling recycled water to farmers is an appealing option often considered

by regulators and treatment plant operators. Farmers can make good use of the

nutrients provided in recycled water. The issues of salt and nutrient management can

be solved with using nutrient and water balances (Duan & Fedler, 2011). Scheduling

and storage can be solved through proper system design. However, this option has

met with limited success because early negotiations between municipalities and


34

agriculturalists often fail to yield a mutually acceptable agreement on cost and water

quality.

In this situation, two or more rational actors are making decisions based on

rational self-interest. Decisions that make sense for the individual or municipality are

rational, but they may not be best for the system as a whole. The municipality is

willing to provide water to the farmers and the farmers can put the water to good

use. Typically, the municipality seeks to recover the cost of producing the water by

supplying it at a small discount relative to the cost of traditional potable water. This

provides incentive to use recycled water while still enabling the supplier to recover

costs. However, agricultural water users are often reluctant to use recycled water.

Typically, they do not pay municipal water rates for irrigation water and are reluctant

to pay more for recycled water than they would pay for traditional sources. This

position neglects the value of the nutrients provided in recycled water. Other issues

like water quality concerns, scheduling misalignments and psychological aversion to

recycled water can make it difficult to persuade farmers to accept recycled water.

2.3.6 Is water recycling a sustainable practice?

To many, the practice of transforming a waste product into a useable resource

would be considered a move towards sustainability. How could using a waste product

for beneficial use not be a sustainable practice? To answer this question we must

consider what could happen in the social-economic-hydrologic system when a new

supply of water is considered.

Sustainability can have several meanings. One widely accepted definition of

sustainable development is “development that meets the needs of the present without

compromising the ability of future generations to meet their own needs” (World

Commission on Environment and Development, 1987, p. 41). In many ways, water is

the driver of development. Its presence can signal farmers (Gohari et al, 2013) and

land developers to increase production and drive consumption upwards. If the use of

recycled water continues to drive consumption upward then it is not necessarily

sustainable. It would be a step towards sustainability if the use of recycled water


35

could offset current water use and preserve the existing supply for future use. This is a

difficult task considering the increased marginal cost of water and the economic

temptation to increase production.

In overdrawn groundwater systems, there is great temptation to use new-found

water sources for economic gain. This may be particularly true with recycled water

because the cost of procuring the resource is higher than the cost of using the existing

sources. This creates a need to increase production to justify the increased cost. The

rational farmer contemplating the use of recycled water must choose from the

following options:

1. Do not accept the recycled water and continue operating in a resource

constrained environment,

2. Accept the recycled water and increase production to help offset the cost,

3. Accept the recycled water and sacrifice profit for the good of the system, or

4. Allow others to accept the recycled water and take advantage of their

sacrifice (free ride).

A rational farmer could reasonably conclude that using more expensive water

to produce the same amount of crop is a bad economic decision. In this situation,

rational self-interest would result in suboptimal conditions for the system in a manner

characteristic of the Tragedy of the Commons (Ostrom, 1990). Unfortunately, this

situation is very common.

A rational farmer could also choose to use recycled water to increase

production. This would provide a rational, economic justification to pay more for the

water. However, if many farmers collectively decide to increase demand to justify the

cost of the new supply, they run the risk of perpetuating the Tragedy of the Commons.

This could serve to increase the systemic overshoot and potentially result in bigger

problems in the future.

Recycling is a key component of sustainability (Caradonna, 2014). Using

recycled water in conjunction with demand management can reduce our reliance on

groundwater and preserve this resource for future generations. However, recycling


36

water in the absence of demand management could result in increased water

consumption.

Meadows, Meadows and Randers (2004), view sustainability and efficiency as

the primary tools for mitigating the negative impacts associated with systemic

overshoot. Others like Diamandis and Kolter (2012) view sustainability as a stopgap

measure, necessary to buy time until technology can provide solutions to our resource

constraints. The use of recycled water may be one of these technical solutions.

Alternatively, it may serve to increase systemic overshoot and perpetuate the Tragedy

of the Commons. In either case, sustainability and efficiency will play an important

role in the future of water and agriculture. For now, all sources of water, including

recycled water should be put to efficient beneficial use.

2.4 System Archetypes in Water

System archetypes describe the structure and patterns of behavior of

commonly occurring systems (Braun, 2002). They are useful in gaining insight into

the underlying structure of different problems. In some cases, this insight can lead to

useful predictions about behavior over time.

According to Braun (2002), there are 10 primary system archetypes. These

archetypes include:

Limits to Growth,

Shifting the Burden,

Eroding Goals,

Escalation,

Success to the Successful,

Tragedy of the Commons,

Fixes that Fail,

Growth and Underinvestment,

Accidental Adversaries, and

Attractiveness Principle

It should be noted that Senge (1990) and Anderson and Johnson (1997) do not

specifically identify the “accidental adversaries” and “attractiveness principle”


37

archetypes. While many of these archetypes may be relevant, the limits to growth,

Fixes that Fail, and Tragedy of the Commons archetypes are of primary interest. A

discussion of how these archetypes pertain to water systems is provided below.

2.4.1 Fixes that Fail

Traditionally humans have managed hydrologic flow variability by increasing

storage and transferring water from one basin to another. Increased storage created by

dams and other reservoirs adds stocks of surface water to the system. Inter-basin

water transfers use these stocks to minimize the impacts of spatial and temporal

variability in the natural hydrologic system by allowing the transfer of water from an

area of surplus to an area of greater need. The addition of recycled water can be

similar to an inter-basin water transfer.

If supply increases derived from inter-basin water transfers can be

representative of the Fixes that Fail archetype (Gohari, et. al, 2013), then it is

reasonable to assume that the addition of recycled water may fit the archetype as well.

These types of solutions provide temporary relief from resource constraints, but

actually increase the growth rate of demand. If the introduction of recycled water

sends signals of abundant water supply to users, they may infer that increasing

extraction is reasonable. Over time, the fix fails to provide a lasting solution because

demand grows to exceed the new supply. Figure 2.2 shows the generic causal loop

diagram of the Fixes that Fail archetype. Figure 2.3 shows how it pertains to inter-

basin transfers.


38

Figure 2.2 Fixes that Fail Generic Archetype (Braun, 2002).

Figure 2.3 Inter-Basin Transfers (Gohari, et. al, 2013).


39

The above causal loop diagram shows how increased water supply through inter-basin

transfer can result in demand growth over time. Demand growth eventually exceeds

that of the new supply. This systemic interaction may explain why technical solutions

do not resolve commons problems.

2.4.2 Limits to Growth

The Limits to Growth archetype is highly relevant to the study of groundwater.

It consists of a single balancing loop and reinforcing loop. The reinforcing loop

accelerates or increases behavior and the balancing loop slows or reduces behavior.

Some limit gradually increases the dominance of the balancing loop until it dominates

the reinforcing loop. Dominance shifts from one loop to another, resulting in changes

in behavior over time. As dominance oscillates, a state of dynamic equilibrium

emerges and the limit of the system is defined. The concept of peak water, developed

by Gleick and Palaniappan, (2010) is a classic example of the Limits to Growth

system archetype. Figure 2.4 below shows the generic causal loop diagram for this

system archetype.

Figure 2.4 Limits to Growth Archetype (Braun, 2002).

Under peak water conditions, limited water availability will result in a slowing action

that will limit the growth of consumption (Gleick & Palaniappan, 2010). The use of


40

recycled water may increase the limit of the system by increasing supply, but it is

unlikely to eliminate limits to growth.

2.4.3 Tragedy of the Commons

The Tragedy of the Commons is a complex system archetype (Anderson &

Johnson, 1997) in which the rational, short-term, self-interest of individual actors

drives resource consumption beyond sustainable levels to the long-term detriment of

the resource system and all the individual stakeholders. Garret Hardin popularized the

concept in his 1968 essay entitled Tragedy of the Commons (Hardin, 1968). Hardin’s

model, while simplistic, illustrates the impact of human social behavior on common

pool resource systems. Figure 2.5 below shows the generic systems archetype.

Figure 2.5 Tragedy of the Commons Generic Archetype (Braun, 2002).

In many ways, this archetype is similar to the Limits to Growth archetype

discussed above. It consists of multiple balancing and reinforcing loops. The


41

reinforcing loops accelerate or increase behavior and the balancing loops slow or

reduce behavior. A resource limit gradually increases the dominance of the balancing

loops. However, in a Tragedy of the Commons, the balancing loop does not

overpower the reinforcing loops. Cost/benefit asymmetries, game theory and basic

human psychology encourage resource users to deplete the resource. Over time, this

can result in depletion or destruction of the resource even if it is renewable.

Groundwater overconsumption is often described as a Tragedy of the

Commons dilemma although some scholars argue that it fails to meet the basic criteria

(Roberts & Emel, 1992). They argue that the assumptions necessary to classify a

dilemma as a Tragedy of the Commons are not always applicable in groundwater

applications. These assumptions are:

1. Participants must have free access to the common pool resource,

2. Participants must be primarily motivated by personal economic interests

and driven to increase the use of the resource for their own gain, and

3. Participants must be unwilling or unable to cooperate for the benefit of the

system.

Researchers like Elinor Ostrom have shown that these assumptions often do not apply

in water resource systems (Ostrom, 1990). Yet, over-exploitation of groundwater

resources remains a significant problem.

In California, the assumptions listed above do apply. There is currently very

little regulation to limit access to groundwater for beneficial use except in adjudicated

groundwater basins (Carle, 2009). Farmers are driven to produce more crops or more

valuable, water-intensive crops. Although many farmers and municipalities appear

willing to cooperate to reduce over-exploitation, the effort is usually ineffective

without external coercion from legal action and/or governmental intervention. As

such, groundwater over-exploitation in California can be considered a commons

dilemma.

Research indicates that the Tragedy of the Commons is a direct result of the

evolution of human psychology (Corral-Verdugo et al, 2002). This basic human

component makes commons dilemmas difficult to resolve. The difficulty originates


42

from the fact that users of a common pool resource face a binary choice set. They can

choose to increase consumption for personal gain at the expense of the system.

Alternatively, they can choose to sacrifice personal gain, for the benefit of all the

users, by maintaining consumption at a sustainable level. In game theory, this is

known as a prisoner’s dilemma.

The prisoner’s dilemma is a game theoretical model involving two players.

Each player has a set of choices. They have an unconditional preference for their own

choice as well as the choice that the other player would make. These preferences go in

opposite directions, which results in a situation where both players would be better off

making a choice that is counter to their preference for personal benefit (Schelling,

2006, p. 216).

The extraction of groundwater for human use often involves a systemic

structure that can lead to a Tragedy of the Commons (Lopez-Corona et al, 2013). In a

common pool groundwater system, users would prefer to increase their extraction for

personal gain. They would also prefer that others reduce their extraction to preserve

the resource. As rational actors, users typically make the choice that will increase

their personal gain, resulting in over consumption of the groundwater resource.

The traditional game theoretical model of a prisoner’s dilemma is overly

simplistic for application to most common pool, groundwater resource systems. These

systems are best described as asymmetrical, multi-player prisoner’s dilemma games.

In multi-player games, free-riders and coalitions can develop (Schelling, 2006, p.

218). A coalition develops when groups of players choose to act together. A free-

rider is an individual that chooses to pursue a course of self-interest while benefiting

from the selfless acts of others. In a groundwater system, a coalition of users could

choose to conserve water and preserve the system. Those who do not act with the

coalition, free-riders, would benefit from the conservation of others without sharing in

the cost.

To further complicate the situation, extraction of groundwater from a common

pool basin can be asymmetrical. In agriculture, this asymmetry can be caused by


43

resource availability and consumption asymmetry (Jacquet et al, 2013). Some

farmers, driven to increase production for economic reasons, may use more water than

others. Some farmers are fortunate to have a better source of water than others are by

virtue of location in the watershed or groundwater basin. Farmers who have the best

sources of groundwater are unlikely to reduce consumption because they receive little

benefit for the sacrifice. These asymmetries can complicate the Tragedy of the

Commons model.

According to Hardin (1968), there are no technical solutions to a Tragedy of

the Commons. Adding water to a system suffering from this tragedy may temporarily

relieve the symptoms, but can be seen as a fix-that-backfires (Gohari et al, 2013)

because it does not address the underlying cause of basic human self-interest.

Overconsumption is likely to continue, resulting in a commons dilemma of even

greater scale.

Economists generally identify privatization and regulation as the two potential

solutions to commons problems (Libecap, 2009). Creating and enforcing private

water rights could help control consumption. However, in California, water rights

have been historically over-allocated and under-enforced. This results in

overconsumption and a reduction in the amount of water allocated to the environment.

Likewise, government regulation has been shown to accelerate resource consumption

in some systems (Ostrom, 2009). Elinor Ostrom (1990) has shown that the most

effective way to achieve sustainability in common pool resource systems, including

groundwater systems, is through local management under very specific conditions.

Technical solutions may relieve the constraints on the system, but they are

unlikely to eliminate the systemic interactions that cause a Tragedy of the Commons

(Meadows, et. al, 2004), (Hardin, 1968). These solutions are a temporary fix that may

be destined to fail (Gohari, et.al, 2013). Long-term solutions to commons dilemmas

require management or governance (Ostrom, 1990) grounded in stewardship.


44

2.5 Groundwater Management

Various hydrologic stresses and competing demands combine to make

groundwater management challenging (Sophocleous, 2010). In the United States

groundwater makes up approximately 22% of the fresh water consumed (Water in the

West, 2013). As groundwater stocks become depleted, users will have to develop new

sources of water, or limit growth to sustainable levels. The following discussion

presents a review of groundwater management. It presents the available groundwater

management tools and introduces concepts of groundwater as savings and credit.

Finally, it explains the role that groundwater credit plays in aggregate groundwater

demand in a contractionary environment.

Groundwater management is a difficult endeavor due to the complex nature of

the system. Globally, there is a trend towards increasing regulation of groundwater

extraction (Findikakis, 2011). Until recently, most countries have viewed

groundwater as part of the land (Carle, 2009). In the United States, groundwater rights

are the jurisdiction of individual states rather than the federal government (Findikakis,

2011). In the Ogallala Aquifer, which covers eight states, groundwater use is

governed by groundwater management districts (Sophocleous, 2000). Landowners in

California have historically been able to extract as much groundwater as they can put

to reasonable and beneficial use under the absolute ownership doctrine (Findikakis,

2011). However, this is beginning to change with the passage of the Sustainable

Groundwater management Act of 2014.

In California, water management has historically focused on increasing supply

and transferring water from locations of abundance to locations of need. This focus on

supply has been unable to keep up with growing demand. In the west, nearly all the

available water is already allocated to exiting users (Goemans & Pritchet, 2014).

Scientists and regulators have begun to recognize the systemic nature of groundwater.

The use of groundwater has wide-ranging impacts on the overall hydrologic system.

Groundwater management is now being recognized as a critical part of “integrated

water management” (Bouwer, 1995).


45

Demand management is an increasingly important part of integrated water

management. Demand management is intended to reduce consumption changing

attitudes and promoting conservation (Findikakis, 2011). It usually employs technical

measure to improve efficiency. Increasingly, market based incentives have been used

to reduce demand through economic means (Stavins, 2003)

Governance of common pool resources must occur before conditions

deteriorate to the point that the resource is no longer useful (Ostrom, et al. 1999). In a

groundwater system, this occurs when an aquifer is degraded through subsidence

and/or pollution. Governance must include protective regulation as well as investment

in alternative resources in order to avoid the systemic problems associated with

growth and underinvestment. Failure to govern common pool groundwater resources

will likely result in a Tragedy of the Commons (Meadows, et. al, 1972).

2.5.1 Groundwater in the United States

Groundwater consumption has become unsustainable in many groundwater

basins in the United States. The High Plains (Ogallala) Aquifer in the Midwest, the

Gulf Coastal Plain aquifer system and California’s Central Valley aquifer system are

three areas where groundwater extraction has led to significant reduction in available

groundwater supply. According to Konikow (2015), the volume of groundwater

stored in the major basins within the continuous 48 states has declined by 1000 Km3

between 1900 and 2008. Between 1950 and 1975, the rate of groundwater extraction

nearly doubled (Hutson, et al., 2004) due to agricultural intensification and

improvements in pumping technologies associated with the “Green Revolution”. This

increase is to be expected based on the increasing irrigated agriculture, increasing

population and technological advances associated with groundwater extraction.

However, the rate of extraction has continued to increase since the year 2000. The

problem of groundwater overexploitation appears to be accelerating. Continued

growth in groundwater consumption is not sustainable in many of the world’s aquifers.

Figures 2.6 and 2.7 below show the rate of groundwater depletion in several

groundwater basins in the United States.


46

Figure 2.6. Groundwater depletion rates from 1900 to 2000. (Konikow L. F., 2015).


47

Figure 2.7. Groundwater depletion rates from 2000 to 2008. (Konikow L. F., 2015).


48

The impact of accelerating rates of depletion varies across the country. Some

areas have higher rates of recharge than other areas. “Extrapolation of the current

depletion rate suggests that 35% of the southern High Plains will be unable to support

irrigation within the next 30 years” (Scanlona, et al., 2012). The northern high plains

has a much greater rate of recharge (Sophocleous, 2000) and can possibly transition to

sustainable consumption.

In 1980, Arizona Governor Bruce Babbitt enacted the Groundwater

Management Act (Arizona Department of Water Resources, 2014). This important

legislation established legal and institutional solutions for reducing groundwater

overdraft in the state (Jacobs & Holway, 2004). This legislation has been successful

in reversing the decline in Arizona groundwater levels (Konikow L. F., 2015).

The Arizona Groundwater Management Act is an important precursor to the

California Sustainable Groundwater Management Act. However, these pieces of

legislation differ in one important area. Since it was enacted before the recent focus

on sustainability, the Arizona Groundwater Management Act focuses on “safe yield”.

The term “safe yield” is different from sustainable yield or sustainable management

(Alley & A.Leake, 2004). “Safe yield” focuses on the volumetric comparison between

extraction and recharge rates. It does not address groundwater quality directly.

Sustainable yield has a similar focus, but also includes emphasis on systemic

environmental factors associated with groundwater consumption. The California

Legislature has elected to focus on sustainability rather than “safe yield”. This

involves management of groundwater for volumetric balance as well as preserving

water quality and ecosystem services associated with the overall hydrologic system.

2.5.2 Groundwater in California

In California, groundwater depletion has increased dramatically since the

1940s largely due to increased agricultural consumption (Konikow L. F., 2015).

Groundwater accounts for approximately 40% of total water use in California in

average years. However, this number increases to 60% during drought years (Water

Education Foundation, 2015). This discrepancy between average-year groundwater


49

consumption and drought groundwater consumption is similar to the use of credit to

maintain spending during periods of decreased cash flow.

Due to California’s reliance on groundwater, the California Department of

Water Resources recognized the need for monitoring and management. In 1975, the

Department published the results of groundwater basin evaluations in Bulletin 118 -75

(California Department of Water Resources, 2015). This bulletin has since been

updated in 1980 and 2003. It provides a summary of the state’s groundwater resources

and identifies critical basins of concern.

In 2009, the State legislature enacted Senate Bill SBx7-6, which amended the

water code to require the Department of Water Resources to collect, analyze and

publish groundwater elevation data (California Department of Water Resources,

2014). As a result, the Department created the California Statewide Groundwater

Elevation Monitoring Program known as CASGEM. The goal of CASGEM is to

“track seasonal and long-term trends in groundwater elevations in California’s

Groundwater Basins” (California Department of Water Resources, 2014). This

information, combined with data from other monitoring efforts has provided a clear

picture of groundwater use in California. The data has been used to prioritize

groundwater basins and identify which basins will be subject to the requirements of

the Sustainable Groundwater Management Act.

Groundwater use varies greatly throughout California. In the Central Coast

Hydrologic Region, nearly 84% of total water consumption comes from groundwater

sources (Water Education Foundation, 2015). By contrast, only 33% of the water

supply for the San Joaquin Hydrologic Region use comes from groundwater.

However, The San Joaquin Hydrologic Region uses nearly twice as much groundwater

and the Central Coast Hydrologic Region. The greatest increase in groundwater

depletion has occurred in the Central Valley Aquifer system.

Figure 2.8 below shows the distribution of water resources throughout

California.


50

Figure 2.8. California Water use by Hydrologic Region (Water Education Foundation,

2015) (Values in thousand acre-feet).


51

2.5.3 Groundwater as Savings

Many people consider groundwater analogous to a savings account. This

analogy may help people understand how groundwater works as a stock, or storage

reservoir for future consumption. However, this analogy may also be inadequate to

fully describe the nature of groundwater. In financial terms, savings can be defined as

income deferred and stored for future use. In hydrologic terms, savings can be defined

as water that is stored rather than consumed. Groundwater savings is water that could

have been consumed, but was stored for future use instead. For this research savings

is defined as surplus, accumulated by forgoing consumption, and placed in storage by

the consumer for use at a future date.

An aquifer is a subterranean water storage reservoir. It is a stock of surplus

water that has accumulated for many years. In undeveloped aquifers, surplus

accumulates when inflow exceeds outflow. Undeveloped aquifers tend to reach a state

of dynamic equilibrium when they are full. A full aquifer will naturally balance

inflows and outflows over time. For example, Figure 2.9 below shows a schematic of

the stocks and flows in the Central Valley Aquifer in California. The aquifer

accumulates surplus water in wet years. However, this water is inaccessible until

humans develop access. A consumer did not deposit the groundwater in storage.

There was no deferment of consumption for use at a later date. As such, the term

savings does not adequately describe groundwater storage.

Groundwater can be considered savings when surface water is collected and

deposited in the aquifer for future use. This is the case when humans induce recharge

through aquifer development or groundwater banking. Induced recharge occurs when

groundwater pumping reduces the volume of water stored in an aquifer. This changes

the state of dynamic equilibrium by allowing the aquifer to store water that would

have otherwise left the system. Groundwater banking occurs when runoff is collected

and allowed to infiltrate into the aquifer rather than flow out of the system.


52

Figure 2.9. Central Valley Aquifer system in predevelopment condition

(United States Geological Survey, 2009)(Values in million acre-feet).

Figure 2.10. Central Valley Aquifer system in post-development condition

(United States Geological Survey, 2009) (Values in million acre-feet).


53

Figure 2.10 above shows the Central Valley Aquifer system in its developed

state. It should be noted that precipitation volume show in Figure 2.9 differs from that

shown in Figure 2.10. This is due to the fact that the period Figure 2.9 reports the

long-term average precipitation. Figure 2.10 reports the average precipitation from

1962 to 2003. The period of groundwater development has taken place during a

period of higher than average precipitation.

Figure 2.10 shows that pumping has reduced storage in the aquifer. This

creates room for surface flows to infiltrate though induced recharge. These surface

flows that could have been consumed, were placed in storage for future use. In this

way, humans have created a groundwater savings account. However, when

groundwater consumption exceeds the rate of natural recharge and the groundwater

savings created by induced recharge, unsustainable drawdown occurs. Accumulated

deficits in excess of natural and induced recharge create groundwater debt. As such,

unsustainable consumption beyond natural and reduced recharge may best be

described as consumption of credit.

2.5.4 Groundwater as Credit

In order to understand groundwater as credit, it can help to start with the

concepts of environmental capital and environmental debt. From a systems

perspective, capital can be defined as “a stock that yields a flow of valuable goods and

services into the future” (Costanza & Daly, 1992). Depletion of this capital stock will

reduce the flow in the future. In financial terms, capital usually refers to money or

assets. In ecological economics the terms environmental capital, or natural capital are

used to discuss stocks and flows of environmental services (Harte, 1995). Costanza

and Daly (1992), considered renewable natural capital and non-renewable natural

capital as the two primary types of environmental capital. Berkes and Folke (1992)

considered environmental services to be a form of environmental capitol. Hartwick

(1997) considered waste sinks to be another form of environmental capital.

Groundwater is a form of renewable natural capital (Berkes & Folke, 1992). It can be


54

used sustainably to yield value without degradation of the stocks. In recent times,

users have begun to reduce the stock of groundwater and therefore the potential for

future yield. This reduction in stock is a form of debt.

The concept of environmental debt arose shortly after the concept of

environment as capital (Azar & Holmberg, 1995). It can be defined as a reduction in

natural capital stocks that is owed to future generations. John Hartwick (1997)

considers the concept analogous to public debt. The accumulation of groundwater

deficits is a form of environmental debt that must be repaid through future recharge.

Accumulating groundwater debt to support current consumption is similar to accessing

financial credit to support current spending.

Credit can be defined as borrowing to support present needs with the

expectation of repayment from future income. The use of groundwater can be seen as

credit because users borrow groundwater to support current water use with the

expectation that it will be repaid with future recharge. Pumping at unsustainable rates

is similar to prolonged deficit spending. The resulting groundwater overdraft is

similar to financial debt that occurs when accumulated deficits exceed accumulated

surpluses (Colander, 2010).

At its best, groundwater credit can provide a reliable source of water to buffer

against the natural variations in the hydrologic cycle (Taylor M. , 2013). This is

similar to the use of financial credit to allow individuals or businesses to continue

spending through income fluctuations. Access to groundwater credit can help

“farmers to overcome barriers to production and profitability” (Taylor M. , 2013) by

allowing production in areas that lack adequate surface supply. However, as with

traditional credit, groundwater credit requires the creation of an equal amount of debt

in the form of lower water tables or decreased storage.

Like financial credit, groundwater credit growth can be considered endogenous

growth. Endogenous means that it comes from within. It is the opposite of

exogenous, which means to come from the outside. While groundwater credit in not

created by users in the true sense, access to new sources of groundwater is created


55

through improved well and pump technologies. When wells run dry, groundwater

users are effectively out of funds. They can access new credit, up to the limits of

technology and the groundwater system, by drilling deeper wells and using stronger

pumps. In this way, growth in groundwater credit resembles the model of endogenous

credit creation to be discussed in section 2.6.3. Figure 2.11 below illustrates how

groundwater can be conceived as credit or savings.

Figure 2.11. Credit and Savings in an Aquifer. Adapted from (California Department

of Water Resources, 2003).

Williams (2008) and Hudson and Donovan (2014) discuss the potential for an

environmental credit crunch. They predict that prolonged use of natural resources at

unsustainable rates will restrict supply in a manner similar to a financial credit crunch.

A financial credit crunch occurs when potential borrowers cannot access credit due to

supply restrictions. This can occur when central banks make contractionary policy

changes or when economic events cause lenders to restrict access to credit. An


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environmental credit crunch could occur when supply of natural resources becomes

limited due to unsustainable consumption. A “groundwater credit crunch” could occur

if the demand for groundwater exceed supply due to physical limits in the groundwater

system or policy measures intended to curtail groundwater consumption.

2.5.5 Groundwater Management Tools

Historically, groundwater management has ranged from no management at all

to management by allocation of groundwater through property rights (Grisser, 1983).

These tools have proven to be ineffective at creating sustainable groundwater basins.

Recently, economists and policy makers have begun to study other management tools

and methods (Viaggi, et. al, 2010), (Stavins, 2003).

The Groundwater Sustainability Act specifies two tools available to create

sustainable groundwater basins. The primary policy tools available to GMAs are

pumping regulation, and pumping taxes. If GMAs wish to curtail the creation of

“groundwater credit” they can set (or increase) minimum groundwater levels (i.e.

reserve requirements), set/increase pumping taxes (making groundwater more

expensive), or directly regulate the amount of groundwater pumped.

Another groundwater policy tool is the use of crop subsidies and/or taxes.

Although this tool is largely unavailable to GMAs, it is a potential open-market policy

that can be used to control groundwater use. Crop subsidies can artificially increase

the demand for agricultural products and thereby the demand for groundwater. Water

intensive crops like cotton are often heavily subsidized. A reduction in crop subsidies

would be similar to reducing quantitative easing by reducing the amount of securities

purchased by the Fed. Alternatively, if the existence of crop subsidies are already in

place, then reducing subsidies could be similar to selling securities to reduce credit

creation.

Groundwater management can be used to control the use of “groundwater

credit” and thereby regulate groundwater consumption. The goal of sustainable

groundwater management should be to use these tools to bring about sustainability in a

way that will avoid or minimize a “groundwater credit crunch”.


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As freshwater supplies diminish and population increases, it will be important

to rethink supply and demand management in California (Gleick, 2010). Supply

management strategies are intended to increase the amount of a resource available for

use. Demand management strategies are intended to reduce (or control) resource use

through conservation, technology, or regulation. Market-based instruments are

another management tool.

Market-based instruments are policies or “regulations that encourage behavior

through market signals rather than through explicit directives (Stavins, 2003). This

type of price-based demand control can be effective at promoting resource

conservation and more cost effective than traditional regulatory approaches (Olmstead

& Stavins, 2009). However, the effectiveness of market-based instruments depends

on the price elasticity of water (Glennon, 2009). Instruments like Pigovian taxes can

help reduce demand by increasing the cost of resources (Viaggi et al. 2010) if water

exhibits sufficient price elasticity. In this way, they can mitigate the negative

externalities associated with overexploitation of common pool resources. Revenue

from these taxes can be used to fund the investment in alternative supply and

conservation measures that will be needed to support growth in agricultural

production. Unfortunately, on April 21, 2015, a California court decision found that

the use of tiered water rates to facilitate conservation violates the state constitution

(Cuniff, 2015) limiting the ability of water managers to use market-based instruments

to manage water.

The groundwater management tools can be used to change groundwater

consumption. Market based instruments can increase the cost of groundwater and

thereby reduce demand. Setting minimum groundwater storage requirements can

reduce the amount of groundwater available. Investing in new water supply sources

(recycling, desalination, and inter-basin transfers) can reduce reliance on natural

groundwater stocks. Subsidizing crops can support demand for lower water use crops

and change the overall demand in the system. These policy levers are similar to those

used to control credit creation and aggregate demand in a monetary system. In order


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to better understand the similarities between the two systems it is necessary to

understand how groundwater can be viewed as a form of credit.

2.5.6 Aggregate Groundwater Demand

According to the conservation of mass, total inflow minus total outflow equals

the change in storage (Maliva, 2014). Mass balance allows calculation of the change

in storage (Storage) according to the following equation (Raeisi, 2008):

IA + IS = OA + D + E + Storage (1)

Where: IA = Subsurface inflow

IS = Surface recharge and seepage

OA = Subsurface Outflow

D = Discharge from wells, springs, and perennial streams

E = Evaporation (Generally negligible)

Storage = Net change in aquifer storage

The left side of this equation represents inflow. The right side represents Aggregate

Groundwater Demand (AGD) and the change in aquifer storage. Each groundwater

system will have different components of inflow and outflow depending on the

specific conditions of the basin in question.

Aggregate Groundwater Demand (AGD) can be seen as the total demand for

all water in the groundwater basin. This includes water for human consumption,

environmental consumption, and storage. It is the aggregate sum of all basin outflows

over a given period and the change in aquifer storage. Using the mass balance

equation, it is possible to derive a simple equation for AGD in a form that is similar to

the financial aggregate demand equation presented in section 2.8.3. This equation is

presented below:

AGD = IA + IS + (Y – X) (2)

Where: AGD = Aggregate Groundwater Demand

IA = Subsurface inflow


X = Total basin outflow

Y = Total basin inflow

(Y – X) = Net change in aquifer storage (excluding other

inflows and outflows)


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Alternatively, Aggregate Groundwater Demand can be modeled based on

Keen’s equation from section 2.8.3.

AGD = Inflow + Storage (3)

In this equation, the change in debt is similar to a change in storage, and inflow is

similar to income.

Modeling the equation for aggregate groundwater demand on Keens equation

for economic aggregate demand rather than Krugman’s conception of aggregate

demand is justified by the inclusion of future expectations. Future expectations clearly

play a role in groundwater demand. Farmers decide which crops to grow based on

expectation about the waters supply. Municipal consumers certainly expect water to

be available for future use.

In order to create sustainable groundwater basins, GMAs must regulate

Aggregate Groundwater Demand (AGD). If a basin is in overdraft, then the GMAs

must reduce AGD to achieve sustainability. This process is similar to contractionary

monetary policy. It will create disequilibrium between supply and demand for

groundwater and result in a form of credit rationing.

2.5.7 Contractionary Groundwater Policy in California

In the past, there has been very little groundwater management for the majority

of California (Carle, 2009). Most groundwater users have been allowed to pump as

much water as they can put to beneficial use. This expansionary policy has led to

unprecedented growth in groundwater consumption. Residents and regulators have

begun to recognize the unsustainable nature of this policy and are in the process of

enacting policy that could contract groundwater use in many basins. This

contractionary policy is similar to contractionary monetary policy used to control

inflation.

The Reasonable use Doctrine requires that water must be put to beneficial use

to establish a water right (Wilson, 2011). Water rights cannot be perfected based on


60

wasteful or unreasonable use of water. According to the reasonable use doctrine, the

excessive use or overconsumption of groundwater from an over drafted groundwater

basin is considered an unreasonable use of water regardless of how efficient or

beneficial the use (Gray, 1994). However, this has not been sufficient to limit the use

of groundwater in many basins. The main recourse for users deprived of groundwater

by others is adjudication. Groundwater adjudication is a form of court- imposed

groundwater management. In an adjudicated basin, the court appoints a “water

master” to allocate pumping rights and manage the groundwater levels in the basin.

Through the legal process, the common pool resource system is converted to a

collection of private property rights.

Some areas in California have developed management districts without

adjudication. The largest and most well know of these is Orange County. In 1933, the

Orange County Water District Act created the Orange County Water District (Orange

County Water District, 2013). The formation of the district did not constitute

adjudication, but rather a mechanism for local control of the groundwater basin. Users

were not required to limit pumping, but the district was authorized to collect fees for

groundwater use. These fees, known as a pumping tax, are used to protect the basin

through groundwater replenishment. Groundwater management in Orange County has

been considered successful (Ostrom, 1990) partly because groundwater users

voluntarily accepted local management.

There are many laws and management systems to govern surface water in

California. However, until recently there have been no statewide policies to manage

groundwater (Carle, 2009). That changed in 2014 with the passage of the

Groundwater Sustainability Act, which requires the creation of Groundwater

Management Agencies (GMAs). These GMAs charged with maintaining the

sustainability of individual groundwater basins through groundwater policy.

The Sustainable Groundwater Management Act (SMGA) is a collection of

three bills signed into law by Governor Brown in 2014. The act is composed of

Assembly Bill (AB) 1739, Senate Bill (SB) 1168, and SB 1319. Assembly member


61

Roger Dickinson of Sacramento proposed AB 1739. State Senator Fran Pavely of the

27th district in southern California proposed SB 1168 and SB 1319.

The Act requires that groundwater resources be managed sustainably for long-

term reliability and multiple economic, environmental and social benefits (Association

of California Water Agencies, 2014). The SGMA defines sustainable groundwater

management as the use of groundwater in a manner that can be maintained without

causing undesirable results. (Water Education Foundation, 2015). An “undesirable

result” can include any of the following:

1. Chronic lowering of groundwater levels

2. Significant seawater intrusion;

3. Significant degradation of water quality; and

4. Significant land subsidence;

The SGMA requires the Department of Water Resources (DWR) to evaluate

and prioritize basins. It requires the creation of local GMAs in high and medium

priority basins by June 30, 2017 and provides regulatory tools to achieve sustainable

groundwater management. These tools include the ability to measure and manage

groundwater extractions and assess fees. The act allows 20 years for GMAs to bring

groundwater management to sustainable levels (Association of California Water

Agencies, 2014).

In basins where groundwater extraction is unsustainable, GMAs may be

required to contract groundwater consumption. This contraction could have

significant social and economic impacts. This new groundwater policy appears to be

analogous to “tightening” monetary policy in which the Federal Reserve (Fed) curtails

credit growth to maintain sustainable economic growth. If GMAs attempt to contract

demand to sustainable levels too quickly, they run the risk of creating a “groundwater

credit crunch”. The goal should be to control the rate of contraction to achieve

sustainable levels without the crippling consequences of a credit crunch. To

accomplish this goal, regulators will need to understand groundwater management as a

system. Knowledge about how to accomplish this goal may be found in monetary

policy and economic theory.


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2.6 Economic Theory

In order to compare groundwater management to monetary policy it is

necessary to understand some of the relevant economic theories. The field of

economics has evolved to at least eight schools of thought (Radzicki, 2003). Each

school holds specific views and opinions of various economic theories. A complete

discussion of these schools and theories is beyond the scope of this work. Three

theories of particular relevance to this discussion are Equilibrium Theory, Loanable

Funds Theory, and the Theory of Endogenous Credit. These theories are the most

relevant to the discussion of systemic similarities between monetary policy and

groundwater management.

Equilibrium theory is important for the comparison between groundwater

management and monetary policy. In a contractionary environment, there may be

disequilibrium between supply and demand. This is the case in credit rationing and

water rationing.

The theory of endogenous credit and the loanable funds theory are also

important for comparing groundwater management and monetary policy. These are

competing theories about the nature of credit. As such, it is important to understand

how each might apply to groundwater in a contractionary environment.

2.6.1 General Equilibrium Theory

General Equilibrium Theory forms the basis for most modern economic

thought (Gintis, 2007). Leon Walras first formulated the theory in 1874. It states that

a set of prices exists in which supply equals demand in all markets (Arrow & Debreu,

1954). It is the theory that “opposing dynamic forces cancel each other out”

(Colander, 2010, pp. G-3) and therefore there is no impetus for change (Samuelson &

Nordhaus, 2001). It is the dominant theory of the current economic paradigm because

it provides an assumption of market equality that simplifies the mathematics of

economics.


63

While most economists agree that equilibrium theory is important in modern

economics, many claim that the assumption of equilibrium is over-applied

(Coddington, 1976), (Friedman, 1955), (Dow, 1995). Historically, the assumption of

equilibrium has been used because no other method was known (Keen, 2008).

According to Ackerman (2002), equilibrium, under the general equilibrium model is

neither unique nor stable. “This conclusion is clearly at odds with established modes

of thought about economics” (Ackerman, 2002, p. 120).

Credit rationing and unemployment are often cited as examples where

equilibrium theory does not hold (Stiglitz & Weiss, 1981). Both phenomena represent

disequilibrium. In the case of credit rationing, demand for credit exceeds supply. In

the case of unemployment, demand for employment exceeds supply.

Economic systems are open systems. As such, true static equilibrium does not

apply (Bertalanffy, 1969). It would be more accurate to apply the concept of dynamic

equilibrium characterized by perpetual disequilibrium and constant fluctuation around

true equilibrium. Disequilibrium is an important concept in Keynesian economic

philosophy.

2.6.2 Loanable Funds Theory

Loanable funds theory states that the supply of credit is based on the amount of

funds deposited by savers and investors in accounts at lending institutions (Mankiw,

2010). This is the dominant theory of credit in mainstream economics and is

supported by the assumption of general equilibrium. In this theory, the interest rate

for credit is in dynamic equilibrium. The rate adjusts based on supply and demand to

ensure that the supply of credit equals the demand.

2.6.3 Endogenous Credit Theory

The endogenous theory of credit as postulated by Lavoie (1984) as well as

Bernardo and Campiglio (2014), states that banks create credit, and thereby money, by

their own actions. Simply put, endogenous credit is created from within the banking

system rather than from external forces or a supply of loanable funds. In this model,


64

banks decide the amount of money that they wish to lend regardless of the funds on

deposit. If the demand for funds exceeds the supply of deposits, the bank will borrow

funds from the central bank to cover the shortfall. In this theory, equilibrium is only

satisfied when the central bank “creates” money for lending. Under endogenous

money theory, “money should be considered as income money and credit money”

(Lavoie, 1984, p. 791). This is the basis for Keen’s (2012) argument that changes in

credit affect aggregate economic demand.

2.7 Monetary Theory

At least eight competing schools of thought exist within the broad field of

economics (Radzicki, 2003). These schools include the Austrian, Classical, Neo-

Classical, Monetarist, Chartalist, Keynesian, Neo-Keynesian and Post-Keynesian

schools among others. These schools of thought represent slightly different

paradigmatic views of the broad discipline of economics (Coddington, 1976). The

evolution of these schools illustrates the evolution of the science of economics through

the Kuhnian concept of normal science (Kuhn, 1962). However, recent debates about

the role of banking and credit in macroeconomic monetary theory have exposed

significant paradigmatic differences within monetary theory (Bernardo & Campiglio,

2014).

While a complete discussion of the various schools of economic thought is

beyond the scope of this work, a discussion of Keynesian, Monetarist, and New

Classical economics is warranted. These schools will be described with respect to

their positions on credit, aggregate demand and equilibrium. Keynesian Theory and

New Classical Theory offer opposing views while Monetarist Theory falls somewhere

in-between (Stein, 1981).

2.7.1 Keynesian Theory

The economist John Maynard Keynes was one of the first to postulate a

systemic link between monetary policy and aggregate economic activity (Snippe,


65

1985). He also clearly identified a link between water and economics. This

connection, known as Hydraulic Keynesianism, “conceives of the economy at the

aggregate level in terms of disembodied and homogenous flows” (Snippe, 1985, p.

470). Keynes believed in a stable relationships between the flow of money (and

credit) and aggregate demand (Coddington, 1976). He focused on short-term,

macroeconomic controls to stabilize the economy and control output (Colander, 2010).

Keynes believed that systemic effects, including negative feedback loops, could affect

economic income. According to Colander (2010), Keynesian theory supports the idea

that monetary and fiscal policy can be used to close the gap between equilibrium

income and potential income. Potential income is the maximum possible income for a

given economy. Equilibrium income fluctuates and is smaller than potential income.

Systemic forces drive economic output to a level that is lower than its potential.

Keynesian theory differs from classical economic theory with respect to

equilibrium and aggregate demand. Keynes was a critic of classical economics and it

reliance on equilibrium theory. He argued that much of classical economics is only

applicable to special cases when equilibrium can be assumed (Keynes, 1936). His

theories were concerned with “general cases” which, in his view, make up the

majority.

2.7.2 Post-Keynesian Theory

Over time, the early Keynesian economic philosophy has evolved into Post-

Keynesian philosophy (Klein J. J., 1982). Post Keynesians believe in a systems

approach with a focus on disequilibrium (Radzicki, 2003). They believe that changes

in aggregate demand will significantly affect economic output while prices and wages

remain relatively constant (Samuelson & Nordhaus, 2001). Finally, they believe that

future expectations play an important role in economic activity and aggregate demand

(Radzicki, 2003).

The recent financial crisis of 2008 has brought a resurgence in Keynesian

philosophy as economists recognized the need for government intervention (Colander,

2010). Keynesians agree with monetarists that monetary policy is the most effective


66

way to provide economic stability at the macro level (Samuelson & Nordhaus, 2001).

However, Post Keynesians believe that fiscal policy also plays an important role.

2.7.3 Monetarist Theory

Monetarists believe that monetary policy is the most effective way to provide

economic stability (Samuelson & Nordhaus, 2001). They contend that aggregate

demand is solely determined by the supply of money. This is an intermediate

philosophy between Keynesian and New Classical extremes (Stein, 1981).

Monetarists subscribe to the Quantity Theory of Money, which states that

prices are directly related to the amount of money in circulation (Friedman, 1987).

This theory is the basis for open market operations called quantitative easing or

quantitative tightening. Monetarist believe that prices increase or decrease based on

the size of the money supply. Keynesians also subscribe to the Quantitative Theory of

Money. However, they contend that the supply of money is determined by aggregate

economic demand rather than direct control of the money supply (Hicks J. R., 1937).

2.7.4 New Classical Theory

The New Classical economic philosophy is based on the assumption of price

and wage elasticity combined with rational expectation. New Classical theorists

believe that fiscal policy and monetary policy cannot effectively change economic

output (Samuelson & Nordhaus, 2001). The philosophy represents the opposite

extreme from Keynesian philosophy (Stein, 1981).

2.8 Monetary Policy

Monetary policy uses the supply of money to affect the economy. Many

countries use a central bank to control monetary policy through fractional reserve

banking. In the United States, the Federal Reserve (Fed) is charged with maintaining

the stability of the financial system through monetary policy. The Fed uses policy

tools to create sustainable economic growth. Central banks have several tools

available to affect aggregate demand and economic output through control of the


67

supply of money and credit. These tools can be used to expand or contract aggregate

economic activity (Klein J. J., 1982).

2.8.1 Monetary Policy Tools

Expansionary monetary policy increases the money supply in order to

stimulate economic activity, whereas contractionary policy does the opposite. These

tools act as levers on the monetary system. Changes in policy cause the system to

change to a new state of dynamic equilibrium and can affect aggregate demand.

Figure 2.12 below shows the tools used by the central banks to implement monetary

policy.

As Figure 2.12 shows, central banks have many tools available. There are

three primary tools used to control the economy, aggregate demand (Nelson, 2002)

and arguably, credit. They are reserve requirements, interest rates, and open market

operations. These tools work together to control the supply of money and credit.

This, in turn affects the economy as a whole.

Open market operations are a way of controlling the supply and demand of

money by buying or selling securities. Currently the Fed relies heavily on Open

Market Operations as the primary monetary policy tool (Klein J. J., 1982). When a

central bank purchases securities it is called quantitative easing. The process increases

the money supply and bank reserves which facilitates the creation of credit (and debt).

When a central bank sells securities it is called quantitative tightening. This process

has the opposite effect on credit.

“Twenty-four of the thirty countries that belong to the Organization for

Economic Co-operation and Development (OECD) employ reserve requirement

systems” (O'Brien, 2007). The reserve requirement is the ratio of a bank’s reserve

assets to deposit liabilities (Klein J. J., 1982). Banks must hold a fraction of their

assets to ensure that adequate funds are available for customer withdrawals. It is a

legal requirement for all member institutions in the Fed. Changes in the reserve

requirement rarely occur due to the strong, destabilizing effects. Increases in the

reserve requirement can force rapid contraction in credit availability and instigate a


68

Figure 2.12. Monetary Policy Tools (adapted from O'Brien, 2007).

Tools for Monetary Policy

Implementation

Standing

Facilities

Reserve Requirement

Systems

Open Market

Operations

Demand for Deposit

Balance at Central Bank Supply of Deposit

Balances at Central Bank

Required

Reserve

Balances

Excess Reserve and/or

Settlement Clearing

Balances

Central Bank’s

Holdings of

Securities and RPs

Loans from

Standing

Facilities

Other Items on

Central Bank’s

Balance Sheet

(Autonomous Factors)

Overnight

Interest Rate

Total Demand for Deposit

Balances at Central Bank Total Supply of Deposit

Balances at Central Bank

Central

Bank

Notes

Government

Deposits at

Central Bank

Check

Float

All Other

Autonomous

Factors


69

credit crunch. However, according to Klein (1982), these sharp contractions

associated with increases in the reserve requirement can be offset by expansionary

open market operations.

Changes in the interest rate affect the cost of money and therefore the cost of

credit. The interest rate that banks pay when they borrow funds depends on who is

loaning the funds. Typically, banks will borrow from other banks at the federal funds

rate, or directly from the Fed at the discount rate. The discount rate is higher than the

federal funds rate. It is “the interest rate that a district Federal Reserve Bank charges

depository institutions when they borrow reserves” (Klein J. J., 1982, p. 263).

Changes in the discount rate or the federal funds rate can affect the availability and

cost of credit. However, these changes have not be ineffective monetary policy tool

unless accompanied by other tools such as open market operations (Klein J. J., 1982).

2.8.2 Credit

Credit, in financial terms, is the use of someone else’s money in the present in

exchange for a promise to repay at a future date (Samuelson & Nordhaus, 2001). In

general, it is the use of “tomorrow’s standard of living to raise today’s standard of

living” (Hudson & Donovan, 2014, p. 6) by borrowing resources in the present with

the expectation of repayment in the future.

The precise modes of credit creation is a subject of recent debate. Economists

have different theories about credit creation and the role of credit in aggregate

demand. A 2012 debate between Paul Krugman and Steve Keen illustrated the

division between competing economic paradigms (Carney, 2012).

Steve Keen is an Australian economist who subscribes to the theory of

Endogenous Credit. He contends that commercial banks control credit creation

(Bernardo & Campiglio, 2014). Keen rejects the Loanable Funds Theory (Keen,

2013) and neoclassical reliance on equilibrium theory. He believes that aggregate

demand is the sum of income plus the change in debt (Keen, 2012).


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Paul Krugman is an American economist, and Nobel Laureate, who strongly

disagrees with Keen. Krugman contends that central banks control credit creation

(Bernardo & Campiglio, 2014). He believes that credit and debt do not factor into

aggregate demand.

The issue of endogenous credit is importance for the comparison to

groundwater credit. In economic terms, it helps link credit to aggregate demand.

Groundwater credit, as discussed in section 2.5.2, can be considered endogenous. As

such, it is possible to link groundwater credit to aggregate groundwater demand.

2.8.3 Aggregate Demand

Aggregate demand (AD) is the demand for all goods and services produced by

an economy at any time and at all price levels (Samuelson & Nordhaus, 2001). The

commonly accepted equation for aggregate demand is:

AD = C + I + G + (X – Y) (Samuelson & Nordhaus, 2001) (4)

Where:

AD = Aggregate Demand

C = Consumption

I = Investment

G = Government Spending

X = Total Exports

Y = Total Imports

(X – Y) = Net Exports or (change in accumulated storage)

Keen and Krugman disagree on the effect of credit on aggregate demand

(Bernardo & Campiglio, 2014). Krugman does not consider credit or debt to be

relevant components of aggregate demand. Keen considers aggregate demand to be

directly related to credit and debt (Keen, 2013). Bernardo and Campiglio (2014) claim

that the difference of opinion can be explained by differences in the definition of

aggregate demand (Boesler, 2012). They claim that Krugman and Keen are both

correct within their own definition of aggregate demand. Krugman considered

aggregate demand to include only realized expenditures, whereas Keen contends that


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aggregate demand also includes planned expenditures or future expectations (Bernardo

& Campiglio, 2014). Colander (2012) agrees with Keen.

According to Keen (2012), aggregate demand can be found by the following

equation:

AD = Income + Debt (5)

2.8.4 Contractionary Monetary Policy

When a government or central bank attempts to control the aggregate

expenditures in an economy it engages in aggregate demand management (Colander,

2010). Expansionary economic policy will result in increased aggregate demand.

Contractionary policy will decrease aggregate demand (Colander, 2010). Monetary

tightening is a contractionary policy that reduces aggregate demand by reducing the

supply of money and credit.

Central banks may attempt to relieve inflationary pressures through

contractionary monetary policy (Klein J. J., 1982). There have been approximately

thirteen monetary tightening cycles in the United States since 1955 (Adrian & Estrella,

2008). Some of these have constrained credit growth too quickly resulting in a “credit

crunch” or “credit crisis.” The goal of tight monetary policy is to facilitate a

controlled contraction rather than a systemic shock with drastic negative

consequences.

2.9 Systems Analysis

A system, in the simplest definition, is a set of “elements standing in

interrelation” (Bertalanffy, 1969, p. 38). Yet, great complexity can result from this

simple definition. The elements of a system can be physical and tangible or they can

be intangible relationships, policies, values or beliefs (Anderson & Johnson, 1997).

Systems can be natural, man-made, or a combination of both. Systems typically

behave in a non-linear manner that is counter-intuitive and difficult to predict. System

dynamics can provide valuable insight for the creation of water resource management


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policies that account systemic interactions and complex human behavior (Winz, et al.

2009).

Systems analysis techniques can be used to identify potential isomorphisms

between two systems. Cantu and Beruvides (2013) propose a two-step methodology

for assessing isomorphological relationships between two systems. The first step uses

systems analysis to document the structural elements and relevant characteristics in

each system. The second step is to determine how these characteristics compare to

each other. Systems analysis begins with the identification of structural elements,

including policy levers, stocks, flows and causal loops present in each system. If the

systems are sufficiently similar in structure, they may be considered homological

systems. Evaluation of system behavior is then used to compare the behavior of each

system over time. If the systems behave in a similar manner, they may be considered

isomorphic.

Our water resource system is an example of a highly complex set of

interrelated elements. The natural hydrologic system provides water for various

ecosystems and human consumption. Physical elements like weather and geology

interact with fragile biological systems and a complex web of human cultural values

and policies. The addition of recycled water to this complex system will cause ripples

that can affect the system in surprising ways.

Water that increases base-flow in streams or improves wetland habitat can

have significant environmental benefit. Water that offsets groundwater pumping can

result in increased sustainability and water security. Groundwater, surface water and

recycled water are all components of a complex hydrologic system. As such, they

cannot be effectively managed independently (Sophocleous, 2000). It will require a

systems perspective.

2.9.1 General Systems Theory

General Systems Theory (GST) appeared in the 1950s in response to a

perceived failure of reductionist science to adequately explain the vast, increasing,

complexity that characterizes our observable world. Various theories and concepts of


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systems developed independently and somewhat spontaneously in disparate scientific

fields like biology, psychology, mathematics and linguistics (Bertalanffy, 1969).

These concepts were collated, developed and refined into General Systems Theory by

German biologist Ludwig von Bertalanffy. His work is the foundation for modern

systems science and systems engineering.

2.9.2 Open and Closed Systems

One of Bertalanffy’s (1969) most important contributions to GST is the

concept of open systems and closed systems. Systems display different behavior

depending on their classification as open or closed. A closed system is self-contained

and does not interact with the external world. A closed system will exhibit decreasing

complexity over time. An open system interacts with the external environment and

grows increasingly complex over time. Our water resource system is an open system.

Inputs in the form of solar energy drive climatic changes, which in turn drive

biological and social changes in a non-linear path towards increasing complexity.

2.9.3 Stock and Flow

Stock and flow variables are important in system dynamics modeling and

economics. Flows are rate terms measured with respect to time (Singh, n.d.). They

are not measurable when model time stops. Flow quantities enter stocks, which

modify their rates when they exit. Stream flow and subsurface flow are examples of

flow variables in hydrologic systems.

Stocks accumulate and release the quantities that make up flows. They are

measureable at a point in time and are measurable when model time stops (Singh,

n.d.). Groundwater storage and money supply are examples of stock variables.

The appropriate classification of variables as either stock or flow is a critical

step in dynamic modeling (Klein L. R., 1950) because they make up the structure of a

system. The combination of stocks and flows in a system can create unusual patterns

of behavior over time (System Dynamics Society, n.d.). These patterns can be


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counter-intuitive and difficult to predict. This is particularly true when stocks and

flows combine with feedback and delay.

2.9.4 Feedback and Delay

Since elements within a system are interrelated, an output or action from one

component of a system will affect the other components of the system. The actions of

these components will eventually loop back to affect the first component in a cyclical

process called feedback. Feedback is one of the fundamental building blocks of

systems and systems dynamics models (Radzicki, 2003). The structure of a complex

system will contain various combinations of balancing and reinforcing feedback loops

that act together to determine the behavior of the system (Anderson & Johnson, 1997).

Groundwater is a renewable resource with a slow-feedback mechanism

resulting in a systemic delay (Green, et al, 2011). A delay in system feedback can

make management of the system difficult (Anderson & Johnson, 1997) because the

results of actions may not be apparent until long after the action is taken. Transient

pumping effects in groundwater systems may change the aquifer recharge and

discharge characteristics over a long period of time (Harou & Lund, 2008).

Feedback is “the return of information about the status of a process” (Anderson

& Johnson, 1997). There are many examples of feedback in our water resource

system. For example, groundwater pumping can reduce stream flows and destroy

wetland habitat. The reduction of wetland habitat can reduce groundwater recharge in

a reinforcing loop. At the same time, reduced groundwater levels leave more room for

storage in the aquifer. This induces more recharge in a balancing loop.

Feedback interactions can occur between human elements in the system as

well. For example, the presence of abundant water can signal agricultural water users

to plant more crops (Gohari, et al. 2013). As water use increases, farmers receive a

signal that water is becoming scarce and act to reduce consumption. Alternating

between balancing and reinforcing loops may lead to a state of dynamic equilibrium.

However, socio-economic pressures and population growth often counteract the desire

to reduce consumption. Additionally, delay between the action of using a resource


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and feedback provided by the system can lead to overuse and depletion of the resource

(Shahbazbegian & Bagheri, 2010). This can lead to a state of perpetual decline of

resource stocks.

2.9.5 Systemic Overshoot

“To overshoot means to go too far, to go beyond limits accidentally – or

without intention” (Meadows, et al, 2004, p. 1). It occurs when the rate of growth in a

reinforcing loop is uncontrolled and the response from the balancing loop is delayed.

Overshoot is likely to occur when growth approaches a natural limit and a delay

prevents a timely corrective response. Groundwater is a renewable resource with a

slow feedback mechanism (Green, et al., 2011). As such, it is highly susceptible to

systemic overshoot.

Delays make it difficult to control systemic behavior (Anderson & Johnson,

1997). They can cause resource consumption to exceed sustainable levels (Meadows

et al, 1972). When a delay is present, systemic overshoot can result in destruction of a

resource pool before the feedback can facilitate an adequate response. Often,

technological measures that relieve the constraints caused by balancing loops can

contribute to systemic overshoot (Meadows et al, 1972). They can reduce the impact

of balancing forces in the short term while doing little to change the natural limits of

the system.

There is a high potential for groundwater consumption to overshoot sustainable

limits because of the recent rapid growth in demand and consumption coupled with a

delay by consumers to reduce consumption. This delay can be caused by failure to

adequately monitor consumption or by the asymmetric cost/benefit relationship

associated with reducing consumption.

2.9.6 Dynamic Equilibrium

According to Bertalanffy (1969), true equilibrium is only attainable in closed

systems. In fact, all closed system must eventually attain complete equilibrium.

However, true closed systems are rare. Economic systems and groundwater systems


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are open systems. As such, theories based on a model of dynamic equilibrium are

more appropriate.

Most systems we encounter, whether biological, social or economic, are open

systems. Equilibrium in open systems is best described as a “(quasi-)stationary” state

of perpetual disequilibrium (Bertalanffy, 1969). It is dynamic rather than static. A

system in dynamic equilibrium will fluctuate around an equifinal condition while

never coming to rest at true equilibrium. This fluctuation, characterized by recurring

false start and/or overshoot (Bertalanffy, 1969), appears as goal seeking behavior over

time (Anderson & Johnson, 1997). In fact, this behavior is a function of an open

system dictated by its systemic structure.

Organisms, as open systems, strive to attain dynamic equilibrium called

homeostasis. The characteristics of this state depend on the structure of the system.

Economic systems and groundwater systems are also open systems. As such, they will

tend toward a dynamic equilibrium dictated by their structure.

External conditions can alter the behavior of a system in the short term.

However, the dynamic equilibrium of a system can only change in when the structure

of the system changes. In one sense, management can be seen as a tool for directing

the short-term response to external conditions. At its best, it can be seen as the

purposeful manipulation of internal structure for the purpose of altering dynamic

equilibrium. Managing a groundwater system for sustainability will require structural

change sufficient to shift the consumptive demand to a new, sustainable, dynamic

equilibrium.

2.9.7 Confidence Testing and Validation

System dynamics has often been criticized for reliance on qualitative

validation procedures (Barlas, 1996). The roots of this criticism are grounded in the

fundamental, philosophical differences between causal and correlational models

(Barlas & Carpenter, 1990). Both types of models are based in mathematics, but they

have different purposes. Therefore, the method of validation for causal models is

different from that of non-causal models. The purpose of this section is to compare


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the different conceptions of validity and discuss the confidence tests used to establish

validity in system dynamics models.

The classical concept of validity originates in the philosophy of logical

empiricism. The system dynamics concept of validity is grounded in the relativist

philosophy of science (Barlas & Carpenter, 1990). As such, system dynamics

researchers and theorists believe that there is no single, objective or absolute test for

validity (Sterman, 1984). At the heart of this philosophical conflict is the difference

between relative validity and absolute validity. Absolute validity is based on

statistically significant agreement with empirical data. Relative validity allows for

agreement relative to the model’s purpose. In the context of system dynamics, the

validity of a model cannot be separated from its purpose. A model is judged to be

valid if it is suitable for its intended purpose and provides result that are sufficiently

accurate for that purpose (Forrester, 1968).

The purpose of non-causal models is to predict with statistically significant

accuracy (Barlas & Carpenter, 1990). Non-causal models are considered valid when

they produce results that agree with observed reality in a statistically significant

manner. This statistical significance is sufficient to establish validity (within a

specified range) regardless of the underlying logic or understanding of causation

(Forrester, 1968). This type of statistical validation approach is considered “external

validation” (Taylor A. , 1980). According to the relativist philosophy of science, the

fact that logical causality is not a prerequisite for validity is a weakness of non-causal

models. Sterman (2000) goes so far as to say that only pure analytical statements can

be fully validated. However, according to the empiricist philosophy of science, this is

considered a strength and an indication of objectivity.

The goal of causal, system dynamics models is to predict and explain (Barlas

& Carpenter, 1990). Often, the explanatory power of a system dynamics model is

more important for policy decisions than the precision of the predicted results.

Historically, those who subscribe to the relativist philosophy of science have been

willing to accept a lower level of correlation with observed data in exchange for the

explanatory power of causality. The threshold for statistical significance is lower to


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reflect less emphasis on predictive precision. Since statistical validation of system

dynamics models is often not possible, these models are generally subject to “internal

validation” (Taylor A. , 1980).

Confidence tests are methods for comparing a model to observed reality for the

purposes of corroboration or refutation (Forrester & Senge,1979). They are distinct

from the classical concept of validation because they can rely on logical comparison

rather than pure statistical agreement between empirical data and model output. While

no model is useful or valid if expected outputs do not coincide with empirical data, a

system dynamics model can be considered valid with a lower level of statistical

significance.

In system dynamics, model building is an iterative process of testing and

validation. The process involves both qualitative and quantitative analysis.

Quantitative analysis ensures that the accuracy of model output is sufficient for the

purpose of the model. Qualitative analysis helps modelers understand the system and

ensures that the results are correct for the “right reason” (Barlas, 1989). Models build

confidence in the model through repeated cycles of validity testing and refinement.

Figure 2.13 below shows a simplified view of the system dynamics modeling process.


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Figure 2.13. Simplified Modeling Process (Qudrat-Ullah & Seong, 2010).

Qualitative Model

A Causal Loop Diagram

Structural

Validity Behavior

Validity

Problem

Purpose and Intended Use of the Model

Quantitative Model

SD-based Computer Simulation Model


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Barlas (1989) identifies the four main aspects of model validity shown below

in Figure 2.13. These aspects include the real system, the model, structural validation

and behavior validation. The real system includes exogenous inputs and non-systemic

forces called “noise”. The model is a mathematical representation of the real system

based on known or assumed parameters and noise characteristics. The primary

methods for establishing model validity are in the structural validity tests and

behavioral validity tests.

Forrester and Senge (1979) identify 17 tests for building confidence in system

dynamics models. They divide these tests into three main categories including

structural validity tests, behavioral validity tests and policy tests. Some or all of these

tests can be used to support an assertion of validity. However, the structural tests and

structurally oriented behavior tests are always required. The following discussion is a

summary of these tests.


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Figure 2.14. Major Aspects of Model Validation (Barlas, 1989).

MODEL VALIDITY

Structural Validation:

1. Comparing the model

equations to the real

system relationships

(“Empirical”

Structure Tests).

2. Comparing the model

equations with the

available theory.

(Theoretical structure

tests). REAL SYSTEM

MODEL

- Mathematical

Equations

- Parameter

Values

- Noise

Characteristics

Exogenous Inputs

Model

Behavior

Observed

Behavior

Unsystemic Forces

(noise)

Behavior Validation:

1. Pattern Prediction

Tests.

2. Structurally oriented

Behavior Tests.


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Structural validity tests are used to verify that the structure of a system

dynamics model is an adequate representation of the structure of the observed system

(Barlas, 1989). The notion of adequacy is subjective and therefore suspect to those that

subscribe to the philosophy of empiricism. However, the notion of adequacy is

relevant when considering the purpose of the model in question. The adequacy of the

model’s representation should match the level of predictive accuracy desired.

According to Forrester and Senge (1979), the fundamental requirement for

establishing structural validity is that the model structure not contradict knowledge

about the structure of the observed system. They identify five tests for structural

verification. These tests are considered part of a core test for overall validity of a

system dynamics model. Table 2.1 below lists the tests of model structure along with

a brief description.

Table 2.1 Tests of Model Structure (Forrester & Senge, 1979).

Test Comment

Structure Verification Compare model structure to observed structure.

Parameter Verification Conceptual and numerical comparison to observed

system.

Extreme Conditions Model should permit extreme conditions considered

in observed system.

Boundary Adequacy

(Structure)

Examine model boundaries and asses plausible

hypothesis about elements excluded from the system.

Dimensional Consistency Dimensional analysis for rate equations and stock unit

dimensions.

“Tests of model behavior are used to evaluate the adequacy of model structure

through analysis of behavior generated by the structure” (Forrester & Senge, 1979, p.

18). These tests typically compare model behavior with observed behavior to increase

confidence in the model structure. Table 2.2 below lists the tests of model behavior

along with a brief description.


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Table 2.2 Tests of Model Behavior (Forrester & Senge, 1979).

Test Comment

Behavior Reproduction Compare model behavior to observed behavior.

Multiple tests include symptom generation, frequency

generation, relative phasing, multiple mode, and

behavior characteristic tests.

Behavior Prediction Compare model behavior to behavior predicted by

causal hypothesis. Tests include pattern prediction,

event prediction and shifting mode prediction.

Behavior Anomaly Identify flaws in the model by analyzing model

behavior that does not match observed behavior.

Boundary Adequacy

(Behavior)

Evaluating behavior in multiple models with

questionable structures included to determine if the

structures should remain outside of the boundary or be

included in the model.

Family Member Compare system behavior to that of known classes of

systems.

Surprise Behavior Identification and analysis of unpredicted behaviors to

determine if it is anomalous or real, but not observed.

Extreme Policy Analysis of dynamic behavior associated with

extreme policy conditions not generally observed.

Behavioral Sensitivity Evaluate the sensitivity of model behavior to changes

in parameter values.

Forrester and Senge (1979) consider the ultimate validity of a system dynamics

model to be related to the model’s ability to perform as a useful policy analysis tool.

Policy implication tests are used to build confidence in a model by comparing the

behavior changes associated with policy changes in the model to changes observed

during actual policy changes. Table 2.3 below lists the tests of policy implications

along with a brief description.


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Table 2.3 Tests of Policy Implications (Forrester & Senge, 1979).

Test Comment

System Improvement Compare policies that lead to systemic improvement

or symptom relief to observed results. Generally used

after other tests support model validity.

Changed-Behavior

Prediction

Compares model behavior during policy change to

observed or hypothesized behavior change.

Boundary Adequacy

(Policy)

Examines how boundary changes effect policy

recommendations to determine if the boundary should

be adjusted.

Policy Sensitivity Indicates the impact of parameter uncertainty on

model output.

“Validation is the process of establishing confidence in the soundness and

usefulness of a model” (Forrester & Senge, 1979, p. 6). Often, causal models

emphasize explanation as a method for informing policy decisions. It is generally

accepted that system dynamics models should be evaluated based on their internal

structural validity and their ability to the produce dynamic behavior patterns observed

in real systems (Hadjis, 2011). As such, predictive precision is not as important as

causality. However, several appropriate statistical validation methods have been

identified (Barlas, 1989).

2.9.8 Statistical Validation Methods

Validation of a simulation model is the process of determining whether a

model is an adequate representation of the system being modeled (Law & Kelton,

1991). Statistical validation methods are traditionally used to measure goodness of fit

to historical data and determine magnitude of various sources of error. Model users

typically expect some form of statistical evidence that the model compares favorably

with historical data (Sterman, 1984). However, in system dynamics, a model can be

considered acceptable for its purpose even though the behavior derived from the

model may be a relatively poor fit when subjected to traditional regression analysis.


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This apparent lack of statistical rigor often found in system dynamics modeling

presents a challenge for modelers. The following discussion explains why traditional

statistical tests are inappropriate for validation of system dynamics models and

identifies several statistical tests that are acceptable for systems dynamics.

The purpose of most system dynamics models is to predict behavior based on

known relationships between elements within the system rather than simply fitting

observed data. Fitting historical data is important. However, system dynamics

modelers consider it as important, or more important, to understand the systemic cause

of the observed behavior. Forrester and Senge (1979) consider standard statistical

hypothesis tests to be generally inappropriate for system dynamics models. They

equate validity with confidence in the explanatory power of a model rather than

statistical correlation with observed truth. However, the process of calibrating a

system dynamics model to fit historical data can be a useful form of dynamic

hypothesis testing (Oliva, 2003).

Traditional statistical hypothesis tests typically rely on assumptions of

normality, stationarity and normality (Barlas, 1989). System dynamics models often

violate these assumptions. Output from these models usually shows high

autocorrelation due to the systemic nature of the model itself. These models are

designed to generate output based on observed correlations. As such, traditional

statistical techniques are often not appropriate for validation of system dynamics

models (Sterman, 1984).

Conventional statistical tests are useful for evaluating systemic structure but

they are not “sufficient grounds for rejecting the causal hypothesis in a system

dynamics model” (Forrester & Senge, 1979, p. 18). According to Barlas (1989), the

traditional t-test, F-test, and 2- test are not applicable for system dynamics model

validation. Similarly, Sterman (1984) considers the use of the traditional regression

analysis to be inappropriate for system dynamics. As such, these statistical tests are

considered supplemental tests for validity. They can be used to enhance confidence in

system dynamics models, but should not be the sole measure of model validity.


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Despite the stated difficulties associated with using traditional statistical

techniques to validate system dynamics models, many researchers, including Forrester

(1968), Barlas (1989) and Sterman (1984), recognize the need for statistical rigor in

the validation process. To that end, Sterman (1984) identifies the root-mean-square

percent error (RMSPE) and Theil inequality statistic as “appropriate summary

statistics for evaluating the historical fit of system dynamics models.” RMSPE can be

used to assess goodness of fit in place of the traditional regression analysis. Theil

inequality statistics provide a method for error decomposition.

Several statistical methods have been used to quantify goodness of fit in

system dynamics. These methods include graphical comparison, Thiel inequality

statistics (bias), regression and RMSPE. However, there is no universally accepted

metric or value for goodness of fit in system dynamics. The acceptable values depend

on the system being modeled, the quality of the observed data, and the purpose of the

model. A review of validated system dynamics models provides a range of

acceptable values for these statistical tests. A summary of the tests and associated

values are presented in Table 2.4 for 10 system dynamics models in which the author

provided validation and verification metrics.

Based on the review summarized in Table 2.4, it is possible to define

acceptable values for use in hypothesis testing. In general an acceptable value for the

bias component of error (UM) is 10% of the total error. Similarly, an acceptable value

for RMSPE is 5%. Although regression is often not appropriate for system dynamics,

a Coefficient of Determination (R2) value of 0.90 or greater demonstrates acceptable

agreement with observed data.


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Table 2.4 Summary of Statistical Metrics in the Literature.

Range of Acceptable Statistics for System Dynamics Models

Statistic Source

Bias (Theil UM) (%)

RMSPE (%)

Coefficient of Determination (R2)

Qudrat-Ullah & Seong, 2010

7% - 9% 3% - 4% N/A

Berendsa & Romme, 2001

54% - 64% N/A 0.75 - 0.99

Qudrat-Ullah, 2011

8% 4%

Li & Simonovic, 2002

N/A N/A 0.88 - 0.97

Dyson & Chang, 2005

N/A N/A 0.89 - 0.99

Lane, Monefeldt & Rosenhead, 2005

N/A 10% N/A

Georgiadis & Besiou, 2008

3% N/A 0.99

Tidwell, et.al., 2004

N/A 7% N/A

Chowdhury& Sahu, 1992

N/A 10% -20% N/A

Olvia, 2003 3% 2% 0.70

Niazi, et. al., 2014

N/A 2% 0.90 - 0.92

2.10 Analogy, Homology and Isomorphology

There are many similarities between the fields of water policy and finance.

Terms like budget, overdraft, and banking are used in both fields. While these terms

have different meanings in different fields, they can be considered analogous because

the similarities are sufficient to enable a general conceptual understanding across both

fields. However, the use of analogy can lead to incorrect understanding and action


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when analogical similarities are used to infer systemic, structural similarities.

(Bertalanffy, 1969). If two fields exhibit sufficient structural and systemic similarity,

they can be said to be homological and isomorphological. The existence of a

homological and isomorphic relationship between two systems can allow knowledge

about one system to be transferred to the other system without the dangers of reliance

on weak analogous similarities.

2.10.1 Analogy

An analogy is “a comparison between two things, typically on the basis of their

structure and for the purpose of explanation or clarification” (Oxford University Press,

Analogy, 2015). Analogies are helpful because they relate well-understood concepts

to foreign or confusing concepts in a way that permits greater understanding. The

term implies a partial similarity or resemblance between objects, concepts or systems

of substantially different structure. Analogous systems may display similar behavior-

over-time. However, this similarity is coincidental. It does not result from underlying

structural or systemic similarities. Analogies are superficial similarities “which are

useless in science and harmful in their practical consequences” (Bertalanffy, 1969, p.

81).

2.10.2 Homology

The term homology is most commonly used in the fields of biology and

mathematics. It is defined as “the state of having the same or similar relation, relative

position, or structure” (Oxford University Press, Homology, 2015). In systems,

homology is a one-to-one relationship between corresponding elements in different

systems. The term implies that two homologous systems are structurally and

functionally similar, but did not necessarily evolve from a common ancestor.

Wagner (1989) identifies three types of homology including idealistic

homology, historical homology and biological homology. Historical homology

implies that similarities are caused by evolution from a common ancestor. Biological

homology is based on a mechanistic, functional relationship rather than genealogical


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similarities (Wagner, 1989). Idealistic homology does not rely on genetic or historic

causes. Wagner (1989) considers structures built from the same archetype to be

idealistically homological.

In systems, the idealistic conception of homology is most relevant. In this case

homology can be justified based on logical structural and/or functional similarities

rather than historic or evolutionary causes. One-to-one mapping of physical structures

and/or their functional relationship to each other is a logical justification for

homology. The elements of homologous systems may be different. Similar elements

may have different structure when viewed individually. However, when viewed as a

system, the structures relate to each other in a similar manner physically, functionally

or logically.

The elements of homologous systems work together to in the same way, but

may result in different behavior. Functional, logical similarity concerns how elements

within a system relate to each other. It does not necessarily mean that homological

systems will behave in the same way. Similar behavior is neither adequate nor

required to prove homology.

2.10.3 Isomorphology

According to Bertalanffy (1969), it is “logical homology” that makes

isomorphology possible. Isomorphology is a term used in the fields of chemistry,

mathematics, systems, biology and psychology. An isomorphism is “an exact

correspondence as regards the number of constituent elements and the relations

between them” (Wordfinder, 2015). Isomorphology, as with homology, it is a one-to-

one relationship between corresponding elements in different systems. The individual

elements may also be structurally different. Unlike homological systems, the elements

of isomorphic systems work together in the same manner and produce similar

behavior-over-time. Isomorphology is distinguished from homology through the

process of identifying “specific conditions and laws” that are valid for all systems of

the same class (Bertalanffy, 1969, p. 86). These general laws can be replaced by laws

that are specific to each system if the systems are of the same class. This requires the


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explanation of the causal relationship between structural elements based on underlying

theory.


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CHAPTER III

RESEARCH 1: SYSTEM DYNAMIC MODEL FOR

SUSTAINABLE GROUNDWATER MANAGEMENT

3.1 Abstract

This research develops system dynamics models for three groundwater systems

in California. Systems analysis techniques were used to develop a structural model of

groundwater systems based on the structure of monetary systems. The system

dynamics models predict changes in groundwater storage for 1-year, 5-year and 10-

year periods based on data from the preceding 10-years. The models were evaluated

by comparing the predicted changes in groundwater storage to the values provided by

the USGS. The models were subjected to structural, behavioral and policy tests to

ensure validity, as well as statistical tests to evaluate predictive performance. The

results of this research support the conclusion that a system dynamics groundwater

model that is based on the structure of monetary policy may be a valid model of a

groundwater system capable of producing behavior-over-time that is sufficient for the

purposes of testing groundwater policy provided that it is an inland system with a

simulation period of five years or less. The results do not support this conclusion for a

coastal system or for a simulation period of ten years.

3.2 Introduction

The primary purpose of this research is to develop a system dynamics model of

a groundwater system for testing groundwater policy. Models were developed for

three separate groundwater systems in the California. The systems under

consideration are the Modesto groundwater region in the Central Valley, the Cuyama

Valley Groundwater Basin in Santa Barbara County, and the Pajaro Valley

Groundwater Basin in Santa Cruz and Monterey Counties. Model output is compared

to simulated groundwater storage data from groundwater models developed by the


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USGS. Output from these models represents the best available information on the

systems in question.

The following sections detail the methods and procedures used for model

development, verification and validation. The hypotheses and data sources are

identified. Analytical procedures and methodological concerns are also discussed.

3.3 Research Methodology

The primary hypothesis for this research states that a system dynamics

groundwater model based on the structure of monetary policy systems can produce

behavior-over-time that matches historical groundwater data with accuracy that is

sufficient for the purposes of testing groundwater policy. However, there is no single

accepted test for the validity of system dynamic models. Traditional, statistical

hypothesis tests are generally not acceptable for system dynamics modeling (Sterman,

1984). Therefore, the methodology for this research relies on a preponderance of

evidence derived from testing sub-hypotheses intended to support or refute the

primary hypothesis.

Three groundwater systems were selected for modeling. Three separate

models were developed for each groundwater system. The system dynamics models

were subjected to a battery of relevant validation tests proposed by Forrester and

Senge (1979). Statistical analysis techniques, determined by Sterman (1984) to be

relevant for system dynamics, were also used to test the validity of the models.

Regression analysis was also used provide a basis for comparison with traditional

statistical methods. Finally, the models were reviewed by experts in groundwater

resources to provide independent support for the structure of the model. The

combination of these tests are used to support or refute the primary hypothesis.

3.3.1 System Dynamics Modeling

The structural model developed in step one is used to create functioning

system dynamics models in Microsoft Excel. These models produce dynamic


93

behavior for three separate groundwater systems in the western United States. The

groundwater basins to be models are the Modesto groundwater region in the Central

Valley, the Cuyama Valley Groundwater Basin in Santa Barbara County, and the

Pajaro Valley Groundwater Basin in Santa Cruz and Monterey Counties. Model

output is compared to historical groundwater depletion data from the USGS. These

models are subjected to a battery of system dynamics validation tests identified by

Forrester and Senge (1979) and Barlas (1989). These tests are discussed in section

3.5. Successfully passing these validity tests helps “build confidence” (Forrester &

Senge, 1979) in the models.

3.3.2 Statistical Analysis

Traditional statistical tests are often not applicable for system dynamics

modeling (Sterman, 1984). They can be useful for evaluating systemic structure, but

not for testing hypotheses (Forrester & Senge, 1979). These tests typically rely on

assumptions of normality, stationarity and normality (Barlas, 1989) that simply do not

apply to system dynamics. The traditional t-test, F-test, and 2- test are not applicable

for system dynamics model validation (Barlas, 1989). Regression analysis is

considered inappropriate for similar reasons (Sterman, 1984).

Despite the difficulties associated with using traditional statistical techniques

to validate system dynamics models, it is important to include statistical analysis in the

validation process. Sterman (1984) identifies two “appropriate summary statistics for

evaluating the historical fit of system dynamics models.” He suggests using root-

mean-square percent error (RMSPE) and Theil inequality statistic. RMSPE are used

to assess goodness of fit. Theil inequality statistics provide a method for error

decomposition. Regression analysis, although not considered applicable for system

dynamics validation, is used provide a basis for comparison with traditional statistical

methods. Detailed statistical analysis procedures are discussed in section 3.9


94

3.4 Hypotheses




sufficient for the purposes of testing groundwater policy.

In this research, a system dynamics model of a groundwater system that is

based on the structure of monetary policy systems serves as the general statement or

theory. It is a dynamic hypothesis in model form. A dynamic hypothesis is a claim

that a causal relationship exists between structure and behavior (Keloharju, 1981). In

this research, the dynamic hypothesis states that a system dynamics model of a

groundwater system that is based on the structure of a monetary system can produce

behavior that is representative of observed behavior in groundwater systems. The

formal process of calibration and validation tests the hypothetical link between system

structure and behavior (Oliva, 2003).

Table 3.1 presents a list of null and alternative hypotheses to be tested with this

methodology.

Table 3.1 Null and Alternative Hypotheses.

No. Null Hypothesis Alternative Hypothesis

1 The system dynamics based on the

general structure of monetary policy

system is not a valid model of the

Modesto regional groundwater

system.

The system dynamics based on the


system is a valid model of the


system.




Cuyama Valley groundwater system.



system is a valid model of the

Cuyama Valley groundwater system.




Pajaro Valley groundwater system.



system is a valid model of the Pajaro

Valley groundwater system.


95

Table 3.1 Null and Alternative Hypotheses, Continued.


4 The system dynamics model of the


system will not produce behavior

representative of physical system as

modeled by the USGS.

The system dynamics model of the


system will produce behavior




Cuyama Valley groundwater system

will not produce behavior




Cuyama Valley groundwater system

will produce behavior representative

of physical system as modeled by the

USGS.


Pajaro Valley groundwater system

will not produce behavior




Pajaro Valley groundwater system

will produce behavior representative

of physical system as modeled by the

USGS.

As previously mentioned, the primary hypotheses listed above cannot be

directly tested. Instead, several sub-hypotheses are tested directly. These sub-

hypotheses are intended to provide evidence used to support or refute the primary

hypotheses. Table 3.2 presents the sub-hypotheses related to hypothesis 1 in null and

alternative from. They apply to all three groundwater system models.

Table 3.2 Null and Alternative Sub-hypotheses for Hypothesis 1.

No. Null sub-hypothesis Alternative Sub-hypothesis

1.1 The model does not pass structure

verification tests.

The model passes structure

verification tests.

1.2 The model does not pass parameter

verification tests.

The model passes parameter

verification tests.

1.3 The model does not pass extreme

conditions tests.

The model passes extreme conditions

tests.

1.4 The model does not pass not pass

boundary adequacy tests

The model passes boundary

adequacy tests


96

Table 3.2 Null and Alternative Sub-hypotheses for Hypothesis 1, Continued.


1.5 The model does not pass dimensional

consistency tests.

The model passes dimensional

consistency tests.

1.6 The model does not pass behavior

reproduction tests through calibration

and comparison.

The model passes behavior

reproduction tests through calibration

and comparison.

1.7 The model does not pass behavior

anomaly tests.

The model does passes behavior

anomaly tests.

1.8 The model does not pass boundary

adequacy tests related to behavior.


adequacy tests related to behavior.

1.9 The model does not pass extreme

policy tests related to behavior.

The model passes extreme policy

tests related to behavior.

1.10 The model does not pass boundary

adequacy tests related to policy.


adequacy tests related to policy.

1.11 The model does not pass policy

sensitivity tests.

The model passes policy sensitivity

tests.

1.12 The model does not pass review from

experts in the field of groundwater

resources.

The model passes review from

experts in the field of groundwater

resources.

Table 3.3 below presents the sub-hypotheses related to hypothesis 2 in null and

alternative from. They apply to all three groundwater system models.

Table 3.3 Null and Alternative Sub-hypotheses for Hypothesis 2.


2.1 Root Mean Square Percent Error

(RMSPE) of greater than 5%

Root Mean Square Percent Error

(RMSPE) of less than 5%

2.2 Systemic bias in the model greater

than 10% of the total error.

Systemic bias in the model less than

10% of the total error.

2.3 Regression coefficient of

determination (R2) of less than 0.90.

Regression coefficient of

determination (R2) of greater than

0.90.

Tables 3.4 and 3.5 below express the sub-hypotheses in mathematical form.


97

Table 3.4 Sub-hypotheses test for Hypothesis 1 in Mathematical Form.

No. Test

1.1 H0 : Structural Verification Test ≠ Pass

H1 : Structural Verification Test = Pass

1.2 H0 : Parameter verification Test ≠ Pass

H1 : Parameter verification Test = Pass

1.3 H0 : Extreme Condition Test ≠ Pass

H1 : Extreme Condition = Pass

1.4 H0 : Boundary Adequacy Test ≠ Pass

H1 : Boundary Adequacy Test = Pass

1.5 H0 : Dimensional Consistency Test ≠ Pass

H1 : Dimensional Consistency Test = Pass

1.6 H0 : Behavior Reproduction Test ≠ Pass

H1 : Behavior Reproduction Test = Pass

1.7 H0 : Behavior Anomaly Test ≠ Pass

H1 : Behavior Anomaly Test = Pass

1.8 H0 : Behavior Boundary Adequacy Test ≠ Pass

H1 : Behavior Boundary Adequacy Test = Pass

1.9 H0 : Extreme Policy Test ≠ Pass

H1 : Extreme Policy Test = Pass

1.10 H0 : Policy Boundary Adequacy Test ≠ Pass

H1 : Policy Boundary Adequacy Test = Pass

1.11 H0 : Policy Sensitivity Test ≠ Pass

H1 : Policy Sensitivity Test = Pass

1.12 H0 : Expert Review ≠ Pass

H1 : Expert Review = Pass


98

Table 3.5 Sub-hypotheses test for Hypothesis 2 in Mathematical Form.

No. Test

2.1 H0 : RMSPE > 5%

H1 : RMSPE ≤ 5%

2.2 H0 : UM > 10%

H1 : UM ≤ 10%

2.3 H0 : R2 > 0.90

H1 : R2 ≤ 0.90

The following table provides a summary of the tests for this research and

indicates the hypotheses and sub-hypotheses relevant for each test.


99

Table 3.6 Test / Hypothesis Matrix.

Test Sub-Hypothesis

Primary

Hypothesis

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.1 1.11 1.12 2.1 2.2 2.3 1 2

Structure Verification x x

Parameter Verification x x

Extreme Conditions x x

Boundary Adequacy (Structure) x x

Dimensional Consistency x x x

Behavior Reproduction x x x

Behavior Anomaly x x

Boundary Adequacy (Behavior) x x

Extreme Policy x x

Boundary Adequacy (Policy) x x

Policy Sensitivity x x

Expert Review x x

Root Mean Square Percent Error x x x x

Theil Inequality Statistics x x x x

Regression x x x x


100

3.5 General Procedures

The approach for this research has three steps. First, systems analysis

techniques are used to develop a structural model of groundwater systems based on the

structure of monetary systems. Second, system dynamics modeling is used to develop

dynamic models capable of reproducing behavior in groundwater systems. In this

step, model calibration and validation support the dynamic hypothesis relating model

structure to behavior. Next, statistical tests were used to evaluate the model. These

tests provide a defensible method of comparing modeled behavior to observed

historical behavior in groundwater systems.

The data provided by the USGS groundwater models provide annual estimates

for net groundwater storage or change in storage for a period of 44-60 years. The

models predict changes in groundwater storage for 1-year, 5-year and 10-year periods

based on the previous 10-year period. In order to evaluate the performance of the

model simulations were run for each successive 5-year and 10-year period based on

the 10 years immediately preceding it. The coefficients in the equations used to

predict the model parameters change in each successive simulation to reflect the

relationship derived from the 10 years of data immediately preceding the period in

question. Model output for each test period is compared to data from the USGS

models.

3.5.1 Year-over-year Simulation

In the 1-year simulation, the model predicts the change in groundwater storage

for the year in question based on the data from the previous 10 years. Input

parameters are taken directly from USGS data. Linear equations are used to predict

the value of internal parameters. The coefficients used in these linear equations are

based on observed relationships in the 10 years immediately preceding the year being

simulated. These coefficients change slightly with each successive simulation to

reflect changes in the next preceding 10-year period. The change in annual storage

from each 1-year simulation are then compared to the USGS data to evaluate the

model.


101

3.5.2 Successive 5-year simulations

In the 5-year simulation, the model predicts the change in groundwater storage

for each year of the 5 years in question based on the data from the previous 10 years.

Input parameters are taken directly from USGS data. Linear equations are used to

predict the value of internal parameters. The coefficients used in these linear

equations are based on observed relationships in the 10 years immediately preceding

the year being simulated. These coefficients change slightly with each successive

simulation to reflect changes in the next preceding 10-year period.

The change in storage is calculated over the 5 years in question and compared

to the USGS data for the same period. The simulated cumulative change in storage is

compared to the actual cumulative change in storage for the same period to evaluate

the model’s ability to predict long-term depletion. The simulated annual change in

storage is also compared to the USGS data on a year-over-year basis for each

successive simulation period to evaluate the model’s ability to predict behavior over

the short term. This process was repeated for all available 5-year periods.

3.5.3 Successive 10-year simulations

In the 10-year simulation, the model predicts the change in groundwater

storage for each year of the 10 years in question based on the data from the previous

10 years. Input parameters are taken directly from USGS data. Linear equations are

used to predict the value of internal parameters. The coefficients used in these linear

equations are based on observed relationships in the 10 years immediately preceding

the year being simulated. These coefficients change slightly with each successive

simulation to reflect changes in the next preceding 10-year period.

Each simulation run uses data from the 10-year period immediately preceding

the simulation period in question. Data from this 10-year calibration period is used to

inform system structure and develop mathematical relationships between variables.

This data was obtained from USGS models developed for each system. Variables

such as rainfall, stream flow, pumpage, seepage, etc. are compared to look for

evidence of correlation. Variables with strong correlation indicate potential systemic


102

links. Mathematical equations expressing this correlation are included in the Excel

model. The data that define these correlated variables are used as the input parameters

for the system.

The change in storage is calculated over the 10 years in question and compared

to the USGS data for the same period. The simulated cumulative change in storage is

compared to the actual cumulative change in storage for the same period to evaluate

the model’s ability to predict long-term depletion. The simulated annual change in

storage is also compared to the USGS data on a year-over-year basis for each

successive simulation period to evaluate the model’s ability to predict behavior over

the short term. This process was repeated for all available 10-year periods.

3.6 Data

Water data, in the form of water use estimates, modeled hydrological and

hydrogeological data was used for model development and validation. A discussion of

this data is presented below.

3.6.1 Water Data

In this research, system dynamics models were developed for three separate

groundwater systems in the western United States. The systems under consideration

are the Modesto groundwater region in the Central Valley, the Cuyama Valley

Groundwater Basin in Santa Barbara County, and the Pajaro Valley Groundwater

Basin in Santa Cruz and Monterey Counties. These basins provide a variety of

policy/parameter changes for testing. Each model estimates storage depletion, or net

change in storage for 1-year, 5-year and 10-year periods based on data from the

previous 10 years. Figures 3.1 to 3.3 below show a graphical representation of the

groundwater data avaialble for the basins in this research. Numerical Data is

presented in appendix B, C and D.


103

Figure 3.1 Groundwater Data for the Modesto Region, California (Philips, Rewis, & Traum, 2015).


104

Figure 3.2 Groundwater Data for the Pajaro Valley, California (Hanson, et. al., 2014).


105

Figure 3.3 Groundwater Data for the Cuyama Valley, California (Hanson, et. al., 2015).


106

3.7 Model Development and Parameters

3.7.1 Model Development

The system dynamics models were developed using Microsoft Excel. The

elements in the models, and the structure of the models, are based on known elements

and relationships from the natural groundwater systems. The relationship between

elements within the model were further refined by examination of the data provided by

the USGS groundwater models for each system. Analysis of the data was used to

develop linear relationships between elements and feedback loops as appropriate. The

linear equations for each parameter are shown in Appendix J.

The structure of a system dynamics model is related to its purpose, the known

relationships between elements in the real system, and the mental model of the

researcher. According to Doyle and Ford (1998), “a mental model of a dynamic

system is a relatively enduring and accessible, but limited, internal conceptual

representation of an external system whose structure maintains the perceived structure

of that system” (p. 17). Different researchers, having different purposes and different

mental models, may develop models with slightly different structure. In this research,

care has been taken to frame the structure of the models as closely as possible to the

general structure of the United States monetary system while preserving the known

relationships within the actual groundwater systems.

The structure of each model was evaluated by groundwater experts to

minimize researcher bias and confirm the adequacy of the model for the purpose of

testing groundwater policy. Additionally, a model was developed using raw data

parameters rather than simulated parameters in order to confirm the structure of the

system. The difference between the annual storage calculated by the model using

only raw data and the annual storage calculated by the USGS represents the mass

balance error inherent in the USGS calculations.

In addition to the correlation analysis above, many variables were evaluated

for autocorrelation. Autocorrelation can be a result of persistence in the parameter

being measured, or it can indicate that one or more variables has been omitted from


107

the model (Chatterjee & Hadi, 2006). In the Cuyama model, strong correlation was

found in three parameters (ET groundwater, Underflow, and Drains). This

autocorrelation was used to predict terms within the groundwater model.

Mathematical equations expressing this autocorrelation were included in the Excel

model.

Once the structure of the system and mathematical equations were developed,

the model was reviewed by groundwater experts. Finally, the model is calibrated by

adjusting the mathematical relationships based on each 10-year period preceding the

simulation.

In general, each hydrologic system contains three components. The landscape

flow system represents water flowing through the surface. The groundwater flow

system represents water flowing below the surface. The total groundwater stock is the

volume of groundwater available. Groundwater storage is the annual volume of water

moved into or out of groundwater stock and into groundwater flow. The structure of

each hydrologic system was confirmed by USGS experts.

The USGS uses different software packages to simulate flow in the

groundwater flow system and the landscape system. Annual groundwater storage

flowing into or out of the groundwater flow system can be calculated by summing the

inflows and outflows at the groundwater flow boundary or the overall system

boundary. However, there are internal differences between the values calculated by

summing at the system boundary and the values calculated by summing at the

groundwater flow boundary due to the different software packages used by the USGS

to simulate each system. The system dynamics models account for this by averaging

the annual change in storage calculated at the system boundary and the groundwater

flow boundary. See Figures 3.4 – 3.6 for more information.

The parameters and variables used in this research are the constituent

components of the groundwater system that make up the mass balance in the system.

These components are general parameters of systems in the same class, but are

variable with respect to the specific system in question.


108

3.7.2 General Water System Parameters

The parameters to be used in the groundwater system model are the

components of the general mass balance equation (1) (Raeisi, 2008). The equation is

restated here for convenience.


The specific parameters that make up the mass balance equation are defined below.





E = Evaporation


As discussed in section 1.8, raw data for these parameters is not always readily

available for the period in question. Simulated data from USGS hydrologic models is

used for the purposes of calibration and comparison. This data represents the best

available information on the systems in question.

The models contain input parameters and simulated parameters. These

parameters are used to calculate the annual change in in storage. The input parameters

represent water supply, demand and initial conditions for the groundwater system.

Simulated parameters are developed within the model using linear equations

developed from the 10 years of data immediately preceding the simulation period.

The simulated parameters are calculated using input parameters, other simulated

parameters, or the previous year’s value in the case of strong autocorrelation.

Not all water applied for irrigation contributes to crop evapotranspiration.

Some of the water returns to the groundwater in the form of deep percolation.

Irrigation efficiency is a measure of the percentage of applied water that is beneficial

for crop growth. This value changes depending on the crop and irrigation type.

Aggregate irrigation efficiency represents a weighted average of the crop types in the


109

system. This simplification allows the model to relate applied water to

evapotranspiration.

Each model represents a unique system. As such, each model has a slightly

different set of parameters. These parameters are described in sections 3.6.3 – 3.6.5

below. System diagrams are included to provide a visual description of the models.

3.7.3 Cuyama System Parameters

The Cuyama groundwater system is the simplest of the three systems in

question. Table 3.7 below shows the parameters used in the model as well as the

parameters used to calculated simulated values.

The Cuyama model requires initial values for ET gw, D, and UF in order to

operate. As previously stated, the coefficients for the linear equations used to simulate

internal parameters are adjusted after each period to account for the next 10 years of

data. See Figure 3.4 for a diagram of the Cuyama System.


110

Table 3.7 Cuyama System Parameters.

Parameter Description Correlated Parameter

Precipitation (P) Annual rainfall over the system

(Acre-Feet)

N/A – Input parameter

Total

Evapotranspiration

(ET all)

The sum of annual

evapotranspiration from irrigation,

precipitation and groundwater

(Acre-feet)


Evapotranspiration

from Irrigation

(ET irr)

Annual evapotranspiration from

applied irrigation water (acre-feet)


Aggregate

Irrigation

Efficiency (IE)

Percent of applied irrigation water

contributing ET irr on an annual

basis (%)

Used to calculate total

pumpage. Relates ET

irr to groundwater

demand.

Pumpage (Pump) Total annual pumpage from

groundwater (acre-feet)

Calculated using ET irr

and IE.

Underflow (UF) Net annual subsurface groundwater

flow into or out of the groundwater

basin (acre-feet)

Correlated to UF from

the previous year

(strong autocorrelation)

Runoff (R) Annual precipitation in excess of

infiltration (acre-feet)

Correlated to

Precipitation

Stream Leakage

(SL)

Annual volume of water flowing

into or out of groundwater into

streams (acre-feet)

Correlated to Runoff

Deep Percolation Net annual volume of water

infiltrating below the rootzone and

into groundwater (acre-feet)

Correlated to

Precipitation

Drains (D) Annual outflow from groundwater

through springs and tile drains (acre-

feet)

Correlated to D from

the previous year


Evapotranspiration

from groundwater

(ET gw)

The annual sum of Evaporation and

transpiration of groundwater by deep

rooted plants (acre-feet)

Correlated to ET gw

from the previous year


Runout (Rout) Annual volume of surface water

flowing out of the system (acre-feet)

Estimated by taking the

difference between R

and SL


111

Figure 3.4 Cuyama Hydrologic System.


112

The Cuyama model calculates the change in storage by summing the

parameters at the boundary to the groundwater system and at the boundary to the

overall system. The annual change in groundwater storage is calculated at the system

boundary using the following equation:

(P – ET all – UF – Rout) x -1 = Storage(Bndry) (6)

The annual change in groundwater storage is calculated at the groundwater flow


(DP + SL – ET gw – D – Pump - UF) x -1 = Storage(GW) (7)

The model calculates the annual change in storage by taking the average of the values

calculated at each boundary using the following equation:

(Storage(GW) + Storage(Bndry) ) = Storage (8)

2

3.7.4 Pajaro System Parameters

The Pajaro groundwater system is more complex than the Cuyama system. It

is a coastal system with significant seawater intrusion making it difficult to estimate

the volume of freshwater storage consumed on an annual basis. It also has a significant

amount of domestic, municipal and industrial pumpage. Table 3.8 below shows the

parameters used in the model as well as the parameters used to calculated simulated

values.

Table 3.8 Pajaro System Parameters.



(Acre-Feet)


Total

Evapotranspiration

(ET all)

The sum of annual ET from

irrigation, precipitation and

groundwater (Acre-feet)



113

Table 3.8 Pajaro System Parameters, Continued.


Evapotranspiration

from Irrigation

(ET irr)

Annual evapotranspiration from

applied irrigation water (acre-feet)


Farm Well

Pumpage (Wf)

Annual volume of pumpage for

irrigation (acre-feet)

Calculated by

multiplying ET irr by

IE. Links ET irr to

groundwater use

Domestic Wells

(Wd)

Annual volume of pumpage for rural

domestic use (acre-feet)


Municipal and

Industrial

Pumpage(M & I)


municipal and industrial use (acre-

feet)


Aggregate

Irrigation

Efficiency (IE)

Percent of applied irrigation (Wf)

water contributing ET irr on an

annual basis (%)

Used to calculate farm

well pumpage (Wf).

Farm Net

Recharge (FNR)

Net annual volume of recharge

(acre-feet). FNR is the net

difference between deep infiltration

and ET gw.

Correlated to

Precipitation

Underflow (UF) Net annual fresh subsurface

groundwater flow into the

groundwater basin from outside the

boundary (acre-feet)

Correlated to Drains

(D). Both UF and D

depend on groundwater

elevations (head).



Correlated to

Precipitation

Stream Leakage

(SL)

Annual volume of water flowing

into or out of groundwater into

streams (acre-feet)

Correlated to Runoff

Total Net Coastal

Inflow (NCI)

The net annual volume of water

flowing into or out of the system to

the ocean

Correlated to

Underflow

Drains (D) Annual outflow from groundwater

through springs and tile drains (acre-

feet)

Correlated to

Precipitation

Runout (Rout) Annual volume of surface water

flowing out of the system (acre-feet)

The difference

between R and SL


114

As previously stated, the coefficients for the linear equations used to simulate

internal parameters are adjusted after each period to account for the next 10 years of

data. See Figure 3.5 for a diagram of the Pajaro System.

The Pajaro model calculates the change in storage by summing the parameters

at the boundary to the groundwater system and at the boundary to the overall system.

The annual change in groundwater storage is calculated at the system boundary using

the following equation:

(P – ET all – UF – Rout +NCI) x -1 = Storage(Bndry) (9)

The annual change in groundwater storage is calculated at the groundwater flow


(UF + NCI - SL – Wf – Wd – M&I + FNR – D) x -1 = Storage(GW) (10)

The model calculates the annual change in storage by taking the average of the values

calculated at each boundary using the following equation:

(Storage(GW) + Storage(Bndry) ) = Storage (11)

2


115

Figure 3.5 Pajaro Hydrologic System.


116

3.7.5 Modesto System Parameters

The Modesto groundwater system is also more complex than the Cuyama

system. It is an inland system with significant deliveries of fresh surface water from

outside the system. It also has a significant amount of domestic and municipal

pumpage. Table 3.9 below shows the parameters used in the model as well as the

parameters used to calculated simulated values.

Table 3.9 Modesto System Parameters.



(Acre-Feet)


Total

Evapotranspiration

(ET all)

The sum of annual

evapotranspiration from irrigation,

precipitation and groundwater

(Acre-feet)


Surface Water

Deliveries (SWD)

Annual volume of fresh water

delivered for irrigation (acre-feet)


Farm Well

Pumpage (Wf)


irrigation (acre-feet)

Calculated by

multiplying ET irr by

IE. Links ET irr to

groundwater use

Domestic Wells

(Wd)

Annual volume of pumpage for rural

domestic use (acre-feet)


Municipal

Pumpage (M)


municipal use (acre-feet)


Aggregate

Irrigation

Efficiency (IE)

Percent of applied irrigation (Wf)

water contributing ET irr on an

annual basis (%)

Used to calculate farm

well pumpage (Wf).

Relates ET irr to

irrigation water

demand.

Net Percolation to

groundwater (Net

Perc)

Net annual volume of recharge

(acre-feet).

Correlated to Farm

Well pumpage (Wf)


117

Table 3.9 Modesto System Parameters, Continued.

Parameter Description Correlated

Parameter

Underflow (UF) Net annual subsurface groundwater flow

into or out of the groundwater basin

(acre-feet)

Correlated to

Runoff (R)



Correlated to

Precipitation

Stream Leakage

(SL)

Annual volume of water flowing into

the groundwater into streams (acre-feet)

Correlated to

underflow (UF).

Reservoir Leakage

(RL)

The net annual volume of water flowing

out of the groundwater system to surface

reservoirs and then out via evaporation

Correlated to Net

Perc.

The USGS model for the Modesto system calculates the change in

groundwater storage differently than the Cuyama and Pajaro systems. Change in

groundwater storage for a given year is calculated by summing the parameters for the

following year. As previously stated, the coefficients for the linear equations used to

simulate internal parameters are adjusted after each period to account for the next 10

years of data. See Figure 3.6 for a diagram of the Modesto System.

The annual change in groundwater storage for year t is calculated at the system

boundary using the following equation for year t + 1:

{(P – ET all – UF – R - RL + SL)} t+1 = {Storage(Bndry)}t (12)

The annual change in groundwater storage for year n is calculated at the

groundwater flow boundary using the following equation for year n + 1:

{(Net Perc – UF – Wf - Wd + SL)} t+1 = {Storage(GW)}t (13)

The model calculates the annual change in storage by taking the average of the

values calculated at each boundary using the following equation:

({Storage(GW)}t + {Storage(Bndry)}t) = {Storage}t (14)

2


118

Figure 3.6 Modesto Hydrologic System.


119

3.8 Model Validation Procedures

According to Forrester and Senge (1979), “validation is the process of

establishing confidence in the soundness and usefulness of a model”. System

dynamics models are typically evaluated on internal structural validity as well as the

ability to match observed behavior (Hadjis, 2011). Structural validity is at least as

important as predictive precision because it helps explain causal relationships.

Forrester and Senge (1979) identify 17 tests for building confidence in system

dynamics models. There are three main categories of tests including structural,

behavioral policy validation tests. However, not all of these tests are required for

every model. Some or all of these tests can be used to support an assertion of validity.

The following discussion is a summary of the tests selected for this research.

3.8.1 Expert Review

The groundwater models were evaluated by experts in groundwater resources

to provide an external check of the proposed logical relationships. This tests helps

protect against bias from the researcher and helps ensure that the structure of the

proposed model matches the physical system. The expert review process also

provides independent support for the structural, behavioral and policy verification tests

for sub-hypotheses 1.1 – 1.13.

USGS researchers Randall Hansen and Scott Boyce confirmed the structure of

the Pajaro and Cuyama models. USGS researcher Steve Phillips confirmed the

structure of the Modesto model. Each expert was asked a series of questions presented

in Appendix H. Results of the expert review are presented in the research log in

Appendix I.

Since the structure of the groundwater models are intended to be based on the

structure of monetary systems, independent expert review of the conceptual monetary

policy model was also required. Dr. Michael McCullough (agricultural economics

faculty from California State Polytechnic University San Luis Obispo) verified the


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structure of the monetary policy model. He was asked a series of questions presented

in Appendix H. Results of the expert review are presented in Appendix I.

3.8.2 Structural Validation Tests

Structural validity tests are used to verify that model structure matches

observed structure (Barlas, 1989). The structural validation tests are used to ensure

that the model structure does not contradict knowledge about the structure of the real

system. Forrester and Senge (1979) identify five tests for structural validation. All of

these tests are required for structural validation. Table 3.10 below lists the tests of

model structure along with a brief description.

Table 3.10 Selected Structural Validity Tests.

Test Purpose Procedure

Structure

Verification

Determine if the structure is

consistent with descriptive

knowledge of the system

(Qudrat-Ullah & Seong,

2010).

Expert Review, Systems analysis,

graphical comparison and logical

argument as described in (Bates &

Beruvides, 2015).

Parameter

Verification

Determine if the model

parameters are consistent with

descriptive knowledge of the

system (Qudrat-Ullah &

Seong, 2010).




Beruvides, 2015).

Extreme

Conditions

Test for logical behavior

under extreme conditions


2010).

Test the model for logical

(expected) results under extreme

conditions. Low rainfall condition

is tested.

Boundary

Adequacy

(Structure)

Determine if the important

structural elements are within

the proposed model (Qudrat-

Ullah & Seong, 2010).




Beruvides, 2015).

Dimensional

Consistency

Determine if the model

provides results in the same

dimensional units as the

physical system (Qudrat-

Ullah & Seong, 2010).

Ensure the model units match the

physical system (acre-feet of

groundwater storage)


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Structural Verification

The models were developed using system analysis techniques to develop the

structural relationships between parameters present in each system. Several iterations

of the models were created and revised after consultation with the USGS experts. The

structure of each model has been verified by USGS Experts.

The model structure was verified using a graphical comparison of model

behavior to observed behavior under parameters present in the physical system. Raw

data from USGS was used in place of simulated data to calculate changes in storage.

This tests the method of method of calculation to ensure that the model is correctly

calculating storage. The results were compared on an annual and cumulative basis.

Plots for each groundwater model are presented in Figures 3.7- 3.12 below.

The Cuyama annual structure test in Figure 3.7 below clearly shows a good fit

between the actual storage depletion and the simulated storage depletion. This

simulation uses actual data parameters rather than simulated parameters. As such the

test indicates that the parameters selected and the structure are correct.

Figure 3.7 Cuyama Annual Structure Test.

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The Cuyama cumulative structure test in Figure 3.8 below also shows a good

fit between the actual storage depletion and the simulated storage depletion. It shows

a 2.3% deviation in cumulative storage over time indicating some error. This may be

due to internal calculations or mass balance errors in the USGS data. However, the

graph indicates a successful test of model structure.

Figure 3.8 Cuyama Cumulative Structure Test.

The Pajaro annual structure test in Figure 3.9 below shows a good fit between

the actual storage depletion and the simulated storage depletion. The fit is not as good

as the Cuyama test; however, the coefficient of determination for this test (R2) is 0.98,

indicating a good fit. This simulation uses actual data parameters rather than

simulated parameters. As such, the test indicates that the parameters selected and the

structure of the system are correct.

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Figure 3.9 Pajaro Annual Structure Test.

The Pajaro cumulative structure test in Figure 3.10 below shows a poor fit

between the actual storage depletion and the simulated storage depletion (R2 = 0.57).

Although the plots move together, the graph shows a significant departure and shift in

between the actual and simulated cumulative storage. This may be due to difficulties

in calculating storage in a coastal system with seawater intrusion. The graph indicates

a possible mass balance error in the USGS data.

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Figure 3.10 Pajaro Cumulative Structure Test.

The Modesto annual behavior test in Figure 3.11 below also shows a good fit

between the actual storage depletion and the simulated storage depletion. The test

indicates that the parameters selected and model structure are correct.

Figure 3.11 Modesto Annual Structure Test.

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The Modesto cumulative structure test in Figure 3.12 below also shows an

acceptable fit between the actual storage depletion and the simulated storage

depletion. It shows a 7.4% deviation in cumulative storage over the 44-year test

indicating some error. This may be due to internal calculations or mass balance errors

in the USGS data. The USGS must meet certain requirements for mass balance

accuracy before model publication. However, the sum of all inflows and outflows

does not always equal zero. When solving for the annual change in storage this small

mass balance error appears as a deviation from the USGS data. Over time this error

can accumulate as shown in Figure 3.12. However, the graph indicates a successful

test of model structure.

Figure 3.12 Modesto Cumulative Structure Test.

All three models both are structurally valid. The Pajaro model behavior is

acceptable on an annual basis, but suspect on a cumulative basis. However, since the

structure and parameters have been verified by USGS experts, this discrepancy may be

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due to mass balance errors in the USGS data and / or difficulties caused when

seawater intrusion masks groundwater storage depletion.

Parameter Verification

The development of the structure of each system also required the verification

of the relevant parameters. Several iterations of the models were created and evaluated

with different parameters. Behavior of the system was tested with USGS data to

ensure that all relevant parameters were included. The parameters in each model have

been verified by USGS Experts. The graphical comparison used to test model

structure in Figures 3.13 – 3.15 also indicate that the parameters selected for the

models are sufficient. All three models pass the parameter verification test.

Extreme Conditions

Each groundwater model was tested under extreme conditions to verify that the

results of the simulation are as expected. The year-over-year simulation models were

tested with extremely low rainfall, in which, an increase in cumulative storage

depletion was expected. In each case, the models behave as expected. Figure 3.13-

3.15 below compare the simulated and actual cumulative storage depletion under the

extreme condition.

In the Cuyama low precipitation test, annual precipitation was reduced by

24,000 acre-feet to simulate extremely low precipitation. All other parameters were

unchanged. As expected, cumulative storage depletion increased in response to

decreased supply. compared to actual cumulative storage depletion over the same

period. See Figure 3.13 below.


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Figure 3.13 Cuyama Low Precipitation Test.

In the Pajaro low precipitation test, annual precipitation was reduced by 72,000

acre-feet to simulate extremely low precipitation. All other parameters were


decreased supply. compared to actual cumulative storage depletion over the same

period. See Figure 3.14 below.

Figure 3.14 Pajaro Low Precipitation Test.

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In the Modesto low precipitation test, annual precipitation was reduced by

337,000 acre-feet to simulate extremely low precipitation. All other parameters were


decreased supply compared to actual cumulative storage depletion over the same

period. See figure 3.15 below.

Figure 3.15 Modesto Low Precipitation Test.

Boundary Adequacy

Behavior of the system was tested with USGS data to ensure that all available

relevant parameters were included within the system boundary. The boundary of each

model has been verified by USGS experts. The graphical comparison used to test

model structure in Figures 3.7 – 3.12 also indicate that the boundary selected for the

models are sufficient. All three models pass the boundary adequacy test.

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Modesto Extreme Conditions Test (Low Precip)




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Dimensional Consistency

All three models calculate the annual change in groundwater storage in acre-

feet. These units are consistent with the data provided by the USGS. Therefore the

models are dimensionally consistent.

All three models pass the battery of structural validation tests. The next section

discusses behavioral validation tests.

3.8.3 Behavioral Validation Tests

Behavioral validation tests are used to compare model behavior with observed

behavior in order to increase confidence in the model structure. Forrester and Senge

(1979) identify eight tests for behavior validation. However, not all test are required

for every model. Table 3.11 below lists the five tests of model behavior selected for

this research.

Table 3.11 Selected Behavioral Validity Tests.


Behavior

Reproduction

Test to ensure that the

model produces symptoms

that are evident in the

physical system (Forrester

& Senge, 1979)

Graphical comparison of model

behavior to observed behavior under

parameters present in the physical

system.

Behavior

Anomaly

Identify potential flaws in

model assumptions

demonstrated by behavior

that does not match

observed behavior

(Forrester & Senge, 1979).

Graphical comparison of model

behavior to observed behavior under

parameters present in the physical

system.

Boundary

Adequacy

(Behavior)


behavioral characteristics

are generated by structures

outside the proposed model

(Forrester & Senge, 1979).

Expert review, systems analysis and

logical argument. Ensure that all

relevant structures are included in

the proposed model.

Extreme Policy Test for logical behavior

under extreme policies


2010).

Test the model for logical

(expected) results under extreme

conditions such as zero pumpage for

irrigation.


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Behavioral validation tests differ from structural validation tests. Structural

test are used to verify that the structure of the model is correct using raw data rather

than allowing the model to simulate behavior. Behavior validation tests are used to

verify that the model produces the correct behavior when simulating changes in

storage.

Behavior Reproduction

Behavior reproduction was tested using a graphical comparison of model

behavior to observed behavior under parameters present in the physical system. In the

previous section, raw data from USGS was used in place of simulated data to calculate

changes in storage. This tests the method of method of calculation to ensure that the

model is correctly calculating storage. In this section, the year-over-year simulation

was used to test model behavior. The results were compared on an annual and

cumulative basis. Plots for each groundwater model are presented in Figures 3.16-

3.21 below.

The Cuyama annual behavior test in Figure 3.16 shows a good fit between the

actual storage depletion and the simulated storage depletion. The test indicates that

the parameters selected are correct and the method of calculation is adequate.

Figure 3.16 Cuyama Annual Behavior Test.

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The Cuyama cumulative behavior test in Figure 3.17 below also shows a good

fit between the actual storage depletion and the simulated storage depletion. It shows

a 0.8% deviation in cumulative storage over time indicating some error. This may be

due to internal calculations or mass balance errors in the USGS data. However, the

graph indicates a successful test of behavior reproduction.

Figure 3.17 Cuyama Cumulative Behavior Test.

The Pajaro annual behavior test in Figure 3.18 below shows a good fit between

the actual storage depletion and the simulated storage depletion. The fit is not as good

as the Cuyama test; however, the coefficient of determination for this test (R2) is 0.84,

indicating a good fit. As such, the test indicates that the parameters selected are

correct and the method of calculation is adequate.

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Figure 3.18 Pajaro Annual Behavior Test.

The Pajaro cumulative behavior test in Figure 3.19 below shows a poor fit

between the actual storage depletion and the simulated storage depletion. Although

the plots move together, the graph shows a significant departure and shift in between

the actual and simulated cumulative storage. This may be due to difficulties in

calculating storage in a coastal system with seawater intrusion. The graph indicates a

failed test of behavior reproduction.

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Figure 3.19 Pajaro Cumulative Behavior Test.

The Modesto annual behavior test in Figure 3.20 below also shows a good fit

between the actual storage depletion and the simulated storage depletion. Although

the fit is not as good as the Cuyama model, the behavior is consistent with the

observed behavior (R2 = 0.88). This test indicates that the parameters selected and the

method of calculation are correct.

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Figure 3.20 Modesto Annual Behavior Test.

The Modesto cumulative behavior test in Figure 3.21 below also shows an

acceptable fit between the actual storage depletion and the simulated storage

depletion. It shows a 4.6% deviation in cumulative storage over the 44-year test

indicating some error. This may be due to internal calculations or mass balance errors

in the USGS data. However, the graph indicates a successful test of behavior

reproduction.

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Figure 3.21 Modesto Cumulative Behavior Test.

The Modesto and Cuyama models both pass the behavior reproduction test.

The Pajaro model behavior is acceptable on an annual basis, but not on a cumulative

basis. It does not pass the behavior reproduction test.

Behavior Anomaly

The above test for behavior reproduction can also be used to test for behavior

anomalies. Based on the graphical fit, the Cuyama and Modesto models pass the

Behavior anomaly test. The Pajaro model, as discussed above, shows anomalous

behavior in the cumulative storage depletion test that is not present in the actual data.

As such, the Pajaro model does not pass the behavior anomaly test.

Boundary Adequacy

Behavior of the system was tested with USGS data to ensure that all available

parameters were included within the system boundary. The behavior tests listed above

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indicate that the parameters included within the model boundaries are adequate.

Although the Pajaro model fails the behavior reproduction test, the annual behavior

indicates that the parameters within the boundary are adequate. The boundary of each

model has been verified by USGS Experts.

Extreme Policy

Each groundwater model was tested under the extreme policy of near-zero

pumpage to verify that the results of the simulation are as expected. The year-over-

year simulation models were tested with 1 acre-foot of annual groundwater pumpage.

Zero pumpage results in a calculation error within the model, so 1 acre-foot was

selected to simulate the extreme policy. In this scenario, a decrease in storage

depletion was expected. In each case, the models behave as expected. Figure 3.22-

3.24 below compare the simulated and actual cumulative storage depletion under the

extreme policy.

In the Cuyama zero pumpage test, annual evapotranspiration from irrigation

(ET irr) was reduced to one acre-foot to simulate near-zero irrigation and pumpage.

All other parameters were unchanged. As expected, cumulative storage depletion

decreased in response to decreased demand when compared to actual cumulative

storage depletion over the same period. However, the simulated groundwater accretion

can only occur until the aquifer is full. Since the storage capacity of the aquifer is

unknown, this is beyond the scope of this research. See Figure 3.22 below.


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Figure 3.22 Cuyama Zero Pumpage Test.

In the Pajaro zero pumpage test, annual evapotranspiration from irrigation (ET

irr) was reduced to one acre-foot to simulate near zero irrigation and pumpage. All

other parameters were unchanged. As expected, cumulative storage depletion


storage depletion over the same period. However, as state above, the simulated

groundwater accretion can only occur until the aquifer is full. Since the storage

capacity of the aquifer is unknown, this is beyond the scope of this research. See

Figure 3.23 below.

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Figure 3.23 Pajaro Zero Ag Pumpage Test.

In the Modesto low pumpage test, annual farm pumpage was reduced by

1,382,000 acre-feet to simulate extremely pumpage. Surface water deliveries were

increased by 1,382,000 to simulate replacing the groundwater consumption with

external water and maintaining the annual evapotranspiration from irrigation (ET irr).

All other parameters were unchanged. As expected, cumulative storage depletion


storage depletion over the same period. However, as state above, the simulated

groundwater accretion can only occur until the aquifer is full. Since the storage

capacity of the aquifer is unknown, this is beyond the scope of this research. See

Figure 3.24 below.

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Figure 3.24 Modesto Low Pumpage Test.

All three models pass the extreme policy test of near-zero agricultural

pumpage. They show significant, rapid accretion of groundwater due to reduced

demand as expected. However, as previously mentioned, the models do not reflect

conditions in which the groundwater basin is full. In these situations, groundwater

accretion would stop, and the inflows and outflows would balance. This condition is

beyond the scope of this research.

The Cuyama and Modesto models pass the battery of behavioral validation

tests. The Pajaro model passes the boundary adequacy and extreme policy tests.

However, it does not pass the behavior reproduction and behavior anomaly tests. The

next section discusses policy implication tests.

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3.8.4 Policy Implication Tests

Policy implication tests are used to compare the behavior caused by parameter

changes in the model to changes observed after policy changes in the real system in

order to build confidence in the model. If the model responds to policy changes as

expected, it increases confidence in the model as a whole. Forrester and Senge (1979)

identify four policy implication tests. However, only two were selected for this

research. Table 3.12 below lists the policy implications tests selected for this research.

Table 3.12 Selected Tests of Policy Implications.


Boundary

Adequacy (Policy)


behavioral characteristics

are generated by policy

levers within the proposed

model (Forrester & Senge,

1979).

Systems analysis and logical

argument. Ensure that all

relevant policy levers are

included in the proposed model.

Policy Sensitivity Determine the models

sensitivity to specific

parameters.

Evaluate how model changes

under various levels of pump tax

and maximum annual

groundwater pumping policies.

Groundwater management

policies used in Active

Management Areas (AMAs) in

Arizona are used as a basis for

testing policy sensitivity.

Policy sensitivity tests are used to evaluate behavioral response to policy

changes. In Arizona, groundwater management policies have included setting

maximum annual pumping limits and assessing fees (pump taxes) for groundwater

use. These fees are used to fund groundwater management activities and conservation

measures. These policies were used to evaluate the policy sensitivity of the proposed

groundwater models.


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Each groundwater model was tested under the combined policy of setting a

maximum allowable volume of groundwater pumpage along with a reduction in

demand associated with conservation efforts. In this scenario, a decrease in storage

depletion was expected. The results of the simulation are compared to the actual

storage depletion on a cumulative.

The year-over-year simulation models were tested by setting the maximum

groundwater consumption (ET irr) to 90% of the average agricultural consumption.

Additionally, aggregate irrigation efficiency is increased by 10% to simulate the

policy using pump taxes to increase conservation measures. In each case, the models

behave as expected. Figure 3.25-3.27 below compare the simulated and actual annual

storage depletion under this policy.

Cuyama Policy Implication Test

In the Cuyama policy implication test, maximum annual evapotranspiration

from irrigation (ET irr) was capped at 38,000 acre-feet per year (90% of average) and

aggregate irrigation efficiency was increased by 10%. All other parameters were

unchanged. See Figure 3.25 below.

Figure 3.25 Cuyama Policy Implications Test.

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-1800000

-1600000

-1400000

-1200000

-1000000

-800000

-600000

-400000

-200000

0

19

60

19

63

19

66

19

69

19

72

19

75

19

78

19

81

19

84

19

87

19

90

19

93

19

96

19

99

20

02

20

05

20

08

Cu

mu

lati

ve C

han

ge in

sto

rage

(A

F)

Water Year

Cuyama Policy Implications Test

Storage Actual (cumulative)



142

Figure 3.25 above shows the response to the combined groundwater policy

based on the Arizona groundwater management policies. The rate of storage depleting

begins to decline in 1977 when the pumpage restriction begins to take effect. As

expected, cumulative storage depletion decreased in response to decreased demand

and increased efficiency when compared to actual storage depletion over the same

period. The Cuyama model passes the policy implications test.

Pajaro Policy Implication Test

In the Pajaro policy implication test, maximum annual evapotranspiration from

irrigation (ET irr) was capped at 23,000 acre-feet per year (90% of average) and

aggregate irrigation efficiency was increased by 10%. All other parameters were

unchanged. See Figure 3.26 below.

Figure 3.26 Pajaro Policy Implications Test.

-150000

-100000

-50000

0

50000

100000

150000

Cu

mu

lati

ve C

han

ge in

sto

rage

(A

F)

Water Year

Pajaro Policy Implications Test




143

As expected, cumulative storage depletion decreased in response to decreased

demand and increased efficiency when compared to actual storage depletion over the

same period. The Pajaro model passes the policy implications test.

Modesto Policy Implication Test

In the Modesto policy implication test, maximum annual evapotranspiration

from irrigation (ET irr) was unchanged because it is not possible to separate ET from

irrigation water from ET from surface water deliveries. Instead, farm well pumpage

was capped at 972,000 acre-feet per year (90% of average) and surface water

deliveries were increased to make up the difference. Aggregate irrigation efficiency

was increased by 10%. All other parameters were unchanged. See Figure 3.27 below.

Figure 3.27 Modesto Policy Implications Test.

As expected, cumulative storage depletion decreased in response to decreased

demand and increased efficiency when compared to actual storage depletion over the

same period. The Modesto model passes the policy implications test.

-4000000

-3500000

-3000000

-2500000

-2000000

-1500000

-1000000

-500000

0

500000

19

70

19

73

19

76

19

79

19

82

19

85

19

88

19

91

19

94

19

97

20

00

20

03

Cu

mu

lati

ve C

han

ge in

sto

rage

(A

F)

Water Year

Modesto Policy Implications Test




144

3.9 Analysis Procedures

The validation and verification tests discussed in section 3.8 are intended to

build confidence in the structure and behavior of the proposed model. However, these

tests do not provide measurable, statistical results. The following tests are considered

appropriate for evaluating system dynamics models intended for testing policy

(Forrester & Senge, 1979). They are intended to provide a statistical measure of the

ability of the proposed model to predict behavior.

3.9.1 Statistical Analysis

Statistical methods were used to compare model behavior to observed behavior

and test hypotheses. However, many traditional statistical techniques are not

appropriate for use with system dynamics models. Instead, “appropriate summary

statistics” (identified by Sterman, 1984) are used to assess the degree of fit and

quantify sources of error. The following statistical methods were choosen because

they are considered appropriate for use insystem dynamics.

3.9.2 Goodness of Fit

Sterman (1984) considers the use of the traditional regression analysis to be

inappropriate for system dynamics. However, regression analysis is used in this

research as a supplementary test of model validity. It is also provides a basis for

comparison with traditional statistical methods. The primary statistical tool for

assessing goodness of fit is the Root Mean Square Percent Error (RMSPE). RMSPE

is used for a year-over-year comparison of output from the system dynamics models to

output from the USGS models. Based on a review of system dynamics modeling

literature shown in section 2.9.8, a RMSPE value of 5% or less is considered

acceptable for the purposes of this model.

Mean Square Error is a common measure of error in forecast models. RMSPE

is a similar statistical technique that provides a dimensionless measure of error

(Sterman, 1984). The equation for RMSPE is presented below:


145

1

𝑛∑ [

(𝑆𝑡−𝐴𝑡)

𝐴𝑡]𝑛

𝑡=12

(6)

Where: n = number of observations

St = Simulated value at time t

At = Actual Value at time t

The groundwater models predict changes in groundwater storage for 1-year, 5-

year and 10-year periods based on input from the previous 10-year period. In order to

evaluate the performance of the model simulations were run for each successive 5-

year and 10-year period based on the 10 years immediately preceding it.

1-Year Simulations

RMSPE for the 1-year simulation is calculated by comparing model output for

the entire test period to data from the USGS over the same period.

5-year Simulations

RMSPE for the 5-year simulation is calculated by comparing model output for

the 5-year test period to data from the USGS over the same period. The model is then

re-run and RMSPE is calculated for the next 5-year period. This process is repeated

for all possible 5-year periods. Finally, the goodness of fit is assessed by taking the

average RMSPE from all the simulations. This eliminates selection bias by

accounting for all the possible simulations.

10-Year Simulations

RMSPE for the 10-year simulation is calculated by comparing model output

for the 10-year test period to data from the USGS over the same period. The model is

then re-run and RMSPE is calculated for the next 10-year period. This process is

repeated for all possible 10-year periods. The goodness of fit is then assessed by

taking the average RMSPE from all the simulations.


146

3.9.3 Cumulative Error

Cumulative error is an important way to evaluate the predictive ability of a

simulation model. It is simply the difference in the cumulative change in storage over

the simulation period compared to the actual change in storage over the same period.

Cumulative error is expressed in acre-feet and as a percentage.

1-Year Simulations

Cumulative error for the 1-year simulation is calculated by comparing the

simulated cumulative change in storage for the entire test period to the actual change

in storage from the USGS over the same period.

5-year Simulations


simulated cumulative change in storage for the 5-year test period to the actual change

in storage from the USGS over the same period. The model is then re-run and

cumulative error is calculated for the next 5-year period. This process is repeated for

all possible 5-year periods. Finally, the average cumulative error is calculated to

assess the overall accuracy of the model. This eliminates selection bias by accounting

for all the possible simulations.

10-Year Simulations


simulated cumulative change in storage for the 10-year test period to the actual change

in storage from the USGS over the same period. The model is then re-run and

cumulative error is calculated for the next 10-year period. As with the 5-year

simulation, this process is repeated for all possible 10-year periods. Finally, the

average cumulative error is calculated to assess the overall accuracy of the model.

3.9.4 Error Decomposition

Sterman (1984) suggests the use of Theil inequality statistics for quantifying

sources of error between modeled and observed behavior. This method can separate


147

and quantify the fractions of total error associated with bias, unequal variance and

unequal covariance.

UM + US + UC = 1 (7)

Where: UM = Fraction of total MSE from bias

US = Fraction of total MSE from unequal variance

UC = Fraction of total MSE from unequal covariance

The equations used to calculate these Theil statistics are provided below:

_ _

UM = __( S – A )2__ (8) 1

𝑛∑(𝑆𝑡 − 𝐴𝑡)2

US = __( SS – SA )2___ (9)

1


UC = __2( 1 – r )SSSA__ (10)

1


Due to the nature of system dynamics modeling, the fraction of total error due

to unequal variance and covariance (US and UC ) is expected to be large. This is due to

the fact that system dynamics models build causal relationships into the model.

Conversely, a system dynamics model that displays minimal systemic bias (i.e. low

UM ) can be said to be an adequate representation of the system in question. Based on

a review of system dynamics modeling literature shown in section 2.9.8, the fraction

of total error due to systemic bias should be less than 10% of the total error described

by the Theil inequality statistics.

1-Year Simulations

Systemic bias for the 1-year simulation is calculated by comparing model

output for the entire test period to data from the USGS over the same period. Equation

8 (above) is applied to calculate UM.


148

5-year Simulations


output for the 5-year test period to data from the USGS over the same period. The

model is then re-run and UM is calculated for the next 5-year period. This process is

repeated for all possible 5-year periods. Finally, UM is calculated by taking the

average UM from all the simulations. This eliminates selection bias by accounting for

all the possible simulations.

10-Year Simulations


output for the 10-year test period to data from the USGS over the same period. The

model is then re-run and UM is calculated for the next 10-year period. This process is

repeated for all possible 10-year periods. UM is then calculated by taking the average

UM from all the simulations.

3.9.5 Regression Analysis

As previously discussed, regression analysis is generally considered

inappropriate for evaluating system dynamics models (Sterman, 1984) due to expected

unequal variance associated with this type of model. However, regression can be a

basis for comparison with traditional statistical methods. For this reason, least squares

regression is performed to compare predicted behavior to behavior provided by the

USGS models over the last 10-years of available data. The coefficient of

determination is calculated. Based on a review of system dynamics modeling

literature shown in section 2.9.8, a coefficient of determination (R2) of 0.90 or greater

is considered adequate for the purposes of this model.

1-Year Simulations

The coefficient of determination (R2)for the 1-year simulation is calculated by

comparing model output for the entire test period to data from the USGS over the

same period.


149

5-year Simulations

R2 for the 5-year simulation is calculated by comparing model output for the 5-

year test period to data from the USGS over the same period. R2 is calculated by

comparing the simulated and actual change in storage on an annual basis over the 5-

year simulation period. The model is then re-run and R2 is calculated for the next 5-

year period. This process is repeated for all possible 5-year periods. Finally, R2 is

calculated by taking the average R2 from all the simulations. This eliminates selection

bias by accounting for all the possible simulations.

10-Year Simulations

R2 for the 10-year simulation is calculated in the same manner as in the 5-year

simulation. It is calculated by comparing the simulated and actual change in storage

on an annual basis over the 10-year simulation period. The model is then re-run and

R2 is calculated for the next 10-year period. This process is repeated for all possible

10-year periods. Finally, R2 is calculated by taking the average R2 from all the

simulations.

The following section presents the results of these analysis procedures.

3.10 Results and Discussion

Three models were developed for each groundwater basin. The 1-year, 5-year

and 10-year predictive models are analyzed using the procedures presented in section

3.9. Each model is tested for goodness of fit (RMSPE), cumulative error, systemic

bias (UM), and the coefficient of determination (R2).

3.10.1 Cuyama Models

The following section presents the results and discussion the 1-year, 5-year and

10-year models for the Cuyama system. The results are presented for RMSPE,

cumulative error, systemic bias and regression analysis for each model.


150

1-Year Simulation

Table 3.12 below summarizes the results of the 1-year simulation for the

Cuyama groundwater model from water year 1960 to 2010. The results of the 1-year

simulation can be found in Appendix G.

Table 3.12 Cuyama 1-year Simulation.

Sum of actual

Storage (AF) -1757766

Sum of

Simulated


Difference (AF) -14516

% Error 0.8%

RMSPE 45.1

R2 0.9

UM 0.9%

n 51

The Cuyama 1-year simulation uses 10 years of data to predict the annual

change in storage for the next year. As Table 3.12 illustrates, this model predicts

change in storage well with the exception of the RMSPE. However, this error is solely

due to the results of the simulation from the year 1993. In water year 1993, the actual

change in storage is 62 acre-feet. The simulated change in storage is -19,972 acre-

feet. This is likely due to a change in the USGS model land use and unusually high

rainfall that occurred in 1993 (Hanson, Flint, Faunt, Gibbs, & Schmid, 2015). If water

year 1993 is removed from the calculation, the RMSPE for the remaining years is

excellent (0.74).

5-Year Simulations


Cuyama groundwater model from water year 1960 to 2010. The results of the



151


Average 5-year Error (AF) -4468

Average 5-year Error (%) -0.9%

Average 5-year UM 42.9%

Average 5-year R2 0.93

Average 5-year RMSPE 17.59

n per simulation 5

# of simulations 47


change in storage for the next 5 years. The model calculates the cumulative error, %

error, UM, R2 and RMSPE for each 5-year period. Table 3.13 presents the average

values for all 49 simulations. The results of each simulation can be found in Appendix

G. As Table 3.13 illustrates, this model predicts change in storage well with the

exception of the RMSPE. However, this error is solely due to the results of five

simulations from 1989 to 1993. There is also significant systemic bias. These

problems are likely due to the inability of the model to react to abrupt changes that are

not present in the 10-year period preceding the simulation.

10-Year Simulations


Cuyama groundwater model from water year 1960 to 2010. The results of the




Average 5-year Error (%) 3.3%




n per simulation 10

# of simulations 42


152





G. As Table 3.14 illustrates, this model predicts change in storage fairly well. While

the average R2 is acceptable, the average cumulative error, UM and RMSPE are not.

This is likely due to the difficulties predicting change in storage for such a long time

period based on only 10-years of input data.

3.10.2 Pajaro Models


10-year models for the Pajaro system. The results are presented for RMSPE,


1-Year Simulation


Pajaro groundwater model from water year 1974 to 2009. The results of the 1-year


Table 3.15 Pajaro 1-year Simulation.

Sum of actual

Storage (AF) -61561

Sum of

Simulated

Storage (AF) -16803

Difference (AF) -44757

% Error 72.7%

RMSPE 2.7

R2 0.84

UM 2.6%

n 36

The Pajaro 1-year simulation uses 10 years of data to predict the annual change

in storage for the next year. As Table 3.15 illustrates, this model does not predict


153

behavior well. The cumulative error is very high. However, RMSPE and UM are

within acceptable limits. R2 is lower than desired for this research. This is likely due

to difficulties in predicting the change in storage for a coastal system, and the

fluctuating nature of the storage data for this system.

5-Year Simulations


Pajaro groundwater model from water year 1974 to 2009. The results of the



Average 5-year Error (AF) 773





n per simulation 5

# of simulations 32

The Pajaro 5-year simulation uses 10 years of data to predict the annual change

in storage for the next 5 years. The model calculates the cumulative error, % error,

UM, R2 and RMSPE for each 5-year period. Table 3.16 presents the average values for

all 32 simulations. The results of each simulation can be found in Appendix G. As

Table 3.16 illustrates, this model does not predict behavior well. The average RMSPE

is within acceptable limits. However, the average percent error and UM are very high,

while the R2 is low.

10-Year Simulations


Pajaro groundwater model from water year 1974 to 2009. The results of the



154







n per simulation 10

# of simulations 27

The Pajaro 10-year simulation uses 10 years of data to predict the annual




G. As Table 3.16 illustrates, this model does not predict behavior well. The average

RMSPE is within acceptable limits. However, the average percent error and UM are

very high, while the average R2 is low. This is likely due to the difficulties

predicting change in storage for such a long time period based on only 10-years of

input data.

3.10.3 Modesto Models


10-year models for the Modesto system. The results are presented for RMSPE,


1-Year Simulation


Modesto groundwater model from water year 1970 to 2003. The results of the 1-year


The Modesto 1-year simulation uses 10 years of data to predict the annual

change in storage for the next year. As Table 3.18 illustrates, this model this model


155

predicts change in storage well. R2 is lower than desirable, but the other test criteria

indicate an acceptable model.

Table 3.18 Modesto 1-year Simulation.

Sum of actual


Sum of

Simulated


Difference

(AF) -166549

% Error 4.6%

RMSPE 0.1

R2 0.88

UM 0.3%

n 34

5-Year Simulations


Modesto groundwater model from water year 1970 to 2003. The results of the








n per simulation 5

# of simulations 30

The 5-year simulation uses 10 years of data to predict the annual change in

storage for the next 5 years. The model calculates the cumulative error, % error, UM,

R2 and RMSPE for each 5-year period. Table 3.19 presents the average values for all

30 simulations. The results of each simulation can be found in Appendix G. As

Table 3.19 illustrates, this model does not predict behavior well. The average RMSPE


156

and R2 are within acceptable limits. However, the average percent error and UM are

very high indicating systemic bias. This is likely a result of small annual mass balance

errors accumulating over the 5-year simulation period.

10-Year Simulations


Modesto groundwater model from water year 1970 to 2003. The results of the








n per simulation 10

# of simulations 25

The Modesto 10-year simulation uses 10 years of data to predict the annual




G. As Table 3.20 illustrates, this model does not predict behavior well on average.

This is likely due to the difficulties predicting change in storage for such a long time

period based on only 10-years of input data.

3.11 Hypothesis Test Results




sufficient for the purposes of testing groundwater policy. As previously mentioned,


157

the primary hypotheses listed above cannot be directly tested. Instead, several sub-

hypotheses are tested directly. These sub-hypotheses are intended to provide evidence

used to support or refute the primary hypotheses. The following Table presents the

results of the sub-hypotheses related to hypothesis 1.

Table 3.21 Sub-hypotheses Results for Hypothesis 1.

Table 3.22 below presents the results of the sub-hypotheses related to

hypothesis 2 for each groundwater model. C1, C5 and C10 represent the 1-year, 5-

year and 10-year models for the Cuyama system respectively. P1, P5 and P10

represent the1-year, 5-year and 10-year models for the Pajaro system. M1, M5 and

M10 represent the1-year, 5-year and 10-year models for the Modesto System.

Cuyama Pajaro Modesto

1.1H0 : Structural Verification Test ≠ Pass

H1 : Structural Verification Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.2H0 : Parameter Verification Test ≠ Pass

H1 : Parameter Verification Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.3H0 : Extreme Condition Test ≠ Pass

H1 : Extreme Condition = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.4H0 : Boundary Adequacy Test ≠ Pass

H1 : Boundary Adequacy Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.5H0 : Dimensional Consistency Test ≠ Pass

H1 : Dimensional Consistency Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.6H0 : Behavior Reproduction Test ≠ Pass

H1 : Behavior Reproduction Test = Pass

Reject H0:

Test = Pass

Fail to reject H0:

Test ≠ Pass

Reject H0:

Test = Pass

1.7H0 : Behavior Anomaly Test ≠ Pass

H1 : Behavior Anomaly Test = Pass

Reject H0:

Test = Pass

Fail to reject H0:

Test ≠ Pass

Reject H0:

Test = Pass

1.8H0 : Behavior Boundary Test ≠ Pass

H1 : Behavior Boundary Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.9H0 : Extreme Policy Test ≠ Pass

H1 : Extreme Policy Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.10H0 : Policy Boundary Test ≠ Pass

H1 : Policy Boundary Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.11H0 : Policy Sensitivity Test ≠ Pass

H1 : Policy Sensitivity Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

1.12H0 : Expert Review ≠ Pass

H1 : Expert Review = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Reject H0:

Test = Pass

Null Sub-Hypothesis

Result

No.


158

Table 3.22 Sub-hypotheses Results for Hypothesis 2.

Cuyama Pajaro Modesto

Root Mean Square

Percent Error

(RMSPE) of greater

than 5%

H0 : RMSPE > 5%

H1 : RMSPE ≤ 5%

C1 Fail to reject H0: RMSPE = 45.1%



P1 Reject H0: RMSPE = 2.7%



M1 Reject H0: RMSPE = 0.1%



Systemic bias in the

model greater than

10% of the total

error.

H0 : UM

> 10%

H1 : UM

≤ 10%

C1 Reject H0: UM

= 0.9%

C5 Fail to reject H0: UM

= 33.4%

C10 Fail to reject H0: UM

= 42.9%

P1 Reject H0: UM

= 2.6%

P5 Fail to reject H0: UM

= 38.6%

P10 Fail to reject H0: UM

= 33.3%

M1 Reject H0: UM

= 0.3%

M5 Fail to reject H0: UM

= 44.6%

M10 Fail to reject H0: UM

= 19.7%

Regression

coefficient of

determination (R2)

of less than 0.90.

H0 : R2 > 0.90

H1 : R2 ≤ 0.90

C1 Reject H0: R2 = 0.90

C5 Reject H0: R2 = 0.93

C10 Reject H0: R2 = 0.91

P1 Fail to reject H0: R2 = 0.84



M1 Accept H0: R2 = 0.88

M5 Reject H0: R2 = 0.92

M10 Accept H0: R2 = 0.83

ResultNull Sub-

Hypothesis Test Statistics


159

3.12 Methodological Concerns

The following section addresses four common methodological issues. They

are reliability, validity, bias and replicability.

3.13.1 Reliability

Reliability is concerned with consistency of results and measurement (Leedy &

Ormrod, 2013). For the purposes of this research, the model is considered reliable

because it is capable of producing the same results given the same parameter values

and initial condition.

3.13.2 Validity

Validity in systems dynamics pertains to the soundness of the model in

question (Forrester and Senge, 1979). The validity of the dynamic groundwater

models was tested and confirmed according to the methods identified in section 3.8.

The models are considered valid because they passes these tests.

3.13.3 Bias

Bias is a significant concern in all research. It is not possible to remove all

bias from research. However, it is important to minimize potential bias to the

maximum extent possible.

In this research, there are two primary forms of bias. The first is internal

(judgmental) bias from the researcher (Sterman, 2000). The systems analysis and

dynamic modeling methods used in this research require significant insight from the

researcher. As such, they are particularly vulnerable to confirmation bias.

Assumptions about the structure of the model are identified and justified through

logical argument to minimize personal bias of the researcher. These assumptions

were confirmed by evidence from observed behavior in the real system. To further

minimize the risk of personal bias, experts in the field of groundwater resources were

consulted to review the system model for structural and behavioral adequacy.


160

Furthermore, validation tests and statistical analysis were also used to confirm the

structure of the system being modeled.

The second form of bias is systemic bias. Data produced by system dynamics

models will typically exhibit some bias when compared to observed data from the real

system (Sterman, 2000). This is due to the nature of feedback and impossible to

eliminate. In this research, statistical methods identified in section 3.8 were used to

quantify systemic bias produced by the dynamic model.

3.13.4 Replicability

Future researchers may wish to replicate the methods and models produced in

this research. This research uses three specific groundwater basins for model

validation. Each basin will have different parameter values. The dynamic model, if

reliable, make it possible to repeat this research. However, if researchers choose to

test the model on other groundwater basins, new parameter values will have to be

developed. Procedures for parameter development are well documented to ensure that

the model can be properly applied by future researchers.

3.13 Discussion and Conclusions

The primary purpose of this research is to develop a systems dynamics model

of the groundwater systems based on the structure of the United States monetary

system. This required the creation of system dynamics models and comparison to

historical groundwater data to determine if a model of this structure can be used for

the purpose of testing groundwater policy. The primary hypothesis for this research

states that a system dynamics groundwater model based on the structure of monetary

policy systems can produce behavior-over-time that matches historical groundwater

data with accuracy that is sufficient for the purposes of testing groundwater policy. To

that end, the following hypotheses were tested:

Hypothesis 1: A system dynamics groundwater model that is based on the

structure of monetary policy systems is a valid model of a groundwater system.


161

Hypothesis 2: A system dynamics groundwater model based on the structure of

monetary policy systems can produce behavior-over-time that matches historical

groundwater data with accuracy that is sufficient for the purposes of testing

groundwater policy.

The following section provides a discussion of the results and their

implications regarding the primary hypotheses.

3.14.1 Discussion of Results

Hypothesis 1 cannot be tested directly. Instead, three separate groundwater

models were developed for three different groundwater basins. These models were

subjected to a battery of verification and validation tests shown in Table 3.2. These

tests are the sub-hypotheses developed to assess the validity of the models in question.

The Cuyama and Modesto models passed all 12 of the tests proposed. These

tests included structural verification, behavioral verification, policy verification and

expert review. Passing all of these tests indicates that these two models are valid.

The Pajaro groundwater model passed 10 of the 12 verification and validation

tests. Although the model passed expert review and many other tests, it failed to

reproduce observed behavior and behavioral anomalies present in the historical data.

Behavior reproduction is important to demonstrating the validity of the underling

systemic structure. As such, the results of the sub-hypothesis tests cast doubt on the

validity of the Pajaro system model.

Hypothesis 2 relies on three sub-hypotheses to assess and quantify the ability

of each model to produce behavior-over-time that matches historical groundwater data

with accuracy that is sufficient for the purposes of testing groundwater policy. Three

groundwater models were developed for each groundwater system to compare the

simulated change in groundwater storage to the actual change in groundwater storage

over different periods of time. The Root Mean Square Percent Error (RMSPE), Theil

inequality statistic for bias (UM), and the coefficient of determination (R2) were

calculated for 1-year, 5-year and 10-year simulations for each groundwater system.


162

The Cuyama 1-year model uses 10 years of data to predict the change in

groundwater storage for the next year. Null hypotheses 2.2 and 2.3, pertaining to

systemic bias and R2, can be rejected outright. Null hypothesis 2.1, pertaining to

RMSPE cannot be rejected outright. However, failure in this test can be attributed to a

large error in only one of the 50 years simulated. Based on a preponderance of

evidence, this model is acceptable for the purposes of testing groundwater policy.


groundwater storage for the next 5 year period. Null hypothesis 2.3, pertaining to R2,

can be rejected. Null hypothesis 2.1 and 2.2, pertaining to RMSPE and UM cannot be

rejected outright. However, failure in the RMSPE test can be attributed to a large

error in only five of the 47 periods simulated. Although the average UM was higher

than desired, the average cumulative error was only 0.9%. This indicates that, while

the portion of error due to systemic bias is large, the magnitude of the error is small.

Figure 3.28 below compares the simulated and actual 5-year cumulative

change in storage for all possible simulation periods. It is a graphical indication that

the structure of the model can produce behavior-over-time that is similar to observed

behavior. Based on a preponderance of evidence, this model is acceptable for the

purposes of testing groundwater policy.

Figure 3.28 Cuyama 5-year Cumulative Change in Storage.

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163


groundwater storage for the next 10 year period. Null hypothesis 2.3, pertaining to R2,

can be rejected. Null hypothesis 2.1 and 2.2, pertaining to RMSPE and UM cannot be

rejected outright. However, failure in the RMSPE test can be attributed to error in 10

of the 42 periods simulated. Although the average UM was higher than desired, the

average cumulative error was only 3.25%, with a maximum of 37%. This may be

acceptable for the purposes of testing policy.

The Pajaro 1-year model is similar to the Cuyama model. However, the

system is much more complicated. It involves significant inflow from the ocean. This

seawater intrusion makes it difficult to estimate changes in fresh groundwater storage.

Null hypotheses 2.1 and 2.2, pertaining to RMSPE and UM, can be rejected outright.

Null hypothesis 2.3, pertaining to R2 cannot be rejected outright. However, an average

R2 value of 0.84 may be acceptable for the purposes of testing groundwater policy.

In the Pajaro 5-year and 10-year models, null hypothesis 2.1, pertaining to

RMSPE, can be rejected. However, null hypothesis 2.2 and 2.3, cannot be rejected.

The average cumulative error was very high in both models. As such, the results of the

sub-hypothesis tests do not support the claim that the these two models are acceptable

for the purposes of testing groundwater policy.

The Modesto 1-year model is similar to the other models. It involves

significant inflow of surface water for irrigation. Null hypotheses 2.1 and 2.2,

pertaining to RMSPE and UM, can be rejected. Null hypothesis 2, pertaining to R2

cannot be rejected outright. However, an average R2 value of 0.88 is still very good

for a highly-variable, natural system. A graphical comparison of the simulated and

actual annual change in storage can be found in section 3.8.3 (Figure 3.21). Based on

a preponderance of evidence, this model is acceptable for the purposes of testing

groundwater policy.


164

In the Modesto 5-year, null hypotheses 2.1 and 2.3, pertaining to RMSPE and

R2, can be rejected. Null hypothesis 2.2, pertaining to UM cannot be rejected. The

average UM was higher than desired.

Figure 3.29 below compares the simulated and actual 5-year cumulative

change in storage for all possible simulation periods. It is a graphical indication that

the structure of the model can produce behavior-over-time that is similar to observed

behavior. Based on a preponderance of evidence, this model is acceptable for the

purposes of testing groundwater policy.

Figure 3.29 Modesto 5-year Cumulative Change in Storage.

In the Modesto 10-year model, null hypothesis 2.1, pertaining to RMSPE, can

be rejected. However, null hypothesis 2.2 and 2.3, cannot be rejected. The average

cumulative error was very high. This models is not acceptable for the purposes of

testing groundwater policy.

3.14.2 Conclusions

The system dynamics models were subjected to a battery of relevant validation

tests. Statistical analysis techniques, relevant for system dynamics, were also used to

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test the validity of the models. Regression analysis was used to provide a basis for

comparison with traditional statistical methods. Several conclusions can be drawn

based on a preponderance of the evidence derived from these tests. It appears that a

system dynamics model that is based on the structure of monetary policy systems may

be a valid model of a groundwater system under certain conditions. Two of the three

models passes all 12 verification and validation tests. These were models of inland

systems with no subsurface coastal influence. A model of this structure may be valid

for inland groundwater systems.

The Pajaro model is a coastal system with significant subsurface inflow from

the ocean. It passed 10 of the 12 tests. While this was insufficient to support the

claim of validity in hypothesis 1, it may indicate that more information is required in

order to develop a model capable of reproducing observed behavior. However, the

results of the test do not support the claim of validity in hypothesis 1. A model of this

structure may not be appropriate for coastal groundwater systems.

The results of the sub-hypothesis tests for hypothesis 2 are also mixed. While

some of the models are capable of producing behavior-over-time that matches

historical groundwater data with accuracy that is sufficient for the purposes of testing

groundwater policy, others are not. This appears to depend on the influence from

coastal inflow, and the length of the prediction desired.

The Pajaro model was only capable of matching historical groundwater data in

the 1-year simulation. However, the results of the behavior reproduction raise

questions about the validity of the model. More research is required to determine if

this model is acceptable for the purposes of testing policy.

None of the 10-year models were capable of matching historical behavior with

accuracy sufficient for the purposes of testing groundwater policy. The overall

cumulative error is too large for the model to be useful. Some of this error is due to

the accumulation of small mass balance errors in the actual data. This small annual

error results in a significant error after 10 years. Also, it may not be possible to


166

predict 10 years of groundwater data based on linear approximations derived from the

previous 10 years.

Models of the inland systems (Cuyama and Modesto) may be capable of

producing behavior-over-time that matches historical groundwater for 1-year and 5-

year simulations. Although they did not pass all of the tests, a preponderance of

evidence indicates that they are likely sufficient for the purpose of testing policy.

Overall, the results of research 1 support the conclusion that a system

dynamics groundwater model that is based on the structure of monetary policy may be

a valid model of a groundwater system capable of producing behavior-over-time that

is sufficient for the purposes of testing groundwater policy provided that it is an inland

system with a simulation period of five years or less. More research is required to

make this claim for coastal systems. However, this conclusion lends support to the

potential isomorphology between groundwater systems and monetary systems to be

discussed in Chapter 4.

3.14 References

Barlas, Y. (1989). Multiple Tests for Validation of System Dynamics Type Simulation

Models. European Journal of Operational Research, 42, 59-87.

Bates, G., & Beruvides, M. (2015). Financial and Groundwater Credit in

Contractionary Environments: Implications for Sustainable Groundwater

Management and the Groundwater Credit Crunch. 2015 International Annual

Conference . Indianapolis, IN: American Society for Engineering

Management.

Chatterjee, S., & Hadi, A. S. (2006). Regression Analysis by Example. Hoboken: John

Wiley & Sons, Inc.

Doyle, J. K., & Ford, D. N. (1998). Mental Models Concepts forSystem Dynamics

Research. System Dynamics Review, 14(1), 3-29.


167

Forrester, J. W., & Senge, P. M. (1979). Tests for Building Confidence in System

Dynamics Models. Cambridge, MA: System Dynamics Group, Massachusetts

Institute of Technology.

Hadjis, A. (2011). Brining Economy and Robustness in Parameter Testing: a Taguchi

Methods-Based approach to Modle Validation. System Dynamics Review, 27,

374-391.

Hanson, R., Flint, L. E., Faunt, C. C., Gibbs, D. R., & Schmid, W. (2015). Scientific

Investigations Report 2014-5150 Version 1.1: Hydrologic Models and Analysis

of Water Availability in Cuyama Valley, California. Reston, VA: U.S.

Geological Survey.

Hanson, R., Lear, W. S., & Lockwood, B. (2014). Scientific Investigations Report

2014-5111: Integrated Hydrologic Model of Pajaro Valley, Santa Cruz and

Monterey Counties, California. Reston, VA: U.S. Geological Survey.

Keloharju, R. (1981). Dynamic or 'Dynamic' Hypothesis? Retrieved from

www.systemdynamics.org:

http://www.systemdynamics.org/conferences/1981/proceed/keloh159.pdf

Leedy, P. D., & Ormrod, J. E. (2013). Practical Research Planning and Design.

Upper Saddle River, NJ: Pearson Education, Inc.

Oliva, R. (2003). Model Calibration as a Testing Strategy for System Dynamics

Models. European Journal of Operational Researc, 151, 552-568.

Philips, S., Rewis, D. L., & Traum, J. A. (2015). Scientific Investigations Report 2015-

5045: Hydrologic Model of the Modesto Region, California, 1960-2004.

Reston, VA: U.S. GeologicalSurvey.

Qudrat-Ullah, H., & Seong, B. S. (2010). How to do Structural Validity of a System

Dynamics Model Type Simulation Model: The Case of an Energy Policy

Model. Energy Policy, 38, 2216-2224.

Raeisi, E. (2008). Ground-water storage calculation in karst aquifers with alluvium or

no-flow boundaries. Journal of Cave and Karst Studies, 70(1), 62–70.

Sterman, J. (2000). Business Dynamics: Systems Thinking and Modeling for a

Complex World. Boston: Irwin McGraw-Hill.


168

Sterman, J. (1984). Appropriate Summary Statistics for Validating the Historical Fit of

System Dynamics Models. Dynamica, 10(II), 51-66.


169

CHAPTER IV

RESEARCH 2: EXPLORATORY STUDY - POTENTIAL

ISOMORPHOLOGY BETWEEN GROUNDWATER AND

MONETARY SYSTEMS

4.1 Abstract

This exploratory research presents a methodology for assessing potential

isomorphology between two different systems. The methodology is used to evaluate

the potential isomorphology between groundwater management policy and monetary

policy using a system dynamics modeling approach. It relies on the system dynamics

models developed in Research 1 to evaluate the potential for isomorphology using a

combination of logical argument, qualitative and quantitative comparison.

Research 1 links the structure of groundwater systems to behavior in

groundwater systems. In this research, the general structure of groundwater systems is

compared to the structure of United States monetary system to evaluate the potential

structural homology between the two systems. Policy levers are added to the dynamic

model to allow behavioral comparison. Finally, the behavior of the groundwater

system models is compared to behavior in the observed monetary system.

Based on this analysis, the structure of groundwater systems appears to be

homologous to the structure of monetary systems. The structure of the non-coastal

groundwater system is capable of reproducing observed behavior. However, the

structure of the coastal groundwater system was not. The behavior of the non-coastal

groundwater systems, which is based on the structure of a monetary system, produces

behavior that is similar to the behavior observed in the United States monetary system

under contractionary policy.

Although this analysis cannot conclude that groundwater systems and

monetary systems are isomorphic, it does provide support for this claim in non-coastal

groundwater systems.


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4.2 Introduction

Water is an important resource existing in various states of stock and flow.

The same can be said for money. Both systems consist of interrelated structures. Both

systems can be managed using policy levers to change system parameters and

therefore affect behavior. There are many similarities between water policy and

finance. Terms like liquidity, budget and overdraft are used in both fields. However,

these terms have different meanings for each system. They are analogous, but not the

same. The ubiquitous analogies between finance and water indicate a strong

possibility for structural homology and systemic isomorphology between groundwater

and monetary systems.

This exploratory research is intended to evaluate the potential for

isomorphology or identify partial isomorphisms using a system dynamics modeling

approach. Identifying an isomorphological relationship between two systems is

valuable because it can allow knowledge about one system to be transferred to the

corresponding isomorphic system. This research uses the system dynamics model

developed in Research 1 to evaluate the potential for isomorphology.

4.3 Research Methodology

This research uses systems analysis techniques to evaluate the potential

homology and isomorphology between groundwater management policy and monetary

policy. Since the publication of General Systems Theory in 1969, there has been little

research concerning isomorphology. As such, there is no widely accepted

methodology for evaluating isomorphisms between distinct systems.

Recently, Cantu and Beruvides (2013) proposed a three-step methodology for

assessing the potential for isomorphological relationships between two systems. The

first step is to identify analogous systems that show potential for structural homology.

The second step is to use systems analysis to identify and document the structural

elements and relevant characteristics in each system. The final step is to compare

elements of each system.


171

This research methodology builds off the work of Cantu and Beruvides (2013).

The general approach is to link structure and behavior in both systems. A combination

of logical argument, qualitative and quantitative comparison are used to evaluate the

potential isomorphology. First, the structure of groundwater systems is linked to the

structure of monetary systems through systems analysis. This process supports the

assertion of structural homology between the two systems. Next, the structure of

groundwater systems is linked to behavior in groundwater systems. This relies on the

model developed in Research 1. Finally, the behavior of groundwater systems, which

is based on the structure of a monetary system, is linked to behavior in the observed

monetary system.

4.3.1 Structural Homology

There is a long history of analogy between money and water. John Maynard

Keynes developed Hydraulic Macroeconomics in the late 1930s (Coddington, 1976).

Keynes identified the systemic link between monetary policy and aggregate demand

(Snipe, 1985). William Phillips creates a physical hydraulic model of the British

economic system in 1949 (Ryder, 2009). Many of the words used in the financial

system are also used in water. It is clear that the analogy is sufficient to justify

exploration of possible systemic isomorphology. According to Bertalanffy (1969),

“If an object is a system, it must have certain general system characteristics,

irrespective of what the system is otherwise. Logical homology makes possible

not only isomorphy in science, but as a conceptual model has the capacity of

giving instructions for correct consideration and eventual explanation of

phenomena.” (p. 85).

Clearly, the first step towards identifying isomorphic systems is to demonstrate the

existence of a systemic, structural homology.

The methodology for this step includes system analysis and comparative

analysis through homological mapping. Systems analysis techniques are used to

identify structural elements of each system including stocks, flows, delays and

feedback loops. Once each system has been analyzed, they are compared to each

other through the process of homological mapping. A combination of logical argument


172

and qualitative comparison is used to support a claim of homology. Step one results in

a structural model of the groundwater system based on known structures in the

monetary system. Procedures for systems analysis and homological mapping are

presented in section 4.5.1. This research builds on procedures used by Bates and

Beruvides (2015).

4.3.2 Behavioral Comparison

The process of model validation described in Research 1 supports the dynamic

hypothesis implicit in the model by confirming the link between system structure and

behavior (Oliva, n.d.). The fact that the behavior generated by a model that is based

on the structure of a monetary system fits observed groundwater system behavior

supports the potential isomorphology. However, these are no direct objective tests for

isomorphology. A direct comparison between modeled groundwater behavior and

observed monetary system behavior is required. The null hypotheses are tested to

determine if changes in model parameters result in behavioral changes in the same

direction as observed changes in the United States monetary system. Rejecting the

null hypothesis supports the primay hypothesis that the systems are isomorphic.

4.4 Hypotheses

The primary hypothesis for this research states that groundwater systems and

monetary systems exhibit sufficient structural and behavioral similarities to support

the assertion that they are isomorphic. However, there is no single objective test for

isomorphology. Therefore, the hypothesis includes three sub-hypotheses intended to

evaluate different aspects of isomorphology including structure and behavior.

The first sub-hypothesis is groundwater systems and the monetary systems


homology. The goal of this exploratory research is to develop support for the potential

isomorphology or identify potential partial isomorphisms rather than prove or disprove


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the existence of isomorphology. Systems analysis techniques and logical argument are

used to support the potential isomorphology.

The second sub-hypothesis is a dynamic hypothesis about the structure and

causal relationships in the groundwater system, and their relation to monetary systems.

It states that a system dynamics model of a groundwater system that is based on the

structure of a monetary system will produce behavior representative of behavior in

groundwater systems. It represents a dynamic hypothesis about the causal relationship

between structure and behavior (Keloharju, 1981). The model developed in Research

1 states that system dynamics models of a groundwater system that is based on the

structure of a monetary system can produce behavior that is representative of behavior

in groundwater systems. In this research, the structure of the dynamic groundwater

model developed in Research 1 is compared to the structure of monetary systems.

This analysis connects monetary system structure with groundwater system behavior.

The third sub-hypothesis states that policy actions (parameter changes) in the

groundwater system will result in changes in aggregate groundwater demand that are

in the same direction as changes in the rate of growth of aggregate economic demand

when similar policy changes are made in the monetary system. This hypothesis links

behavior of groundwater systems to behavior of monetary systems and is the final step

in demonstrating potential system isomorphology.

The validation of the groundwater model in Research 1 provides support for

the dynamic hypothesis linking structure and behavior, but cannot serve as an

objective hypothesis test for the existence of isomorphology between groundwater and

monetary systems. To achieve this, a testable hypothesis about the behavior of the

two systems is required. The third sub-hypothesis is testable when broken down into

smaller specific hypotheses. Under this methodology “the model is a general

statement and a hypothesis is a proposition that narrows that statement” (Greene,

2011, p. 109). By systematically changing model parameters, the model is restricted

to discrete testable components. The behavior generated by the models under discrete,

restricted simulations can be tested against observed behavior in the monetary system

by direct comparison. See Table 4.1 for a list of research hypotheses.


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Table 4.1 Null and Alternative Hypotheses.


1 Structural elements in the

groundwater management system

cannot be logically mapped to

structural elements in the monetary

policy system on a one-to-one basis.

Structural elements in the groundwater

management system can be logically

mapped to structural elements in the

monetary policy system on a one-to-

one basis.

2 Policy levers in the groundwater

management system cannot be

logically mapped to structural

elements in the monetary policy

system on a one-to-one basis.

Policy levers in the groundwater

management system can be logically

mapped to structural elements in the

monetary policy system on a one-to-

one basis.

3 The form of mathematical equations

governing groundwater systems

differ from monetary systems.

The form of mathematical equations

governing groundwater systems is the

same as monetary systems.

4 An increase in the groundwater

storage requirement parameter in the


model will result in changes in

aggregate groundwater demand that

are in not the same direction as

observed changes in the rate of

growth of economic demand when

the reserve requirement is increased.

An increase in the groundwater storage

requirement parameter in the



aggregate groundwater demand that are

in the same direction as observed

changes in the rate of growth of

economic demand when the reserve

requirement is increased.

5 An increase in the groundwater

pumping tax parameter in the


model will not result in changes in

aggregate groundwater demand that

are in the same direction as observed


economic demand when interest rates

are increased.

An increase in the groundwater

pumping tax parameter in the



aggregate groundwater demand that are

in the same direction as observed


economic demand when interest rates

are increased.

6 A decrease in the total water supply

parameter in the groundwater

management system model will result

in changes in aggregate groundwater

demand that are not in the same

direction as observed changes in the

rate of growth of economic demand

when the money supply is decreased.

A decrease in the total water supply

parameter in the groundwater

management system model will result

in changes in aggregate groundwater

demand that are in the same direction

as observed changes in the rate of

growth of economic demand when the

money supply is decreased.


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4.5 Procedures

4.5.1 Systems Analysis and Structural Homology

This research procedure uses systems analysis techniques to demonstrate the

underlying structural homology between groundwater management policy and

monetary policy. Identifying systems with homologous structure is a critical first step

in identifying systems that are isomorphic. However, there is no single objective test

for confirming idealistic homology. The proposed methodology for this step includes

systems analysis and system comparison. There are four main steps in this procedure.

1. System analysis techniques are used to identify structural elements within

each the system.

2. Causal loop diagrams are created for each system.

3. The structure of each system is compared to assess the degree of structural

homology using logical argument.

4. The form of the governing mathematical equations in each system are

compared to assess similarities.

Expert review is also used to confirm the general structure of the United States

monetary system and the groundwater systems.

The above procedure is used to test sub-hypotheses 1, 2 and 3 shown in Table

4.1. The results are presented in section 4.8.

4.5.2 Behavioral Comparison Procedures

Once the potential for structural homology is confirmed, it is possible to test

the behavior of the groundwater systems under contractionary conditions. Models

from research 1 are modified to include the relevant policy levers. The models are

then tested to determine the direction of change under various contractionary policies.

Finally, the direction of change is compared to the direction of change observed

during periods of contractionary monetary policy in the United States. The following

is a list of the behavioral tests intended to test sub-hypotheses 4, 5, and 6 from Table

4.1.

1. Add a minimum storage requirement to the groundwater models from

research 1 to simulate a change in the reserve requirement and asses the

direction of change in aggregate groundwater demand.


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2. Add a pump tax to the groundwater models from research 1 to simulate

increasing the discount rate and asses the direction of change in aggregate

groundwater demand.

3. Increase the amount of to the groundwater models from research 1 to

simulate open market operations and asses the direction of change in

aggregate groundwater demand.

This research will test the Cuyama and Modesto groundwater systems only.

The Pajaro model was deemed invalid and not capable of producing behavior with

sufficient accuracy for testing policy in research 1. Furthermore, only the 1-year and

5-year simulation models are tested. The 10-year models were not capable of

producing behavior with sufficient accuracy for testing policy.

The direction of change in aggregate groundwater demand is compared to the

direction of change in aggregate (economic) demand observed in during the periods of

contraction listed in Table 4.2 below. The results are presented in section 4.9.

Table 4.2 End Dates of Monetary Tightening Periods (Adrian & Estrella, 2008).

Oct. 1957 Aug. 1969 July. 1974 Aug. 1984 Jul. 2000

Nov. 1959 Aug. 1971 Apr. 1980 Mar. 1989

Nov. 1966 Sept. 1973 Jun. 1981 Apr. 1995

4.6 Parameters and Variables

The parameters and variables used in the groundwater system are presented in

section 3.7. In this research, the parameters are economic. They are the constituent

components of aggregate demand. These parameters are discussed in more detail

below.

4.6.1 Economic Parameters

The parameters to be used in the monetary system model are the components

of the economic aggregate demand equation (3) (Samuelson & Nordhaus, 2001). The

equation is restated here for convenience.


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AD = C + I + G + (X – Y) (3)

The specific parameters that make up the aggregate demand equation are defined

below.


C = Consumption

I = Investment


X = Total Exports

Y = Total Imports


As discussed in section 4.7, data for these parameters is readily available for

the period in question. Economic data is presented in Appendix E.

4.7 Data

Two types of data will be required for this research. Water data is discussed in

section 3.6.1. Economic data is required for behavioral comparison. A discussion of

this data is presented below.

4.7.1 Economic Data

In contrast to water data, there is an abundance of economic data available for

this research. Data for the economic parameters identified in section 4.6 is taken from

the Bureau of Economic Analysis (United States Department of Commerce, n.d.), and

the United States Federal Reserve (Board of Governors of the Federal Reserve

System, n.d.), (Federal Reserve Bank of St. Luis, n.d.).

For the purpose of comparing economic and groundwater systems in a

contractionary environment, this research is limited to periods of contractionary

monetary policy. According to Adrian and Estrella (2008), there have been thirteen

monetary tightening cycles in the United States since 1955. Table 4.2 lists the end of

known periods of monetary tightening.


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Calculated aggregate demand from these time periods represents the observed

behavior of the monetary system. The direction of change in aggregate demand

during and after the periods of monetary tightening is compared to the direction of

change in groundwater demand predicted by the dynamic groundwater model.

4.8 Structural Homology Analysis

In order to assess the potential structural homology, system analysis techniques

were used to identify structural elements within each the system. The elements in the

groundwater system are compared to the elements in the monetary system through

homological mapping. Causal loop diagrams are then created for each system. The

form of the mathematical equations governing each system are assessed and

compared. The structure of each groundwater system is compared to the monetary

system. Finally, logical argument and graphical comparison are used to assess the

degree of structural homology.

Homological Mapping

The first step in this research was systems analysis identify the structural

elements in the monetary system and the correlating elements in the groundwater

systems. This process relies on systems analysis and logical argument. The structural

elements in the groundwater system are related similar elements in the monetary

system through homological mapping.

Each system consists of stocks and flows. The primary stock in a system is the

finite amount of either money or water within the system In the monetary system, the

primary stock is the monetary base. This is the total amount of currency in the system.

In the groundwater system, the primary stock is the water supply. This is the total

volume of water available in the system.

The primary stock can exist within each system as a set of interrelated stocks

and flows. In the monetary system, currency exists as a stock in the banking system, or


179

as a flow of money in circulation. In a groundwater system, water exists as a stock of

groundwater, or in various states of surface or subsurface flow.

In the monetary system it is possible to develop a stock of debt when the

accumulated deficits in the banking stock exceed the accumulated surpluses. In a

groundwater system, it is possible to develop a groundwater debt, known as storage

depletion, when the accumulated outflows from the groundwater stock exceed the

accumulated flows into the groundwater stock.

Aggregate demand is the “total planned or desired spending in the economy

during a given period” (Samuelson & Nordhaus, 2001, p. 756). It is the sum of all the

consumption, investment, government spending, and net exports (exports minus

imports) in an economic system. Aggregate groundwater demand can be described as

the total planned or desired water consumption in a given year. It is the sum of the

consumptive use, storage, runout and net subsurface flow in a hydrologic system.

From this analysis is can be logically argued that groundwater is similar to

currency stored in a bank, and that total income in an economic system is similar to

total inflow in a hydrogeologic system. It can also be argued that accumulated deficits,

or debt, in the banking stock is similar to accumulated groundwater deficits.

Table 4.3 below lists the important structural elements in monetary systems

and the corresponding structural element in groundwater systems. An argument is

presented to justify the reason that these elements are similar.


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Table 4.3 Structural Elements.

Monetary

Component

Groundwater

Component

Argument

Income Inflow Currency entering the system as income is similar to

water entering the system from precipitation or

surface water deliveries.

Monetary Base Water Supply The total amount of currency in the monetary

system is similar to the total amount of water in the

groundwater system.

Bank Stock Total

Groundwater

Stock

The total funds on deposit in a reserve bank is

similar to the total volume of groundwater in an

aquifer.

Debt Groundwater

Debt

The cumulative amount of currency loaned into

circulation, minus the amount repaid is similar to

the cumulative amount of groundwater pumped into

the surface flow system minus the amount

infiltrated back into the groundwater system.

Accumulated deficits minus accumulated surpluses

Money in

Circulation

Surface Flows Currency flowing through the system for commerce

and consumption is similar to water flowing through

the surface water system for irrigation and domestic

consumption.

Aggregate

Demand

Aggregate

Groundwater

Demand

The demand for all goods and services produced by

an economy is similar to the total demand for all

water in the groundwater basin.

Credit Stock Available

Groundwater

Stock

The amount of loanable funds (total deposits minus

reserve) in the banking system is similar to the

volume of accessible groundwater available for

pumping in a groundwater system.

There are three primary policy levers available in the monetary system. The

Federal Reserve can influence aggregate economic demand by changing the overnight

interest rate, changing the reserve requirement, or conducting open market operations.

Open market operations involve buying or selling assets to increase or decrease the

amount of currency in the system.

The Groundwater Sustainability Act of 2014 requires the creation of

Groundwater Management Agencies (GMAs) to regulate individual groundwater


181

basins. These GMAs have the power to regulate pumping, assess fees or pump taxes,

and purchase water from other supplies. These policy levers are similar to those

available to the Federal Reserve discussed above.

Table 4.4 below lists the policy levers in the monetary system and the

corresponding policy levers that are potentially available in groundwater systems. An

argument is presented to justify the reason that these elements are similar.

Table 4.4 Policy Levers.

Monetary

Component

Groundwater

Component

Argument

Interest Rate Pumping Tax The cost of accessing credit in the monetary system

is similar to a cost or tax on the use of groundwater.

Reserve

Requirement

Minimum

Groundwater

Storage

Requirement

The minimum amount of currency that must be kept

in reserve is set by FED policy. This is similar to a

GMA setting a minimum storage requirement for a

groundwater system.

Open Market

Operations

Water Market

Operations

Buying or selling securities to change the monetary

base and/or support demand of specific securities is

similar to buying or selling water or subsidizing

specific crops.

The above analysis argues that there are significant similarities between

elements in the monetary system and groundwater systems. A similar argument can

be made for policy levers. Although the policy levers discussed do not currently exist

in most groundwater systems, the passage of the Sustainable Groundwater

Management Act makes it possible for GMAs to use these types of policy levers. The

next step in this research is to assess how these structural elements and policy levers

relate to each other.

Causal Loop Diagrams

The structure of a system can be graphically illustrated using causal loop

diagrams. These diagrams show the relationship between various elements within the

system. Elements are linked to other elements by causal relationships. In this way,


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these diagrams show how changes in one element effect the other elements in the

system. The overall structure of the system may vary slightly depending on the mental

model of the researcher, but the general structure of the system cannot change

drastically without changing the nature of the system.

Figures 4.1 and 4.2 show the general structure of a groundwater system and

monetary system respectively. The general structure of the monetary system has been

verified by Dr. Michael McCullough, associate professor of agricultural economics at

Cal Poly San Luis Obispo. The general structure of groundwater systems was

developed using system analysis techniques in research 1.

These systems show significant similarities. By analyzing the diagrams, it is

possible to see how various elements in the monetary system correspond to

homologous elements in the groundwater system. These systems show significant

similarities. The logical similarities identified through homological mapping appear to

be supported by this analysis. Most of the homologous structural elements hold

similar positions and causal relationships in each system.

The primary difference between the systems appears when comparing net

exports and net underflow. In the groundwater system, net underflow is linked

directly to the volume of water in storage. A change in groundwater debt levels

results in a change in net underflow in the opposite direction. An increase in

groundwater debt results in a decrease in net underflow. No similar link exists in the

monetary system. This research does not show a logical connection between debt

levels and net exports.

Despite this difference, Figures 4.1 and 4.2 show significant similarities. It can

be logically argued that the structural elements and their relationship to each other are

similar. This analysis supports the conclusion that these two classes of systems may

be structurally homologous.


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Figure 4.1 Groundwater System Diagram.

Groundwater

System Surface Water

System


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Figure 4.2 Monetary Policy Diagram.

Currency in

storage

Currency in circulation


185

Governing Equations

The next step in this research is to compare the mathematical equations that

govern each system. Similarities in the form of these equations provides further

support for structural homology. These equations have been discussed in previous

sections, but are restated here for convenience.

Groundwater storage is dictated by the conservation of mass. The sum of the

inflows must equal the sum of the outflows plus any change in groundwater storage.

Mass balance allows calculation of the change in storage (Storage) according to the

following equation (Raeisi, 2008):


Where: IA = Subsurface inflow




E = Evaporation (Generally negligible)


The left side of this equation represents inflow. The right side represents Aggregate

Groundwater Demand (AGD) plus the change in aquifer storage. By substituting

outflows for AGD, the mass balance equation can be rewritten as:

AGD = IA + IS + (Y – X) (2)

Where: AGD = Aggregate Groundwater Demand



X = Total basin outflow

Y = Total basin inflow

(Y – X) = Net change in aquifer storage (excluding other

inflows and outflows)

This equation can be further reduced by substituting for inflows and change in

storage as follows:

AGD = Inflow + Storage (3)


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The equation for aggregate demand (AD) is commonly accepted as:

AD = C + I + G + (X – Y) (Samuelson & Nordhaus, 2001) (4)

where:


C = Consumption

I = Investment


X = Total Exports

Y = Total Imports


The form of this equation is similar to the mass balance equation (1) above.

According to Keen (2012), aggregate demand can also be found by the following

equation:

AD = Income + Debt (5)

The form of this equation is similar to that of equation 3 above.

By comparing these equations, it can be argued that change in debt in the

monetary system is similar to a change in storage in the groundwater system. It can

also be argued that income is similar to inflow.

Structural Comparison

The process of homological mapping through systems analysis and logical

argument supports the assertion of structural homology. Despite small differences in

the models, the development and analysis of causal loop diagrams also supports this

conclusion. The similarity between the forms of the equations governing each system

provides additional support. Based on a preponderance of this evidence, these general

systems appear to be structurally homologous. The next step in this research is to

evaluate the behavior of each system when subjected to contractionary policy changes

in order to assess the potential isomorphology.


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4.9 Behavioral Comparison

The above analysis illustrates that a conceptual, structural model of a

groundwater may be of the same general form as a monetary system. The next step in

this research is to compare the behavior of each system under similar contractionary

policy. The three policy scenarios tested are interest rate increase / pump tax, reserve

requirement increase, and open market operations.

The following analysis presents a behavioral comparison of groundwater and

monetary systems to evaluate sub-hypotheses 4, 5, and 6 from Table 4.1. Gross

Domestic Product (GDP) is used as a proxy for aggregate demand (AD). GDP and

AD are quantitatively the same. The parameters for calculating GDP are the same as

those for AG shown in section 2.8.3. Therefore, a change in GDP is equal in

magnitude and direction to a change in AD.

4.9.1 Interest Rate Increases

The United States Federal Reserve (FED) has the ability to change the interest

rate charged to member banks on federal funds. In a contractionary environment, the

interest rate is increased in order to increase the cost of credit, and thereby reduce

demand. An interest rate increase has occurred in all 13 of the monetary tightening

periods shown in Table 4.2. In five cases, the GDP declined and growth receded after

tightening. In five cases, the rate of GDP growth declined, although growth did not

recede. In one case GDP growth was unchanged. In two cases, GDP increased. Table

4.5 below shows the period of interest rate increase and the corresponding direction of

change in aggregate demand.

The analysis of GDP response to interest rate increase is presented graphically

in Appendix F. Although the economic response to an interest rate increase is not

consistent in all cases, the majority of the tests indicate that the rate of growth of

aggregate demand decreases when interest rates are increased. This indicates that the

systemic response to interest rate increases is in the downward direction.


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Table 4.5 Aggregate Demand Response to Interest Rate Increase.

Period Ending Direction of Change in Rate of Aggregate Demand Growth

Oct. 1957 Decline in Aggregate Demand.

Nov. 1959 Decline in Aggregate Demand.

Nov. 1966 Decline in Aggregate Demand Growth Rate.

Aug. 1969 Decline in Aggregate Demand.

Aug. 1971 Decline in Aggregate Demand Growth Rate.

Sept. 1973 Decline in Aggregate Demand Growth Rate.

July 1974 Decline in Aggregate Demand.

Apr. 1980 Increase in Aggregate Demand.

June 1981 Decline in Aggregate Demand.

Aug. 1984 No Change.

Mar. 1989 Decline in Aggregate Demand Growth Rate.

Apr. 1995 Increase in Aggregate Demand.

July 2000 Decline in Aggregate Demand Growth Rate.

Groundwater System Behavior Comparison

Based on the systems analysis and homological mapping demonstrated in

section 4.8, adding a pump tax on groundwater, or increasing the cost of groundwater

is analogous to increasing the interest rate in the monetary system. However, data on

the effect of pump taxes on groundwater consumption is unavailable, and estimating

the impact of pump taxes on groundwater consumption is beyond the scope of this

research. For the purposes of this research, it is assumed that an increase in the cost of

groundwater will decrease groundwater consumption. In order to simulate this

condition, this research assumes that a pump tax will be sufficient to reduce


189

evapotranspiration due to irrigation. This simulates a reduction in groundwater

demand for irrigation due to the increased cost of groundwater. The reduction in

demand is arbitrary, but sufficient to demonstrate the systemic response. For this

simulation, it is arbitrarily assumed that the pump tax starts in water year 1980 in

order to examine the resulting change in behavior.

To simulate this policy, the evapotranspiration parameters for applied

irrigation water were adjusted annually to produce the desired decrease in demand.

The expected response to this contractionary policy in a groundwater basin would be a

decrease in the rate of groundwater depletion after the period when the pump tax is

enacted. This behavioral test was performed the Cuyama and Modesto groundwater

systems. The results of the test are described below.

Cuyama

In this simulation, the Cuyama groundwater system is subjected to a 20%

reduction in evapotranspiration due to irrigation beginning in water year 1980. The

system was assumed to be unchanged until 1980. Once the pump tax is enacted,

evapotranspiration due to irrigation, and the resulting agricultural pumpage were

adjusted downward annually by 20% to simulate decreased demand. Aggregate

irrigation efficiency was assumed to remain constant at 63.4%. All other parameters

were unchanged. The results of this simulation are shown in Figure 4.3 below.


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Figure 4.3 Cuyama Pump Tax Test.

In this simulation, the pump tax took effect in water year 1980. At this point,

the contractionary policy results in a reduction in evapotranspiration for irrigation of

20% annually. The resulting groundwater pumpage is adjusted annually accordingly.

As Figure 4.3 shows, the result of this policy is a decrease in the rate of groundwater

depletion after 1980, corresponding to a reduction in aggregate groundwater demand.

Although the magnitude of the pump tax was insufficient to stop groundwater storage

depletion, the resulting change in behavior is in the same direction as the change in

aggregate economic demand when the interest rate was increased. This supports the

sub-hypothesis that changes in the cost of groundwater credit will result in changes in

aggregate groundwater demand that are in the same direction as changes in the rate of

growth of aggregate economic demand under increased interest rates.

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Modesto

In this simulation, the Modesto groundwater system is subjected to a 10%

reduction in evapotranspiration due to irrigation beginning in water year 1980. The

system was assumed to be unchanged until 1980. Once the pump tax is enacted,


adjusted downward annually by 10% to simulate decreased demand. Aggregate

irrigation efficiency was assumed to remain constant at 62.0%. All other parameters


Figure 4.4 Modesto Pump Tax Test.

In this simulation, the pump tax took effect in water year 1980. At this point,

the contractionary policy results in a reduction in evapotranspiration for irrigation of

10% annually. The resulting groundwater pumpage is adjusted annually accordingly.

As Figure 4.4 shows, the result of this policy is a general decrease in groundwater

depletion corresponding to a reduction in aggregate groundwater demand. In this

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case, the magnitude of the pump tax was sufficient to stop groundwater storage

depletion resulting in groundwater accretion. The resulting change in behavior is in

the same direction as the change in aggregate economic demand when the interest rate

was increased. This supports the sub-hypothesis that changes in the cost of

groundwater credit will result in changes in aggregate groundwater demand that are in

the same direction as changes in the rate of growth of aggregate economic demand

under increased interest rates.

4.9.2 Reserve Requirement Increase

According to the Board of Governors of the Federal Reserve (n.d.), there have

been nine periods of reserve rate increase from 1960 to 1980. In eight of these

periods, the resulting change in the rate of GDP growth has been in the downward

direction. Table 4.6 below shows the periods of reserve rate increase and the resulting

direction of change in aggregate demand.

Table 4.6 Aggregate Demand Response to Reserve Requirement Increase (Adapted

from (Board of Governors of the Federal Reserve System, n.d.).

Date of Increase Magnitude of Increase Direction of Change in Aggregate

Demand Growth

Nov.1960 $380,000,000 Increase

July 1966 $ 420,000,000 Decrease

Sept. 1966 $445,000,000 Decrease

Jan. 1698 $550,000,000 Decrease

April 1969 $660,000,000 Decrease

July 1973 $850,000,000 Decrease

Oct. 1973 $465,000,000 Decrease

Nov. 1978 $3,000,000,000 Decrease

Nov. 1980 $1,400,000,000 Decrease


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Groundwater System Behavior Comparison

Based on the systems analysis and homological mapping demonstrated in

section 4.8, increasing the reserve requirement in the monetary system is similar to

setting a maximum allowable storage depletion for the groundwater basin. In order to

test system behavior under this policy, a target for maximum allowable depletion was

arbitrarily set at 50% of the observed maximum depletion for each groundwater

system. To simulate this policy, system demand parameters were adjusted annually to

target the 50% reserve requirement. The expected response to this contractionary

policy in a groundwater basin would be an abrupt decrease in the rate of groundwater

depletion when the reserve requirement is reached. This behavioral test was

performed the Cuyama and Modesto groundwater systems. The results of the test are

described below.

Cuyama

The Cuyama groundwater system is dominated by agricultural groundwater

consumption. To simulate a policy of setting a 50% reserve requirement, the

maximum allowable cumulative groundwater depletion was set at 1,053,000 acre-feet.

The system was assumed to be unchanged until cumulative depletion reached this 50%

threshold. Once the reserve maximum allowable depletion target was reached,


adjusted annually to target the 50% reserve requirement. Aggregate irrigation

efficiency was assumed to remain constant at 75.8%. All other parameters were

unchanged. The results of this simulation are shown in Figure 4.5 below.


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Figure 4.5 Cuyama Reserve Requirement Test.

In this simulation, the cumulative groundwater depletion reached the 50%

reserve requirement in water year 1990. At this point, the contractionary policy

required a decrease in groundwater consumption for irrigation to maintain the reserve.

Evapotranspiration due to irrigation and the resulting groundwater pumpage were

adjusted annually to target the 50% reserve. As Figure 4.5 shows, the result of this

policy is a decrease in aggregate groundwater demand. Cumulative depletion reached

a dynamic equilibrium around the target cumulative depletion of 1,053,000 acre-feet.

The resulting change in behavior is in the same direction as the change in aggregate

economic demand when the reserve requirement was increased. This supports the

sub-hypothesis that changes in the reserve requirement in the groundwater system will

result in changes in aggregate groundwater demand that are in the same direction as

changes in the rate of growth of aggregate economic demand.

Modesto

The Modesto groundwater system is also dominated by agricultural

groundwater consumption. However, Modesto also imports surface water to augment

agricultural demand. To simulate a policy of setting a 50% reserve requirement, the

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maximum allowable cumulative groundwater depletion was set at 2,241,000 acre-feet.

The system was assumed to be unchanged until cumulative depletion reached this 50%

threshold. Once the reserve maximum allowable depletion target was reached,

agricultural pumpage as adjusted annually to target the 50% reserve requirement.

Evapotranspiration remained unchanged and surface water deliveries were increased

to offset the reduction in agricultural groundwater pumpage. All other parameters


Figure 4.6 Modesto Reserve Requirement Test.

In this simulation, the cumulative groundwater depletion reached the 50%

reserve requirement in water year 1988. At this point, the contractionary policy

required a decrease in groundwater consumption for irrigation to maintain the reserve.

Annual groundwater pumpage was adjusted annually to target the 50% reserve.

Surface water deliveries were increased to offset the loss of groundwater. As Figure

4.6 shows, the result of this policy is a decrease in aggregate groundwater demand.

The resulting change in behavior is in the same direction as the change in aggregate

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economic demand when the reserve requirement was increased. This test also

supports the sub-hypothesis that changes in the reserve requirement in the


in the same direction as changes in the rate of growth of aggregate economic demand.

4.9.3 Open Market Operations

Open market operations are a flexible monetary policy tool that can be used to

target either interest rates, the money supply, or both. The Federal Open Market

Committee (FOMC) sets targets for the federal funds rate and conducts ongoing open

market operations in an attempt to meet these targets. In a contractionary

environment, the FOMC could use open market operations to increase the cost of

credit, by targeting the interest rate, and decrease the money supply by selling

securities. Most recently, the FOMC has used open market operations to purchase

securities in an effort to support certain areas of the economy and increase the money

supply. This expansionary policy is known as quantitative easing. However, due to

the ongoing nature of open market operations, it is difficult to identify specific time

periods when this tool was used in a contractionary manner.

Theoretically, increasing the interest rate and decreasing the money supply

through open market operations should result in a downward change in aggregate

demand, or the rate of growth in aggregate demand, depending on the magnitude of

the changes and the condition of other forces in the economy. The analysis in section

4.9.1 show that, in general, an increase in the cost of credit results in a decrease in

aggregate demand or its rate of growth. However, due to the fact that open market

operations are adjusted daily, and executed through a wide variety of tools, this

research has been unable to isolate the impact on aggregate demand. Therefore, it is

not possible to determine the direction of change in aggregate demand as a direct

result of contractionary open market operations. Sub-hypothesis number 6 cannot be

tested.


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4.10 Hypothesis Test Results

The primary hypothesis for this research states that groundwater systems and

monetary systems exhibit sufficient structural and behavioral similarities to support

the assertion that they are isomorphic. The hypothesis includes three sub-hypotheses

intended to evaluate different aspects of isomorphology including structure and

behavior. Six tests were used to evaluate these sub-hypotheses. The following is a

discussion of the results of these tests.

The first sub-hypothesis is groundwater systems and the monetary systems


homology. System analysis techniques were used to identify structural elements

within each the system. Homological mapping, causal loop diagrams and a

comparison of the governing mathematical equations were used to compare the

general structure of the two systems. The results of tests 1.1 – 1.3 are summarized in

Table 4.7 below.

Table 4.7 Results for Sub-hypothesis 1.

Through logical argument and graphical comparison, these tests show a high degree of

structural homology.

The second sub-hypothesis is a dynamic hypothesis about the structure and

causal relationships in the groundwater system, and their relation to monetary systems.

It states that a system dynamics model of a groundwater system that is based on the

structure of a monetary system will produce behavior representative of behavior in

groundwater systems. Research 1, described in Chapter 3, shows that two of the three

No. Null Sub-Hypothesis Result

1.1H0 : Structural Elements cannot be mapped ≠ Pass

H1 : Structural Elements can be mapped = Pass

Reject H0:

Test = Pass

1.2H0 : Policy Levers cannot be mapped ≠ Pass

H1 : Policy Levers can be mapped = Pass

Reject H0:

Test = Pass

1.3H0 : Governing Mathematical Equations differ in form ≠ Pass

H1 : Governing Mathematical Equations similar in form = Pass

Reject H0:

Test = Pass


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system models evaluated are valid and capable of producing behavior matching

observed behavior to a degree that is sufficient for testing groundwater policy. The

structure of these models was based on the structure of the monetary system.

Therefore, there is evidence to connect monetary system structure with groundwater

system behavior in the two non-coastal groundwater systems.

The third sub-hypothesis states that policy actions (parameter changes) in the


in the same direction as changes in the rate of growth of aggregate economic demand

when similar policy changes are made in the monetary system. The behavioral

comparison analysis in section 4.9 above indicates that the direction of change in the

rate of growth of aggregate economic demand in response to contractionary monetary

policy is generally downward. Although this downward change occurred in only 10 of

the 13 tightening periods tested, the conclusion agrees with monetary theory. In the

three periods where contractionary monetary policy did not result in a downward

change in aggregate demand growth, it is likely that the magnitude of the policy

changes was insufficient to overcome other economic factors.

The direction of change in aggregate economic demand was compared to the

direction of change in aggregate groundwater demand under similar policy changes for

the Cuyama and Modesto groundwater system models. In each case, the direction of

change in aggregate groundwater demand was also downward. This provides support

for the conclusion that the systems, based on similar structures, also exhibit similar

behavior in a contractionary environment. The results of tests 1.4 – 1.6 are shown in

Table 4.8 below.


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Table 4.8 Results for Sub-hypothesis 3.

4.11 Methodological Concerns

The following section addresses the common methodological concerns of bias

and replicability.

4.11.1 Bias

Bias is a significant concern in all research. It is important to minimize

potential bias to the maximum extent possible. In this research, the primary concern is

internal (judgmental) bias from the researcher (Sterman, 2000). The systems analysis

and dynamic modeling methods used in this research are particularly vulnerable to

confirmation bias. Assumptions about the structure of the model are identified and

justified through logical argument to minimize personal bias of the researcher. These

assumptions were confirmed by evidence from observed behavior in the real system.

Experts in the field of groundwater resources and economics were consulted to review

the systems to confirm the structure and underlying assumptions.

Cuyama Modesto

1.4

Increase in Groundwater Storage

Requirement:

H0 : Direction of change not the same ≠ Pass

H1 : Direction of change is the same = Pass

Downward Change:

Test = Pass

Reject H0

Downward Change:

Test = Pass

Reject H0

1.5

Increase in Groundwater Pump Tax:



Downward Change:

Test = Pass

Reject H0

Downward Change:

Test = Pass

Reject H1

1.6

Water Market Operations:



Not Enough Data:

Test = NA

Not Enough Data:

Test = NA

No. Null Sub-HypothesisResult


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4.11.2 Replicability

Future researchers may wish to replicate the methods and models produced in

this research. The economic analysis relies on data found in the appendix. This

analysis can be replicated. However, the data for the groundwater systems are specific

to each system. The results for these specific systems may be replicated with the data

provided. However, the results may not apply to all systems. Each basin will have

unique parameter values. If researchers choose to test the model on other groundwater

basins, new parameter values will have to be developed. Procedures for parameter

development are well documented to ensure that the model can be properly applied by

future researchers.

4.12 Discussion and Conclusions

The primary goal for this research is to provide support for the assertion that

groundwater systems and monetary systems are isomorphic. As previously stated,

there is no single objective test for isomorphology. This research uses a combination

of logical argument, qualitative and quantitative comparison to evaluate the potential

isomorphology. The analysis of systemic structure and resulting behavior under

contractionary conditions support this claim.

The structure of groundwater systems appears to be homologous to the

structure of monetary systems. The structure of the non-coastal groundwater system is

capable of reproducing observed behavior. This links the structure of the monetary

system to behavior in the groundwater system. Finally, the behavior of groundwater

systems, which is based on the structure of a monetary system, is linked to behavior in

the observed monetary system under contractionary policy.

Although this analysis cannot conclude that groundwater systems and

monetary systems are isomorphic, it does provide support for this conclusion in non-

coastal groundwater systems. More research is required to test the methodology

employed and expand the research to other groundwater systems.


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4.13 References

Adrian, T., & Estrella, A. (2008). Monetary Tightening Cycles and the Predictability

of Economic Activity. Economics Letters, 99(2), 260-264.





Management.

Bertalanffy, L. v. (1969). General System Theory. New York: George Braziller, Inc.

Board of Governors of the Federal Reserve System. (n.d.). federalreserve.gov.

Retrieved from Economic Research and Data:

http://www.federalreserve.gov/econresdata/statisticsdata.htm

Cantu, J., & Beruvides, M. (2013). Isomorphological Analysis: The Tough Knocks of

Experience Found Through Practice. American Society for Engineering

Management 2013 International Annual Conference. Bloomington, MN:

American Society for Engineering Management.

Coddington, A. (1976). Keynesian Economics: The Search for First Principles.

Journal of Economic Literature, 14(4): 1258-1273.

Green, T., Taniguchi, M., Kooi, H., Gurdak, J., Allen, D., & Hiscock, K. (2011).

Beneath the Surface of Global Change: Impacts of Climate Change on

Groundwater. Journal of Hydrology, 405, 532-560.




Oliva, R. (n.d.). web.mit.edu. Retrieved from Empirical Validation of a Dynamic

Hypothesis: http://web.mit.edu/jsterman/www/RO1.html

Ryder, W. H. (2009). A System Dynamics View of the Phillips Machine. Proceedings

of the 27th International Conference of the System Dynamics Society,

http://systemdynamics. org/conferences/2009/proceed/papers, (p. (Vol 1038)).

Retrieved from http://systemdynamics. org/conferences/2009/proceed/papers


202

Samuelson, P., & Nordhaus, W. (2001). Economics. New York: McGraw-Hill Higher

Education.

Snippe, J. (1985). On the Scope of Hydraulic Macroeconomics: Some Reflections on

Alan Coddington's Keynesian Economics. Economist - Netherlands, 133(4):

467-483.



United States Department of Commerce. (n.d.). Bureau of Economic Analysis.

Retrieved from National Economic Accounts:

http://www.bea.gov/national/index.htm


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CHAPTER V

GENERAL CONCLUSIONS AND RECOMMENDATIONS FOR

FUTURE RESEARCH

5.1 General Conclusions

The research discussed in chapters 3 and 4 has helped to develop an

understanding of groundwater management and monetary policy from the systems

perspective as well as an understanding of the systemic, structural similarities between

groundwater management and monetary policy systems. It has shown that it is

possible to develop system dynamics models using simple linear equations to predict

complex groundwater system behavior at a level that is sufficient for testing

groundwater policy in two non-coastal systems. It has also provided a new way of

understanding the various policy levers available to manage groundwater. The

outcomes of this research include the following:

1. A systems analysis of three groundwater systems to identify the structural


2. A systems analysis of the monetary system to identify the structural


3. A homological comparison between groundwater management and

monetary policy systems based on system structure, underlying theory and

mathematics.

4. An isomorphological comparison between the groundwater management

and monetary policy systems based on systemic behavior-over-time.

5. A conceptual model of groundwater systems to improve understanding a

decision-making.

6. A model-based assessment tool for testing various policy measures related

to sustainable groundwater management.

Research 1 shows that it is possible to create valid system dynamics models for

two non-coastal groundwater systems. Although the coastal system model passed

most of the verification and validation tests, the inability of the model to adequately

reproduce behavior casts doubt about its validity. These models may be capable of


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predicting system behavior well enough to be used for testing groundwater policy.

The R2 values for the two valid, non-coastal, system models ranged from 0.83 to 0.93

depending on the system and length of the simulation period. These values compare

favorably to the other system dynamics models shown in Table 2.4.

Although the systematic bias (Um) and Root Mean Square Percent Error

(RMSPE) were higher than desired, the models appear to be accurate enough for the

purpose of testing policy. Systematic bias in the 1-year models ranged from 0.3% to

2.6% of the total error. This is lower than the other models shown in Table 2.4.

Systematic bias in the 5-year and 10-year models ranged from 19.7% to 44.6%of the

total error. This is higher than desired, but may be explained by the accumulation of

small mass balance errors in the USGS model output.

RMSPE in the 1-year models ranged from 0.1% to 45.1%. However, the large

error in the Cuyama model was due to a single anomalous year (1993). Removing this

year from the calculation yield RMSPE values ranging from 0.15% to 4.9% for all

three models and all three simulation periods. This compares favorably to the models

shown in Table 2.4.

The models developed in research 1 are simple models based on linear

relationships between various parameters. The simplification of a complex system

into simple linear components may help managers to better understand groundwater

systems and make it easier for them to test groundwater policy. Although it may be

possible to develop models with higher predictive accuracy, these simple models may

be relatively inexpensive to develop, yet adequate for testing policy.

The most important parameters for modeling groundwater system behavior in

non-coastal systems appear to be precipitation, runoff, stream leakage, underflow and

net percolation. These parameters are also important in coastal systems. However,

the most important parameter in coastal systems appears to be coastal inflow. This

parameter can mask actual groundwater consumption by replacing fresh groundwater

with seawater. Coastal inflow can be a confounding variable in coastal systems.

More research is required in order to account for this parameter in coastal systems.


205

Based on this research, it appears that increasing the cost of credit and setting a

maximum allowable groundwater depletion level are two policy levers that may be

capable of reducing aggregate groundwater demand. Although the actual response to

an increase in the cost of groundwater is beyond the scope of this research, it appears

that this policy action would reduce aggregate groundwater demand if increasing the

cost of groundwater actually curtails consumption as assumed. Additional research is

required to simulate the change in groundwater consumption due to an increase in the

cost of groundwater.

Research 2 is an exploratory study to evaluate the potential isomorphic

relationship between groundwater systems and monetary systems. Systems analysis,

homological mapping and behavioral comparison were used to assess isomorphology.

The research suggests that there are significant systemic similarities between these two

types of systems. Many structural elements in groundwater systems are in the same

place, and have similar functions in monetary systems. The same can be said of two

the three primary policy levers. There was not enough information to compare system

behavior under the third policy lever (open market operations).

Although it is not possible to prove that groundwater systems and monetary

systems are isomorphic, this exploratory research provides support for the assertion of

isomorphology. The structure of the systems appear to be homological. The systems

are governed by mathematical equations of similar form. The systems show changes

in behavior that are similar when subjected to similar policy changes. Based on a

preponderance of evidence, these systems may be of the same general class. More

research is required to provide additional support for the assertion of isomorphology.

However, this research may allow groundwater managers to better understand

groundwater systems by applying knowledge of monetary systems. Our collective

knowledge about monetary policy is much more developed than our knowledge about

groundwater policy. Knowledge about monetary systems and the effects of monetary

policies, particularly in a contractionary environment, may be useful for developing

appropriate and effective groundwater policy.


206

Taken as a whole, this research increases our knowledge of groundwater and

groundwater management. It lends support to the similarities between water and

money identified by Keynes (Coddington, 1976) and Phillips (Ryder, 2009). By

identifying the systemic similarities between groundwater and credit, this research also

provides support for the idea that groundwater is a form of environmental credit

(Hudson & Donovan, 2014). This research is based on the concept of isomorphology

developed by Bertalanffy in 1969. It also extends the methodology for identifying

potential isomorphology developed by Cantu and Beruvides (2013) by adding a

behavioral component to the analysis. Finally, this research provides a tool for

helping managers to better understand groundwater systems and test policies that may

facilitate a transition to sustainable groundwater management. With additional

research, the models developed herein may help California groundwater managers

comply with the requirements of the Sustainable Groundwater Management Act.

5.2 Recommendations for Future Research

The research presented in this dissertation indicates that it is possible to

simulate complex groundwater system behavior using a systems dynamics approach

with simple linear equations. It also provides support for the claim that groundwater

systems and monetary systems are isomorphic. However, additional research is

necessary to build upon these conclusions.

Additional research is needed to improve the approach to groundwater system

modeling developed in research 1. Additional non-coastal groundwater systems

should be modeled using the system dynamics approach to confirm the results of this

research. Research should also distinguish between non-coastal systems that import

significant amounts of water from those systems that do not.

It is possible that these models will be improved by developing separate

equations for wet and dry years because the relationships between precipitation, runoff

and infiltration vary with changes in precipitation. A model that can account for this

variation may predict changes in groundwater storage better. Future research should


207

examine the difference in system response in wet years from the response in dry years.

Developing different equations for simulate the response in wet years may improve

behavior reproduction.

The models developed in this research use simple linear relationships to predict

the behavior of system parameters. Linear relationships were used to make the models

simple, easy to understand, and relatively easy to develop. It is possible that the

accuracy of the models developed in this research may be improved using nonlinear

equations. Using nonlinear equations may allow models to perform better during

extreme conditions. Future research should evaluate the impact of using nonlinear

equations on predictive accuracy and ease of use.

It is also important to recognize that groundwater system response may change

as the systems approach full storage. It is likely that outflow will increase as aquifers

approach capacity. This condition is not considered in the models developed for this

research. Future research should investigate how outflow and inflow change when the

aquifer is full or near full in order to better simulate sustainable conditions.

Based on this research, it appears that coastal systems may behave differently

than non-coastal systems. This may be due to the influence of seawater intrusion. It is

possible that changes in pumping location, sea level and the use of injection wells for

coastal barriers may need to be considered to simulate coastal systems. More research

is required to understand and simulate the impact of coastal inflow in coastal

groundwater systems.

Open market operations are commonly used in monetary policy. In this

research, it was not possible to isolate the effects of open market operations on

aggregate economic demand. As such, it was not possible to compare the behavior in

groundwater systems under contractionary conditions. However, groundwater policies

that are analogous to open market operations may be useful for transitioning to

sustainable groundwater use. Additional research should examine how water market

operations could be used to support desirable crops while simultaneously reducing


208

aggregate groundwater demand. This research should examine regions where there

has been a transition to lower water-use crops.

In order to better simulate the effect of policy changes in groundwater systems,

future research should focus on modeling the human response to changes in the cost

and availability of groundwater. It may be possible to improve these models by

extending the existing research about water price elasticity to groundwater basins and

examining how people have responded to abrupt water price increases in other areas.

Understanding the changes in consumption in areas where a physical lack of water has

reduced consumption may serve as a model for understanding of the societal response

to restrictions caused by contractionary policy. Understanding the response to pump

taxes and minimum groundwater storage requirements will allow for the development

of better models to test policies. This research indicates that the response to these

policies may be similar to the economic response to changes in the cost and

availability of credit. Testing and quantifying the human response to these policies

may lend additional support to the assertion that these systems are isomorphic.

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248

APPENDIX

Appendix A - Definitions

Analogy - “A comparison between two things, typically on the basis of their structure

and for the purpose of explanation or clarification” (Oxford University Press,

Analogy, 2015).

Aggregate Demand- The “total planned or desired spending in the economy during a

given period” (Samuelson & Nordhaus, 2001, p. 756).

Contraction – Reduction in groundwater demand or withdrawal.

Credit – “The ability to use tomorrow’s standard of living to raise today’s standard of

living” (Hudson & Donovan, 2014, p. 6) by borrowing resources in the present with

the expectation of repayment in the future.

Debt –“Accumulated deficits minus accumulated surpluses” (Colander, 2010, pp. G-

1)

Delay – The length of time required for feedback to move between two components in

a system (Anderson & Johnson, 1997).

Dynamic Equilibrium – A “(quasi-)stationary” state of perpetual disequilibrium

(Bertalanffy, 1969).

Dynamic Hypothesis - a claim that a causal relationship exists between structure and

behavior (Keloharju, 1981).

Endogenous Credit – Credit created through the internal actions of lending

institutions and central banks rather than the supply of loanable funds provided by

savings.

Feedback – “The return of information about the status of a process” in a system

(Anderson & Johnson, 1997).

Flow – A system component with quantity measured as a unit over a given time period

(System Dynamics Society, n.d.).


249

General Equilibrium Theory – Modern Economic theory the theory that “opposing

dynamic forces cancel each other out” (Colander, 2010, pp. G-3).

Homology- “The state of having the same or similar relation, relative position, or

structure” (Oxford University Press, Homology, 2015).

Isomorphism - “An exact correspondence as regards the number of constituent

elements and the relations between them” (Wordfinder, 2015).

Loanable Funds Theory - Theory that states, “saving is the supply of loans”

(Mankiw, 2010, p. 65).

Overshoot – To go too far, to go beyond limits accidentally – or without intention”

(Meadows, et al, 2004, p. 1).

Recycled Water - Treated wastewater that is reused for beneficial purposes (Newton,

et al., 2009).

Savings - surplus, accumulated by forgoing consumption, and placed in storage by the

consumer for use at a future date.

Stock – A system component that accumulates quantities over time and is measurable

at any point in time (System Dynamics Society, n.d.).

System - A set of “elements standing in interrelation” (Bertalanffy, 1969, p. 38).

System Structure - "the totality of the relationships that exist between system

variables (Barlas, 2007).


250

Appendix B- Groundwater Data for the Modesto Region (Philips, Rewis, & Traum, 2015)

Water

Year

Pre-

cipitation

Surface

Water

Delivery

Ground-

water

Uptake

by Plants

Crop

Consump-

tive Use

Runoff

to

Streams

Municipal

&

Drainage

Pumping

Private

Agricultural

Pumping

1960 495913 1118203 69986 -1699972 -4355 -200774 -1124125

1961 463930 1007202 56282 -1671557 -4196 -179475 -1234110

1962 581953 1139404 54496 -1642372 -4957 -193113 -1109390

1963 784223 1000823 51525 -1678309 -3881 -187953 -825138

1964 624325 1118420 49550 -1691189 -4708 -225280 -1053968

1965 688184 1068056 49898 -1663256 -4596 -207464 -1006512

1966 435281 1165420 53562 -1710209 -4674 -258372 -1223674

1967 719594 1037321 52554 -1709064 -4553 -220970 -1026145

1968 704951 1122251 47343 -1731073 -4846 -230747 -1065697

1969 923037 1117230 63249 -1678826 -5947 -215346 -998087

1970 952123 1157973 66313 -1740263 -6002 -243143 -1042392

1971 477973 1158038 54907 -1634996 -4445 -249928 -1030914

1972 424369 1191505 49086 -1669646 -4871 -247645 -1200732

1973 999508 1125759 65594 -1725413 -6001 -208365 -951111

1974 584786 1119510 68238 -1709097 -4150 -237528 -936166

1975 534901 1130928 62668 -1651551 -4094 -224686 -895131

1976 337370 1141770 48948 -1637749 -3859 -227030 -1044143

1977 378515 909959 32669 -1657183 -4297 -393649 -1365608

1978 1003832 1025340 45579 -1747640 -5471 -159502 -985674

1979 740917 1170766 53899 -1724224 -5291 -196512 -1013989

1980 602404 1109532 61230 -1606106 -5050 -223504 -1016586

1981 813696 1169298 57510 -1770226 -5541 -203741 -1030470

1982 1062939 1025838 70340 -1710477 -5346 -211426 -783000

1983 1415737 950125 88289 -1665235 -6941 -250849 -783757

1984 457609 1279633 86273 -1702347 -4655 -278004 -972655

1985 486432 1227370 68370 -1702279 -4586 -302142 -999979

1986 641208 1124680 78162 -1677911 -4938 -225801 -967420

1987 621157 1116717 60321 -1744902 -4904 -302698 -1104257

1988 493301 971580 41684 -1720412 -4903 -418147 -1382846

1989 388807 1036138 32758 -1689828 -4119 -214849 -1211632

1990 416140 1027187 29473 -1670104 -4389 -222239 -1227578


251

Water

Year

Net

Percolation

to

Groundwater

Net

Stream

Seepage to

Ground-

water

Net

Subsurface

Boundary

Flow

Net Change

in

Groundwater

Storage

Reservoir

leakage ET all

1960 1183674 -87819 -72653 -306940 11921 -1769958

1961 1188073 -52402 -29028 -67501 15924 -1727839

1962 1323625 -39340 -49283 -88861 12259 -1696869

1963 1049526 -45360 -79936 -104436 15498 -1729834

1964 1264625 -45942 -43871 -75902 13847 -1740739

1965 1241870 -24523 -79272 -291060 14271 -1713154

1966 1282337 -46579 -44772 -122578 15302 -1763770

1967 1208516 29574 -113554 -71442 16095 -1761619

1968 1320316 -38273 -57041 149515 13732 -1778416

1969 1464053 92673 -193777 97057 13621 -1742075

1970 1552681 -51006 -119083 -239792 12025 -1806576

1971 1189711 -51945 -96715 -221092 14574 -1689902

1972 1319124 -18289 -73550 179112 14404 -1718732

1973 1493444 -27490 -127366 -233097 12433 -1791007

1974 1085408 -24068 -120743 -206814 14488 -1777335

1975 1052517 -10833 -128681 -330354 15143 -1714219

1976 1048073 -26579 -80675 -616020 15874 -1686697

1977 1177163 -26919 -7007 235622 15684 -1689852

1978 1405880 107360 -132441 36530 13543 -1793218

1979 1360155 682 -113805 -80449 13251 -1778123

1980 1265176 60680 -166215 45994 15524 -1667336

1981 1414901 -26038 -108657 206838 13939 -1827736

1982 1285485 111568 -195790 368794 12000 -1780817

1983 1578023 154779 -329402 -326166 12654 -1753524

1984 1164111 -49314 -190304 -270585 10995 -1788620

1985 1183814 -23714 -128563 -137655 14018 -1770649

1986 1191378 45453 -181264 -271489 13653 -1756073

1987 1267198 -25937 -105795 -558025 13904 -1805223

1988 1306792 -9646 -54178 -351574 16973 -1762096

1989 1120439 4590 -50123 -298757 16079 -1722586

1990 1177891 6339 -33170 -278288 15979 -1699577


252

Water

Year

Pre-

cipitation

Surface

Water

Delivery

Ground-

water

Uptake

by Plants

Crop

Consump-

tive Use

Runoff

to

Streams

Municipal

&

Drainage

Pumping

Private

Agricultural

Pumping

1991 550004 886545 25166 -1661789 -4739 -221673 -1303747

1992 663201 948505 25900 -1697102 -5591 -206386 -1378486

1993 863229 993985 33965 -1672570 -5728 -178649 -1114722

1994 554191 1016728 30747 -1703065 -4615 -196157 -1183151

1995 1083820 967613 46111 -1600322 -6667 -176547 -1036965

1996 1046815 1011455 52839 -1735477 -6185 -192065 -1046771

1997 565041 1103857 60230 -1609931 -5762 -241243 -1212442

1998 1176237 823495 66076 -1568063 -5839 -200235 -850506

1999 438307 993463 59387 -1550628 -4579 -185443 -1096471

2000 780617 952701 58249 -1631662 -5170 -189579 -1018396

2001 778903 1006795 50837 -1690914 -5676 -193061 -1165056

2002 534380 1035043 47443 -1641040 -5280 -215085 -1245051

2003 492010 999019 46236 -1628477 -4660 -185567 -1169098

2004 616814 1066295 49388 -1670746 -5224 -192156 -1155918

Water

Year

Net

Percolation

to

Groundwater

Net

Stream

Seepage to

Ground-

water

Net

Subsurface

Boundary

Flow

Net Change

in

Groundwater

Storage

Reservoir

leakage ET all

1991 1252847 -3298 -2417 -101512 15734 -1686956

1992 1470588 5587 7186 145471 13013 -1723003

1993 1457124 43139 -61422 -193937 11836 -1706535

1994 1221614 5079 -41322 439952 14463 -1733812

1995 1640143 174720 -161398 207429 15114 -1646433

1996 1521814 75052 -150601 -86702 12806 -1788316

1997 1441549 100066 -174631 218994 11577 -1670161

1998 1367949 157541 -255755 -293640 16087 -1634139

1999 1136030 -1138 -146618 -63383 13985 -1610016

2000 1267230 27446 -150084 -27167 15252 -1689911

2001 1433584 7471 -110104 -187317 12224 -1741751

2002 1357669 9836 -94685 -229703 11398 -1688483

2003 1204847 12037 -91922 -81840 13527 -1674714

2004 1343374 14993 -92132 0 14807 -1720134


253

Appendix C - Groundwater Data for the Pajaro Valley (Hanson, Lear, & Lockwood, 2014)

Water

Year ET all Precip ET irr

Farm

Wells

Domestic

Wells

M & I

Pumpage

Annual

Storage

Under-

flow

1964 -83862 112491 -28257 -35614 -234 -4952 -3481 4730

1965

-

109514 223805 -27789 -35614 -1002 -4978 -13141 4017

1966 -73887 116484 -31292 -41206 -1032 -4935 4252 4225

1967 -91774 309216 -19234 -28270 -958 -4958 -37534 2982

1968 -80081 131680 -22657 -32394 -1073 -5264 5323 3101

1969 -83178 310322 -21431 -30536 -1039 -5360 -23694 2336

1970 -83740 233564 -22860 -31868 -1114 -6126 -7355 2222

1971 -83552 145776 -29538 -38112 -1203 -6505 12761 2642

1972 -73195 83562 -31418 -41389 -1326 -7410 24100 3463

1973 -82721 278570 -23084 -32475 -1248 -6941 -21257 2645

1974

-

104295 296367 -18153 -25461 -1213 -6468 -21201 2178

1975

-

103550 140171 -27210 -34565 -1397 -6300 14863 2896

1976 -98536 82614 -26701 -34315 -1598 -6409 27838 3700

1977 -86603 72844 -26960 -34650 -1705 -6911 24145 4277

1978 -93320 287156 -20899 -30376 -1601 -7397 -23740 3323

1979 -72477 161041 -22138 -32535 -1713 -8298 2693 3182

1980 -98686 259639 -18256 -26257 -1734 -8292 -13782 2825

1981 -70273 146159 -23289 -33682 -1886 -8624 7717 3066

1982

-

109996 333405 -18076 -25718 -1802 -9132 -25756 2491

1983

-

110838 399863 -19794 -27942 -1679 -9227 -27708 2080

1984 -76462 132136 -31377 -40672 -2071 -8417 23036 2821

1985 -96109 139177 -28950 -37209 -2227 -8150 19223 3388

1986

-

107794 197223 -24679 -31662 -2155 -9216 720 3367

1987 -78745 83552 -28702 -37210 -2390 -10259 24362 3937

1988

-

104027 163117 -27947 -35786 -2520 -9433 13817 4073

1989 -90085 115770 -27838 -35987 -2490 -9687 16338 4400

1990 -98232 97194 -26017 -33230 -2571 -9711 20177 4693

1991 -78810 117796 -28914 -36802 -2592 -9046 9311 4832

1992 -92543 135224 -29180 -36711 -2609 -9215 6675 4714

1993

-

115941 279947 -27047 -34568 -2527 -9072 -21298 3961

1994

-

112925 123713 -35220 -54601 -2653 -9164 18182 4859


254

Water

Year

ET

gw Drains

Stream

Leakage

Total

Runoff

FNR

Net

Total

Net

Coastal

Inflow

1964 -3374 -2054 9430 -51820 17367 2141

1965 -3440 -4192 16378 -124509 32602 1366

1966 -3413 -3275 12064 -67395 24804 1559

1967 -3367 -6822 25882 -204715 46396 -323

1968 -3379 -4692 11699 -67515 22860 -22

1969 -3567 -9878 19380 -214585 48948 -1085

1970 -3769 -8228 16964 -150435 37910 -1033

1971 -4229 -5818 12932 -83047 24956 -297

1972 -3688 -3670 5120 -40752 19730 787

1973 -3493 -7459 19982 -188518 46161 -559

1974 -3486 -8941 19998 -180867 41828 -1432

1975 -4001 -5166 12414 -58419 19954 -301

1976 -3519 -3179 1484 -13617 11949 834

1977 -2916 -2325 1216 -15209 13037 1484

1978 -3226 -5012 21905 -190145 40259 177

1979 -3205 -4085 12759 -101353 26486 301

1980 -3360 -5487 18425 -160244 32405 -210

1981 -3420 -4243 11805 -91552 24985 294

1982 -3519 -6614 25778 -214625 39825 -692

1983 -4107 -10880 27153 -273747 49236 -1485

1984 -4897 -5899 13349 -82583 22318 -303

1985 -3984 -4002 11230 -67736 20406 483

1986 -3797 -4047 19514 -103939 23991 581

1987 -3364 -2915 7744 -34094 16213 1567

1988 -3243 -2798 8246 -80177 22613 1680

1989 -2875 -2199 6415 -50924 18853 2017

1990 -2264 -1719 1701 -25083 14682 2437

1991 -2311 -1722 7908 -63202 21113 2673

1992 -2266 -1751 9905 -66150 21859 2759

1993 -1405 -4068 21181 -165870 40494 1746

1994 -1189 -2382 8858 -46206 31379 3000


255

Water


Farm

Wells

Domestic

Wells

M & I

Pumpage

Annual

Storage

Under-

flow

1995

-

141706 320147 -31905 -46230 -2436 -8754 -20787 4021

1996

-

130323 244856 -36414 -55684 -2511 -9423 -3400 4162

1997 -79616 215373 -27178 -39300 -2549 -9355 -13899 3697

1998

-

145518 418894 -19051 -28875 -2250 -8701 -35883 2504

1999

-

112147 165059 -23152 -35621 -1957 -9437 7192 2943

2000

-

113558 260300 -23939 -37578 -1808 -9447 -5651 2833

2001

-

124867 173071 -25396 -36683 -1670 -9371 10590 3322

2002 -71940 105057 -25075 -37778 -1644 -9951 10396 3729

2003 -94856 161692 -22334 -33512 -1663 -9938 764 3614

2004 -85191 141259 -26996 -39187 -1581 -10082 5137 3760

2005

-

148790 231741 -21522 -28276 -1466 -9427 -6512 3363

2006

-

135882 250948 -23198 -33620 -1428 -9476 -9253 3147

2007

-

131289 255026 -26640 -38499 -1465 -9576 -666 2908

2008

-

108866 119158 -28712 -39544 -1485 -9630 17852 3781

2009

-

120531 151841 -29688 -38761 -1481 -9636 10066 3881

Water

Year

ET

gw Drains

Stream

Leakage

Total

Runoff

FNR

Net

Total

Net

Coastal

Inflow

1995 -1658 -4758 22244 -183971 50935 1726

1996 -1873 -4615 19375 -134676 47725 2066

1997 -2931 -5238 19823 -140863 42722 1097

1998 -3871 -10196 24463 -250379 57914 -681

1999 -3535 -4918 16121 -69032 27186 224

2000 -3970 -7232 16525 -148518 43895 -100

2001 -3387 -4481 12858 -66398 26129 537

2002 -2792 -3959 11726 -52913 26413 1089

2003 -2842 -4287 14619 -78895 28789 924

2004 -2870 -4271 14126 -72784 31438 1196

2005 -3133 -4414 18990 -91613 26846 638

2006 -3541 -6069 20100 -120123 37189 299

2007 -3800 -7045 14501 -129334 42570 44

2008 -3236 -3880 10463 -37090 23465 1216

2009 -2936 -3543 10761 -54403 26552 1369


256

Appendix D - Groundwater Data for the Cuyama Valley (Hanson, Flint, Faunt, Gibbs, & Schmid, 2015)

Water


Annual

Storage

Under-

flow

ET

gw Drains

1950 -78341 47267 -23533 -55319 -4634 -13806 -1246

1951 -77157 46406 -26110 -59009 -4783 -11520 -1271

1952 -96978 105343 -25784 -10126 -4675 -8168 -1177

1953 -74504 61319 -26976 -35537 -4545 -7324 -1121

1954 -79023 58603 -27654 -45419 -4473 -6387 -1116

1955 -72615 55281 -27444 -42239 -4386 -5478 -1114

1956 -76694 52907 -26476 -38238 -4347 -5114 -1109

1957 -85484 62719 -25176 -36933 -4253 -4907 -1097

1958

-

123159 140092 -19035 9192 -4311 -3524 -1139

1959 -75713 49544 -26355 -35932 -4189 -4994 -1120

1960 -64744 36518 -27206 -42594 -4131 -4823 -1096

1961 -58848 40708 -26919 -37744 -4089 -4798 -1123

1962 -68889 105411 -22739 13800 -4120 -3615 -1193

1963 -75339 46239 -28027 -47595 -4022 -4393 -1162

1964 -76360 47317 -28913 -48886 -3977 -4217 -1154

1965 -94817 68488 -27231 -43447 -3910 -3874 -1153

1966 -79588 65195 -30750 -16270 -3981 -4002 -1201

1967 -99493 79181 -28189 -18738 -3954 -3821 -1195

1968 -73173 47547 -30082 -47036 -3907 -3965 -1167

1969

-

110825 137798 -32442 25764 -3950 -4016 -1198

1970 -65603 35553 -28710 -48402 -3853 -3861 -1160

1971 -76682 56129 -27451 -29270 -3893 -3676 -1239

1972 -49851 33126 -29638 -34934 -3877 -3934 -1266

1973 -95771 83960 -27392 -3757 -3917 -3382 -1293

1974 -79790 61813 -27467 -27579 -3896 -3597 -1285

1975 -85538 63994 -26797 -20381 -3834 -3469 -1276


257

Water

Year Ag Wells

Annual

Storage

Stream

Leakage

Total

Runoff

Deep

Perc

1950 -46800 55319 6008 -27075 -4740

1951 -54256 59009 6845 -29815 -5634

1952 -54355 10126 42407 -54987 -15710

1953 -52830 35537 20612 -41033 -9627

1954 -57982 45419 16791 -36140 -7674

1955 -57376 42239 16865 -36847 -8812

1956 -55751 38238 17290 -25900 -10886

1957 -52933 36933 15352 -24201 -10680

1958 -55169 -9192 50261 -50088 -22678

1959 -52463 35932 16133 -22997 -10744

1960 -56952 42594 13249 -22578 -10964

1961 -56326 37744 14441 -29304 -13650

1962 -63065 -13800 50490 -67551 -35493

1963 -59063 47595 11492 -25388 -9278

1964 -60908 48886 11885 -26344 -9286

1965 -57500 43447 14007 -25827 -8828

1966 -64208 16270 43666 -40307 -13362

1967 -59497 18738 39442 -32771 -10129

1968 -63085 47036 14654 -31104 -10225

1969 -64369 -25764 70169 -66351 -28770

1970 -59445 48402 10850 -23826 -9123

1971 -56954 29270 26005 -30343 -10264

1972 -61440 34934 21453 -35103 -13875

1973 -57231 3757 49851 -36480 -12289

1974 -57348 27579 27202 -31745 -11336

1975 -44512 20381 26580 -19785 -5861


258

Water

Year ET all Precip

ET

irr

Annual

Storage

Under-

flow

ET

gw Drains

1976 -81928 60706

-

26539 -32988 -3766 -3358 -1243

1977

-

117307 79389

-

49486 -51673 -3719 -3420 -1226

1978

-

133719 146122

-

52963 1375 -3760 -3116 -1257

1979

-

119558 93450

-

54248 -33652 -3767 -3270 -1284

1980

-

126521 101665

-

53294 -36702 -3720 -3215 -1264

1981

-

107141 64105

-

56773 -62960 -3662 -3436 -1196

1982

-

118607 89403

-

52007 -53897 -3635 -3126 -1166

1983

-

149141 153604

-

49621 -1318 -3671 -2800 -1210

1984

-

107198 56876

-

60390 -68755 -3566 -3571 -1146

1985

-

101491 61382

-

55721 -57379 -3535 -3540 -1023

1986

-

122478 79250

-

55845 -52078 -3499 -3115 -942

1987 -98576 46097

-

57628 -67143 -3420 -2964 -825

1988

-

146455 115452

-

54214 -46943 -3438 -2577 -889

1989 -97266 49613

-

58572 -65234 -3380 -2742 -829

1990 -82604 24237

-

58564 -70501 -3320 -2627 -692

1991 -91784 83658

-

52072 -23487 -3339 -2288 -718

1992

-

114247 88753

-

52246 -30724 -3354 -2224 -786

1993

-

123941 121590

-

56380 62 -3340 -2294 -866

1994

-

107850 61366

-

56699 -63227 -3264 -2338 -827

1995

-

124846 161142

-

52888 20977 -3332 -2318 -908

1996

-

103608 60604

-

60571 -60444 -3278 -2628 -818

1997

-

110795 72812

-

59296 -54217 -3268 -2489 -783

1998

-

162649 216068

-

50288 26818 -3314 -2081 -893

1999

-

114445 77245

-

53091 -57816 -3216 -2194 -791


259

Water

Year

Ag

Wells

Annual

Storage

Stream

Leakage

Total

Runoff

Deep

Perc

1976 -44009 32988 13850 -18283 -5496

1977 -66582 51673 13249 -25922

-

10059

1978 -76584 -1375 61407 -66368

-

24408

1979 -76428 33652 37231 -41072

-

13830

1980 -75621 36702 33884 -41061

-

12951

1981 -80822 62960 14575 -29662

-

11637

1982 -74963 53897 16761 -35388

-

12333

1983 -70245 1318 56985 -58488

-

19582

1984 -82389 68755 11139 -25664

-

10676

1985 -74313 57379 17351 -29302 -7068

1986 -72554 52078 22479 -27168 -5640

1987 -74226 67143 9171 -20611 -5203

1988 -70214 46943 23904 -36064 -6365

1989 -77266 65234 12714 -25448 -6123

1990 -75769 70501 6862 -15789 -4912

1991 -70382 23487 34870 -46224

-

18415

1992 -71172 30724 37611 -38761 -9252

1993 -75060 -62 63562 -58261

-

18118

1994 -77839 63227 14874 -26314 -6232

1995 -70469 -20977 66749 -78487

-

31303

1996 -78524 60444 17951 -31595 -6800

1997 -76939 54217 22530 -34865 -7036

1998 -67450 -26818 68117 -89399

-

32474

1999 -70650 57816 12961 -30550 -6095


260

Water

Year ET all Precip

ET

irr

Annual

Storage

Under-

flow

ET

gw Drains

2000

-

110405 67461

-

55968 -53782 -3216 -2183 -726

2001

-

119379 105168

-

55280 -32531 -3247 -2008 -784

2002 -81527 27400

-

56433 -70240 -3140 -2227 -634

2003

-

118173 83732

-

53235 -53183 -3155 -1938 -624

2004 -91904 43297

-

58730 -64462 -3122 -1968 -589

2005

-

143169 212801

-

52009 52813 -3196 -1754 -718

2006

-

128794 108632

-

44713 -26381 -3172 -1977 -716

2007 -80854 27578

-

55629 -67910 -3079 -2407 -575

2008 -81464 101198

-

49703 7005 -3127 -2337 -574

2009 -95199 58696

-

47370 -45213 -3044 -2148 -546

2010

-

110813 79630

-

49980 -34908 -3041 -2023 -543

Water

Year

Ag

Wells

Annual

Storage

Stream

Leakage

Total

Runoff

Deep

Perc

2000 -74368 53782 19961 -27715 -6839

2001 -74062 32531 38722 -52402 -8621

2002 -71933 70240 6585 -19343 -1189

2003 -68034 53183 17396 -32825 -3056

2004 -73911 64462 12873 -26564 -2183

2005 -69047 -52813 93193 -105794

-

34394

2006 -57844 26381 34311 -36527 -3261

2007 -71521 67910 7040 -19491 -2648

2008 -62849 -7005 53372 -61922

-

22612

2009 -58872 45213 16726 -22970 -2768

2010 -65366 34908 33657 -33300 -2518


261

Appendix E - Economic Data for the United States

Quarter

GDP

(Bil 2009 $)

GDP Change (Bil

2009 $) Quarter

GDP

(Bil 2009 $)

GDP Change

(Bil 2009 $)

1951q1 2,304.5 31.1 1959q1 2,976.6 54.3

1951q2 2,344.5 40.0 1959q2 3,049.0 72.4

1951q3 2,392.8 48.3 1959q3 3,043.1 (5.9)

1951q4 2,398.1 5.3 1959q4 3,055.1 12.0

1952q1 2,423.5 25.4 1960q1 3,123.2 68.1

1952q2 2,428.5 5.0 1960q2 3,111.3 (11.9)

1952q3 2,446.1 17.6 1960q3 3,119.1 7.8

1952q4 2,526.4 80.3 1960q4 3,081.3 (37.8)

1953q1 2,573.4 47.0 1961q1 3,102.3 21.0

1953q2 2,593.5 20.1 1961q2 3,159.9 57.6

1953q3 2,578.9 (14.6) 1961q3 3,212.6 52.7

1953q4 2,539.8 (39.1) 1961q4 3,277.7 65.1

1954q1 2,528.0 (11.8) 1962q1 3,336.8 59.1

1954q2 2,530.7 2.7 1962q2 3,372.7 35.9

1954q3 2,559.4 28.7 1962q3 3,404.8 32.1

1954q4 2,609.3 49.9 1962q4 3,418.0 13.2

1955q1 2,683.8 74.5 1963q1 3,456.1 38.1

1955q2 2,727.5 43.7 1963q2 3,501.1 45.0

1955q3 2,764.1 36.6 1963q3 3,569.5 68.4

1955q4 2,780.8 16.7 1963q4 3,595.0 25.5

1956q1 2,770.0 (10.8) 1964q1 3,672.7 77.7

1956q2 2,792.9 22.9 1964q2 3,716.4 43.7

1956q3 2,790.6 (2.3) 1964q3 3,766.9 50.5

1956q4 2,836.2 45.6 1964q4 3,780.2 13.3

1957q1 2,854.5 18.3 1965q1 3,873.5 93.3

1957q2 2,848.2 (6.3) 1965q2 3,926.4 52.9

1957q3 2,875.9 27.7 1965q3 4,006.2 79.8

1957q4 2,846.4 (29.5) 1965q4 4,100.6 94.4

1958q1 2,772.7 (73.7) 1966q1 4,201.9 101.3

1958q2 2,790.9 18.2 1966q2 4,219.1 17.2

1958q3 2,855.5 64.6 1966q3 4,249.2 30.1

1958q4 2,922.3 66.8 1966q4 4,285.6 36.4

Quarterly GDP (Seasonally adjusted annual rates) (Federal Reserve Bank of St. Luis, n.d.)


262

Quarter

GDP

(Bil 2009 $)

GDP Change (Bil

2009 $) Quarter

GDP

(Bil 2009 $)

GDP Change

(Bil 2009 $)

1967q1 4,324.9 39.3 1975q1 5,292.4 (64.8)

1967q2 4,328.7 3.8 1975q2 5,333.2 40.8

1967q3 4,366.1 37.4 1975q3 5,421.4 88.2

1967q4 4,401.2 35.1 1975q4 5,494.4 73.0

1968q1 4,490.6 89.4 1976q1 5,618.5 124.1

1968q2 4,566.4 75.8 1976q2 5,661.0 42.5

1968q3 4,599.3 32.9 1976q3 5,689.8 28.8

1968q4 4,619.8 20.5 1976q4 5,732.5 42.7

1969q1 4,691.6 71.8 1977q1 5,799.2 66.7

1969q2 4,706.7 15.1 1977q2 5,913.0 113.8

1969q3 4,736.1 29.4 1977q3 6,017.6 104.6

1969q4 4,715.5 (20.6) 1977q4 6,018.2 0.6

1970q1 4,707.1 (8.4) 1978q1 6,039.2 21.0

1970q2 4,715.4 8.3 1978q2 6,274.0 234.8

1970q3 4,757.2 41.8 1978q3 6,335.3 61.3

1970q4 4,708.3 (48.9) 1978q4 6,420.3 85.0

1971q1 4,834.3 126.0 1979q1 6,433.0 12.7

1971q2 4,861.9 27.6 1979q2 6,440.8 7.8

1971q3 4,900.0 38.1 1979q3 6,487.1 46.3

1971q4 4,914.3 14.3 1979q4 6,503.9 16.8

1972q1 5,002.4 88.1 1980q1 6,524.9 21.0

1972q2 5,118.3 115.9 1980q2 6,392.6 (132.3)

1972q3 5,165.4 47.1 1980q3 6,382.9 (9.7)

1972q4 5,251.2 85.8 1980q4 6,501.2 118.3

1973q1 5,380.5 129.3 1981q1 6,635.7 134.5

1973q2 5,441.5 61.0 1981q2 6,587.3 (48.4)

1973q3 5,411.9 (29.6) 1981q3 6,662.9 75.6

1973q4 5,462.4 50.5 1981q4 6,585.1 (77.8)

1974q1 5,417.0 (45.4) 1982q1 6,475.0 (110.1)

1974q2 5,431.3 14.3 1982q2 6,510.2 35.2

1974q3 5,378.7 (52.6) 1982q3 6,486.8 (23.4)

1974q4 5,357.2 (21.5) 1982q4 6,493.1 6.3

Quarterly GDP (Seasonally adjusted annual rates)


263

Quarter

GDP

(Bil 2009 $)

GDP Change (Bil

2009 $) Quarter

GDP

(Bil 2009 $)

GDP Change

(Bil 2009 $)

1983q1 6,578.2 85.1 1991q1 8,865.6 (41.8)

1983q2 6,728.3 150.1 1991q2 8,934.4 68.8

1983q3 6,860.0 131.7 1991q3 8,977.3 42.9

1983q4 7,001.5 141.5 1991q4 9,016.4 39.1

1984q1 7,140.6 139.1 1992q1 9,123.0 106.6

1984q2 7,266.0 125.4 1992q2 9,223.5 100.5

1984q3 7,337.5 71.5 1992q3 9,313.2 89.7

1984q4 7,396.0 58.5 1992q4 9,406.5 93.3

1985q1 7,469.5 73.5 1993q1 9,424.1 17.6

1985q2 7,537.9 68.4 1993q2 9,480.1 56.0

1985q3 7,655.2 117.3 1993q3 9,526.3 46.2

1985q4 7,712.6 57.4 1993q4 9,653.5 127.2

1986q1 7,784.1 71.5 1994q1 9,748.2 94.7

1986q2 7,819.8 35.7 1994q2 9,881.4 133.2

1986q3 7,898.6 78.8 1994q3 9,939.7 58.3

1986q4 7,939.5 40.9 1994q4 10,052.5 112.8

1987q1 7,995.0 55.5 1995q1 10,086.9 34.4

1987q2 8,084.7 89.7 1995q2 10,122.1 35.2

1987q3 8,158.0 73.3 1995q3 10,208.8 86.7

1987q4 8,292.7 134.7 1995q4 10,281.2 72.4

1988q1 8,339.3 46.6 1996q1 10,348.7 67.5

1988q2 8,449.5 110.2 1996q2 10,529.4 180.7

1988q3 8,498.3 48.8 1996q3 10,626.8 97.4

1988q4 8,610.9 112.6 1996q4 10,739.1 112.3

1989q1 8,697.7 86.8 1997q1 10,820.9 81.8

1989q2 8,766.1 68.4 1997q2 10,984.2 163.3

1989q3 8,831.5 65.4 1997q3 11,124.0 139.8

1989q4 8,850.2 18.7 1997q4 11,210.3 86.3

1990q1 8,947.1 96.9 1998q1 11,321.2 110.9

1990q2 8,981.7 34.6 1998q2 11,431.0 109.8

1990q3 8,983.9 2.2 1998q3 11,580.6 149.6

1990q4 8,907.4 (76.5) 1998q4 11,770.7 190.1

Quarter

GDP

(Bil 2009 $)

GDP Change (Bil

2009 $)

1999q1 11,864.7 94.0

1999q2 11,962.5 97.8

1999q3 12,113.1 150.6

1999q4 12,323.3 210.2

2000q1 12,359.1 35.8

2000q2 12,592.5 233.4

2000q3 12,607.7 15.2

2000q4 12,679.3 71.6

2001q1 12,643.3 (36.0)

2001q2 12,710.3 67.0

2001q3 12,670.1 (40.2)

2001q4 12,705.3 35.2




264

Appendix F – Economic Analysis

2,700.0

2,720.0

2,740.0

2,760.0

2,780.0

2,800.0

2,820.0

2,840.0

2,860.0

2,880.0

2,900.0

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter

Tightening Period # 1

GDP 2009 dollars (bil)

End of Tightening

Decline inAggregate Demand

3,000.0

3,020.0

3,040.0

3,060.0

3,080.0

3,100.0

3,120.0

3,140.0

1959q3 1959q4 1960q1 1960q2 1960q3 1960q4

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



Decline in Aggregate Demand

End of Tightening


265

3,700.0

3,800.0

3,900.0

4,000.0

4,100.0

4,200.0

4,300.0

4,400.0

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



4,560.0

4,580.0

4,600.0

4,620.0

4,640.0

4,660.0

4,680.0

4,700.0

4,720.0

4,740.0

4,760.0

1968q4 1969q1 1969q2 1969q3 1969q4 1970q1

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter




End of Tightening

Decline in GDP Growth Rate

End of Tightening


266

4,750.0

4,800.0

4,850.0

4,900.0

4,950.0

5,000.0

5,050.0

1971q1 1971q2 1971q3 1971q4 1972q1

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



Increase in GDP Growth Rate

5,100.0

5,150.0

5,200.0

5,250.0

5,300.0

5,350.0

5,400.0

5,450.0

5,500.0

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



End of Tightening

Decline in GDP Growth Rate

End of Tightening

General Decline in Aggregate Demand


267

5,200.0

5,250.0

5,300.0

5,350.0

5,400.0

5,450.0

1974q1 1974q2 1974q3 1974q4 1975q1

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter




6,300.0

6,350.0

6,400.0

6,450.0

6,500.0

6,550.0

1980q1 1980q2 1980q3 1980q4

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



End of Tightening

End of Tightening

Increase in Aggregate Demand


268

6,350.0

6,400.0

6,450.0

6,500.0

6,550.0

6,600.0

6,650.0

6,700.0

1981q2 1981q3 1981q4 1982q1 1982q2

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter




6,900.0

7,000.0

7,100.0

7,200.0

7,300.0

7,400.0

7,500.0

7,600.0

1984q1 1984q2 1984q3 1984q4 1985q1 1985q2

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



End of Tightening

End of Tightening No Change in GDP Growth Rate


269

8,100.0

8,200.0

8,300.0

8,400.0

8,500.0

8,600.0

8,700.0

8,800.0

8,900.0

9,000.0

9,100.0Q

uar

terl

y G

DP

(2

00

9 D

olla

rs B

il)

Quarter



General Decline in GDP Growth Rate

9,400.0

9,600.0

9,800.0

10,000.0

10,200.0

10,400.0

10,600.0

10,800.0

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



Increase in Aggregate Demand

End of Tightening

End of Tightening


270

12,100.0

12,200.0

12,300.0

12,400.0

12,500.0

12,600.0

12,700.0

12,800.0

2000q1 2000q2 2000q3 2000q4 2001q1 2001q2 2001q3

Qu

arte

rly

GD

P (

20

09

Do

llars

Bil)

Quarter



End of Tightening

General Reduction of GDP Growth Rate


271

Appendix G – Simulation Results

Water

Year

Actual

Storage

Simulated

StorageError % Error

Water

Year

Actual

Storage

Simulated


1960 -42594 -48711 6118 -14% 1986 -52078 -52265 187 0%

1961 -37744 -39664 1920 -5% 1987 -67143 -70323 3180 -5%

1962 13800 -1297 15097 109% 1988 -46943 -30914 -16030 34%

1963 -47595 -42844 -4751 10% 1989 -65234 -66035 801 -1%

1964 -48886 -43761 -5125 10% 1990 -70501 -77732 7231 -10%

1965 -43447 -34802 -8645 20% 1991 -23487 -33424 9937 -42%

1966 -16270 -32940 16670 -102% 1992 -30724 -40103 9379 -31%

1967 -18738 -27962 9224 -49% 1993 62 -19972 20035 32237%

1968 -47036 -39685 -7351 16% 1994 -63227 -58520 -4706 7%

1969 25764 18386 7379 29% 1995 20977 19870 1107 5%

1970 -48402 -46778 -1624 3% 1996 -60444 -57082 -3363 6%

1971 -29270 -32596 3326 -11% 1997 -54217 -49763 -4453 8%

1972 -34934 -42520 7586 -22% 1998 26818 48960 -22142 -83%

1973 -3757 -15932 12175 -324% 1999 -57816 -43938 -13879 24%

1974 -27579 -29305 1726 -6% 2000 -53782 -52370 -1412 3%

1975 -20381 -19876 -504 2% 2001 -32531 -27771 -4760 15%

1976 -32988 -18654 -14334 43% 2002 -70240 -70120 -120 0%

1977 -51673 -34435 -17239 33% 2003 -53183 -42777 -10407 20%

1978 1375 4524 -3149 -229% 2004 -64462 -66506 2044 -3%

1979 -33652 -30728 -2924 9% 2005 52813 41058 11755 22%

1980 -36702 -31050 -5653 15% 2006 -26381 -26187 -194 1%

1981 -62960 -51015 -11945 19% 2007 -67910 -72784 4873 -7%

1982 -53897 -36801 -17096 32% 2008 7005 -10873 17878 255%

1983 -1318 1876 -3195 242% 2009 -45213 -47361 2148 -5%

1984 -68755 -64206 -4549 7% 2010 -34908 -39860 4952 -14%

1985 -57379 -55684 -1695 3%

Cuyama 1-Year Simulation


272


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated

UM R2 RMSPE Difference

(AF)

%

Error

1960 1964 -163019 -187600 40% 0.99 0.51 24581 -15%

1961 1965 -163872 -170055 3% 0.99 0.51 6183 -4%

1962 1966 -142398 -158811 8% 0.88 0.70 16413 -12%

1963 1967 -174936 -186423 5% 0.75 0.56 11487 -7%

1964 1968 -174377 -185117 4% 0.74 0.55 10740 -6%

1965 1969 -99726 -132411 26% 0.89 0.62 32685 -33%

1966 1970 -104682 -144710 41% 0.95 0.63 40028 -38%

1967 1971 -117682 -137548 21% 0.98 0.36 19866 -17%

1968 1972 -133877 -141806 4% 0.99 0.28 7929 -6%

1969 1973 -90598 -120169 57% 0.97 1.66 29571 -33%

1970 1974 -143941 -165368 43% 0.94 1.49 21427 -15%

1971 1975 -115920 -144131 65% 0.86 1.53 28212 -24%

1972 1976 -119638 -135275 16% 0.59 1.51 15637 -13%

1973 1977 -136377 -125011 5% 0.88 1.46 -11366 8%

1974 1978 -131246 -105074 36% 0.84 2.73 -26172 20%

1975 1979 -137319 -88251 73% 0.89 3.49 -49068 36%

1976 1980 -153640 -91976 88% 0.95 2.45 -61664 40%

1977 1981 -183612 -130661 82% 0.97 1.75 -52951 29%

1978 1982 -185836 -138348 67% 0.93 1.05 -47487 26%

1979 1983 -188529 -134869 76% 0.92 2.68 -53660 28%

1980 1984 -223632 -176782 69% 0.97 0.21 -46851 21%

1981 1985 -244310 -193108 72% 0.97 0.53 -51202 21%

1982 1986 -233428 -190489 67% 0.96 0.51 -42939 18%

1983 1987 -246674 -223056 96% 1.00 1.10 -23618 10%

1984 1988 -292299 -262718 57% 0.90 0.16 -29581 10%

1985 1989 -288778 -268618 33% 0.91 0.15 -20160 7%

1986 1990 -301900 -301485 0% 0.94 0.16 -415 0%

1987 1991 -273309 -283295 4% 0.80 0.23 9986 -4%

1988 1992 -236889 -246352 4% 0.78 0.24 9463 -4%

1989 1993 -189884 -238167 69% 0.97 151.42 48284 -25%

1990 1994 -187876 -236834 63% 0.96 161.62 48958 -26%

1991 1995 -96399 -152318 66% 0.95 170.72 55920 -58%

1992 1996 -133356 -174137 44% 0.96 162.81 40782 -31%

1993 1997 -156849 -176723 15% 0.97 144.18 19874 -13%

1994 1998 -130093 -97537 41% 0.98 0.36 -32556 25%

1995 1999 -124682 -84690 50% 0.97 0.37 -39993 32%


273


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1996 2000 -199441 -155595 57% 0.99 0.38 -43846 22%

1997 2001 -171527 -122860 62% 0.99 0.41 -48667 28%

1998 2002 -187551 -144940 51% 0.99 0.40 -42610 23%

1999 2003 -267552 -227462 73% 0.86 0.18 -40090 15%

2000 2004 -274198 -249695 59% 0.93 0.13 -24503 9%

2001 2005 -167603 -152922 21% 0.99 0.13 -14681 9%

2002 2006 -161454 -151567 11% 0.99 0.12 -9887 6%

2003 2007 -159124 -154326 3% 0.99 0.12 -4798 3%

2004 2008 -98936 -134858 53% 0.99 1.16 35922 -36%

2005 2009 -79687 -118207 58% 0.98 1.18 38520 -48%

2006 2010 -167407 -203718 58% 0.95 1.16 36311 -22%

Average of Simulations 43% 0.93 17.59 -4468 -1%


274


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1960 1969 -262745 -343203 41% 0.93 0.67 80458 -31%

1961 1970 -268553 -330169 25% 0.93 0.65 61616 -23%

1962 1971 -260079 -314164 19% 0.93 0.63 54085 -21%

1963 1972 -308813 -344757 12% 0.92 0.48 35944 -12%

1964 1973 -264975 -323297 25% 0.90 1.70 58322 -22%

1965 1974 -243667 -307052 32% 0.90 1.65 63384 -26%

1966 1975 -220601 -301189 52% 0.93 1.66 80588 -37%

1967 1976 -237319 -278052 21% 0.92 1.45 40732 -17%

1968 1977 -270254 -275032 0% 0.91 1.34 4778 -2%

1969 1978 -221844 -225144 0% 0.87 2.06 3301 -1%

1970 1979 -281260 -264064 4% 0.75 2.68 -17196 6%

1971 1980 -269560 -245369 7% 0.66 2.74 -24191 9%

1972 1981 -303250 -262203 17% 0.75 2.88 -41046 14%

1973 1982 -322213 -245995 38% 0.77 2.81 -76218 24%

1974 1983 -319775 -202231 73% 0.87 4.79 -117544 37%

1975 1984 -360951 -229014 82% 0.93 4.50 -131937 37%

1976 1985 -397950 -252171 89% 0.96 3.36 -145779 37%

1977 1986 -417040 -292483 86% 0.96 2.68 -124557 30%

1978 1987 -432510 -336490 80% 0.97 1.98 -96020 22%

1979 1988 -480828 -360288 81% 0.91 1.91 -120540 25%

1980 1989 -512411 -406826 80% 0.94 0.22 -105585 21%

1981 1990 -546209 -439454 80% 0.93 0.40 -106755 20%

1982 1991 -506737 -424158 64% 0.92 0.39 -82579 16%

1983 1992 -483563 -446966 25% 0.92 0.79 -36597 8%

1984 1993 -482183 -481755 0% 0.88 86.24 -427 0%

1985 1994 -476654 -490937 3% 0.87 88.72 14282 -3%

1986 1995 -398298 -432997 15% 0.92 88.14 34699 -9%


275


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1987 1996 -406665 -444898 18% 0.92 87.08 38233 -9%

1988 1997 -393738 -419285 9% 0.92 85.25 25547 -6%

1989 1998 -319976 -364409 22% 0.94 107.07 44432 -14%

1990 1999 -312558 -356901 19% 0.93 114.28 44343 -14%

1991 2000 -295839 -342531 21% 0.93 120.72 46691 -16%

1992 2001 -304883 -331757 8% 0.93 115.13 26874 -9%

1993 2002 -344399 -340127 0% 0.94 101.95 -4272 1%

1994 2003 -397645 -332160 48% 0.97 0.28 -65485 16%

1995 2004 -398880 -338581 43% 0.97 0.28 -60299 15%

1996 2005 -367044 -299883 49% 0.98 0.29 -67161 18%

1997 2006 -332981 -260211 53% 0.98 0.31 -72770 22%

1998 2007 -346675 -283025 43% 0.98 0.30 -63649 18%

1999 2008 -366488 -332682 17% 0.97 0.57 -33806 9%

2000 2009 -353885 -341750 3% 0.98 0.60 -12135 3%

2001 2010 -335011 -333493 0% 0.97 0.62 -1518 0%

Average of Simulations 33% 0.91 24.82 -20232 3.3%


276

Water

Year

Actual

Storage

Simulated


Water

Year

Actual

Storage

Simulated


1974 21201 23225 -2024 -10% 2000 5651 16827 -11176 -198%

1975 -14863 -16252 1389 -9% 2001 -10590 -10805 215 -2%

1976 -27838 -26391 -1447 5% 2002 -10396 1353 -11749 113%

1977 -24145 -23334 -810 3% 2003 -764 5023 -5787 757%

1978 23740 21663 2077 9% 2004 -5137 1809 -6947 135%

1979 -2693 3431 -6124 227% 2005 6512 -2909 9421 145%

1980 13782 16305 -2523 -18% 2006 9253 6196 3057 33%

1981 -7717 515 -8231 107% 2007 666 7159 -6493 -975%

1982 25756 28315 -2559 -10% 2008 -17852 -15030 -2822 16%

1983 27708 42636 -14928 -54% 2009 -10066 -12847 2781 -28%

1984 -23036 -8666 -14371 62%

1985 -19223 -16162 -3061 16%

1986 -720 -7036 6316 -877%

1987 -24362 -21035 -3327 14%

1988 -13817 -14195 377 -3%

1989 -16338 -17710 1372 -8%

1990 -20177 -23649 3472 -17%

1991 -9311 -10414 1102 -12%

1992 -6675 -12878 6203 -93%

1993 21298 6760 14538 68%

1994 -18182 -34337 16155 -89%

1995 20787 12977 7810 38%

1996 3400 -4952 8352 246%

1997 13899 21310 -7411 -53%

1998 35883 54510 -18627 -52%

1999 -7192 -8216 1024 -14%

Pajaro 1-Year Simulation


277


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1974 1978 21905 17270 0.39 1.00 0.06 4636 21%

1975 1979 45799 38952 0.20 0.98 1.10 6847 15%

1976 1980 17154 6264 0.45 0.99 1.11 10890 63%

1977 1981 -2968 -20609 0.51 0.96 1.20 17641 -594%

1978 1982 -52869 -64710 0.26 1.00 1.11 11841 -22%

1979 1983 -56837 -83061 0.61 0.92 1.14 26224 -46%

1980 1984 -36494 -75997 0.70 0.93 0.58 39504 -108%

1981 1985 -3489 -46283 0.74 0.95 0.60 42795

-

1227%

1982 1986 -10485 -38892 0.37 0.90 3.29 28407 -271%

1983 1987 39633 8190 0.42 0.90 2.94 31443 79%

1984 1988 81158 63311 0.24 0.46 3.10 17847 22%

1985 1989 74461 77478 0.03 0.92 3.67 -3017 -4%

1986 1990 75415 90084 0.45 0.85 3.93 -14669 -19%

1987 1991 84006 91940 0.23 0.69 0.21 -7934 -9%

1988 1992 66319 84843 0.63 0.67 0.60 -18523 -28%

1989 1993 31204 61797 0.63 0.96 0.64 -30593 -98%

1990 1994 33048 76622 0.67 0.84 0.72 -43574 -132%

1991 1995 -7915 53888 0.72 0.78 0.85 -61803 781%

1992 1996 -20627 59064 0.88 0.85 2.88 -79691 386%

1993 1997 -41201 40012 0.85 0.83 2.96 -81214 197%

1994 1998 -55787 -38180 0.10 0.96 1.56 -17606 32%

1995 1999 -66777 -60957 0.02 0.91 1.44 -5820 9%

1996 2000 -51641 -75835 0.22 0.92 1.47 24194 -47%

1997 2001 -37650 -76062 0.45 0.98 1.14 38412 -102%

1998 2002 -13355 -43784 0.35 0.98 1.05 30429 -228%

1999 2003 23292 9998 0.25 0.90 1.12 13294 57%

2000 2004 21237 -2944 0.60 0.89 1.95 24181 114%

2001 2005 20376 14833 0.03 0.16 2.16 5542 27%

2002 2006 532 -13358 0.12 0.02 3.74 13890 2611%

2003 2007 -10529 -18036 0.05 0.00 5.48 7507 -71%

2004 2008 6559 2661 0.02 0.62 4.29 3897 59%

2005 2009 11487 21715 0.14 0.75 3.97 -10228 -89%

Average of Simulations 39% 0.80 1.94 773.39 43%


278


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1974 1983 -34932 -71754 44% 0.96 0.93 36822 -105%

1975 1984 9306 -39105 45% 0.94 0.89 48411 520%

1976 1985 13665 -37130 52% 0.95 0.90 50795 372%

1977 1986 -13453 -57127 37% 0.91 2.45 43674 -325%

1978 1987 -13236 -50444 30% 0.91 2.77 37208 -281%

1979 1988 24321 -16743 35% 0.91 2.68 41064 169%

1980 1989 37967 505 28% 0.92 2.39 37461 99%

1981 1990 71926 38937 19% 0.91 2.22 32989 46%

1982 1991 73521 55500 6% 0.91 2.34 18020 25%

1983 1992 105953 92841 3% 0.84 2.12 13111 12%

1984 1993 112363 124695 3% 0.72 2.24 -12332 -11%

1985 1994 107509 162718 39% 0.70 2.66 -55209 -51%

1986 1995 67499 154774 54% 0.74 2.87 -87275 -129%

1987 1996 63379 158425 53% 0.67 2.18 -95046 -150%

1988 1997 25118 127610 61% 0.72 2.17 -102492 -408%

1989 1998 -24582 84683 67% 0.83 2.16 -109265 444%

1990 1999 -33728 78183 71% 0.84 2.15 -111911 332%

1991 2000 -59556 49761 69% 0.81 2.13 -109317 184%

1992 2001 -58277 55654 75% 0.85 2.10 -113931 195%

1993 2002 -54557 58452 68% 0.79 2.15 -113009 207%

1994 2003 -32495 -9887 7% 0.92 1.66 -22608 70%

1995 2004 -45540 -46964 0% 0.88 1.18 1424 -3%

1996 2005 -31265 -46056 3% 0.89 1.17 14791 -47%

1997 2006 -37118 -69934 14% 0.91 1.02 32816 -88%

1998 2007 -23885 -50844 11% 0.89 3.42 26960 -113%

1999 2008 29850 28365 0% 0.67 2.50 1486 5%

2000 2009 32724 23513 2% 0.65 3.02 9211 28%

Average of Simulations 33% 0.84 2.09 -18006 37%


279

Water

Year

Actual

Storage

Simulated


Water

Year

Actual

Storage

Simulated


1970 -239792 -179743 -60048 25% 1996 -86702 -144643 57941 -67%

1971 -221092 -303649 82557 -37% 1997 218994 411671 -192677 -88%

1972 179112 184682 -5570 -3% 1998 -293640 -168873 -124767 42%

1973 -233097 -118494 -114603 49% 1999 -63383 47477 -110860 175%

1974 -206814 -91269 -115545 56% 2000 -27167 -14073 -13094 48%

1975 -330354 -307037 -23317 7% 2001 -187317 -196196 8880 -5%

1976 -616020 -635014 18994 -3% 2002 -229703 -203618 -26085 11%

1977 235622 164704 70918 30% 2003 -81840 -114818 32978 -40%

1978 36530 -324 36854 101%

1979 -80449 -100816 20367 -25%

1980 45994 22065 23930 52%

1981 206838 253311 -46473 -22%

1982 368794 492650 -123857 -34%

1983 -326166 -203684 -122483 38%

1984 -270585 -221888 -48697 18%

1985 -137655 -103901 -33754 25%

1986 -271489 -222001 -49488 18%

1987 -558025 -501225 -56799 10%

1988 -351574 -381574 30000 -9%

1989 -298757 -377019 78262 -26%

1990 -278288 -369745 91457 -33%

1991 -101512 -278549 177037 -174%

1992 145471 -13350 158820 109%

1993 -193937 -238301 44364 -23%

1994 439952 271653 168299 38%

1995 207429 207517 -89 0%

Modesto 1-Year Simulation


280


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF)

%

Error

1970 1974 -721683 -523932 0.22 0.79 0.39 -197751 27%

1971 1975 -812245 -624323 0.22 0.85 0.37 -187922 23%

1972 1976 -1207173 -958228 0.52 0.97 0.31 -248945 21%

1973 1977 -1150663 -962249 0.18 0.92 0.39 -188413 16%

1974 1978 -881036 -791897 0.07 0.96 0.41 -89139 10%

1975 1979 -754671 -856954 0.26 0.99 0.45 102283 -14%

1976 1980 -378323 -562217 0.77 1.00 0.58 183893 -49%

1977 1981 444535 342564 0.13 0.87 0.70 101971 23%

1978 1982 577706 712405 0.12 0.99 0.56 -134699 -23%

1979 1983 215011 506639 0.41 0.93 0.37 -291628 -136%

1980 1984 24875 336345 0.57 0.96 0.34 -311470

-

1252%

1981 1985 -158774 236026 0.84 0.98 0.31 -394801 249%

1982 1986 -637101 -220365 0.84 0.99 0.32 -416737 65%

1983 1987 -1563920 -1319705 0.59 0.94 0.24 -244215 16%

1984 1988 -1589328 -1496592 0.22 0.95 0.17 -92736 6%

1985 1989 -1617500 -1609217 0.00 0.90 0.18 -8283 1%

1986 1990 -1758133 -1810281 0.04 0.77 0.17 52149 -3%

1987 1991 -1588155 -1831693 0.31 0.98 0.75 243537 -15%

1988 1992 -884660 -1415179 0.76 0.94 0.98 530519 -60%

1989 1993 -727022 -1368012 0.86 0.92 1.09 640989 -88%

1990 1994 11687 -788497 0.84 0.97 1.07 800184 6847%

1991 1995 497404 -289360 0.85 0.94 1.01 786764 158%

1992 1996 512213 -199712 0.81 0.97 0.85 711925 139%

1993 1997 585737 111654 0.58 0.88 0.60 474082 81%

1994 1998 486034 311223 0.15 0.90 0.47 174811 36%

1995 1999 -17302 140379 0.20 0.92 0.64 -157681 911%

1996 2000 -251898 78682 0.41 0.89 0.97 -330579 131%

1997 2001 -352512 76243 0.58 0.93 1.07 -428755 122%

1998 2002 -801209 -451258 0.63 0.77 1.21 -349952 44%

1999 2003 -589409 -412849 0.43 0.82 0.86 -176561 30%



281


WY

Start

WY

End

Cumulative

Storage

Actual

Cumulative

Storage

Simulated


(AF) % Error

1970 1979 -721683 -1435634 0.00 0.90 0.81 713951 -99%

1971 1980 -812245 -1165156 0.00 0.92 0.82 352911 -43%

1972 1981 -1207173 -537489 0.13 0.95 0.48 -669684 55%

1973 1982 -1150663 -100503 0.22 0.91 0.57 -1050160 91%

1974 1983 -881036 -513708 0.01 0.73 0.60 -367328 42%

1975 1984 -754671 -982808 0.04 0.84 0.49 228137 -30%

1976 1985 -378323 -270597 0.13 0.95 0.48 -107726 28%

1977 1986 444535 6379 0.06 0.89 0.57 438156 99%

1978 1987 577706 -983826 0.00 0.90 0.52 1561533 270%

1979 1988 215011 -1122904 0.05 0.87 0.41 1337915 622%

1980 1989 24875 -1125008 0.31 0.94 0.30 1149884 4623%

1981 1990 -158774 -1688267 0.08 0.94 0.28 1529492 -963%

1982 1991 -637101 -2098240 0.02 0.87 0.63 1461138 -229%

1983 1992 -1563920 -2473876 0.00 0.81 0.40 909956 -58%

1984 1993 -1589328 -2843615 0.15 0.47 0.90 1254287 -79%

1985 1994 -1617500 -2135805 0.07 0.50 1.20 518305 -32%

1986 1995 -1758133 -1753787 0.07 0.61 0.92 -4346 0%

1987 1996 -1588155 -2290444 0.50 0.96 0.90 702289 -44%

1988 1997 -884660 -1401761 0.56 0.86 0.84 517101 -58%

1989 1998 -727022 -1582253 0.64 0.87 0.94 855231 -118%

1990 1999 11687 -1264184 0.51 0.73 1.04 1275871 10917%

1991 2000 497404 -603560 0.38 0.75 1.28 1100964 221%

1992 2001 512213 -770806 0.53 0.85 2.15 1283019 250%

1993 2002 585737 -927337 0.42 0.87 2.12 1513074 258%

1994 2003 486034 -283352 0.05 0.88 0.49 769386 158%



282

Appendix H – Expert Review Questions

Test Questions

Structure

Verification

Is the structure of the model consistent with your knowledge of

the system?

Parameter

Verification

Are the model parameters consistent with your knowledge of

the system?

Behavior Is the behavior of the model consistent with your expectations

about the behavior of the system?

Boundary

Adequacy

(Structure)

Are any important structural elements left out of the proposed

model? Should any structural elements be removed from the

model?

Dimensional

Consistency

Are the dimensions and units within the model consistent with

the results?


283

Appendix I – Research Log

Call with Randy Hansen 9-21-16

Test Questions Response

Structure

Verification

Is the structure of the model

consistent with your knowledge

of the system?

Yes. However, Stream Leakage

and net underflow can go in

both directions.

Parameter

Verification

Are the model parameters


of the system?

Yes.

Behavior Is the behavior of the model

consistent with your expectations


Yes.

Boundary

Adequacy

(Structure)

Are any important structural

elements left out of the proposed

model? Should any structural

elements be removed from the

model?

No.

Dimensional

Consistency

Are the dimensions and units

within the model consistent with

the results?

Yes. We use cubic meters and

then convert to AF.

Additional Comments: Consider simulating wet years and dry years separately.

Probably not possible to simulate change in storage this way for the Pajaro system.

Coastal inflow makes it difficult.


284

Call with Steve Phillips 9-13-16


Structure

Verification



of the system?

Yes.

Parameter

Verification



of the system?

Yes.




Yes.

Boundary

Adequacy

(Structure)





model?

Yes. Add reservoir leakage.

Dimensional

Consistency



the results?

Yes.

Additional Comments: Crop consumptive use equals ET irrigation – Groundwater

uptake.


285

Meeting with Dr. Mike McCullough 9-22-16


Structure

Verification



of the system?

Yes.

Parameter

Verification



of the system?

Yes.




NA. The structure should

produce the predicted behavior.

Boundary

Adequacy

(Structure)





model?

No.

Dimensional

Consistency



the results?

Yes.


286

Appendix J – Linear Equations

Cuyama Linear Equations

Parameter Precipitation to Runoff Runoff to Stream

Leakage Precipitation to Deep

Perc.

Period Slope Intercept R2 Slope Intercept R2 Slope Intercept R2

1950 1959 -0.293 -15026 0.65 -1.089 -17173 0.71 0.160 -146 0.88

1951 1960 -0.299 -14440 0.67 -0.992 -12604 0.70 0.136 2239 0.81

1952 1961 -0.295 -14841 0.67 -0.962 -10752 0.74 0.113 4622 0.69

1953 1962 -0.349 -12554 0.60 -0.895 -8765 0.79 0.198 1024 0.54

1954 1963 -0.357 -10934 0.64 -0.933 -9571 0.83 0.198 1259 0.56

1955 1964 -0.362 -10058 0.66 -0.955 -9883 0.85 0.197 1672 0.59

1956 1965 -0.366 -8250 0.66 -0.978 -9853 0.89 0.191 1807 0.55

1957 1966 -0.362 -9456 0.63 -1.033 -10477 0.84 0.190 1909 0.54

1958 1967 -0.352 -10429 0.63 -1.025 -8656 0.76 0.180 2194 0.49

1959 1968 -0.535 -1040 0.71 -0.949 -7817 0.70 0.278 -3127 0.54

1960 1969 -0.464 -5475 0.81 -1.139 -13498 0.82 0.230 -542 0.64

1961 1970 -0.458 -6027 0.81 -1.159 -14646 0.82 0.236 -1047 0.66

1962 1971 -0.475 -4279 0.82 -1.129 -12495 0.81 0.254 -3050 0.71

1963 1972 -0.354 -11937 0.74 -1.442 -22281 0.87 0.164 2218 0.68

1964 1973 -0.336 -12880 0.71 -1.446 -20178 0.79 0.155 2505 0.63

1965 1974 -0.331 -13245 0.70 -1.399 -17764 0.78 0.154 2541 0.62

1966 1975 -0.338 -12328 0.65 -1.195 -8591 0.70 0.157 2112 0.59

1967 1976 -0.348 -9617 0.61 -1.171 -8136 0.72 0.161 1127 0.55

1968 1977 -0.337 -9683 0.56 -1.198 -10830 0.74 0.161 1135 0.55

1969 1978 -0.388 -5995 0.73 -1.097 -6778 0.82 0.163 808 0.67

1970 1979 -0.337 -8813 0.63 -1.011 -4472 0.73 0.119 3153 0.53

1971 1980 -0.346 -7586 0.62 -0.942 -1553 0.72 0.121 2575 0.52

1972 1981 -0.356 -6520 0.63 -0.974 -3724 0.69 0.121 2605 0.51

1973 1982 -0.494 7121 0.89 -0.970 -4086 0.66 0.181 -3275 0.83

1974 1983 -0.434 2930 0.89 -1.015 -7163 0.83 0.152 -1129 0.82

1975 1984 -0.443 4131 0.92 -1.055 -9578 0.83 0.150 -965 0.82

1976 1985 -0.416 558 0.91 -1.197 -16804 0.93 0.146 -476 0.83

1977 1986 -0.402 -788 0.90 -1.252 -19097 0.94 0.144 -550 0.75

1978 1987 -0.392 -2505 0.94 -1.231 -18024 0.94 0.147 -783 0.79

1979 1988 -0.313 -7491 0.88 -1.296 -20286 0.90 0.092 2580 0.43

1980 1989 -0.301 -8311 0.89 -1.262 -19607 0.91 0.093 2194 0.48

1981 1990 -0.295 -8519 0.91 -1.169 -16290 0.90 0.088 2461 0.50


287

Cuyama Linear Equations (continued)

Parameter Precipitation to Runoff Runoff to Stream

Leakage Precipitation to Deep

Perc.


1982 1991 -0.305 -8840 0.82 -1.134 -15090 0.91 0.096 2318 0.43

1983 1992 -0.309 -8919 0.82 -1.189 -15172 0.93 0.093 2254 0.42

1984 1993 -0.356 -6475 0.75 -1.311 -18408 0.92 0.091 2595 0.30

1985 1994 -0.356 -6324 0.74 -1.297 -17669 0.92 0.099 1504 0.34

1986 1995 -0.434 -1229 0.86 -1.075 -10814 0.93 0.170 -2959 0.63

1987 1996 -0.428 -3007 0.87 -1.098 -12618 0.93 0.170 -2533 0.66

1988 1997 -0.422 -3804 0.86 -1.097 -12819 0.92 0.172 -2964 0.64

1989 1998 -0.411 -5899 0.97 -0.944 -7425 0.91 0.172 -2144 0.88

1990 1999 -0.414 -4932 0.96 -0.953 -8299 0.90 0.176 -2919 0.86

1991 2000 -0.424 -3314 0.95 -0.946 -7805 0.89 0.190 -4973 0.87

1992 2001 -0.431 -2333 0.96 -0.942 -7820 0.88 0.196 -6959 0.91

1993 2002 -0.418 -4333 0.96 -0.972 -10428 0.92 0.189 -5864 0.91

1994 2003 -0.417 -3461 0.96 -0.925 -10569 0.98 0.190 -6780 0.88

1995 2004 -0.406 -5262 0.96 -0.932 -11093 0.98 0.190 -6858 0.89

1996 2005 -0.435 -3043 0.96 -0.956 -12111 0.99 0.180 -6543 0.95

1997 2006 -0.435 -1473 0.94 -0.942 -10304 0.97 0.181 -7841 0.89

1998 2007 -0.426 -2775 0.94 -0.945 -10540 0.97 0.173 -6671 0.88

1999 2008 -0.462 -1806 0.89 -1.008 -12000 0.97 0.171 -5506 0.72

2000 2009 -0.466 -1581 0.90 -0.984 -9883 0.98 0.172 -5626 0.73

2001 2010 -0.464 -1776 0.90 -0.976 -8743 0.96 0.174 -6406 0.72


288

Pajaro Linear Equations

Parameter Precipitation to Runoff Runoff to Stream Leakage Precipitation to FNR


1964 1973 -0.761 28714 0.99 -0.084 5002 0.86 0.160 -146 0.88

1965 1974 -0.734 24018 0.98 -0.084 4975 0.86 0.136 2239 0.81

1966 1975 -0.756 29072 0.98 -0.080 5640 0.85 0.113 4622 0.69

1967 1976 -0.795 39651 0.98 -0.092 3560 0.87 0.198 1024 0.54

1968 1977 -0.801 40951 0.98 -0.091 2921 0.88 0.198 1259 0.56

1969 1978 -0.804 41772 0.98 -0.095 2319 0.90 0.197 1672 0.59

1970 1979 -0.789 38271 0.98 -0.104 1876 0.93 0.191 1807 0.55

1971 1980 -0.779 37573 0.98 -0.104 1875 0.93 0.190 1909 0.54

1972 1981 -0.775 36068 0.97 -0.105 1571 0.94 0.180 2194 0.49

1973 1982 -0.781 39274 0.98 -0.107 1585 0.95 0.278 -3127 0.54

1974 1983 -0.777 39282 0.99 -0.101 2200 0.94 0.230 -542 0.64

1975 1984 -0.773 35663 0.98 -0.100 2669 0.93 0.236 -1047 0.66

1976 1985 -0.768 33547 0.99 -0.102 2186 0.95 0.254 -3050 0.71

1977 1986 -0.748 29106 0.98 -0.094 4070 0.88 0.164 2218 0.68

1978 1987 -0.732 24516 0.99 -0.083 5969 0.90 0.155 2505 0.63

1979 1988 -0.734 26825 0.98 -0.087 5089 0.87 0.154 2541 0.62

1980 1989 -0.744 30516 0.99 -0.090 4488 0.87 0.157 2112 0.59

1981 1990 -0.760 34861 0.98 -0.098 3284 0.87 0.161 1127 0.55

1982 1991 -0.759 35494 0.99 -0.099 3082 0.87 0.161 1135 0.55

1983 1992 -0.767 36481 0.98 -0.094 3348 0.83 0.163 808 0.67

1984 1993 -0.679 25262 0.95 -0.136 682 0.82 0.119 3153 0.53

1985 1994 -0.696 30831 0.97 -0.131 1031 0.82 0.121 2575 0.52

1986 1995 -0.675 28246 0.98 -0.121 1487 0.87 0.121 2605 0.51

1987 1996 -0.672 27985 0.98 -0.120 1168 0.93 0.181 -3275 0.83

1988 1997 -0.697 30746 0.97 -0.128 295 0.95 0.152 -1129 0.82

1989 1998 -0.674 26708 0.98 -0.104 2439 0.91 0.150 -965 0.82

1990 1999 -0.681 29702 0.97 -0.096 4152 0.84 0.146 -476 0.83

1991 2000 -0.664 24528 0.97 -0.082 6221 0.83 0.144 -550 0.75

1992 2001 -0.698 35816 0.97 -0.074 7683 0.84 0.147 -783 0.79

1993 2002 -0.683 31630 0.96 -0.070 8499 0.86 0.092 2580 0.43

1994 2003 -0.678 31217 0.96 -0.068 8672 0.86 0.093 2194 0.48

1995 2004 -0.662 26221 0.96 -0.062 9812 0.88 0.088 2461 0.50

1996 2005 -0.655 28025 0.92 -0.057 10564 0.79 0.096 2318 0.43

1997 2006 -0.645 27744 0.91 -0.057 10718 0.75 0.093 2254 0.42

1998 2007 -0.641 30676 0.94 -0.053 10640 0.67 0.091 2595 0.30

1999 2008 -0.566 18716 0.87 -0.056 10140 0.43 0.099 1504 0.34

2000 2009 -0.575 21259 0.87 -0.065 8916 0.53 0.170 -2959 0.63


289

Pajaro Linear Equations (continued)

Parameter Precipitation to Drains Drains to Underflow Underflow to NCI


1964 1973 -0.024 -1036 0.68 0.312 4985 0.82 1.324 -4032 0.98

1965 1974 -0.022 -1559 0.69 0.279 4739 0.80 1.406 -4296 0.97

1966 1975 -0.022 -1804 0.80 0.246 4445 0.78 1.401 -4291 0.96

1967 1976 -0.022 -1972 0.83 0.209 4153 0.85 1.421 -4344 0.95

1968 1977 -0.027 -1169 0.94 0.250 4429 0.87 1.346 -4127 0.97

1969 1978 -0.023 -1603 0.74 0.255 4493 0.88 1.334 -4103 0.97

1970 1979 -0.021 -1729 0.68 0.285 4588 0.90 1.322 -4039 0.96

1971 1980 -0.018 -1921 0.65 0.285 4570 0.87 1.332 -4068 0.95

1972 1981 -0.018 -1629 0.71 0.272 4506 0.86 1.366 -4172 0.95

1973 1982 -0.017 -1677 0.69 0.282 4542 0.86 1.325 -4062 0.96

1974 1983 -0.020 -1126 0.77 0.236 4323 0.84 1.365 -4200 0.97

1975 1984 -0.018 -1716 0.71 0.235 4309 0.80 1.308 -4000 0.97

1976 1985 -0.018 -1474 0.74 0.236 4334 0.82 1.306 -3981 0.97

1977 1986 -0.019 -1260 0.71 0.230 4293 0.81 1.325 -4020 0.96

1978 1987 -0.018 -1423 0.69 0.212 4178 0.83 1.541 -4626 0.97

1979 1988 -0.020 -970 0.74 0.234 4317 0.83 1.568 -4675 0.99

1980 1989 -0.021 -695 0.75 0.265 4545 0.83 1.518 -4533 0.99

1981 1990 -0.023 -392 0.78 0.287 4731 0.85 1.491 -4460 0.99

1982 1991 -0.024 -30 0.78 0.308 4925 0.87 1.492 -4489 1.00

1983 1992 -0.028 571 0.79 0.301 4974 0.88 1.532 -4627 0.99

1984 1993 -0.010 -1673 0.17 0.465 5466 0.92 1.506 -4490 0.98

1985 1994 -0.012 -1087 0.46 0.524 5668 0.82 1.513 -4495 0.97

1986 1995 -0.012 -870 0.75 0.356 5295 0.64 1.435 -4132 0.96

1987 1996 -0.013 -767 0.79 0.242 5065 0.58 1.307 -3540 0.92

1988 1997 -0.016 -288 0.77 0.259 5151 0.77 1.379 -3867 0.93

1989 1998 -0.022 770 0.85 0.266 5211 0.95 1.475 -4288 0.98

1990 1999 -0.022 486 0.78 0.286 5220 0.83 1.455 -4170 0.98

1991 2000 -0.023 496 0.73 0.301 5264 0.83 1.491 -4292 0.99

1992 2001 -0.021 -16 0.66 0.290 5141 0.75 1.547 -4487 0.99

1993 2002 -0.017 -1210 0.59 0.275 5030 0.68 1.552 -4521 0.99

1994 2003 -0.018 -1163 0.70 0.268 4966 0.66 1.540 -4505 0.99

1995 2004 -0.017 -1713 0.67 0.218 4634 0.59 1.517 -4438 0.98

1996 2005 -0.020 -1136 0.82 0.202 4473 0.60 1.499 -4388 0.98

1997 2006 -0.021 -1139 0.88 0.187 4320 0.70 1.390 -4051 0.98

1998 2007 -0.021 -1162 0.89 0.186 4270 0.77 1.376 -4004 0.98

1999 2008 -0.018 -1628 0.73 0.252 4613 0.73 1.299 -3731 0.99

2000 2009 -0.019 -1314 0.73 0.265 4738 0.90 1.370 -3984 1.00


290

Modesto Linear Equations

Parameter Precipitation to Runoff Runoff to Net Perc. Underflow to Stream

Leakage


1960 1969 -0.002 -3585 0.22 -192.326 354265 0.93 -0.937 -97326 0.78

1961 1970 -0.002 -3154 0.39 -203.908 303483 0.95 -0.803 -87147 0.72

1962 1971 -0.002 -3300 0.35 -211.087 263678 0.96 -0.818 -93853 0.65

1963 1972 -0.002 -3585 0.29 -210.848 266216 0.96 -0.836 -95362 0.64

1964 1973 -0.003 -3295 0.70 -190.407 369418 0.95 -0.757 -90023 0.58

1965 1974 -0.003 -3156 0.67 -204.675 290652 0.95 -0.768 -94751 0.54

1966 1975 -0.003 -3030 0.69 -218.360 214144 0.94 -0.765 -96848 0.53

1967 1976 -0.003 -2791 0.78 -221.390 193729 0.96 -0.826 -104434 0.52

1968 1977 -0.003 -2915 0.82 -218.909 208302 0.96 -0.508 -69335 0.39

1969 1978 -0.003 -3049 0.81 -219.411 200715 0.97 -0.639 -72690 0.30

1970 1979 -0.003 -3106 0.79 -227.215 166874 0.97 -0.347 -47609 0.09

1971 1980 -0.002 -3238 0.72 -217.525 205797 0.96 -0.566 -61020 0.26

1972 1981 -0.003 -3203 0.73 -219.567 194551 0.96 -0.537 -56048 0.26

1973 1982 -0.002 -3149 0.77 -212.759 214185 0.96 -0.748 -74551 0.43

1974 1983 -0.003 -3077 0.86 -184.517 343972 0.95 -0.688 -63106 0.68

1975 1984 -0.002 -3281 0.87 -183.613 347090 0.94 -0.590 -56212 0.48

1976 1985 -0.002 -3426 0.89 -176.813 385892 0.94 -0.594 -57981 0.47

1977 1986 -0.002 -3585 0.89 -174.985 390677 0.89 -0.572 -53345 0.44

1978 1987 -0.002 -3632 0.87 -181.646 353938 0.89 -0.707 -81343 0.45

1979 1988 -0.002 -3670 0.88 -173.315 397790 0.88 -0.687 -84208 0.59

1980 1989 -0.002 -3542 0.88 -169.978 411139 0.91 -0.600 -66355 0.53

1981 1990 -0.002 -3494 0.90 -167.633 425440 0.91 -0.513 -51811 0.48

1982 1991 -0.002 -3496 0.90 -159.707 461925 0.92 -0.440 -34846 0.45

1983 1992 -0.003 -3406 0.92 -174.292 403923 0.89 -0.334 -25234 0.38

1984 1993 -0.003 -3085 0.84 -229.737 143757 0.88 0.090 6502 0.04

1985 1994 -0.003 -2997 0.83 -223.515 180611 0.90 -0.069 293 0.03

1986 1995 -0.003 -2916 0.92 -211.652 239747 0.95 -0.553 -13246 0.37

1987 1996 -0.003 -3048 0.93 -203.473 288810 0.99 -0.732 -20274 0.50

1988 1997 -0.003 -3261 0.82 -200.808 302846 0.99 -0.784 -16438 0.75

1989 1998 -0.002 -3542 0.73 -194.217 325535 0.95 -0.701 -7842 0.83

1990 1999 -0.002 -3698 0.72 -205.043 259600 0.93 -0.621 -7068 0.64

1991 2000 -0.002 -3820 0.65 -213.407 206625 0.91 -0.579 -7462 0.55

1992 2001 -0.002 -3963 0.61 -221.576 159105 0.91 -0.600 -15143 0.48

1993 2002 -0.002 -3989 0.62 -218.784 170213 0.93 -0.742 -39991 0.49

1994 2003 -0.002 -3870 0.66 -214.024 194272 0.94 -0.861 -61776 0.56

1995 2004 -0.002 -4023 0.65 -220.944 155332 0.94 -1.006 -85860 0.59


291

Modesto Linear Equations (continued)

Parameter Net Perc to Res. Leakage Farm Pumpage to

Underflow

Period Slope Intercept R2 Slope Intercept R2

1960 1969 -0.005 20833 0.16 -0.193 -282617 0.23

1961 1970 -0.008 24307 0.58 -0.202 -295171 0.23

1962 1971 -0.007 23198 0.56 -0.167 -261089 0.13

1963 1972 -0.007 22901 0.66 -0.134 -230167 0.11

1964 1973 -0.008 24847 0.71 -0.312 -425334 0.35

1965 1974 -0.006 22622 0.62 -0.290 -407016 0.42

1966 1975 -0.006 21860 0.63 -0.275 -393210 0.47

1967 1976 -0.006 22018 0.73 -0.249 -364806 0.30

1968 1977 -0.006 21917 0.81 -0.281 -395980 0.60

1969 1978 -0.006 21842 0.81 -0.280 -400984 0.65

1970 1979 -0.006 22361 0.83 -0.260 -371783 0.88

1971 1980 -0.006 21829 0.66 -0.269 -385175 0.74

1972 1981 -0.006 21590 0.65 -0.270 -387274 0.75

1973 1982 -0.006 21753 0.50 -0.300 -419275 0.81

1974 1983 -0.005 20939 0.49 -0.422 -553914 0.69

1975 1984 -0.004 19216 0.18 -0.433 -573861 0.70

1976 1985 -0.004 18528 0.13 -0.459 -604235 0.75

1977 1986 -0.002 15488 0.02 -0.451 -603076 0.77

1978 1987 0.000 13138 0.00 -0.534 -681009 0.68

1979 1988 0.000 13485 0.00 -0.370 -529412 0.68

1980 1989 -0.002 16443 0.02 -0.391 -552196 0.74

1981 1990 -0.003 17640 0.04 -0.412 -568325 0.77

1982 1991 -0.003 18228 0.04 -0.433 -591935 0.82

1983 1992 -0.004 18831 0.08 -0.490 -662128 0.89

1984 1993 -0.005 20434 0.09 -0.391 -536613 0.81

1985 1994 -0.008 24652 0.34 -0.351 -481877 0.76

1986 1995 -0.004 19507 0.14 -0.392 -535508 0.75

1987 1996 -0.005 21729 0.29 -0.379 -519478 0.70

1988 1997 -0.006 23194 0.33 -0.373 -523387 0.47

1989 1998 -0.006 22402 0.31 -0.498 -668884 0.74

1990 1999 -0.004 19583 0.16 -0.499 -673887 0.74

1991 2000 -0.003 18646 0.11 -0.478 -651074 0.73

1992 2001 -0.003 17466 0.07 -0.445 -618698 0.68

1993 2002 -0.002 16584 0.04 -0.379 -550867 0.51

1994 2003 -0.001 15463 0.02 -0.381 -557785 0.60

1995 2004 -0.001 15078 0.01 -0.348 -525083 0.64