procedures to perform dam rehabilitation analysis in aging

Procedures to Perform Dam Rehabilitation Analysis in Aging Dams

Michael A. Bliss

Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Master of Science

In Civil and Environmental Engineering

David F. Kibler (Chair) William E. Cox

Joseph E. Dove

18 May 2006 Blacksburg, Virginia

Keywords: Dam Rehabilitation Analysis, Hydrologic and Hydraulic Analysis, Incremental Economic Analysis, Linear Programming, Dam Safety.

© 2006, Michael A. Bliss

ii

Procedures to Perform Dam Rehabilitation Analysis in Aging Dams

Michael A. Bliss

(ABSTRACT)

There are hundreds of existing dams within the State of Virginia, and even thousands

more specifically within the United States. A large portion of these dams do not meet

the current safety standard of passing the Probable Maximum Flood. Likewise, many of

the dams have reached or surpassed the original design lives, and are in need of

rehabilitation. A standard protocol will assist dam owners in completing a dam

rehabilitation analysis. The protocol provides the methods to complete the hydrologic,

hydraulic, and economic analysis. Additionally, alternative augmentation techniques are

discussed including the integration of GIS applications and linear programming

optimization techniques. The standard protocol and alternative techniques are applied

to a case study. The case study includes a set of flood control dams located in the

headwaters of the South River watershed in Augusta County, VA. The downstream

impacts of the flood control dams on the city of Waynesboro are demonstrated through

the hydrologic and hydraulic analysis.

iii

Table of Contents Abstract�� ii Table of Contents��.. iii List of Figures��. v List of Tables��.. vi Acknowledgement��.. vii Dedication�� viii Chapter 1: Introduction�� 1

1.1 Problem Background�� 1 1.2 Statement of Objectives��.. 2 1.3 General Framework Description�� 3 1.4 Introduction to South River Watershed��. 4 1.5 Outline�� 4

Chapter 2: Related Works��.. 7 2.1 Dam Safety�� 7 2.2 Risk Analysis��. 10 2.3 Probable Maximum Floods��. 11

2.4 Linear Programming��. 13 2.5 Dam Remediation Strategies��.. 14

Chapter 3: Hydrologic Model for Upper South River and Application to Dam Removal Question�� 17

3.1 South River Watershed�� 18 3.2 Required Data for Model Creation��. 20

3.2.1 Watershed Parameters��. 20 3.2.2 Channel Properties�� 21 3.2.3 Reservoir and Dam Properties��. 22 3.2.4 Reservoir Rating Table��.. 25 3.2.5 Rainfall Data from IFLOWS Gages��. 26 3.2.6 Surveyed High Water Marks from Recent Storms�� 27 3.2.7 Lyndhurst Gaging Station Stream Flows�� 27

3.3 Hydrologic Model Creation��.. 29 3.3.1 Basin Model Creation�� 30

3.3.1.1 Sub-basin Icon Data�� 30 3.3.1.2 Reach Icon Data��.. 31 3.3.1.3 Reservoir Icon Data��. 32

3.3.2 Weather Model Creation�� 33 3.3.2.1 User Hyetographs�� 33 3.3.2.2 NRCS Hypothetical Storms�� 36

3.4 Model Calibration��.. 36

iv

3.5 Simulating the Results of Dam Removal..�� 43 3.6 Summary�� 47

Chapter 4: Traditional Economic Analysis of Dam Rehabilitation by Flood Damage Curve Integration�� 49

4.1 General Approach to Economic Analysis��.. 49 4.2 Specific Steps to an Economic Analysis�� 53 4.3 Federal Planning Guidance��. 57 4.4 Case Study Economic Analysis��.. 58 4.5 Summary of Traditional Economics Analysis�� 67

Chapter 5: Use of GIS Software as a Hydro-economic Tool in Dam Rehabilitation Analysis��.. 68

5.1 Overview of GIS as a Tool for Analysis��. 68 5.2 Discussion of Existing Relevant GIS Software��. 70 5.3 Automating the Economic Analysis�� 73 5.4 FEMA�s HAZUS Multi-Hazard Model��. 74 5.5 Case Study Application of HAZUS-MH Software��. 76 5.6 Summary of Integration of GIS Software with Rehabilitation Analysis��... 85

Chapter 6: Linear Programming as an Alternative Analysis Technique��.. 87

6.1 An Alternative Economic Analysis for Dam Rehabilitation��.. 88 6.2 Application of Linear Programming�� 93 6.3 Expansion of Alternative Economic Analysis Through Linear Programming��... 96

6.3.1 Model Formulation��.. 96 6.3.2 Test Example��.. 100 6.3.3 Results from Simulation Runs��.. 103 6.3.4 Discussion of New Linear Program Techniques�� 104

6.4 Summary��. 105 Chapter 7: Summary, Conclusions, and Recommendations��.. 107 7.1 Summary�� 107 7.2 Conclusions��... 109 7.3 Recommendations�� 110 . Bibliography�� 112 Appendices Appendix A HEC-HMS Data��.. 115 Appendix B South River Model Output Data��... 136 Appendix C Linear Programming Test Example��. 139 Vita�� 148

v

List of Figures

Figure 1.1: South River Watershed, Sub-basins and Dams��.. 5 Figure 2.1: Taum Sauk Reservoir Breach; �Reprinted with permission of the St. Louis Post-Dispatch, copyright 2005.� Graphic from the news article: �Swept away, rescued more than a billion gallons of water��, December 15, 2005, Todd C. Frankel and Tim Rowden��. 8 Figure 2.2: Extreme 12 hour Historical Storms in U.S. ��.. 13 Figure 2.3: Parapet Wall Remediation (USACE, 2004)��. 15 Figure 2.4: Articulated Blocks in place on VA Tech Campus�� 16 Figure 3.1: South River Watershed, Sub-basins and Dams��. 19 Figure 3.2: Cross Section Template��. 22 Figure 3.3: Robinson Hollow Dam, Upstream Side Reservoir��. 23 Figure 3.4: Canada Run Inlet Structure�� 23 Figure 3.5: Happy Hollow Outlet Structure��.. 23 Figure 3.6: Robinson Hollow Original Plan View�� 24 Figure 3.7: Lofton Lake Auxiliary Spillway��.. 24 Figure 3.8: IFLOWS Gage at Stoney Creek Dam��. 26 Figure 3.9: Hurricane Isabel Hydrograph�� 28 Figure 3.10: HEC-HMS Primary Menu Screen�� 29 Figure 3.11: HEC-HMS Basin Model Editing Screen��. 30 Figure 3.12: Reach Editor Screen, Basin Model��. 32 Figure 3.13: Reservoir Editor Screen, Basin Model�� 33 Figure 3.14: Meteorological Model Editor, HEC-HMS�� 34 Figure 3.15: South River Watershed, Rainfall Data Applied to Sub-basins for HEC-HMS Model��. 35 Figure 3.16: South River Watershed, HEC-HMS Schematic Diagram�� 37 Figure 3.17: South River Watershed, Landuse within Watershed�� 40 Figure 3.18: South River Watershed, NRCS Soil Curve Number Data for Sub-basins�� 41 Figure 3.19: Real Time Data from USGS on 29 NOV 05 Storm��... 43 Figure 3.20: Q2 Side by Side Comparison at Dam Sites�� 44 Figure 3.21: Q100 Side by Side Comparison at Dam Sites�� 45 Figure 3.22: South River Watershed, Reduction of Discharge by Dams for Q100. 46 Figure 3.23: Gage Height Comparison��.. 46 Figure 4.1: Example Economic Benefit Determination��.. 50 Figure 4.2: Economic Analysis Flow Chart��.. 56 Figure 4.3: NRCS Damage Frequency Curve (Faulkner, 2006)��.. 63 Figure 5.1: Augusta County, VA GIS Web-site�� 70 Figure 5.2: HAZUS-MH Start Menu��.. 74 Figure 5.3: Augusta County Study Region in HAZUS-MH�� 76 Figure 5.4: Census Blocks in HAZUS-MH��... 77 Figure 5.5: Stream Network in HAZUS-MH��. 78 Figure 5.6: Flood Inundation Zone for Hillsborough, NC��.. 79 Figure 5.7: Common Reach for Inch Branch and Toms Branch Dams��.. 81 Figure 5.8: Comparison of HAZUS-MH and NRCS Flood Zones�� 82 Figure 5.9: Example Damage HAZUS-MH Damage Report�� 83 Figure C.1: Regression Plot for People at Risk Parameter��.. 139 Figure C.2: Regression Plot for Damage without Modification��. 140 Figure C.3: Regression Plot for Damage with Modification��.. 141 Figure C.4: Regression Plot for Modification Cost v. % PMF�� 138

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List of Tables

Table 3.1: South River Watershed Data��.. 20 Table 3.2: South River Manning�s n Values�� 21 Table 3.3: Lyndhurst GS Data��... 28 Table 3.4: Hurricane Isabel Rainfall��. 36 Table 3.5: Initial Simulation Runs��. 38 Table 3.6: Simulation Changes��. 39 Table 3.7: Calibration Results�� 42 Table 4.1: Example Economic Analysis��... 53 Table 4.2: NRCS Damage Summations (Faulkner, 2006)�� 62 Table 4.3: NRCS Tabulated Data for Figure 4.3 Damage Frequency Curve (Faulkner, 2006)�� 63 Table 4.4: NRCS Average Annual Damages for Sponsor Breaches (Faulkner, 2006)�� 64 Table 4.5: NRCS Average Annual Damages for Toms Creek Rehab. (Faulkner, 2006)�� 65 Table 4.6: NRCS Incremental Analysis on Sponsor Breaches (Faulkner, 2006).. 66 Table 4.7: NRCS Incremental Analysis on Rehabilitation Options (Faulkner, 2006)�� 66 Table 5.1: Lyndhurst Gaging Station Comparison��. 80 Table 5.2: HAZUS-MH Comparison to HEC-HMS at Dam Sites��. 81 Table 5.3: Flood Inundation Comparison��. 82 Table 5.4: Property Exposure Estimates Comparison��84 Table 5.5: Total Structure Damages Comparison��.. 85 Table 6.1: South River LS and LM Calculations�� 90 Table 6.2: South River LCS and LCM Calculations�� 91 Table 6.3: LB Results��.. 91 Table 6.4: South River Economic Calculations��.. 92 Table 6.5: Hypothetical Data for South River Dam Rehabilitations��. 94 Table 6.6: Summary of Results��. 103 Table A.1: South River Watershed Sub-Area Data�� 115 Table A.2: South River Manning�s n Values�� 117 Table A.3: Back Creek Manning�s n Values�� 117 Table A.4: South River Cross Section Data�� 118 Table A.5: Rating Table Data��. 122 Table A.6: IFLOWS Rainfall Data��.. 128 Table A.7: Hurricane Isabel High Water Marks��... 134 Table B.1: Simulation Output, CN = 65��. 136 Table B.2: Simulation Output, CN = 60��. 137 Table B.3: Simulation Output, CN = 55��. 138 Table C.1: People at Risk (PAR) Regression��.. 139 Table C.2: Flood Damage Regressions�� 140 Table C.3: Construction Cost Regression�� 141 Table C.4: Run#1: Original Data; Not Feasible��.. 142 Table C.5: Run#2: Flood Damage Switched; Not Feasible��.. 143 Table C.6: Run#3: Flood Damage Switched, no construction costs; Feasible Solution��... 144 Table C.7: Run#4: Additional Condition Xs > 25; Feasible Solution��. 145 Table C.8: Run#5: PARM is reduced to zero to check LB; Feasible Solution��.. 146 Table C.9: Run#6: Take PAR out of equation, Economic only; Feasible Solution 147

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Acknowledgements

I want to thank Dr. Kibler for providing mentorship and support through my

studies the past two years. I�m honored to have been associated with such an

outstanding professional who genuinely supports anyone he comes in contact with. I am

also grateful for the assistance from Dr. Cox and Dr. Dove, who have also provided

great insight to me.

I received much assistance from several agencies in providing pivotal data for

the development of the South River case study. I would like to thank Mr. Matthew

Lyons, State Conservation Engineer, Natural Resources Conservation Service (NRCS),

in providing the NRCS dam rehabilitation proposal for the South River watershed. Also

for the detailed economic information provided to me by Mr. David Faulkner, NRCS

economist. Mr. Fred Garst, GIS Analyst, NRCS, provided me with applicable GIS data

files to South River watershed products. Finally, I would like to thank Mr. Otis Bilkins

from the Headwaters Water and Soil Conservation District for providing me with critical

high water marks from major storm events.

Finally, I want to thank my family who support me everyday. My wife and

children mean the world to me, and I couldn�t have finished this without sacrificing time

away from them.

viii

Dedication

I dedicate this work to my soldiers of B Company, 11th Engineer Battalion, who I

am humbled and privileged to have led into battle during the start of Operation Iraqi

Freedom in 2003. They were the finest unit a commander could ever want, and they

fought with the utmost heroism and honor. We think daily of our fallen Bulldogs:

Bulldog 2-7: SFC Paul Smith (KIA, 04 APR 03) (Medal of Honor Recipient)

Bulldog 2-3: SSG Lincoln Hollinsaid (KIA, 07 APR 03)

Bulldog 1-6D: PFC Jason Meyer (KIA, 07 APR 03)

They are not forgotten!

Chapter 1: Introduction 1

Chapter 1: Introduction

1.1 Problem Background

There are hundreds of existing dams within the State of Virginia, and even

thousands more within the United States. The issue of dam safety, with respect to the

aging inventory of the existing dams, is an ongoing struggle that garnered national

interest back in the 1970s. The U.S. Army Corps of Engineers (USACE), mandated by

Congress, inspected over 8,000 non-federal dams in the late 1970s and early 1980s.

Almost one third of the dams did not meet the current Probable Maximum Flood (PMF)

design criteria (USACE, 1982).

Even with national interest for what is now over 30 years, the problem remains a

huge issue. The magnitude of the issue is best highlighted by the following statements

taken from the American Society of Civil Engineers (ASCE) 2005 �Report Card for

America's Infrastructure� (ASCE, 2005):

• Since 1998, the number of unsafe dams has risen by 33% to more than 3,500.

• The number of dams identified as unsafe is increasing at a faster rate than those being repaired.

• Such dam failures as Silver Lake Dam in Michigan in 2003 ($100 million in

damages and economic losses of $1 million per day) and the Big Bay Lake Dam in Mississippi in March 2004 (100 homes destroyed) are current reminders of the potential consequences of unsafe dams.

• The total investment to bring U.S. dams into safety compliance or to remove

obsolete dams tops $30 billion. The ASCE Report Card also states that in general dams owned by government agencies

are as expected in better condition then privately owned dams. Economic

considerations become extremely critical for privately owned dams. These independent

dam owners often do not possess the necessary capital to remediate aging dams to

meet current safety standards.


A recent newspaper article for the Roanoke Times exemplifies the dilemma

facing private dam owners. The article is about the Rainbow Forest Lake in Roanoke,

Virginia that is owned by a private home owners� association. The reservoir dam has

existed safely for over 45 years, included during the flood of record in 1985. However,

the dam does not meet the emergency spillway requirement of passing 75% of the PMF

for its size classification. The home owner�s association, with only about 100 members,

is faced with a few courses of actions. The cheapest option, at $41,000, is draining the

lake which would significantly impact the appeal of the lakeside property. A full

remediation project of the emergency spillway is estimated to cost $178,400. Even with

the complete remediation, there is not a guarantee that future changes will not be

needed based upon the continually changing hydrologic conditions in the watershed.

(Poindexter, 2005)

In order to proceed with dam rehabilitation analysis, dam owners perform a

detailed incremental hazard evaluation of the dam. This evaluation quantifies the risks

involved with courses of actions, as well as assesses the economic impacts of the same

courses of actions. A general framework for a procedure to complete this analysis could

greatly benefit the dam owners. Such a framework would demonstrate to the owners

methods to complete the incremental risk analysis. This general framework is the

overall focus for this thesis.

1.2 Statement of Objectives

With the background problem explained, there are two main objectives that

guided this work: 1. Develop a standard protocol to assist dam owners in performing decision

analysis for dam rehabilitation for dams that are out of safety compliance.

2. Develop a method to prioritize courses of actions for dam remediation.


The desired standard protocol is a needed framework for dam owners to implement in

completing dam rehabilitation analysis. The second objective is to demonstrate different

methods of performing the economic risk analysis in evaluation of the rehabilitation

courses of actions.

1.3 General Framework Description

The analysis process from a general framework perspective is not intricate by

nature. The problem(s) is defined to include an area of interest with existing structures.

In this case, an aging dam(s) is not in compliance with existing Dam Safety regulations,

is in need of repairs or rehabilitation, or possibly has exceeded the original project

design life. Either way, the initial step in the process is to perform hydrology & hydraulic

(H&H) analysis in order to represent the past, current, and future conditions of the

dam(s) in question. Potential remediation courses of actions are then considered and

monetary amounts of project benefits and costs are calculated.

Using the project benefits and costs from the H&H analysis, economic analysis is

then performed in an iterative manner to rank the courses of actions, and thus allow for a

decision to be made. The Economic analysis may lead to infeasible situations in which

the course of action must be changed, and the H&H analysis redone. Eventually, the

desired end state is achieved, and a decision for future work is made. What is a simple

description of the process requires complicated approaches, techniques, and

assumptions to reach the desired end-state of a recommended course of action to solve

the problem. The process is also time consuming and rigorous due to the complexity in

attempting to replicate real world conditions.


1.4 Introduction to South River Watershed

To demonstrate the complexity of the analysis process, a case study watershed

of the headwaters portion of the South River in Augusta County, Virginia was selected

as the case study watershed of interest for this thesis. Within the South River

Watershed (SRW), the Headwaters Soil & Water Conservation District (HSWCD)

maintains 12 existing agricultural flood control dams. All but two of the dams were built

in the 1950s, and therefore are candidates for rehabilitation. The dams are primarily

used for flood control purposes and benefit the local town of Waynesboro, VA and its

surrounding areas (See Figure 1.1) The 12 dams were originally planned, funded, and

constructed by the former Soil Conservation Service (SCS), now the National Resources

Conservation Service (NRCS), under the 1954 Watershed Protection and Flood

Prevention Act (Public Law 83-566, 1954). As will be further detailed, a simulation

model for the entire watershed was initially created to assess the impacts of the 12 dams

on the city of Waynesboro. Later work narrowed the focus onto three of the dams

currently being considered for dam rehabilitation through the NRCS.

1.5 Outline

This thesis is organized into six remaining chapters. The next chapter is a review

of related works and relevant references for this thesis. The initial step for completing

the incremental risk analysis is the hydrology and hydraulic analysis in order to represent

the watershed of interest. Incremental risk analysis is defined as the difference in

impacts incurred from any changes that are made, and the current condition of the

hydraulic structure (Interagency Committee on Dam Safety (ICDS), 2004b). The H&H

analysis preformed for the South River Watershed is presented in Chapter 3. The H&H

analysis must be linked to Economic Analysis in order to arrive at

Cha

pter

1: I

ntro

duct

ion

5


recommended courses of action. Chapter 4 provides a discussion of traditional

economic analysis techniques, and a review of the NRCS�s recently completed analysis

within the South River watershed. With today�s continual advancement in Geographic

Information Systems (GIS) software and GIS data, new analysis should incorporate the

available information to assist with the rehabilitation analysis. Chapter 5 presents a

discussion of potential uses of existing GIS software tools, and focuses in on evaluating

the Federal Emergency Management Agency�s (FEMA) risk mitigation software HAZUS-

MH. Incorporating data from Chapter�s 3 and 4, Chapter 6 discusses Linear

Programming techniques as an optimization decision making tool. Finally, closing

remarks and conclusions are summarized in Chapter 7.

Chapter 2: Related Works 7

Chapter 2: Related Works

The topic of dam rehabilitation assessment and analysis encompasses several

different functional areas that are necessary to achieve a complete representation of the

hydraulic structures of interest. There are different facets that must be accounted for

while executing a decision making process for dam rehabilitation. A major factor in this

regard is dam safety as it pertains to the protection of the general public. There are also

several different guideline documents at different levels of government, like Federal

government regulations vs. State regulations for dam construction. The purpose of this

chapter is to summarize these important sources of information.

We begin with the topic of dam safety, which is an important part of dam

rehabilitation. As part of the decision making process of dam rehabilitation, risk analysis

becomes the next area of emphasis for information. Following after this topic, is the

concept of the probable maximum flood (PMF) which is a critical design metric for dam

safety. Next we present the mathematical optimization technique of linear programming.

We briefly comment on the rehabilitation material like roller compacted concrete (RCC).

Finally, we conclude with some key information sources provided for the South River

watershed.

2.1 Dam Safety

As mentioned in the Introduction, a current assessment of the problem the

American Society�s of Civil Engineer�s Infrastructure released in March of 2005

highlights the need for rehabilitation of thousands of dams across the United States

(ASCE, 2005). Additionally, the issue faced by private dam owners is demonstrated by

the news article published in the Roanoke Times in January 2005 (Poindexter, 2005).

Finally, a vivid reminder of the importance of dam safety is demonstrated by the


catastrophic failure of the Taum Sauk Hydroelectric Plant�s Reservoir in Lesterville, MO

on December 13, 2005 (Frankel and Rowden, 2005). This horrific event sent a 10 ft high

wall of water through a nearby camp ground that was (fortunately) occupied only by the

Park Ranger�s family, all of whom were rescued safely. (See Figure 2.1)

Figure 2.1: Taum Sauk Reservoir Breach; �Reprinted with permission of the St. Louis Post-Dispatch, copyright 2005.� Graphic from the news article: �Swept away, rescued more than a billion gallons of water��, December 15, 2005, Todd C. Frankel and Tim Rowden�

John Peterson, formally of the U.S. Dept. of Agricultural, presented a paper

during the 2004 International Conference on Geosynthetics and Geoenvironmental

Engineering (Bombay, India), that included a good historical background for flood control

legislation in the United States (Peterson, 2004). Interestingly, he authored the Public


Law Statue 106-472 (PL 114, 2000) in 2000 that allowed for federal money to be used to

rehabilitate dams that were built by the Soil Conservation Service (now the National

Resources Conservation Service). This public law does not help all of the dam owners

in Virginia of course, but the dams in the South River Watershed actually are impacted

by this public law. Peterson also references the U.S. Bureau of Reclamation�s (BUREC)

Risk Based Profiling System in his paper as a systematic approach to prioritizing efforts

for rehabilitation.

The current Federal Government guidance for Dam Classification is Technical

Report 333 by FEMA (ICDS, 2004b). Originally, published in 1998 and updated in 2004,

the report states that all dams should be classified into one of three categories: High,

Significant, or Low hazard. To eliminate the gray area between High and Significant

classifications, dams are classified as High if one loss of life is probable from a dam

failure. A companion document also published during the same time is Technical Report

94 by FEMA (ICDS, 2004a). FEMA 94 gives in-depth details on how to select the Inflow

Design Floods through the incremental hazard evaluation process. Both of these FEMA

documents along with three other documents on Dam Safety were direct products of the

National Dam Safety Program Act of 1996.

The original overarching dam safety guidance traces back to the research

completed in the late 1970s and early 1980s as a result of President Carter�s influence

and concern for Dam Safety. The first publication from the National Research Council�s

Committee on the Safety of Existing Dams was published in 1983 (NRC, 1983). The

committee recognized the need to perform risk-based decisional analysis because of the

limited capital always available for rehabilitation. The described risk analysis is not only

technically based, but also must be economics-based. The second publication is the

National Research Council�s 1985 publication on the Safety of Dams (NRC, 1985). This

book includes an entire chapter on how to perform Risk Analysis while designing a dam.


Also, the committee acknowledged risk-based decisions were not commonly used prior

to 1985, but recognized the value of performing these types of analyses.

2.2 Risk Analysis

The United States Society on Dams (USSD) recognized the important aspects of

performing risk analysis. In 2003, the USSD published a discussion white paper: �Dam

Safety Risk Assessment: What Is It? Who�s Using It and Why? Where Should We Be

Going With It?� The purpose was to provide some uniform guidance for dam owners.

As previously mentioned, the BUREC published an updated Risk Based Profiling

System (RBPS) in 2001 (Cyganiewicz and et al., 2005). This systematic approach

allows for a rapid assessment of a particular dam in order to set remediation priorities

amongst multiple dams. The approach solves the following equation:

Risk = (Probability of Load)(Probability of Adverse Action)(Consequences).

Each parameter is evaluated and assigned points based upon a 1000 point maximum.

This assessment is particularly useful when management of limited funds is critical to

maximize the benefits of committed capital. The assessment is rapid in that a field

engineer can complete the assessment in a one to two day time period. The RBPS

incorporates the BUREC standard for estimating loss of Life (Graham, 1999). This

standard makes an assessment of the Population at Risk (PAR) given a certain warning

time of the emergency, and the population residing in the particular flood plain.

A comprehensive examination of estimating loss of life was completed by Duane

McClelland and David Bowles from the Institute of Dam Safety Risk Management, Utah

State University. The final paper was prepared for the Institute for Water Resources, of

the USACE (Bowles and McClelland, 2002). McClelland and Bowles reviewed the

current practices for estimating loss of life. They began with Brown and Graham�s work

at the Bureau of Reclamation in the early 1980s. Their research became the BUREC


standard. Brown and Graham performed regressions on known dam failures to create

general equations for estimating PAR. McClelland expanded upon Brown and Graham�s

pioneering work (Dekay and McClelland, 1991). They included a few additional dam

failures that Brown and Graham omitted to generate two additional equations for dam

situations where the watershed is within a steep valley.

McClelland and Bowles additionally reviewed a more recent approach used by

the completed by BC Hydro (B. A. and H. BAI, 2001) that attempts to go beyond

statistical regressions for estimating Loss of Life. They�ve created a model based upon

probabilities that a person in a particular area will survive the flood wave from a dam

break. The model is more complex in that the warning time is combined with flood wave

routing, and probability rules are applied to each individual population. This method is

still being developed by BC Hydro, but the potential to provide a more accurate model

beyond derived equations is encouraging.

The first major approach to risk analysis was provided by a committee organized

by the American Society of Civil Engineers (ASCE Task Committee, 1988). This task

force�s primary goal was to evaluate and provide a uniform way to select of selecting the

safety design flood. This committee was formed in response to the risk analysis

approaches presented by the National Research Council�s published work in the 1983

and 1985 on Dam Safety. The ASCE report did provide a thorough approach to risk

analysis, but provided dam owners with a good reference guide for future design work.

2.3 Probable Maximum Floods

The first three references involving the Probable Maximum Flood (PMF) argue

against the validity and purpose of the PMF being used as the design criteria for dams.

Lave et al. (1990b) argue the extremely low probability of the PMF being exceeded and

causing economic damages is not worth the construction costs of retrofitting an existing


dam. A companion article, also by Lave et al. (1990a), provided a case study

rehabilitation project of a dam. Lave et al. described how for the case study dam the

emergency spillway was never used in 25 years of operation. Yet to meet the current

PMF required standard, the dam was modified. The large rehabilitation costs only

yielded small economic benefits.

A follow up to Lave et al. (1990b) culminated with a discussion paper published

by Graham (2000) that proposes a procedure for evaluating dam modifications. Graham

(2000) recognized that economic analysis must be performed. Fundamentally, this

analysis should answer the following question: Is spending construction costs going to

be exceeded by the benefits gained? This is typically not an easy issue to address as

the value of human life must be estimated. Graham (2000) also argues that meeting the

PMF design standard is not always the best course of action of many dam projects.

However, this discussion paper provides a logical mathematical framework that can be

used as a basis for completing the economic analysis of a water resources project.

Harrison (2000) and (2003) demonstrated that PMPs and PMFs do happen in the

United States. There are five storms in the Mid-Atlantic region where for a 10 square

mile area, 75% of the calculated PMP was observed (Figure 2.2). For one 12 hour

storm in Smethport, PA, the PMP was exceeded by 19% (Harrison, 2000). It is also

showed that calculated PMFs for Northern Appalachian, Central Appalachian, and South

Central Texas regions are observed frequently (Harrison, 2003).


Figure 2.2: Extreme 12 hour Historical Storms in U.S.

2.4 Linear Programming

Linear programming is a solution technique for problems that involve multiple

courses of action that are in competition for limited resources. A goal that is usually

desired is to maximize profits or minimize production costs. Within the confines of the

problem, the limited resources translate to constraints that must be addressed within the

linear program. Through formulation of a linear program an �optimal� solution can be

found by solving mathematical equations to achieve the desired goal.

Null and Lund (2005) describes how optimization linear programming was used

to justify the decommissioning of a reservoir for the Hetch Hetchy water supply system in

the Yosemite National Park. The course of action to remove the dam was proven not to


have an impact on the water supply system�s ability to meet future year 2100 city

demands. The author�s method of justification for dam removal may prove to be useful

for certain situations.

Lund (2002) is focused on Risk-based Optimization with Floodplain Planning

(Lund, 2002). The author approaches the long standing issue of integrating economical

issues with permanent and emergency flood control options. A two part general linear

program is formulated that allows for the permanent and emergency courses of actions.

This general linear program must then be applied to a given situation by creating the

constraints.

Finally the textbook, �Operations Research: Principles and Practices� provides

the background mathematical method of linear programming formulation (Ravindran et

al., 1987). This background contained within the textbook gives in depth instruction on

developing linear programs and integer programs for the purpose of modeling complex

systems.

2.5 Dam Remediation Strategies

Roller Compacted Concrete (RCC) is extremely relevant for current dam

construction, regardless if it is a new project or a repair of an existing structure. All three

of the sources support the use of RCC in water resource projects because of its ease of

placement; it can be mixed on site, and the lasting physical properties of the end

product. Bass (2000) and (2003) demonstrate the usefulness of RCC. The United

States Society on Dams (USSD) also recognized the value of using RCC in dam

projects. They published a reference book on RCC, with an entire section on dam

rehabilitation (Obermeyer and Johnson, 2003).

While RCC can be used to armor the entire dam or a spillway, RCC can also be

used to raise the height of the dam which is a remediation technique. Raising the dam


can also be accomplished with mechanically stabilized soils up to 10 to 15 feet. Another

technique is constructing a parapet concrete wall on the crest of an existing dam. The

USACE Engineer Manual for design of dams states that in general the most cost

effective technique to raise a dam is the parapet wall (USACE, 2004). Figure 2.3 is an

example of a parapet wall looks like (USACE, 2004).

Figure 2.3: Parapet Wall Remediation (USACE, 2004)

Similar to armoring a spillway with RCC, another technique is to use an

articulated concrete block (ACB) mat system. The ACB requires a geotextile fabric

under layment, and typically is covered with a grass and topsoil over layment. The

middle section includes concrete blocks that are geometrically shaped in order to

interlock in a set pattern (See Figure 2.4). The entire matrix is more stable then a typical

grass lined spillway, and the construction costs can be considerably less (NRCS, 2005).


Figure 2.4: Articulated Blocks in Place on VA Tech Campus

Chapter 3: Hydrologic Model for Upper South River 17 and Application to Dam Removal Question

Chapter 3: Hydrologic Model for Upper South River and Application to Dam Removal Question

To begin a dam rehabilitation process, one must first evaluate the existing

conditions. The process begins with the physical characteristics of the dam itself, such

as the intake and outlet structures, the storage capacity behind the dam, and the

structural integrity of the dam. They all must be assessed and quantified. The

characteristics of the watersheds upstream and downstream of the hydraulic structure

must be determined. The existing intermittent creeks, streams, and main channel

reaches must be characterized by channel geometry, slope, roughness, etc. The

necessary information requirements are significant, but there is a valid end state result

from obtaining the data. That end state is a working model representing the existing

conditions within the study area of interest. Establishing the current conditions is critical

in order to perform analysis on proposed future work to fix problems occurring with a

dam in question.

There are numerous hydrologic and hydraulic simulation programs existing in

today�s industry. Many generally accepted models are products of Federal Government

Agencies, such as the U.S. Army Corps of Engineers (USACE), Bureau of Reclamation

(BUREC), and National Resources Conservation Service (NRCS), all of whom manage

numerous existing dams across the United States. The model to be discussed in this

chapter is the USACE�s Hydrologic Engineering Center � Hydrologic Modeling System

(HEC-HMS). A widely accepted simulation program, HEC-HMS is capable of

transforming a prescribed precipitation event into surface water run-off hydrographs, and

routing the corresponding river flood hydrographs through the entire watershed.

Additionally, the model simulates various hydraulic structures present within the

watershed, as well as the situation where the structures are removed.


3.1 South River Watershed

As previously stated, the South River Watershed near Waynesboro, VA is used

as a case study. There was a dual purpose for the selection of this watershed. The first

purpose fulfilled a request of the co-sponsors, the Headwaters Soil & Water

Conservation District (HSWCD) and the city of Waynesboro, that we analyze the 12

existing dams in the watershed. Their specific request was to evaluate the downstream

hydrologic impacts of the 12 dams on the city of Waynesboro during flooding events.

The second purpose narrows the area of interest to the watersheds specifically involved

with 3 of the dams currently being considered for rehabilitation. These purposes are

linked to a common interest. The demonstrated impacts of the city of Waynesboro could

lend critical public support for the proposed rehabilitation of the 3 dams.

The headwater portion of the South River (Upper South River) is comprised of a

watershed drainage area of about 126 square miles. The watershed is further divided

into 69 sub-basins raging from 0.1 to 4.6 square miles (See Figure 3.1). The 12

Agricultural Flood Protection Dams regulate only 12 sub-basins out of the 69 total, or

27% of the 126 square mile drainage area. The 12 dams were originally planned,

funded, and constructed by the former Soil Conservation Service (SCS), now the

National Resources Conservation Service (NRCS), under the 1954 Watershed

Protection and Flood Prevention Act (PL 83-566, 1954). They were all completed in the

1950s to early 1960s, and were built to a 50 year design life that is currently exceeded

on several of the dams. Under PL 83-556, the SCS was empowered to build dams to

provide flood protection for agricultural lands, and then turn over the dams to local

entities to maintain. Hence, the Headwaters Soil & Water Conservation District, along

with the City of Waynesboro, currently is responsible for most of these 12 dams. As

would be expected many of the aging dams require significant upgrades to meet current

Virginia Dam Safety Regulation standards. Also under the 2000 Watershed

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Rehabilitation Bill (PL 106-472, 2000), the 12 dams qualify for partial Federal Funding to

rehabilitate the dams, but still require 35% funding by the local entity. Therefore,

knowing the impact of the 12 dams on the greater city of Waynesboro is important to

gain the required 35% local funding (Peterson, 2004).

3.2 Required Data for Model Creation

3.2.1 Watershed Parameters

The model parameter data pertaining to current conditions was obtained from

several different sources. A logical starting point is defining the watershed parameters

for each of the 69 sub-basins comprised within the entire South River Watershed. The

state of Virginia NRCS Conservation Engineering Office provided the data for the 69

sub-basins, based upon hydrologic analysis performed in 1991 (NRCS, 2005). Table

3.1 is an excerpt for three sub-areas taken from that report:

Table 3.1: South River Watershed Data

Sub Area

Drainage Area

SCS Curve #

Initial Infiltr. T conc.

Reach Length

Elev Drop

Reach

Reach Channel

Slope (#) (Sq Mi) (#) (in) (hr) (ft) (ft) (ft/ft) 1 3.41 66 1.030 1.51 - - - 2 2.72 66 1.030 1.41 - - - 3 0.42 66 1.030 0.55 4050 48 0.012

The previous NRCS work provided drainage area, the Soil Conservation Service (SCS)

Curve Number, time of concentration, and, if applicable, the length of main channel

reach within each of the 69 sub-basins.

The drop in elevation of the main channel was obtained from two resources. The

primary resource was the major flood study of record for the South River Watershed that

was completed in 1974 (SCS, 1974). This study�s purpose was to map the flood

inundation zones within the watershed as a prelude to establishment of flood insurance


rate maps. Detailed elevations of the channel bed are presented in this study. If a reach

was not on the main channel included in the study, channel depths were extrapolated

from a topographic map. Explanation of each of the above parameters, including how to

compute the depth of initial infiltration, will be discussed in the Model Creation section.

3.2.2 Channel Properties

There are 42 reaches within the 69 sub-areas that comprise the watershed.

Some of the reaches constitute main channels of the South River and Back Creek, while

others are secondary connecting streams. The Manning�s �n� Values, representing the

characteristic roughness of the channel beds, were also obtained from the 1974 flood

study. These values are compiled by cross section on the main channels of the South

River and Back Creek. Table 3.2 is an excerpt from Table A.2 in Appendix A. Tables

A.2 and A.3 compiled all the given �n� values for which averages were obtained.

Table 3.2: South River Manning's n Values

Section Description

Main Channel

n

Left Bank

n

Right Bank

n 419 Right after Canada Run SA38 0.069 0.053 0.053 420 Before RR in SA 38 0.069 0.078 0.060

Another important channel property contained in the flood study was an example

cross section for the typical reach within the South River watershed. The basic cross

section became the template for each of the reaches within the watershed (See Figure

3.2). The cross section was adjusted two ways to better replicate the geographic

location of the reaches. The first adjustment was for the actual channel bed elevation at

the beginning of the reach from Table A.1. The second adjustment was to the width of

the main channel. The width of the main channel was changed depending on where it

fell within the watershed. For example, a reach closer to the headwaters would not be

as wide as a reach near the bottom of the watershed (See Table A.4 for section data.)


Reach #9 Cross Section

14621464146614681470147214741476

0 100 200 300

Distance (feet)

Elev

atio

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et)

Series1

Figure 3.2: Cross Section Template

3.2.3 Reservoir and Dam Properties

The 12 agricultural flood control dams must be represented in the hydrology

models. A basic understanding of the structures themselves is required in order to

explain the needed parameters to input into the simulation model. The first part of this

section details the basic components of the dams within the South River Watershed.

All of the 12 dams are earthen, ranging from heights of 25 to 91 feet (See Figure

3.3). The surface area of the normal pool for the reservoirs varies from 5 to 11 acres.

During flood events the storage capacity of the reservoirs increases to a range of 223 to

1052 acre-feet. Since all of the dams were constructed by the SCS over a 10 year

period, the dams are all similar in design. Each includes a sedimentation pool upstream

of the dam, an intake structure, a principal spillway outlet structure, and an at least one

auxiliary spillway.


Figure 3.3: Robinson Hollow Dam, Upstream Side Reservoir

All of the dams include a concrete single stage inlet tower (See Figure 3.4).

Water enters the intake tower from side inlets controlling the normal pool level for the

reservoirs. The principal spillway on all of the dams is a 24 inch diameter pipe, ranging

from 175 to 525 feet in length. The pipes run through the center of the dam to an outlet

pool. The outlet structure in most of the dams is simply the principal spillway pipe

releasing into a rip-rap lined receiving pool (See Figure 3.5).

Figure 3.4: Canada Run Inlet Structure Figure 3.5: Happy Hollow Outlet Structure

The auxiliary spillways, also called emergency spillways, are all grass lined

channel by-passes on either one side or both sides of the dam itself. The primary

purpose of these spillways is to safely pass extreme flood waves in order to protect the


dam from overtopping which could cause catastrophic structural failure. Figure 3.6

shows the design plan view for the Robinson Hollow Dam from the original design

documents. The auxiliary spillway is highlighted with hatches beside the dam.

Figure 3.6: Robinson Hollow Original Plan View

Some of the spillways are quite large as the design required a smaller depth within

the channel, but the volume of water to pass was large. To compensate for a depth

restriction, the spillway width is increased. This is shown in Figure 3.7:

Figure 3.7: Lofton Lake Auxiliary Spillway


3.2.4 Reservoir Rating Table

The key to understanding how water flows through the reservoirs begins with

quantifying the storage capacity of the reservoir. This quantification involves knowing

the geometry of the reservoir pond, and then calculating the volume of impounded water

to obtain the total capacity. Unfortunately, the volume never remains constant as the

height of water in the reservoir is always changing during a storm event. To overcome

this, a relationship is developed between the reservoir surface elevation (usually in feet

of water behind the dam) and the storage capacity (usually in acre feet) (Mays, 2001).

The second part of understanding the reservoir is the amount of discharge that

occurs from both the principal and the auxiliary spillways. The flow rate through the

spillways is a function of the geometry of the spillway, and the head difference between

headwater and tail water pools. The total head in this case is usually the elevation head

of the headwater pool, since there is rarely a tail water pool below the dam. Another

relationship can then be generated relating the reservoir surface height to the flow rate

out the spillways. Not every dam has a continuous flow rate out of the principal spillway.

In some cases the reservoirs must reach an initial height before the spillway begins to

discharge. The discharge relationship accounts for such nuances, and incorporates

different discharge rates at different reservoir elevations (Mays, 2001).

The storage capacity and discharge relationships are combined into what is

called a rating table. The common factor between the two relationships is the water

surface height of the reservoir. Rating tables can be generated if the engineering data

for the dam and the reservoir is provided. For the South River case study, the NRCS

provided the rating tables for all 12 of the dams (NRCS, 2005). The original data tables

are compiled in Table A.5.


3.2.5 Rainfall Data from IFLOWS Gages

In order to calibrate the model, rainfall data from past storm events is required.

Fortunately, there are six Integrated Flood Observing and Warning System (IFLOWS)

rain gages located within the watershed. The IFLOWS program is managed by the

National Weather Service and is meant to assist local officials in predicting floods. Five

of the IFLOWS rainfall gages are co-located on reservoirs, and the other is located near

the Canada Run Dam. The gages provide real time rainfall data at these locations, and

for the five co-located ones, the water level height in the reservoir is also monitored.

Figure 3.8 is a picture of the IFLOWS gage at the Stoney Creek Dam:

Figure 3.8: IFLOWS Gage at Stoney Creek Dam

The real time IFLOWS web-site is found at the following address:

http://www.afws.net/ . Following the map links to Virginia, and then Augusta County, the

past 24 hour data is viewable. Additionally, the historical data beginning in 2001 is

maintained in a rainfall archive. Therefore for recent rainfall events, hourly rainfall data

can be compiled into rainfall hyetographs. For model calibration, three recent storms

were used: 1. Hurricane Isabel, 18 September 2003. 2. Hurricane Jeanne, 28


September 2004. 3. Hurricane Frances, 08 September 2004. One additional storm that

occurred on November 29, 2005 was also used to confirm the model calibration. The

compiled rainfall data is shown in Table A.6 in Appendix A.

3.2.6 Surveyed High Water Marks from Recent Storms

The HSWCD provided additional key data for the above recent storms in the form

of surveyed high water marks at the reservoirs. Due to the severity of these storms,

HSWCD personnel recorded the elevations left by the debris lines in the reservoir and,

when applicable, the auxiliary spillway. The data for Hurricane Isabel proved to be most

complete, and also corresponded to the largest storm out of the four selected. The

Isabel data became important for model calibration. The Hurricane Isabel high water

mark data is included in Table A.7 of Appendix A.

3.2.7 Lyndhurst Gaging Station Stream Flows

The final link for model calibration is stream flow data for the South River.

Fortunately, like the IFLOWS rainfall gages, the watershed includes a U.S. Geological

Survey (USGS) stream gage station within the city limits of Waynesboro, VA. The

USGS tracking number for the gage is #0126000, and is called �South River Near

Waynesboro, VA.� The South River passes under the Lyndhurst Street bridge right near

the location of the gage. Consequently, the gage is also referred to as the Lyndhurst

Gaging Station. The real time data for the gage is available at the USGS web-site:

http://waterdata.usgs.gov/va/nwis/uv/?site_no=01626000&PARAmeter_cd=00065,00060,62620,00062.

The historical data is archived for the Lyndhurst Gaging Station at the Richmond

USGS office. The flow data corresponding to the selected IFLOWS storms was

obtained. The data was a time series hydrograph, in which the flow was given in cubic

feet per second. The critical information to compare was the magnitude of the peak of

the hydrograph, and the timing of the peak. The peak flow rate and timing will assist


with model calibration. Refer to Table 3.3 for the summary data, and Figure 3.9 for the

Hurricane Isabel Hydrograph.

Figure 3.9: Hurricane Isabel Hydrograph

Table 3.3: Lyndhurst GS Data

Storm Peak Q

(cfs) Time Isabel 13,800 19 0400 SEP 03

Jeanne 6460 28 1530 SEP 04 Frances 1380 08 2145 SEP 04

29-Nov-05 4720 29 1500 NOV 05


3.3 Hydrologic Model Creation

The next step following the gathering of required information was to input into the

HEC-HMS simulation program to construct the watershed model. Every HEC-HMS

model requires three separate components in order to execute a simulation: the Basin

Model, the Meteorological Model, and the Control (See Figure 3.10).

Figure 3.10: HEC-HMS Primary Menu Screen

The Control simply sets a reference date, a time period for the simulation, and the

computational time step. To be consistent with time sensitive data like the rainfall and

stream flow data, the control time periods were adjusted to reflect the true time of the

rainfall event. When design storms were used, the present time period was used for the

Control. (Scharffenburg and Felming, 2005)

The Basin Model represents the physical watershed to be modeled, and requires

the most robust data. The Meteorological Model replicates the storm event, and how the

rainfall is distributed across the watershed with respect to time. Both the Basin Model

and Meteorological Models require further explanation in the next sections.


3.3.1 Basin Model Creation

The Basin Model for the entire watershed including the reservoirs was first

generated. To begin, a new Basin Model was created within HEC-HMS. HEC-HMS

automatically brings up a working schematic pallet for editing (Figure 3.11). For this

model, only four component icons were used: the sub-basins, reaches, junctions, and

reservoirs. The sub-basins correspond to the 69 sub-areas within the entire watershed.

The reaches are the main channel streams or rivers passing through a given sub-basin.

The junctions represent starting and ending points for the reaches. As seen in Figure

3.11, multiple reaches can enter a junction or node. Junctions do not require data, and

are merely a merging point within the simulation. Once all of the icons are drawn onto

the Basin Model Screen, necessary data must be entered for the icons to correctly

replicate the watershed system.

Figure 3.11: HEC-HMS Basin Model Editing Screen

3.3.1.1 Sub-basin Icon Data

The sub-basin data from Table A.1 must be entered for each of the sub-basins.

The first part of the sub-basin data involves the amount of water that is absorbed into the

soil. In this case, the SCS Rainfall-Runoff Relation was used, based upon the known


Curve Numbers for the sub-basins. HEC-HMS requires the CN and the Initial

Abstraction (Ia) amount. Ia is found by the following equation (Mays, 2001):

Ia = 0.2 x S, where S = 1000 / CN � 10.

With the amount of run-off established from the CN, the run-off must be

transformed to a hydrograph. For this part, the SCS synthetic unit hydrograph method

was used. Synthetic hydrographs are constructed within the simulation program based

upon the Time of Concentration (Tc) parameter. The Tc represents the longest time of

travel from the ridge to outlet within the sub-basin taken by a single drop. One final part

that must be accounted for is the base flow rate within the sub-basins. Since, this is

typically only a small portion of the storm hydrographs a modest assumption of 0.5 cubic

feet per second was used for the entire watershed (Mays, 2001).

3.3.1.2 Reach Icon Data

The reaches, representing streams and river channels, are important in

transporting the sub-basin run-off down stream. The reaches replicate what the channels

do in the real world. All of the sub-basins in the model are assumed to drain to a single

point, represented by the junctions. With the exception of the 69th sub-basin, all of the

sub-basins are then routed along a reach between two junctions. The 69th sub-basin

links to the final junction of the model, but would be further routed to the next sub-basin

downstream. The HEC-HMS simulation first transforms the surface run-off to a

hydrograph at the assigned junction, and this hydrograph must be routed through the

reaches to final junction.

HEC-HMS is capable of several different methods of routing a hydrograph within

a reach. For this simulation, we chose to use the Muskingum-Cunge 8 Point method.

The Muskingum-Cunge method is a variation of the kinematic wave method which

incorporates the Muskingum method of routing (Mays, 2001). The method relies upon

derived Muskingum coefficients for each channel in order to perform the routing. The 8


Point part of the method, extrapolates the Muskingum coefficients from the known

channel cross sections in Table A.4 (See Figure 3.12).

Figure 3.12: Reach Editor Screen, Basin Model

The reach length from Table A.1 must be included for the routing. The energy

slope was assumed to be equivalent to the slope of the channel bed, also included in

Table A.1. The final information is the channel roughness characteristic represented by

average Manning�s �n� values from Tables A.2 and A.3.

3.3.1.3 Reservoir Icon Data

The key information for the reservoirs already mentioned before is the rating

table. The rating table becomes the basis for the routing of a hydrograph into the

reservoir and through the outlet structures. The HEC-HMS program performs a level

pool routing of the inflow hydrograph based upon the inputted rating table. The only

other requirement to begin the process is to establish the Normal Pool elevation of the


reservoir surface water. This is the assumed starting point for the routing (See Figure

3.13).

Figure 3.13: Reservoir Editor Screen, Basin Model

3.3.2 Weather Model Creation

The last component needed to complete a HEC-HMS simulation is the Weather

Model. Weather Models represent the precipitation event within the model. There exists

within HEC-HMS eight different methods to create a precipitation event (Scharffenburg

and Felming, 2005). For this case study, only two methods were used: 1. User

Hyetographs (actual rainfall gage data) 2. NRCS Hypothetical Storm.

3.3.2.1 User Hyetographs

For the User Hyetographs approach, the rainfall data gathered from the NOAA

IFLOWS gages was used. One rainfall gage was created for the six gages within the

watershed for each storm event. The 15 minute increment rainfall data was manually


inputted into HEC-HMS using the Precipitation Gage Manager tool. The rainfall data

was checked after the first simulation runs to confirm accuracy of the data. The

accuracy can be checked by comparing the total rainfall amount in the simulation to the

known amount in the data. Any discrepancies were adjusted when encountered.

The creation of the rainfall gages doesn�t constitute a complete Weather Model.

The second step is to create one Weather Model for the separate storm events. In

choosing the User Hyetograph method, a list of the sub-basins within the watershed is

brought up in the editor screen (See Figure 3.14). Each of the sub-basins must be

associated with a rainfall gage in order to complete a Weather Model. There are many

established techniques for rainfall distribution, such as Mean Aerial Precipitation or

Thiessen Polygons. For this case study the rainfall amounts were spatially similar (one

exception will be discussed in the Model Calibration section). Therefore, gages were

assigned to sub-basins based upon geographic proximity. Figure 3.15 shows how the

gages were assigned to the sub-basins within the storm Weather Models.

Figure 3.14: Meteorological Model Editor, HEC-HMS

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3.3.2.2 SCS Hypothetical Storm

The second approach used for the Weather Model is the NRCS Hypothetical

Storm method. This method uses the synthetic method for generating a synthetic storm

based upon a given amount of precipitation. For the South River Watershed, the Type II

hyetograph is appropriate. The rainfall depths were obtained from the National Weather

Services (NWS) NOAA Atlas 14. The NOAA Atlas 14 compiles the precipitation

frequency data for the United States. The rainfall depths for a given return period were

determined based upon the Stuart�s Draft location, located in the center of the

watershed. The rainfall depths can be downloaded from the NWS web-site:

http://hdsc.nws.noaa.gov/hdsc/pfds/index.html. Five weather models were created for the 2,

10, 50, 100, and the 500 year return periods.

3.4 Model Calibration

The finished HEC-HMS model is represented in the schematic shown in Figure

3.16. With the model complete for the case study, simulations could now be run. The

largest of the storms, Hurricane Isabel, was the first Weather Model used. As previously

mentioned, there was a problem with the Hurricane Isabel gage data. During Isabel, the

Upper Sherando IFLOWS gage registered 20 inches of rain, an extreme amount. As

shown in Table 3.4, the other gages only recorded from 6.5 to 9 inches of precipitation

during the same event.

Table 3.4: Hurricane Isabel Rainfall

IFLOWS Gages ID # Total (in)

Toms Branch 1200 6.92 Sherando 1201 8.44 Robinson Hollow 1202 7.08 Stoney Creek 1207 6.59 Upper Sherando 1240 20.12 Mills Creek 1248 9.04 Pavg 7.614

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Applying the Upper Sherando gage data to the Upper Sherando Reservoir sub-basin

yielded a flood wave peak that was over five feet higher then what was actually

observed (compared to surveyed debris lines). Additionally, when applying the same

rainfall over surrounding sub-basins, the total flow observed at the Lyndhurst Gaging

Station (Junction 42 in the model) was over 50,000 cubic feet per second (cfs). This

drastically exceeded the recorded observed peak flow by the USGS gage of 13,800 cfs.

To alleviate this issue of extreme isolated rainfall, the Upper Sherando Gage data

was ignored. The Mills Creek gage data was applied instead as shown in Figure 3.15.

The appropriate changes were made in HEC-HMS, and the simulation model was rerun

for Hurricane Isabel. The results of this run were lower, with a total flow of 28,840 cfs.

This is more reasonable, but the target flow of 13,800 was again greatly exceeded. At

this point, Hurricanes Jeanne and Frances were run to confirm any similar observations.

As shown in Table 3.5, all of the storm events were coming in higher then the observed

flows at the Lyndhurst Gaging Station, and the timing of the peaks were slightly off.

Consequently, other changes to the model were needed in order to calibrate the model.

Table 3.5: Initial Simulation Runs

Storm Actual Observed

(Target) Simulation #1 Original Data;

(No Changes)

Peak Q

(cfs) Time Peak Q

(cfs) Time %Difference Isabel 13,800 19 0400 SEP 03 28840 19 0230 SEP 03 2.09

Jeanne 6460 28 1530 SEP 04 11185 28 1530 SEP 04 1.73 Frances 1380 08 2145 SEP 04 7925 08 2045 SEP 04 5.74

Based upon the obtained data, the Curve Number (CN) was the other key model

parameter that when adjusted could lower the flow rates enough. The individual curve

numbers for the South River Watershed average to a value of 65. The entire 69 sub-

basins� CNs were lowered from the average 65 to 55, and then to 45. In comparing the

simulation results to the target flows in Table 3.5, the best matches were for the CN

average of 45, as shown in Table 3.6:


Table 3.6: Simulation Changes

Storm Simulation #2

(CN = 50; SAs above Dams Original Data) Simulation #3

(CN = 45; SAs above Dams Original Data)

Peak Q

(cfs) Time %Difference Peak Q

(cfs) Time %Difference Isabel 17185 19 0400 SEP 03 1.25 13571 19 0415 SEP 03 0.98

Jeanne 3662.7 28 1530 SEP 04 0.57 2375 28 1530 SEP 04 0.37 Frances 2994 08 2045 SEP 04 2.17 2057 08 2045 SEP 04 1.49

A NRCS Curve Number of 45 is extremely low and is not reflective of the actual

conditions. To confirm this, the land use map, in Figure 3.17, was compared with the

corresponding CN map, Figure 3.18. In Figure 3.17, the darker shaded areas represent

more urbanized terrain closer to the city of Waynesboro. The lighter shades

corresponded to the areas located within the George Washington National Forest. In

checking the NRCS-provided curve numbers in Figure 3.18, it was found that the higher

curve numbers (shown in darker shades) matched the urbanized areas of the land use

map. Therefore, without a more detailed analysis, the provided curve numbers were

assumed to be fairly representative of the real conditions.

The calibration issue remained a problem, as the model output was still not

matching the observed storms. Another potential explanation for the discrepancies is

the topic of antecedent moisture. The concept when applied verifies what the moisture

conditions were prior to the storm event. The storm conditions are segregated into three

categories: normal, extremely dry, or extremely saturated. The NRCS Curve Number

can be changed significantly based upon the antecedent moisture conditions. For the

arid situation, if there was less then 1.4 inches of rain observed 5 days prior to the storm

event during the growing season, then a CN of 65 could be lowered to 45 (McCuen,

2005). In checking the storms, Hurricanes Isabel and Jeanne met this criterion. The

observed antecedent moisture for the storms was less them 1.4 inches of rain, thus

justifying the lowering of the CN from 65 to 45.

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The determination of the antecedent moisture conditions left some doubt to

which average SCS CN should be used for the model. To confirm the model calibration

a different way, design storms were used. The simulated discharges Q2, Q10, Q25,

Q100, and Q500 at the model Lyndhurst gaging station were obtained for the average

CNs 55, 60, and 65. The Q2, Q10, Q25, Q100, Q500 were also computed by statistical

flood frequency analysis, based on Log-Pearson Type III distribution and the USGS

historical records for the gaging station. In comparing the simulated with the observed

data, it was found that the simulation results for the average CN of 65 was the best fit

(See Table 3.7).

A final check of the model used an average CN of 65. Rainfall data from a recent

intense storm on November 29, 2005 was used. The model produced a peak flow of

5869 cfs at the Lyndhurst gaging station. Since the storm took place in November, the

dormant season, the antecedent moisture criterion is more stringent at less then 0.5 inch

to meet arid conditions. None of the rainfall gage data met this criterion, so the average

CN of 65 was assumed to be valid. An actual observation by a USGS observer on the

afternoon of the 29th of November, converts to a discharge value of 4720 cfs. The real

time data for the gage continued upwards to a peak of 6600 cfs observed on the USGS

web-site (Figure 3.18). However, this peak was readjusted later by the USGS, to the

lower value of 4720 cfs. In comparison to either value, the model produced a

Table 3.7: Calibration Results Return CN = 55 CN = 60 CN = 65 Historical Period Q (cfs) Q (cfs) Q (cfs) Q (cfs)

Q2 1057 1834 2651 2770 Q10 4182 6063 8077 9568 Q50 11111 14789 18879 21902 Q100 15703 20600 25653 29777 Q500 31942 39145 46847 56810


reasonable intermediate estimate of 5869 cfs. Thus the model was considered to be

calibrated sufficiently for purposes of this study.

Figure 3.19: Real Time Data from USGS on 29 NOV 05 Storm

3.5 Simulating the Results of Dam Removal

Reiterating the first purpose for creating the model, it is intended to demonstrate

the impacts of the 12 agricultural dams on the watershed. With the difficult part of

validating the simulation model finished, replicating the pre-structure conditions in HEC-

HMS is much simpler. To establish the pre-structure conditions, the reservoir icons in

the HEC-HMS are removed from the simulation. In a sense, they are taken �off-line�,

and do not impact the hydrologic calculations in a simulation run. The HEC-HMS model

now represents the watershed as if the dams were not present. The difference between


the pre-structure and post-structure discharge rates quantifies the impacts the dams

have on the watershed.

The design storms used to calibrate the model at an average CN value of 65

were used again on the �dams not present� model. Discharge rates were recorded from

the simulation runs for the Q2, Q10, Q25, Q100, and Q500 storm events. In order to

fully assess the impacts of the dams it was necessary to first examine the local area

impacts in the immediate vicinity of the dams. Then flow rates at key junctions along the

downstream reaches were selected in order to allow for a tracking of the diminishing

impacts. Finally, the combined impacts of all 12 agricultural dams were determined at

the Lyndhurst gaging station. All of the simulation output data for average CNs 55, 60,

and 65, for both pre- and post-structure conditions, is presented in Appendix B.

To examine the impacts of the dams the Q2 and Q100 storm events are used to

show the impacts of storms that occur frequently (on average every 2 years), and storms

that occur rarely (on average every 100 years). Figures 3.20 and 3.21 show a side by

side comparison at each of the dams for the Q2 and Q100 storm events. The

comparisons show the dams significantly reduce the flow rates below what would occur

if the dams were not present. Also, the reduction becomes more significant in the

extreme events as the dams reach their full design storage capacity.

Q2 Comparison; CN = 65

050

100150200250300350400

Dams

Q (c

fs) Q2 w Dams

Q2 w/o Dams% Reduction

83% 81%81%

78%

71%87%

58%79%65%

85%82%

74%

Poor C

reek

Lofto

nLak

eSt

oney

Cr.W

ilda La

keCan

ada R

unW

ayne

s Nurs

Up She

rand

oTo

ms Br.

Mills C

r.Hap

py H

ollow

Rob. H

ollow

Inch

Br.


050

100150200250300350400

Dams

Q (c

fs) Q2 w Dams

Q2 w/o Dams% Reduction

83% 81%81%

78%

71%87%

58%79%65%

85%82%

74%

Poor C

reek

Lofto

nLak

eSt

oney

Cr.W

ilda La

keCan

ada R

unW

ayne

s Nurs

Up She

rand

oTo

ms Br.

Mills C

r.Hap

py H

ollow

Rob. H

ollow

Inch

Br.

Figure 3.20: Q2 Side by Side Comparison at Dam Sites



0500

100015002000250030003500

Dams

Q (c

fs) Q100 w Dams

Q100 w/o Dams

% Reduction

97%97%

97%

95%82%

95%92%

98%

97%97%95%

96%Po

or C

reek

Lofto

nLak

eSt

oney

Cr.W

ilda La

keCan

ada R

unW

ayne

s Nurs

Up She

rand

oTo

ms Br.

Mills C

r.Hap

py H

ollow

Rob. H

ollow

Inch B

r.


0500

100015002000250030003500

Dams

Q (c

fs) Q100 w Dams

Q100 w/o Dams

% Reduction

97%97%

97%

95%82%

95%92%

98%

97%97%95%

96%Po

or C

reek

Lofto

nLak

eSt

oney

Cr.W

ilda La

keCan

ada R

unW

ayne

s Nurs

Up She

rand

oTo

ms Br.

Mills C

r.Hap

py H

ollow

Rob. H

ollow

Inch B

r.

Figure 3.21: Q100 Side by Side Comparison at Dam Sites

In tracking the flow rates moving down stream from the dams, the effect of the

dams diminishes. The reduction percentage decreases as discharge flow moves toward

the Lyndhurst gaging station at the bottom of the watershed. This is directly related to

the increasing flows from the unregulated sub-basins (no dams in the sub-basin) that

merge with the outlet streams from the dams. As shown in Figure 3.1 and stated

previously, only 27% of the entire watershed is regulated by the 12 dams. Figure 3.22

shows how the discharge reduction decreases while moving down stream. The

reductions are represented by circles that are graduated by size, thus a smaller circle

represents smaller reductions.

The final focus is at the Lyndhurst gaging station, which is the officially recognized

site for the city of Waynesboro flood warnings system. Flood stages in Figure 3.23 were

obtained by applying the USGS rating at the Lyndhurst gaging station to the modeled

Q2, Q10, Q50, Q100, and Q500, with the average CN of 65. The highest observed

floods in 1969 and 1985, produced a gage height of 15.3 feet in 1969 and 1985. Based

upon Figure 3.23, these two storms would occur on average about every 40 years.


Gage Height Comparison at Lyndhurst Gaging Station; CN = 65

0

5

10

15

20

25

30

35

40

45

50

2 10 50 100

500

Flooding Return Period

Gag

e H

eigh

t (ft)

Gage Height w Dams

Gage Height w/o Dams

Jeanne, SEP 04

Frances, SEP 04

29 NOV 05

Flood Stage 9.5'

Isabel, SEP 03

Major Flood 13'05 NOV 85

Figure 3.23: Gage Height Comparison


The recent hurricane storm events highlighted in Figure 3.23 (Isabel, Jeanne,

Frances) are intended to show the impacts of the existing dams during actual storms.

Hurricane Isabel produced an observed high water mark of 13.6 feet at the Lyndhurst

Gaging Station, corresponding to a return period of about 30 years. If the dams were not

present this high water mark would have been about 16.5 feet, corresponding to a 50-

year flood with the dams in place, as indicated in Figure 3.23. In other words, the same

flood that used to occur on average every 30 years without the dams now can be

expected to occur on average just once every 50 years.

We can look at the 100-year flood in a similar way. From Figure 3.23, one sees

that the simulated 100 year flood peak �with dams� occurs at a gage height of

approximately 22 feet. Transferring this gage height horizontally to the upper �without

dams� curve, a gage height of 22 feet would occur on average every 50 years. Thus,

the effect of the dams is to reduce what used to be the 100 year flood stage (before

dams) back to the 50 year flood stage.

3.6 Summary

After the first purpose of creating the HEC-HMS model was accomplished, the

impacts of the 12 dams were demonstrated. The 12 dams in the upper South River

watershed effectively reduce flood events in areas located immediately below the dam

structures. The results coincides with the original NRCS/SCS purpose of providing flood

protection for agricultural lands. The flood reduction benefit of the 12 dams diminishes

as we move downstream approaching Waynesboro. However, the dams do provide a

significant flood reduction at Lyndhurst gaging station that undoubtedly extends well into

the city limits. This flood reduction is above and beyond the primary purpose of the

dams as planned for by the SCS in the 1950s.


The completion of the simulation model also fulfills the second purpose of

performing smaller scaled analysis on three out of the 12 dams: Toms Branch, Inch

Branch, and Robinson Hollow Dams. If only these three dams were to be considered,

the HEC-HMS model could have been significantly scaled back to replicate only the sub-

basins impacted by these dams. The purpose of the model would remain unchanged,

as the impacts of the dams would still need to be shown. However, as will be shown in

the next chapter, any proposed structural changes to the dams must be incorporated

into the simulation model of the entire watershed to show the hydrologic impacts of

making the dam improvements.

Chapter 4: Traditional Economic Analysis of Dam Rehabilitation 49 by Flood Damage Curve Integration

Chapter 4: Traditional Economic Analysis of Dam Rehabilitation by Flood Damage Curve Integration

The significant problems with the current inventory of dams in the United States

were highlighted in Chapter 1. Consequently due to the large number of remediation

projects needed, it can be assumed that projects are being considered for remediation

because of their failure to meet the appropriate dam safety regulation. Because funding

is always a constraint, remediation courses of action must be analyzed economically.

Unlike proposed new water projects, the course of action to �do nothing� is really not an

option. The existing hydraulic structure is known to be out of compliance with

established safety regulations, and it is probable that a controlled breach would have to

be completed by the owner. As a result, the �do nothing� option will have associated

construction costs in order to complete the breach which must be considered during the

economic analysis.

This chapter will begin with a general description of an economic framework used

to assess water projects. A step-by-step description of an economic process will follow

the general description intending to be used as reference tool for future work. The

NRCS�s proposed remediation projects for the Toms Branch, Inch Branch, and Robinson

Hollow Dams requires a discussion of the Federal Government�s water project planning

document Principles & Guidelines (P&G). This will lead to an explanation of the NRCS�s

technique for economic analysis. The chapter will conclude with a summary of the

economic analysis process.

4.1 General Approach to Economic Analysis

Water projects, especially those that are publicly funded, require economic

analysis of the benefits and costs. Since the projects already exist, economic analysis


may have been done previously. A conventional approach to analyze proposed courses

of action is by means of the benefit-cost ratio and its variations. For water projects,

benefits are measured in flood damages avoided annually as a result of the presence of

the project. This shows the importance of knowing the hydrologic impacts of the dams.

In the South River case study for the flood of record, damages for the �with� and

�without� dams can be established. The net difference between these two conditions is

a net benefit of flood damages avoided (Franzini et al., 1964).

The magnitude of damages avoided changes with the magnitude of the resulting

flood wave from a given storm. Lower probability of occurrence storm events (low risk)

produce higher flood damages, but occur infrequently. Typically, a proposed water

project is intended to meet a certain level of protection, like avoiding damages from the

100 year flood. However, the damages for each return period like Q2, Q10, Q25, Q50,

Q100, and Q500 are determined for each course of action. The flood damage in dollars

is then plotted versus the exceedence probability for the desired course of action and the

�no project� case. The economic benefit is then equal to the area between the two

curves as shown in Figure 4.1 (Franzini et al., 1964).

Damage - Frequency Curves

0

10

20

30

40

50

60

0 50 100

Probability of Exceedence

Dam

age

($10

00)

Natural FlowRegulated Flow

Damages Avoided

Damage - Frequency Curves

0

10

20

30

40

50

60

0 50 100

Probability of Exceedence

Dam

age

($10

00)

Natural FlowRegulated Flow

Damages Avoided

Figure 4.1: Example Economic Benefit Determination


Determining the flood damages within a watershed is not a simple task. The

flood damages are inherently linked to the flood inundation area resulting from the

routed flood wave. A certain magnitude storm, like the 25 year storm, produces a Q25

flood wave that floods a certain area. To determine the area impacted, hydraulic

simulation programs, like USACE�s HEC-River Analysis System (HEC-RAS) are used to

calculate the water surface profile of the resulting flood wave at known cross sections in

the flood plain. The cross sections are linked to the topography of the river in question,

and the end results are inundation zones for each return period. The final step is to

inventory the existing infrastructure in the inundation area like residential homes,

commercial buildings, highways, bridges, or any other item that might get damaged by

flooding. The extent of monetary damage is usually measured as a function of depth of

inundation. This in turn is usually assessed by established damage curves (like FEMA�s

or USACE�s). For example if a structure is flooded by five feet on the main floor, then

the assigned damage might be 50% of assessed property value (Mays, 2001).

Establishing the infrastructure inventory that is impacted by flooding is no simple

task. The required time and effort is extensive as detailed on-site surveys must be

conducted to establish high water marks from flood waves. The process of gathering the

necessary tax parcel information has improved with the availability of GIS databases, but

this is a function of the local government�s efforts. There are guidelines that are

followed, but the assessment of damages is certainly more an �art� rather than pure

science. For example, trying to predict a local gas station�s loss of business based upon

the 25 year flood as opposed to the 100 year flood is not a black and white calculation.

Creating feasible courses of actions will be iterative in nature. Infeasible courses

of actions can be eliminated, most likely by a simple cost comparison. For example, one

course of action could be to replace the entire dam which would undoubtedly be more

expensive than attempting to remediate the existing dam. For this chapter we assume


that the best remediation courses of actions were created, and the hydrology and

hydraulic models were completed to reflect the flooding changes caused by the courses

of actions. This leads to an annual sum of damages (flood damages will be reduced, but

not completely eliminated in all projects) and project costs for each course of action.

Likewise, the annual benefits (primarily flood damages avoided) can be summed for

each course of action. Benefit-cost ratios can now be calculated for comparison.

It must be noted that the benefit-cost ratios are not the only indicator that should

be used. An incremental approach can establishes better indicators of which course of

action would be best. The courses of action are placed in increasing order by annual

benefits. Beginning with the course of action that had the lowest benefits, it is compared

to the next course of action. Net change in benefits between the two courses of action is

computed, along with the net change in costs. The following ratio is then computed:

∆ Benefits / ∆ Costs see if ratio is > one.

If the ratio is greater then one, the second course of action is worth the change in

benefits at the set change in costs. This completes one increment of the analysis, and

the analysis continues until one course of action yields a ratio that is less then one. At

this point the second course of action is not worth doing because a dollar of benefit is at

expense of more then a dollar of cost (Franzini, et al, 1964).

Table 4.1 presents out an example of incremental analysis based upon five

possible courses of action. If one were to strictly use the benefit-cost ratio, course of

action II would produce the greatest ratio at 1.35. However, course of action III actually

provides a change in benefits-cost ratio of 1.25 when compared incrementally with

course of action II. Course of action IV only provides a change in benefits-ratio of 0.33,

and therefore should not be selected over course of action III. This demonstrates the

importance of using incremental economic analysis for comparison of the course of

actions (Franzini, et al, 1964).


Table 4.1: Example Economic Analysis

Courses of

Actions

Annual

Benefits

Annual

Costs

Benefit-

Cost ∆ Benefits ∆Costs ∆ B / ∆ C

(#) ($) ($) (Ratio) ($) ($) (Ratio)

I 150,000 128,104 1.17

60,000 27,944 2.15

II 210,000 156,048 1.35

65,000 52,016 1.25

III 275,000 208,064 1.32

25,000 76,088 0.33

IV 300,000 284,152 1.06

40,000 52,006 0.77

V 340,000 336,158 1.01

4.2 Specific Steps to an Economic Analysis

The following section is intended to layout a step by step process to be used as a

guideline for completing economic analysis for a dam remediation project. The steps are

numbered with additional comments in bullet format. A summary flow chart is shown at

the end of the section (See Figure 4.2).

1. Identify a dam, and the need for remediation of some sort.

2. Establish remediation courses of action, and associated costs. (Iterative process)

• Consider the �controlled breach� course of action for dam remediation.

• Narrow down unrealistic solutions like replacing the entire dam.

3. Establish area of interest.

• Include all relevant watersheds and flooding areas are directly impacted by the

dam. (Chapter 3 analysis)

• Begin with FEMA�s 100 and 500 year flood studies as a starting point.


4. Generate water surface elevations for the downstream flood waves for each course

of action.

• Complete hydrology and hydraulic calculations, and use accepted simulation

models.

• Transfer water surface profiles to flood inundation maps to determine depth of

flooding at impacted properties.

5. Gather economic data for area of interest.

• Gather tax parcel data for any property that might be impacted by flooding.

Includes property value and structures value. Must adjust to current market value.

• Identify any infrastructure like roads, bridges, retaining walls that might be

impacted by flooding. Obtain construction and replacement costs.

• Identify any commercial property that might be impacted. Estimate potential

business loss per day from closures. Identify structure and property costs.

• Determine if any recreational activities that occur within the area of interest.

Estimate daily value for such activities.

• Acquire census income data to establish income lost by population impacted.

6. Field survey at known junctions the high water bench marks from hydrologic and

hydraulic simulation results.

• Establish the flood inundation zone through bench marks.

7. Survey all structures in flood inundation areas, and establish high water marks.

• Determine the elevation of the point of entry, and establish at what elevation water

enters into the structure.

• Identify structures structure that have basements, as less damage might occur if

the main level is not necessarily flooded first.


8. Sum up all accounted for damages for each course of action, for each level of

flooding Q2, Q25, Q50, Q100, Q500, etc.

• Include property damages and clean up costs. Adopt structural damage

assessment technique such as based upon �x� water level in the structure�s 1st floor, �x�

percent damage of structure value is incurred. (direct damages)

• Include any revenue lost from businesses. (indirect damages)

• Include loss in property value if the course of action removes a reservoir, if

applicable. (intangible damages)

• Include losing recreational value lost by removing reservoir, if applicable.

• Add detour costs to commuters, if flooding results in closure of main traffic roads.

(secondary damages)

9. Construct Damage Frequency Curves for each course of action. (See Figure 4.1)

10. Compute Average Annual Damages from the Damage Frequency Curves.

• Use integration approximations like trapezoidal rule to determine area under the

curves.

11. Establish damages avoided for remediation courses of actions.

• Subtract course of action damages from the status quo.

12. Conduct incremental analysis for the courses of actions.

• Compute ∆ Benefits / ∆ Costs ratio or other equivalent metric.

• Evaluate and rank courses of action based upon calculated decision metric, like

∆ Benefits / ∆ Costs.


Identify Remediation Problem1.

Establish Courses of Action2.

Establish Flood Area of Interest3.

Create Flood Water Surface Profiles4.

Gather Economic

Data5.

Establish High WaterMarks on

Cross Sections6.

Survey 1st FloorElevations for

Structures7.

Sum Damages for Return Periods8.

Construct Damage Freq. Curves9.

Compute Average Annual Damages10.

Compute Damages Avoided11.

Complete Incremental Analysis12.

Identify Remediation Problem1.

Establish Courses of Action2.

Establish Flood Area of Interest3.

Create Flood Water Surface Profiles4.

Gather Economic

Data5.

Establish High WaterMarks on

Cross Sections6.

Survey 1st FloorElevations for

Structures7.

Sum Damages for Return Periods8.

Construct Damage Freq. Curves9.

Compute Average Annual Damages10.

Compute Damages Avoided11.

Complete Incremental Analysis12.

Figure 4.2: Economic Analysis Flow Chart

Referring to Figure 4.2, the first four steps entail engineering design work, cost

estimating, and hydrologic simulation analysis. The middle steps (Steps 5-7) can be

completed simultaneously, and are usually the most time consuming. Detail surveying

and gathering economic information is resource and time intensive. The remaining

steps are the steps to complete the economic analysis. The end state of the process is

a rank order of recommended courses of action.


4.3 Federal Planning Guidance

The case study includes the NRCS�s planning for the three case study dams.

Since the NRCS is a part of the federal Department of Agriculture, the NRCS must follow

the federal planning guidelines for water resources projects. The guideline document

was published in 1983, and is called �The Economic and Environmental Principles and

Guidelines for Water and Related Land Resources Implementation Studies (P&G).� The

NRCS completed the economic analysis for the case study watershed following the P&G

planning guidance.

The P&G planning guidance provides a framework for federal agencies to follow.

All analysis is placed into four categories or �accounts.� The first two are more

economically focused being the national economic development (NED) and the regional

economic development (RED) accounts. The other two accounts include the

environmental quality (EQ) and the other social effects (OSE). The NRCS performed

the economic analysis while adhering to the P&G standard. For the case study the RED

analysis equaled the NED analysis since the case study is a localized project, and really

does not have impact at the national level (WRC, 1983).

NRCS economic analysis was clearly guided by the P&G document in two areas

of emphasis. The first area is computation and assignment of recreational value

associated with the courses of action. The P&G gives step by step instructions on how

to assess recreational benefits from a water resources project. The second area is the

break down of costs between what the federal agency can fund, and what must be

funded by the local entity. The NRCS uses a standard spreadsheet file that breaks

down the costs for each course of action, and further breaks down the cost allocations.

This streamlines the process for the NRCS and ensures the P&G regulation is followed

(Faulkner, 2006).


4.4 Case Study Economic Analysis

This section details the NRCS�s economic analysis as part of the decision

making process to rehabilitate three of the dams in the South River watershed. The

three dams, Robinson Hollow, Toms Branch, and Inch Branch are all located in the

eastern portion of the watershed. They all discharge to the Back Creek branch of the

South River and are located in the George Washington National Forest. The dams were

originally classified as low hazards back in the 1950s and 60s. Urbanization by the mid-

1980s down stream of the dams impacted the hazard classification of the dams.

Consequently, the dam safety criteria changed for the dams in the late 1980s, and the

dams are now classified as high hazard. The following sub-sections follow the above

general framework to demonstrate how the traditional economic approach is applied.

1. Identify Remediation Problem: The three dams do not meet the Virginia State

regulation for dam safety, as they are unable to safely pass the probable maximum flood

(PMF) through the auxiliary spillway without significant risk of structural failure. The

NRCS determined that under current conditions, the Robinson Hollow, Toms Branch,

and Inch Branch dams could only pass 55%, 60%, and 50% of the PMF respectively

(NRCS, 2005). Since 1987, these dams have been operating under �conditional

permits� from the VA Dam Safety Division.

Further analysis performed by the NRCS included modeling the watersheds with

the NRCS Water Resources Site Analysis Program (SITES). One of the key capabilities

of the SITES simulation program is its ability to model erosion of the auxiliary spillway

during extreme storm events. By providing soil sample data from the spillways, the

NRCS personnel could apply the SITES model to predict severe erosion could occur

during major storm events. Thus not only were the dams unable to pass the PMF, the


auxiliary spillways might also fail during the same event. This constituted the two key

remediation problems. (NRCS, 2005)

2. Establish Courses of Action: The NRCS ruled out two courses of action rather

quickly. The first one was to relocate or flood proof structures in the breach zones below

the dams. The NRCS determined that it would be infeasible to move or flood proof the

identified 263 structures in the inundation zone below the dams. The second course of

action was the decommissioning of the dams, meaning that the dams would be

completely removed and the area returned to a natural state. The costs associated with

the decommissioning for all three dams totaled around $4.7 million.

This left two other options, to remediate the dams or to �sponsor breach� the

dams. A sponsor breach is simply cutting a notch in the dams to allow water to flow

freely through the dam; in a sense a pre-emptive, controlled breach rather then an

unexpected one. The remediation courses of action were compared to the �sponsor

breach� course of action for the economic analysis.

As discussed in Chapter 2, there are several different techniques for dam

rehabilitation. To meet the PMF standard the dam height can be raised, the auxiliary

spillways increased, or the dam itself could be armored. Combinations of these

techniques allows for large permutations of possible courses of action. These dams are

located in most cases in steeply confined valleys, tied in nicely to large hill masses.

Expansion of the spillways for all three dams would require significant earth moving

operations, and possible blasting of rock. The associated cost quickly rules out this

possibility. Likewise armoring the dam with material like RCC would cost significantly

more then raising the dam. Consequently the NRCS, settled on a combination of raising

the dam with a parapet wall (USACE recommended as most cost effective), and

armoring the auxiliary spillways to prevent erosion.


There is one additional comment about the courses of actions considered by the

NRCS. Although, one remediation technique was selected for each of the dams and

optimally designed, the three projects were also considered as a whole. The NRCS

considered doing nothing, completing all three, completing combinations, etc. Thus, the

end state economic analysis contained numerous courses of actions for which

incremental analysis could be performed. (NRCS, 2005)

3. Establish Flood Area of Interest: Once the courses of action were determined, the

modifications to the dams could be simulated in the SITES model. Simulating all of the

courses of actions produced flow rates at established junctions. The NRCS chose to

use the SITES simulation software, but the hydrology model presented in Chapter 3

would work also.

4. Generate Water Surface Profiles: The NRCS then converted the flow rates to flood

stages at the junctions by surveying the main channels. The hydraulic simulation

program HEC-RAS was then used by the NRCS to create a flood inundation zone for

each course of action.

5. Gather Economic Data: The lead economist for this NRCS project, David Faulkner

spent significant time and effort gathering necessary economic information in order to

conduct the analysis. He began with the tax parcel information for the 263 homes, 13

business structures, 2 church buildings, and 6 farm buildings. He interviewed local

realtors in order to establish a fair market value amount for replacement costs.

There are 13 bridges and 6 public roads in the inundation zones. Mr. Faulkner

obtained from the appropriate departments of transportation to establish replacement

costs. Mr. Faulkner conducted interviews of the business owners to determine what

amount business income could be loss during flood events. He also checked on the

recreation value of the properties around the reservoirs, and the impacts of losing water

front property.


This only highlights the extremely thorough efforts performed by Mr. Faulkner to

gather the economic data. His efforts, and any similar future efforts, are time and

resource intensive. The compilation of the data took place over several months. Any

effort to obtain data will not encompass everything, and so reasonable assumptions

must be made to fill in missing gaps in the economic information. (Faulkner, 2006)

6. Survey High Water Marks on Cross Sections. 7. Survey 1st Floor Elevations on

Structures: These two steps can be performed together by methodically working

through the inundation zone. The high water marks from the HEC-RAS simulation were

established on the actual ground at the key junctions. Working from these known high

water marks to a given structure one can determine the high water marks that could be

expected to occur on the property. Water damage within the structure can be

established by comparing the high water marks to surveyed 1st flood elevations. This

process is also time and resource intensive, and likewise took several months to

complete. (Faulkner, 2006)

8. Sum Damages for Return Periods: With the labor intensive portion of the process

complete, the compilation of the data is the next step. For each return period and

course of action the following three categories were totaled: 1. Structure Damages 2.

Content Damages 3. Infrastructure Damages. These three categories constitute the

bulk of the assessed damages. (See Table 4.2)

Other lesser damages were also calculated and compiled. Fishing and hunting

recreation activity estimates were completed for each dam using the prescribed method

in the P&G. The decommissioning of the three dams would lower the value of the

properties adjacent to the reservoirs, and so these were accounted for as losses.

Personal and Business Incomes were estimated and included in the total damages.

Finally, the clean up costs and public management of the clean up effort rounded out the

lesser damages accounted for by the NRCS. (Faulkner, 2006)


9. Construct Damage Frequency Curves: The totaled damages from step 8 are

tabulated against the corresponding storm return period. Interpolation was completed

for the 75 and 400 year return periods to allow for better definition to the damage

frequency curve. The damage frequency curves are then plotted for all of the courses of

action. The NRCS decommissioning of all three dams course of action damage

frequency curve is shown in Figure 4.3, as well as the associated tabulated data in Table

4.3.

Table 4.2: NRCS Damage Summations (Faulkner, 2006)


Figure 4.3: NRCS Damage Frequency Curve (Faulkner, 2006) (Note: FWOT = Future With Out Treatment; FWT = Future With Treatment)

Stor

m E

vent %

Chance of

Occur-rence

Structure Damages

Content Damages

Private Clean-up

Costs

Public Clean-up

Costs

Lost Business Income

and Personal Income

Disrup-tion of Traffic

and EMS + vehicle damage Costs

Infrastruc-ture Clean-

up and Damage Repair Costs

Agricul- tural

Impacts Debris

Clean-up Costs

Public Admin-stration Costs

Total Damages

1 100% $0 $0 $0 $0 $0 $0 $0 $0 $0 $05 20% $16,053 $8,686 $64 $0 $0 $0 $335 $0 $0 $25,13810 10% $83,277 $50,453 $384 $197 $0 $0 $12,225 $0 $0 $146,53625 4% $237,771 $136,178 $1,440 $247 $0 $0 $73,566 $0 $0 $449,20250 2% $499,224 $274,392 $3,328 $592 $0 $1,350 $185,919 $254 $129 $965,18875 1.33% $729,501 $412,392 $6,432 $1,036 $5,486 $3,412 $274,454 $357 $193 $1,433,263

100 1% $959,778 $549,745 $10,496 $1,578 $27,576 $4,601 $362,988 $460 $515 $1,917,737400 0.25% $1,567,835 $950,220 $33,229 $4,182 $62,752 $7,024 $513,771 $1,107 $1,494 $3,141,614500 0.20% $2,959,810 1825806 $72,576 $8,876 $129,305 $9,446 $921,439 $2,307 $3,220 $5,932,785All n/a $7,053,249 $4,207,872 $127,949 $16,708 $225,119 $25,833 $2,344,697 $4,485 $5,551 $14,011,463

Table 4.3 NRCS Tabulated Data for Figure 4.3 Damage Frequency Curve (Faulkner, 2006)

10. Compute Average Annual Damages: The NRCS examples above in Figure 4.3

and Table 4.3 represent the �status quo� course of action. For the NRCS analysis this

becomes the �natural flow� curve shown in Figure 4.1, or stated differently as the

expected damages if the project was not present. To obtain an estimate of the expected


annual damages for the status quo case, one has to integrate numerically the area

under the damage probability curve in Figure 4.1. This approach was used by the NRCS

and is shown in Table 4.4. The total estimated average annual damages for the �status

quo� is $162,210.

Table 4.4 NRCS Average Annual Damages for Sponsor Breaches (Faulkner, 2006)

Storm Event

Definition (Years)

Freq of each Storm Event - % Chance of Occurrence

Change in Freq

(Probability)

Damages in Present Values ($)

Average Damages in Present Values ($)

Contribution to Average

Annual Damages ($)

1 100.00% --- $0 --- --- --- --- 0.80 --- $12,569 $10,055 5 20.00% --- $25,139 --- --- --- --- 0.10 --- $85,837 $8,584 10 10.00% --- $146,536 --- --- --- --- 0.06 --- $297,869 $17,872 25 4.00% --- $449,202 --- --- --- --- 0.02 --- $707,194 $14,144 50 2.00% --- $965,187 --- --- --- --- 0.07 --- $1,999,063 $7,994 75 1.33% --- $1,432,939 --- --- --- --- 0.00 --- $1,675,338 $5,584

100 1.00% --- $1,917,737 --- --- --- --- 0.01 --- $3,925,261 $31,402

500 20.00% --- $5,932,784 --- --- Estimated Direct Average Annual Damages: $95,635 Lost Incidental Recreation Value each year: $11,381

Lost Property Value (amortized over perpetuity): $55,193 Total Estimated Average Annual Damages: $162,210

The same process was repeated for each course of action. These become the

�regulated flow� curves in Figure 4.1. The same finite difference method was performed

to compute the average annual damages shown in Table 4.5 for the Rehabilitation of

Tom�s Creek only. The calculated average annual damages totaled $84,920.


Table 4.5 NRCS Average Annual Damages for Toms Branch Rehab. (Faulkner, 2006) Storm Event

Definition (Years)

Freq of each Storm Event - % Chance of Occurrence

Change in Freq

(Probability)

Damages in Present Values ($)

Average Damages in Present Values ($)

Contribution to Average

Annual Damages ($)

1 100.00% --- $0 --- --- --- --- 0.80 --- $1,638 $1,310 5 20.00% --- $3,276 --- --- --- --- 0.10 --- $36,927 $3,693 10 10.00% --- $70,578 --- --- --- --- 0.06 --- $148,502 $8,910 25 4.00% --- $226,426 --- --- --- --- 0.02 --- $313,259 $6,265 50 2.00% --- $400,093 --- --- --- --- 0.07 --- $541,174 $3,608 75 1.33% --- $682,256 --- --- --- --- 0.00 --- $830,203 $2,767

100 1.00% --- $978,151 --- --- --- --- 0.01 --- $2,241,914 $17,935

500 20.00% --- $3,505,676 --- --- Estimated Direct Average Annual Damages: $44,488 Lost Incidental Recreation Value each year: $4,572

Lost Property Value (amortized over perpetuity): $35,859 Total Estimated Average Annual Damages: $84,920

11. Compute Damages Avoided: The damages avoided represents the area between

the natural flow and regulated curves in Figure 4.1. So for the above example the

difference between the status quo and Tom�s Branch rehabilitation is $162,210 -

$84,920, or $77,290, as shown at the bottom of Table 4.5.

12. Complete Incremental Analysis: The NRCS performed some additional analysis

to establish the best order to decommission the dams, as well as the best order to

rehabilitate the dams. This is a subtle point to note, but there is a project length time for

each course of action that shifts slightly when the annual damages occur. Once the

order was determined, this set the increment analysis order. The NRCS compiled the

average annual costs and benefits similar to Table 4.1, as shown in Tables 4.6 and

Tables 4.7


Table 4.6 NRCS Incremental Analysis on Sponsor Breaches (Faulkner, 2006)

Structure

Average Annual

Cost (&) Incremental

Cost ($)

Average Annual Benefits

($) Incremental Benefits ($)

Net Average Annual Benefits

($) B/C Ratio

($)

Inch Branch $14,860 --- $1,216 --- -$13,644 0.08

Inch Branch and Robinson Hollow $35,415 $20,555 $2,432 $1,216 -$32,983 0.07

Inch Branch, Robinson Hollow and Toms Branch $58,495 $23,080 $3,614 $1,182 -$54,881 0.06

Table 4.7 NRCS Incremental Analysis on Rehabilitation Options (Faulkner, 2006)

Structure

Average Annual

Cost (&) Incremental

Cost ($)

Average Annual Benefits

($) Incremental Benefits ($)

Net Average Annual Benefits

($) B/C Ratio

($)

Inch Branch $57,536 --- $16,938 --- -$40,598 0.29

Inch Branch and Robinson Hollow $120,548 $63,012 $45,318 $28,380 -$75,230 0.38

Inch Branch, Robinson Hollow and Toms Branch $221,393 $100,845 $120,498 $75,180

-$100,895 0.54

The NRCS chose to use the Benefit to Cost ratio as the metric for the

incremental analysis. So as observed in Table 4.6, the B/C ratio is decreasing as each

dam is decommissioned. This makes sense as the flood benefits of the existing dam are

removed, and each increment would increase the damages. We can observe this in

Table 4.7 where they are increasing with each increment. Based upon the B/C ratio of

0.54 the rehabilitation of all three dams yields the highest benefit to cost ratio.

We can check the NRCS calculations by computing the ∆ (B / C) ratios for the

increments. The ratio for the Robinson Hollow and Inch Branch is 0.44, and for the


rehabilitation of all three 0.75. Both of the ratios are less then 1, and so the incremental

analysis is supposed to end if the ratio is less then one. This is also the case when

computing the B/C ratio, as the benefits should outweigh the costs. David Faulkner

discussed this exact issue, and explained that special permission was needed in order to

proceed with the recommended course of action that yielded a B/C ratio less then one

(Faulkner, 2006). So, if we ignore the ratios being less then one, either method yields

the same resulting recommendation to rehabilitate all three dams.

4.5 Summary of Traditional Economic Analysis

This chapter provides a general framework that is one way of approaching the

necessary economic analysis for proposed rehabilitation projects. The framework was

first discussed on a conceptual level followed by a step-by-step flow chart shown in

Figure 4.2. The framework was validated by the NRCS case study for the proposed

rehabilitation projects for the Toms Branch, Inch Branch, and Robinson Hollow Dams.

As demonstrated, the NRCS economic analysis fit nicely into the general framework.

As indicated in the discussion of the NRCS benefit-cost ratios, these

rehabilitation projects did not have B/C ratios above one. Yet, the NRCS approved the

recommendation despite the B/C ratios. This is an excellent example of a continuous

debate. The debatable issue is justification of rehabilitation projects to meet the required

design probable maximum flood derived from the theoretical probable maximum

precipitation. In the opinion of the NRCS, the project benefits warranted the additional

cost expenditures. This is supported by the conclusions from Chapter 3 in that the dams

do impact and reduce flooding within the watershed. Therefore, the decision metrics like

the B/C ratios are only tools, and the final decisions must account for all mitigating

factors surrounding the projects in question.

Chapter 5: Use of GIS Software as a Hydro-economic Tool 68 in Dam Rehabilitation Analysis

Chapter 5: Use of GIS Software as a Hydro-economic Tool in Dam Rehabilitation Analysis

In performing rehabilitation analysis from both the engineering and economic

stand points, an individual can benefit from the use of integration of Geographic

Information Systems (GIS). Even if a person were only to perform a watershed

delineation today using a paper map, chances are that paper map was produced from

GIS technology at some point. With the continuous improvement in Geographic

Information Systems (GIS) technology, and the ever increasing number of GIS

databases, ignoring a potential source of information could be counter-productive. With

that said, one must be able to evaluate the credibility of the GIS data source, the

capability of the GIS application software being used, and the extent to which such GIS

applications should be used.

This chapter will discuss the topic of integrating GIS into rehabilitation analysis.

The first section provides an overview of potential GIS software that is available that

might assist with the creation of simulation models. The second section provides a

software specific discussion of products available that could be used in performing

rehabilitation analysis. One particular GIS based simulation software that was evaluated

was the Federal Emergency Management Agency�s (FEMA) risk mitigation software

HAZUS Multi-Hazard (HAZUS-MH). The HAZUS software methodology will be

described as an introduction to its capabilities. Following the introduction to the HAZUS

software, a discussion about the application to the case study will be presented. Finally,

the chapter concludes with summary comments.

5.1 Overview of GIS as a Tool for Analysis By definition, a Geographic Information System database is comprised of data

that is spatially referenced. In creating the HEC-HMS model in Chapter 3, input


parameters for the sub-basins, like the NRCS curve number, were numerically lumped

together by an accepted approach. In the past, input parameters needed to be lumped

together in order to expedite the modeling process by reducing the amount of data to

input into the simulation, and by reducing the computational time of the models.

Advancement in personal computer technology for processor speeds has negated the

need for smaller models to reduce computational time. However, data input can remain

time-consuming, even by today�s standards.

GIS databases allow users to store large amounts of spatially oriented data, such

as soil types. An engineer can now represent data as distributed parameters rather then

as lumped parameters. Provided the GIS database source is relatively error free,

simulation results can be enhanced using distributed parameters as input data

(Whiteaker et al., 2006). Public GIS sources are becoming widely available. For

example, the USGS alone provides downloadable digital elevation maps (DEMS),

satellite imagery, national atlas roads, counties, topographic quad sheets, and many

other databases.

Recognizing the usefulness of GIS databases, counties and larger cities across

the United States have public accessible GIS internet web-sites. Augusta County in

Virginia, the South River case study county, provides such a web-site as shown in

Figure 5.1 (http://www.co.augusta.va.us/website/AugustaInternetGIS/viewer.htm). These web-

sites function not only as great reference maps, but relevant data can also be obtained

in the data layers. In the Augusta County web-site, critical GIS data on Tax Parcel

information (georeferenced shapes and data information), the 500 year flood plane,

existing structure locations, and the shapes of the existing structures are available. This

data could be directly used in conjunction with the creation of the hydrology model and

the economic analysis discussed in Chapters 3 & 4.


Figure 5.1 Augusta County, VA GIS Web-Site

5.2 Discussion of Existing Relevant GIS Software

The major purpose of GIS was the expansion of a typical database, like one

might create using a program like Microsoft Access, by linking the data to a geospatial

reference point. Thus, a software program to merge traditional databases with maps

was needed. There are several different commercial software programs that have

evolved that will allow the user to manipulate GIS data. A widely used GIS software

program is produced by the Environmental Systems Research Institute (ESRI),

headquartered in Redlands, California. The ESRI software suite named ArcGIS (version

9.0 or 9.1) provides the necessary programs to view, edit, organize, and analyze GIS

data. All GIS related work performed for this work was completed using the ArcGIS

software suite (Longley et al., 2005).

Mastering the ArcGIS software is only part of the battle to employing the full

potential of available GIS data. The process of gathering the data from the various

sources, like Augusta County and the USGS, requires persistence and patience. Often


a user remains at the mercy of the local internet connection and the source data server

in being able to download files quickly. The GIS data files are often extremely large and

may require breaking the data into smaller files. Another potential problem in dealing

with GIS data is ensuring the data projection and reference coordinate systems are the

same. Otherwise the different data layers will not be compatible when trying to perform

an analysis. All of these issues are usually mastered by a proficient GIS technician. The

time spent gathering the existing data vastly exceeds anyone trying to conduct new

surveys to obtain all of the same information (Wiley et al., 2005).

The ArcGIS software suite contains applications that can immediate expedite the

hydrologic and hydraulic modeling. For example, having obtained the necessary data

layers, watershed boundaries can be delineated manually, the area can be calculated for

the watershed, the centroid of the watershed can be found, and the longest travel

distance within watershed can be determined. These semi-automated applications are

much more efficient then the original manual methods. Another powerful aspect of the

current ArcGIS software suite is a model creation capability. If a particular order of

applications or data calculation is to be repeated, the user can create a model in visual

basic to accomplish this. For example, once the watershed is delineated manually, a

model could be set up that automatically computes the area, the centroid, and longest

distance travel distance for the watershed (Wiley et al., 2005).

The modeling techniques are encouraged by ESRI, as the ArcGIS software

remains the base platform for the data manipulations. New models are perfected for all

different areas of emphasis like geology, water utilities, groundwater, hydrology, and etc.

ESRI takes full advantage of these products, and markets them as software packages,

training packages, and provides technical support. A relevant hydrology and hydraulic

model marketed by ESRI is called Arc Hydro (CRWR, 2001).


The Arc Hydro data model performs five different tasks within three broad

hydrology categories called: hydro description, hydro connectivity, and hydro modeling.

The five tasks the data model is capable of performing are: 1. Network. 2. Drainage. 3.

Channels. 4. Hydrography. 5. Time Series. The first three functions establish how

water moves through a given watershed, and outputs parameters that allows for a

simulation model to be created. The Hydrography tool links the data from the first three

functions to map locations remaining consistent with the enhanced spatial reference

gained by using GIS. The Time Series tool ties together the first four functions to create

outflow hydrographs. From the description of the software alone, the potential

usefulness of Arc Hydro as an alternate means of modeling is quite apparent (CRWR,

2001).

The USACE Hydrologic Engineering Center (HEC) has recognized the

importance of geospatial data in its recent model development activities. The HEC

developed two ArcGIS applications for hydrology and hydraulics called HEC-GeoHMS

and HEC-GeoRAS. These two programs work with GIS databases like Arc Hydro, but

with a primary purpose to generate input parameter data for the simulation programs

HEC-HMS and HEC-RAS discussed previously. So, the arduous task of compiling and

inputting data into the hydrology model described in Chapter 3 could potentially have

been streamlined into a more automated method using HEC-GeoHMS (HEC, 2004). On

completing the HEC-HMS work, the engineer could then route along the flood inundation

zone HEC-GeoRAS. The HEC-GeoRAS performs two functions. The first function

being like HEC-GeoHMS in that input parameter data is generated in HEC-GeoRAS for

HEC-RAS. Additionally, the output data from HEC-RAS can then be inputted back into

HEC-GeoRAS in order to visualize the hydraulic routing along the reaches in question

(HEC, 2005).


Using the above simulation programs as described still requires manual transfer

of input/output data, and therefore could be described as semi-automated. Ideally, one

software package that could accomplish all of the tasks might prove to be quite useful.

The Center for Research in Water Resources (CRWR), of the University of Texas

recently published a way of accomplishing a full automation process using ArcGIS and

the HEC software (Whiteaker, 2006). The researchers demonstrated that Flood

Inundation Maps can be created from NEXRAD rainfall maps and the HEC software

suite. They created a model in GIS that interacts with the four software programs HEC-

HMS, HEC-GeoHMS, HEC-RAS, and HEC-GeoRAS. Their research study and

corresponding analysis is not an exact match for the analysis of dam rehabilitation, but

never the less their approach in gaining a more automated process is quite promising.

5.3 Automating the Economic Analysis

Already highlighted in Chapter 4, the economic analysis process is rigorous and

time consuming. Any potential ways to automate or streamline the process would be

welcome. In the absence of a widely accepted software simulation program, in house

spread sheets are used by agencies like the NRCS (Faulkner, 2006). The NRCS does

have a flood damage assessment software packages called URB1 and ECON2, but they

are extremely outdated. The HEC software for economic flood damage analysis that is

used by USACE Districts is the program HEC-Flood Damage Analysis (HEC-FDA).

HEC-FDA provides a risk based analysis for flood reduction studies that are

performed regularly by USACE offices. The purpose for HEC-FDA is to assist the user

during the feasibility stage of the USACE�s project planning cycle. A user of HEC-FDA

must complete the hydrology and hydraulic analysis in order to generate discharge-

frequency curves and water surface elevation profiles. This mandatory H&H input data

is first coupled with the building inventory, and then the program computes the


equivalent annual damages for the model situation. HEC-FDA is meant to be a decision

tool. The results are meant to provide a quick assessment in order to determine whether

the project is going to be feasible, and therefore can save USACE planners time by not

continuing to plan projects that are not economically viable. (HEC, 1998)

FEMA wrestled with the same automation issues in designing a GIS based

software that can assist local emergency managers across the United States plan for

natural disasters, like flooding. FEMA�s intent was to provide a software package that

could be used by different levels of experienced users. Therefore the program is

capable of running simulations by personnel who possess very limited knowledge of the

science behind some of the models, like a typical emergency planner, but is also

versatile enough to allow technical experts to provide almost all of the input parameters.

The next section will describe the characteristics of FEMA�s HAZUS-MH model.

5.4 FEMA�s HAZUS Multi-Hazard Model

The FEMA HAZUS Multi-Hazard model

contains three major models for the primary

natural disasters experienced in the U.S.:

earthquakes, winds, and flooding (Figure 5.2).

The model is capable of replicating all three

disasters in a given location; however, the

model is not capable of simultaneously running

more then one disaster. HAZUS-MH is an

interactive GIS application that requires the

ArcMAP 9.0 software platform. Our discussion

only focuses on the flood model. (National

Institute of Building Sciences (NIBS), 2003b) Figure 5.2 HAZUS-MH Start Menu


A person using the HAZUS-MH flood model is able to create a study area up to

the size of four counties. The software package when distributed by FEMA includes

data files for every county in the United States. After selection of a study area, the

program creates the necessary background GIS layers including county boundaries,

census population blocks, and building inventory databases. The user must provide an

elevation DEM in order for the program to establish the stream network. The stream

network is created similarly as the Arc Hydro�s Network tool. With an overall network

completed, the user establishes specific reaches to analyze. In turn the program

calculates a discharge frequency curve for the desired reaches, and creates flood

inundation polygons with a water surface profile for the reach. This leads to the damage

analysis portion of the flood model. The damage model performs an economic analysis

based upon the flood inundation polygon, and summarizes all of the expected direct and

indirect damages. (NIBS, 2003a)

The HAZUS-MH flood model requires a modest amount of input from the user to

complete a basic flood analysis. This is very close to a fully automated process, but as

such there are many problems in completing the basic level analysis. For instance, the

calculated damages are based upon aggregate 2000 U.S. census data that is compiled

by census blocks, and are not site specific data one could obtain from county tax parcel

databases. However, the flood model is capable of integrating user provided data for

infrastructure and building inventories for completing the damage analysis. This requires

a more sophisticated understanding of the software, and requires more time for data

parameter inputting. The next section will describe how the model was applied to the

South River Case Study as a means of evaluating the flood damage assessment

capabilities of the HAZUS-MH flood model.


5.5 Case Study Application of HAZUS-MH Software

The potential for HAZUS-MH flood model to assist engineers and economists in

performing rehabilitation analysis was evaluated. To accomplish the evaluation, the

flood model was applied to the same South River case study. This section provides

details as to how the HAZUS-MH software works, as well as some discussion of the

strengths and weaknesses of the program. The desired end state is a comparison of the

damage assessment provided by HAZUS-MH versus comparison to the NRCS�s

assessment discussed in Chapter 4.

The first step in setting up the flood model is to select the study region. By

selecting Augusta County, the user requests the HAZUS-MH upload appropriate data

files for the county (Figure 5.3). Embedded in the flood model is the 2000 U.S. census

data broken into census blocks, in which for the urban setting is equivalent to one city

block. The census data determines the population break-down by annual income as

well as the type of residence found in the census blocks (Figure 5.4). The break-down

percentages of types of residences is determined from another national database that

determines the type of homes, like single family versus apartment complexes. (NIBS,

2003a)

Figure 5.3 Augusta County Study Region in HAZUS-MH


Figure 5.4: Census Blocks in HAZUS-MH

Although the way HAZUS-MH handles the census data within the blocks is

grounded in reasonable assumptions, they do not represent exact numbers and

locations. They are only aggregate numbers, based upon regional regression equations.

This key point must be understood when interpretation of the output data is completed.

The flood model when operated in the basic 1st level mode, only estimates the structure

inventory. The basic analysis would not provide enough detail to make decisions for

rehabilitation feasibility for a single dam. The real tax parcel information would have to

be inputted, which implies it must be gathered first. However, the basic 1st level analysis

would be more effective on a larger scale where the use of default aggregate numbers

would be mitigated. A large levee system encompassing a county size watershed is an

example where such an analysis might be used.

For any case study that is initiated in the flood model, the initial stream network

must be created for the entire study area. This is performed in the HAZUS-MH program

via raster analysis on the DEM. Without going into further details as to the technical

aspects of the raster analysis, the end result from this step is a network of reaches


(Figure 5.5). The stream network analysis of course is impacted by the resolution of the

DEM that is inputted into the flood model. In most cases, the stream network does not

perfectly match the existing streams and rivers spatially, but the process does not create

�false� streams either (NIBS, 2003a).

Figure 5.5: Stream Network in HAZUS-MH

The next step in the process is to identify the reaches that the user wants to

analyze; these are called �case studies� in the HAZUS-MH model. For this

demonstration we created two case studies, one for the Toms Branch and Inch Branch

dams. The reaches below the dams were selected all the way down to the Lyndhurst

Gaging station. Once the case study is completed, the software performs a hydrologic

analysis. The hydrologic analysis involves several complex computations that include

generating expected discharges from return period precipitation events, establishing a

flood inundation zone boundary, determining the water surface profile, and the flood

depth (NIBS, 2003a).


There are some discussion points for the HAZUS-MH hydrologic analysis. The

software program establishes the flow network when it created the stream network. The

primary computation performed during the hydrologic analysis is establishing the

discharge-frequency table. The program uses regional USGS regression equations to

compute discharges for each return period event, for each node of the stream network.

Additionally, the program checks if there are existing USGS gaging stations within the

stream network where a historical statistically-based discharge frequency table is

available. If a USGS gaging station is present, the flood model is extremely accurate in

matching the flood inundation zone to FEMA�s established flood zones as demonstrated

in an example in Hillsborough, NC (See Figure 5.6)

Figure 5.6: Flood Inundation Zone for Hillsborough, NC

More often then not, the study area of interest will not have a USGS gaging

station present for a given case study. The validity and accuracy of the regional

regression equations come into question. There are more accurate methods and

simulation models that perform the hydrologic and hydraulic analysis, like HEC-HMS and


HEC-RAS. For an advanced user, the HAZUS-MH is versatile in that H&H data from

other sources can be inputted into the model. There is a Flood Information Tool (FIT)

that allows the user to manually generate the flood inundation zone, but this tool requires

that cross channel and water surface profile data be known. The more advanced modes

of the HAZUS-MH require more user inputs and fewer semi-automation options. (NIBS,

2003a)

These inherent capabilities and weaknesses in the hydrologic analysis

notwithstanding, the HAZUS flood model output for the Toms Branch and Inch Branch

Dams was compared with HEC-HMS output presented in Chapter 3. As shown in Table

5.1, the calculated discharges from both dams were equal at each return period. This is

a telling feature of HAZUS, and can be attributed to the fact that the discharges are

routed through flow networks to a final reach, which happens to be the same reach for

both dams (see Figure 5.7). Since the raster analysis methodically computes the

discharge-frequency curve continually through the entire set of reaches, having a

common end reach causes the results to be equal. In comparing the HAZUS-MH to the

HEC-HMS model runs where the dams are present in the model, we see that the

HAZUS-MH results are slightly lower for the Q2 and Q10 events, but are considerably

less at for the Q50, Q100, and Q500 events, as shown in Table 5.1:

Table 5.1: Lyndhurst Gaging Station Comparison

Return HAZUS: Inch

Branch HAZUS: Toms

Branch HEC-HMS Period Q (cfs) Q (cfs) Q (cfs)

Q2 2,879 2,879 2,651

Q10 6,914 6,914 8,077

Q50 13,158 13,158 18,879

Q100 16,582 16,582 25,653

Q500 26,254 26,254 46,847


Figure 5.7: Common Reach of Inch Branch and Toms Branch Dams

The HAZUS-MH flood model was also checked for performance in the

headwaters reaches where the dams are located. The HAZUS-MH flood model, unlike

HEC-HMS, is not capable of reporting individual reaches when completing a multiple

reach analysis. New case studies were created in which only the reach containing the

dam was selected. The results from the hydrologic analysis for each of the dams are

shown in Table 5.2. The HAZUS-MH flood model results closely matched the HEC-HMS

outputs for the dam sites. Note, this time the HEC-HMS simulation results came from

the �without� dams present. This observation is expected since the flood model does

have a simple approach to simulating the presence of a hydraulic structure that is not

activated in the basic 1st level analysis.

Table 5.2: HAZUS-MH Comparison to HEC-HMS at Dam Sites HAZUS: HEC-HMS HAZUS: HEC-HMS Return Inch Branch Inch Branch Toms Branch Toms Branch Period Q (cfs) Q (cfs) Q (cfs) Q (cfs)

Q2 217 232 439 378 Q10 606 717 1,173 1,134 Q50 1,289 1,467 2,402 2,333 Q100 1,651 1,867 3,037 2,975 Q500 3,023 2,981 5,418 4,773


One final hydrologic discussion is the inundation zones created by the HAZUS-

MH for the Inch Branch and Toms Creak Dams. The NRCS dam rehabilitation analysis

included an estimated breach inundation zone shown yellow in Figure 5.8. In comparing

the HAZUS-MH 500 year flood zone to the NRCS breach zone, there are some good

Figure 5.8: Comparison of HAZU-MH and NRCS Flood Zones

correlations. The differences in the zones are due in part to the magnitude of the Q500

used in HAZUS-MH versus the initial breach discharges used by the NRCS (Table 5.3).

The NRCS breach zone was constructed using much larger initial discharges,

representing the large flood wave created from an unexpected dam break. This type of

event under most situations should create a larger flood inundation zone, as shown in

Table 5.3 in this instance.

Table 5.3: Flood Inundation Comparison

HAZUS-MH 500 yr

flood

NRCS Inch

Branch Dam Break

NRCS Toms

Branch Dam Break

Q (cfs) 26,254 51,000 90,000


Once the flood inundation zone is created in the HAZUS-MH flood model, the

next step is to compute damages. The flood model begins with comparing the flood

zone boundaries to the census inventory. The depth grid establishes the level of

flooding within a census block, which in turn are translated to damages through the use

of depth to percent damage curves. The damage curves are based upon established

USACE curves, and are adjusted to the region. The user also has the option to modify

the damage curves to reflect local conditions, if so desired. The rest of the process

replicates what was described in Chapter 4 by the NRCS. The flood model is capable of

creating a suite of output reports that can be viewed and printed (Figure 5.9).

Figure 5.9: Example Damage HAZUS-MH Damage Report


As highlighted previously when performing a 1st level analysis, the structure/

building damages are estimated by the use of aggregate census block data. To assess

the 1st level analysis, the results from HAZUS-MH were compared with the NRCS�s

economic analysis. The property exposure values, based upon the baseline inventories

are shown in Table 5.4. The HAZUS-MH model drastically overestimates the exposed

property value, directly attributable to the estimation method the flood model uses for

inventories. The software program can overcome this issue, but this would require

inputting of real tax parcel information into the model. This also requires additional time

and effort, and a higher level of expertise for the HAZUS-MH model. Obviously, the use

of highly aggregated census block data in HAZUS-MH cannot capture local structural

damages, as it was in the NRCS flood damage evaluation.

Another comparison from an economic stand point was the calculated total

damages caused by the flooding. Table 5.5 shows the calculated damages from the

HAZUS-MH flood model and the NRCS economic analysis. The 500 year damages

from the flood were compared with the sunny day breaches from the NRCS analysis

because the 500-year is believed to represent the extreme event in both methods. At

the extreme events, the estimates were closer, but the return periods are not exactly the

same since the breach events occur at percentages of the PMF. Looking at the Q10,

Q50, and Q100 events, results from the HAZUS-MH flood model are drastically larger

than the NRCS estimates. This matches the observed trend with the building exposure

estimates. Further comparisons can be assumed to yield similar results in the HAZUS-

Table 5.4: Property Exposure Estimates Comparison

HAZUS

Inch Branch NRCS

Inch Branch HAZUS

Toms Branch NRCS

Toms Branch Total Property

Exposure ($1000) 45,831 12,083 81,431 22,083


MH. Without local input data, the HAZUS-MH model will grossly over-estimate the

damages resulting from a flood.

Table 5.5: Total Structure Damages Comparison Damages ($1000)

Return Period

HAZUS Inch

Branch

NRCS Inch

Branch

HAZUS Toms

Branch

NRCS Toms

Branch Q10 1,200 3 2,040 25 Q50 1,690 439 3,230 959 Q100 2,050 996 3,830 1,872 500yr/Breach 2,800 2,463 5,550 5,707

5.6 Summary of Integration of GIS Software with Dam Rehabilitation Analysis

This chapter was intended to demonstrate the importance of using the large

quantities of information available in GIS databases. From a general information view, it

seems obvious that any planning or decision making process must consider all relevant

data. However, as seen in the previous section, the benefits of using automated GIS-

based software in performing complex hydrologic, hydraulic, and economic analyses can

be debated. Ideally, GIS models would approach full automation, and the results would

be black and white. As demonstrated in using the HAZUS-MH flood model application to

South River, the technology advancement although quite significant, still has room for

improvement.

On the surface, the HAZUS-MH flood model appears to be a nice solution in

automating the rigorous and time consuming task of performing a dam rehabilitation

analysis. However, the use of level-1 automatic data input is highly problematic, since

so little user input is required, and the simulation results do not include enough fidelity

for making a decision on a dam rehabilitation process. Performing the necessary

analysis in order to input data in HAZUS-HM flood model for the hydrologic analysis and

the economic analysis yields minimal added benefits. Since added benefits are minimal,

one would certainly question if the �automated� method is worthwhile. Especially, when


the reliability of the results is questionable, and would have to be verified through a

second means anyways.

The HAZUS-MH flood model was not originally intended to be used in an intense

civil works feasibility analysis. The model is meant for emergency management and

county level planners to use as a tool for disaster mitigation, and we are not commenting

on the model�s ability to meet this intent. There is some merit in using the model for

some preliminary analysis like establishing the stream network in a GIS format. The

simulation computations of the 100 and 500 year flood inundation zones gives a good

visualization of where the flooding areas might occur based upon topography. Since the

500 year flood inundation zone will be similar to an extreme dam break event, the 500

year flood zone created in GIS could be intersected with the GIS tax parcels, structures,

roads, and bridges to give the engineer reference points for potential damages that

might occur in a breach inundation zone. The next chapter explores the concept of

optimization in selecting a course of action through the method of linear programming.

Chapter 6: Linear Programming as an Alternative Analysis Technique 87

Chapter 6: Linear Programming as an Alternative Analysis Technique

The three South River case study dams are classified as �High� risk by the

NRCS. In the event of a catastrophic failure of any of the dams, it is probable that there

would be at least one life lost due to flooding. The three dams are not in compliance

with the VA Dam Safety Regulation (VDCR, 2004). So, the dam rehabilitation analysis

was forced into two possible solutions. The dams could be �sponsor� breached, or the

dams could be retrofitted to pass the calculated PMF.

The mandatory safety criteria for a �High� risk dam is the passage of the PMF as

stated within the Federal Dam Safety Criteria (NRC, 1985), as well as by the VA Dam

Safety Regulation (§ 4 VAC 50-20). However, if dams are classified as �significant� by

Federal guidance (FEMA 333), or Class III by VA standard, then the passage

requirement can be reduced to as low as ½ the calculated PMF. Justification in the form

an engineer analysis is required to demonstrate that increasing the passage of the ½

PMF to the full PMF does not gain any further reduction in flood damages. This

justification analysis creates the potential need for other analysis tools such as

optimization through Linear Programming techniques. Such a tool would be able to find

the optimal solution based upon the constraints of the problem.

This chapter will begin with an argument presented by Wayne Graham from the

BUREC. As discussed in Chapter 2, his argument focuses on the question: �Is the

benefit of rehabilitating a dam to meet the PMF criteria worth the costs?� Graham puts

forth a simple analysis that can be applied to dams being considered for rehabilitation

(Graham, 2000), and this technique was applied to the South River dams. The next

section introduces Linear Programming techniques and where they could be used to

assist with selection of the best course of action. The following section includes an


expansion of Graham�s simple analysis in combination with Linear Programming.

Finally, summary remarks are discussed in the final section of the chapter.

6.1 An Alternative Economic Analysis for Dam Rehabilitation

Graham (2000) articulated an argument that modifying existing dams to meet the

required safety criterion of passing the PMF is more often not worth the large amounts of

project costs. He criticizes the PMF design criterion under the following four concepts

(Graham, 2000):

1. Spillway enlargements can increase downstream flooding resulting in an increase in average annual flood losses. 2. Benefit-cost ratios could be low. 3. Dam safety modifications could cause accidental deaths. 4. The cost-per-life-saved is high. Essentially, Graham (2000) questions the value of safety that is added by rehabilitating a

dam to meet what represents a statistically calculated maximum event. Also in

completing the dam rehabilitation, there could be increases in flood damages during

lesser extreme events that occur more frequently. The model format is based upon not

doing any modification, leaving the �status quo�, in comparison to the proposed

modification:

1. Economic Benefits: EB = ES � EM Where EB = Economic benefits derived from modification ES = Annualized Economic loss by flooding (Status quo) EM = Annualized Economic loss by flooding (Modification plan) 2. Life Benefits: LB = LS � LM - LC Where LB = Life benefits derived from modification LS = Annualized Life loss caused by flooding (Status quo) LM = Annualized Life loss caused by flooding (Modification plan) LC = Annualized Life loss caused from Construction spending (0.14 lives per $100 million expended)


3. Cost-per-life-saved = LB is positive Parameter found: (CM � EB) / LB

Benefit-per-life-lost = LB is negative Parameter found: (CM � EB) / LB

Where CM = Cost of Modification

4. Decision Guidance:

a. If EB and LB are negative, reject project.

b. If 0 < EB < CM and LB is negative, reject project.

c. If EB < CM and LB is positive, compute Cost-per-life saved.

d. If EB > CM and LB is negative, compute Benefit-per-life lost.

e. If EB > CM and LB is positive, proceed with project.

Graham�s simple economic analysis incorporates a sensitive subject that is often

avoided by our society: assigning a monetary value to human life. Whether we wish to

address this issue from a monetary stand point or not, the fact remains the public

welfare remains the driving force behind the dam safety. What Graham accounts for is

that historically workers are killed during construction projects, and that this fact should

be accounted for when deciding to initiate a new project.

An example problem was provided by Graham (2000), which is used later in this

chapter to demonstrate an expansion of the above analysis. However, this simple

economic analysis is quite applicable to the South River dams. The Chapter 4 NRCS

economic analysis was completed to support the recommended project proposal to

rehabilitate the three South River dams to meet current the PMF standard. This creates

a question: �Would Graham�s economic analysis when applied to the South River case

study support the NRCS�s conclusion to proceed with the dam rehabilitation?� The rest

of this section seeks to answer this question.

To begin the analysis, the number of residents to be impacted by flooding must

be identified within the flood inundation zone. From the NRCS economic analysis, there

are 191 homes with 955 residents who could be affected by the Toms Branch dam, and


72 homes with 360 residents for the Inch Branch and Robinson Hollow dams (NRCS,

2005). Following the procedure in BUREC regulation �A Procedure for Estimating Loss

of Life Caused by Dam Failure (Graham, 1999)�, a regression equation was selected

based upon certain on-site conditions of the dams. For example, the selection criteria

include earthen vs. concrete type of dam, viable emergency action plan in place, dam

visibility during storm events, etc. Accounting for all of the selection criteria, the BUREC

regulation suggested estimating the People at Risk (PAR) by the following equation

(Graham,1999): PAR = (Residents in Flood Zone).6.

Table 6.1 shows the calculated PAR (Sponsor Breach) which would be for the

situation where the dam rehabilitation did not occur. The probability the PMF would

occur in a single year is one chance in 286,000, and the loss of life is either zero or 34 in

the case of the Robinson Hollow Dam. Therefore, the annualized loss of life for flooding,

LS, is 34 divided by 286,000 equaling 0.00012. The available NRCS study did not

include the impacted residents in the flood zone based up the new projected inundation

zone. Even with the rehabilitated dams, some lives would be lost as a result of the

increased flows released by the emergency spillway, and therefore it was assumed the

residents in the flood zone would be decreased to a third of the original number. This

led to the calculation of the PAR (w Rehab) and the LM parameter in Table 6.1 (Graham,

2000)

Table 6.1: South River LS and LM Calculations

Residents in Flood

Zone PAR

(Sp. Breach) LS PAR

(w Rehab) LM Rob. Hollow 360 34 0.00012 18 0.00006 Toms Branch 955 61 0.00021 32 0.00011 Inch Branch 360 34 0.00012 18 0.00006 Combined 1315 74 0.00026 38 0.00013

The next parameters to determine were the lives lost due to construction.

Normally, the Lc parameter impacts only the modification because the �status quo� did


not include any construction. For the South River dams, the minimal acceptable action

was to complete a sponsor breach of the dams which did have associated costs. The

NRCS calculated average annual costs for both the Sp. Breach and w Rehab are shown

in Table 6.2 (NRCS, 2005). The LCS and LCM parameters are calculated by multiplying

by the ratio of 0.14 per $100 million.

With the all of the necessary parameters calculated, the Life Benefits, LB could be

calculated. The LB were found by the following formula: LB = LS � LM - LCS - LCM. The

results are shown in Table 6.3. All of the calculated Life Benefits were negative,

meaning the dam rehabilitation projects would not create any Life Benefits. Graham�s

economic analysis usually did not include the LCS parameter. In removing this term, the

Toms Branch Dam now creates a positive Life Benefit.

Table 6.3: LB Results

LB Adjusted

LB Rob. Hollow -0.00004 -0.00002 Toms Branch -0.00003 0.00002 Inch Branch -0.00017 -0.00008 Combined -0.00034 -0.00018

The other part of the analysis is the Economic Benefits, EB. Table 6.4 compiles

the economic parameters that were obtained from the NRCS economic analysis (NRCS,

2005). The Economics Benefits were computed using the following formula: EB = ES �

EM. Individual ES values were assumed, as the NRCS data only provided a combined

annualized flood damages for the status quo. All of the courses of action yielded

Table 6.2: South River LCS and LCM Calculations

Avg Cost

(Sp. Breach) LCS Avg Cost (w Rehab) LCM

Rob. Hollow $14,860 2.08E-05 $57,536 8.06E-05 Toms Branch $35,415 4.96E-05 $63,112 8.84E-05 Inch Branch $58,495 8.19E-05 $100,745 1.41E-04 Combined $108,770 0.000152 $221,393 3.10E-04


negative economic benefits, but the combined impacts yielded positive impacts. The

Economic Benefits must then be compared with the Project Costs, CM.

Table 6.4: South River Economic Calculations ES EM EB CM Robinson Hollow $20,276 $84,920 ($64,644) $57,536 Toms Branch $121,658 $126,288 ($4,630) $63,112 Inch Branch $20,276 $128,474 ($108,198) $100,744 Combined $162,210 $38,330 $123,880 $221,392

Following Mr. Graham�s decision guidance, the Robinson Hollow and Inch

Branch Dams proposals should be rejected immediately as both the EB and LB

parameters were negative. For the Toms Branch Dam, the LB was positive if the LCS

parameter was not included, but the EB were negative. Thus, this course of action

should be rejected also. Finally, the combined course of action (rehabilitate all three

dams) yielded a positive EB that was less then the CM. Since the LB was negative, the

computed Cost-per-life saved is approximately $528 million (Graham, 2000).

Graham�s analysis proved to be easily applied to the South River dams situation.

As shown in the results from the South River application, completing the rehabilitation of

just one of the dams would not be a wise investment. What is interesting is that the

NRCS proposal to rehabilitate all three dams will occur at the expense of $528 million for

the amount of lives saved. Likewise, the NRCS computed Benefit-Cost ratios that were

less then one, and thus calculated that project costs would indeed exceed project

benefits. We can conclude that Graham�s method of analysis in this situation is

supported by traditional benefit-cost analysis. This ultimately requires a decision

maker(s) to determine if the cost is worth the added safety measures. Graham would

most likely argue the $528 million is not a wise investment in order to achieve the PMF

standard.


6.2 Application of Linear Programming

Obtaining an optimal solution for constrained problems through linear

programming technique is a proven powerful technique. By definition, linear

programming exhibits the following characteristics (Ravindran et al., 1987):

• All decision variables are non-negative. • The desired goal for selecting the optimal solution must be expressed as a linear

function of the decision variables, and is called the objective function. • Constraints are expressed as linear equations or inequalities.

The formulation of the linear program model follows three basic steps, but

requires practice in becoming proficient at application to real problems. The three basic

steps are as follows (Ravindran et al., 1987):

Step 1: Identify the unknown decision variables to be determined, and assign algebraic symbols to represent the variables. Step 2: Identify all known constraints for the given problem, and express them as linear equations or inequalities using the unknown variables. Step 3: Identify the objective function, and represent it as a linear function of the decision variables.

For simple linear programs, the problems can be solved by algebra or by completing row

operations. If numerous constraints or courses of actions are created then an

optimization software program is usually employed. The Solver application contained

within the software program Microsoft Excel is an example of an optimization program.

One application where optimization might have been used was during the

NRCS�s dam rehabilitation design efforts. The selection of the remediation method was

determined from a set of possible solutions. For example there was the �sponsor

breach� course of action, remediation of the dam to pass the PMF course of action, or

even implement a warning system. More specifically, the NRCS design analysis looked

at three specific dam rehabilitation solutions. The NRCS possible solutions included: 1.

Widening the emergency spillway, 2. Raising the height of the dam with a parapet wall,


3. Armoring the emergency spillway to resist erosion failure, 4. Combination of the first

three courses of action. The NRCS concluded that the combination of parapet wall and

armoring the emergency spillway was the best recommended course of action. Not

knowing how the NRCS design engineers arrived at this conclusion, the linear

programming technique might have been employed to solve this decision.

The linear programming technique was applied to a hypothetical situation for one

of the South River dams. It is assumed that for the South River dams armoring of the

spillway will need to be completed, whether any action is taken. There is a fixed cost for

armoring the spillway that can be reduced to a unit cost per linear foot of emergency

spillway. The remaining other 3 courses of action remain valid: widening the emergency

spillway, raising the height of the dam, and a combination of the first two. The following

data table would then have to be determined to give a starting point:

Table 6.5: Hypothetical Data for South River Dam Rehabilitation COA 1 COA 2 COA 3

Raise Dam w. Parapet

Wall

Widen the Emergency

Spillway

Combination of Raise &

Widen

Cost per Linear Foot Mod. a1$ b1$ c1$

Increase Q per Linear Foot Mod. a2$ b2$ c2$

Armoring E. Spillway Cost per Linear Foot Mod. a3$ b3$ c3$

Following the linear program formulation steps, step 1 requires identification of

variables for the problem. The above hypothetical data is expressed as a metric by

linear foot of modification. The amount of linear foot modification required for each

course of action is unknown, and therefore becomes logical variables. The variables X1,

X2, and X3 are assigned as unknown variables. For step 2, all constraints on the

problem must be identified and expressed as an equation or inequality. Ideally, the total

cost should equal or be greater then flood reduction benefits to yield a benefit-cost ratio


of 1. This sets the first constraint for the problem. The second constraint would be the

increase in discharge, Q which should be greater then or equal to the required Q in order

to pass the PMF. Using the variables the following constraint inequalities are created:

Con1: (A1$ * X1) + (B1$ * X2) + (C1$ * X3) < Flood Reduction Benefits $

Con2: (A2$ * X1) + (B2$ * X2) + (C2$ * X3) > Q, passage of PMF

In order to handle the inequalities, two new variables are introduced, X4 and X5. The X4

and X5 variable represent a large number that when added or subtracted to the function

makes the inequality valid as an equation. This changes Con1 and Con2 to:

Con1: (A1$ * X1) + (B1$ * X2) + (C1$ * X3) - X4 = Flood Reduction Benefits $

Con2: (A2$ * X1) + (B2$ * X2) + (C2$ * X3) + X5 = Q, passage of PMF

To complete Step 3, the objective function must be determined. For this

hypothetical situation, the armoring of the emergency spillway is contingent upon the

width of the emergency spillway. The width of the emergency spillway will vary based

upon the optimal solution, but the goal would be to minimize this cost. Therefore the last

row in Table 6.5 becomes the objective function:

Minimize (Z): (A3$ * X1) + (B3$ * X2) + (C3$ * X3) + 0*X4 + 0*X5

The X4 and X5 variables are also included in the objective function as they were added

into the constraints. They are given a coefficient constant of zero, so as not change the

objective function value.

The final linear program to be solved for the hypothetical South River dam

situation would be:

Minimize (Z): (A3$ * X1) + (B3$ * X2) + (C3$ * X3) + 0*X4 + 0*X5

Subject to:

Con1: (A1$ * X1) + (B1$ * X2) + (C1$ * X3) - X4 = Flood Reduction Benefits $

Con2: (A2$ * X1) + (B2$ * X2) + (C2$ * X3) + X5 = Q, passage of PMF


This linear program could then be entered into Excel Solver to determine the optimal

solution values for X1, X2, and X3 that would minimize the Armoring cost. The power of

the linear program technique is that each solution process can be tailored to a given

situation. Thus, the linear programming techniques could be applicable in other areas of

the design process where a best solution analysis is required. The next section shows

how linear programming is used to expand Mr. Graham�s economic analysis.

6.3 Expansion of Alternative Economic Analysis Through Linear Programming

A working model was created by the expansion of Mr. Graham�s economic

analysis approach. The intent was to create a method of reflecting the best of course

action to complete a dam rehabilitation project. Mr. Wayne Graham�s equations were

the basis for which the model was created (Graham, 2000). His published article

included a case study that provided data that was adapted to test the new expansion of

the analysis.

The ultimate goal for the model was to create a linear program that solves a set

of constraints to maximize the Economic Benefits of the proposed remediation project.

As Mr. Graham�s analysis determined, the Economic Benefits should outweigh the

Construction Costs. Coupled with the Economic Benefits is the Life Benefits, which

must be positive in order for a project to be completed. Therefore, the maximization of

economic benefits became the objective function. The model formulation, the test

example, and the final results will be discussed further in the following sections.

6.3.1 Model Formulation

Mr. Graham�s key parameters on which he focuses are the Economic Benefits

(EB) and Life Benefits (LB). The following decision guidance is summarized:

1. If EB and LB are negative, reject project.

2. If 0 < EB < CM and LB is negative, reject project.


3. If EB < CM and LB is positive, Compute Cost-per-life saved.

4. If EB > CM and LB is negative, Compute Benefit-per-life lost.

5. If EB > CM and LB is positive, Proceed with project.

The parameter CM represents the construction of cost for the modification of the

existing dam. From the above guidance, the last condition is the most desirable goal in

which a dam owner needs. The dam owners must make a change to the dam in order to

meet the current dam safety restrictions for the type of dam they own. The third and

fourth conditions allow the user to quantify the cost of meeting the safety restrictions by

only partially meeting the fifth condition.

In looking at the fifth condition, the Objective Function logically became to

maximize Economic Benefits (EB):

Objective Function (Z): Maximize EB

The other key part to the fifth condition in the above guidance is the Life Benefits (LB)

must be positive. LB becomes a variable, and by the standard form for linear

programming, all variables must be non-negative.

Constraints for the Objective Function were formulated beginning with the two

key decision variables EB and LB. The first constraint is:

Con1: LS � LM � LC � LB = 0 (1)

Simply stated, life benefits (LB) equal life lost under the status quo (LS), minus life lost

under modification (LM), minus life lost due to construction (LC). The variables LS, LM,

and LC create other constraints, and therefore will be discussed later on.

The second constraint is based upon the Economic Benefits:

Con2: ES � EM � EB = 0 (2)

The Economic Benefits equal the Economic Losses (ES) from the status quo, minus the

Economic Losses (EM) from the modifications. Similarly as with Con1, the additional

variable ES and EM create other constraints to be further discussed.


For the variables LS and LM, the loss of life is a function of warning time (WT) and

the number of people at risk (PAR) in the flood plain. As previously discussed, the

BUREC regulation provides guidance for estimating the loss of life (Graham, 1999). The

low and high values for WT are in the situation of where no warning is given or if there

are greater then 90 minutes of WT. In the case of no warning time, the results are

catastrophic and average at 50% loss of life from exposed population. In the case with

greater then 90 minutes of warning, almost all loss of life is avoided, or a 0.2% loss of

life on average. So, WT becomes a constant that is set based upon expected warning

time. However, the PAR remains variable as it depends on the magnitude of the flood in

most cases. So the following constraints were determined:

Con3: LS � WTS x PARS = 0 (3)

Con4: LM � WTM x PARM = 0 (4)

The loss of life due to construction is a function of the construction costs (CM). A

construction life lost constant is determined (CL). This sets the next constraint:

Con5: LC � CL x CM (5)

To get at the variables EM and ES an assumption was made. The value of the

Economic Flood Losses is assumed to be a function of the magnitude of the flood (ie. %

PMF). Therefore, a damage value is estimated for varying flood magnitudes, usually

percentage of the PMF for consistency. Performing a regression on these values, based

on the assumption, the result is an equation for a line. Thus the following constraints

were created:

Con6: -ES + (mS) x (XS) + bS = 0 (6)

Con7: -EM + (mM) x (XM) + bM = 0 (7)

The variables XS and XM represent the percentage of PMF for the status quo and the

modification conditions. The constants mS, bS, mM, and bM are generated from data

and analysis from the status quo and the modification conditions.


Similar logic is needed to estimate the people at risk (PAR) variables. As the

magnitude of the flood increases, the PAR should increase. In reality, this is not as

simple as stated because PAR is a function of two factors. The first factor is the

magnitude of the flood that is passed through the dam spillway. In the modification

case, the enlargement of the spillway causes the PAR value to increase due to more

volume of water passed at lower flood conditions. The second factor is the ultimate dam

failure caused by overtopping. As stated above the warning time plays largely into the

amount of people affected also. For simplicity with this linear program formulation, it is

assumed that the above two factors are already calculated to create a single value of

PAR for each flood wave magnitude. Thus a linear regression is performed to give the

following constraints:

Con8: -PARS + (mPARS) x (XS) + bPARS = 0 (8)

Con9: -PARM + (mPARM) x (XM) + bPARM = 0 (9)

The constants mPARS, bPARS, mPARM, and bPARM are generated from data and

analysis from the status quo and the modification conditions.

The next constraint also involved an assumption. The construction cost involves

a certain initial cost to achieve a minimum modification. From that minimum

modification, to achieve the full desired construction result is a function of material and

labor. For example, to raise a dam one foot costs the initial overhead to begin the

project. Each additional foot can be determined largely upon the additional materials

and labor hours required. Again for simplicity, an initial cost is set for the project, and

modification costs are assumed to increase as the percentage of PMF increases. This

set the constraint:

Con10: -CM + (mCM) x (XM) + bCM (10)

The constants mCM and bCM are generated from data and analysis from the status quo

and the modification conditions.


One final constraint required was for the variables XS and XM, the percentage of

PMF. These are two variables as they impact differently based upon the comparison of

the status quo versus the modification plan. However, in reality the flood magnitude

would be constant, and thus Xs and Xm must be equal. This leads to the last constraint:

Con11: XS � XM = 0 (11)

In summary the linear program includes the Objective Function, 11 main

constraint equations, and 12 variables. Of course for the standard form, the variables

are assumed to be non-negative which creates an additional 12 constraints. The linear

program is shown below:

Objective Function (Z): Maximize Eb

Subject To: Con1: LS � LM � LC � LB = 0 (1) Con2: ES � EM � EB = 0 (2) Con3: LS � WTS x PARS = 0 (3) Con4: LM � WTM x PARM = 0 (4) Con5: LC � CL x CM (5) Con6: -ES + (mS) x (XS) + bS = 0 (6) Con7: -EM + (mM) x (XM) + bM = 0 (7) Con8: -PARS + (mPARS) x (XS) + bPARS = 0 (8) Con9: -PARM + (mPARM) x (XM) + bPARM = 0 (9) Con10: -CM + (mCM) x (XM) + bCM (10) Con11: XS � XM = 0 (11)

Variables: LS, LM, LC, LB, ES, EM, EB, PARS, PARM, CM, XS, XM > 0

With formulation of a model complete, the next step is to test the model to analyze the

linear program. The next section describes the test model used.

6.3.2 Test Example

Graham (2000) provided a demonstration of the economic analysis. The overall

purpose of his discussion was to show that dam modifications to achieve compliance

with the current dam safety regulations are not a worthy investment. With that objective

in mind, we realize that his example is geared towards demonstrating his purpose.


However, his example gave a starting point on putting together a test for the linear

program.

The test example is based on some real data and also assumptions made by Mr.

Graham. The example is a Dam located in Colorado that in 1993 was being considered

for a modification project. A new spillway combined with a nine-foot dam heightening

involved a total cost of $31 million. The new spillway was a 200 foot sill, set 45 feet

below the dam crest. Assuming a worst case expected flow out of that spillway, the

calculated discharge rate is approximately 8,800 cubic feet per second (cfs). That is a

large amount flow that is now allowed to pass through the dam. For this example a

Warning Time (WT) of 0.002 was assumed, and the constant for construction losses

(CL) is 0.014.

In the article example, 100,000 people were assumed to be at risk in the

floodplain, which allowed for the simple warning time adjustment to arrive at a single

value PAR value. A single value was not the desired end-state for the model. So data

was created to replicate the PAR for given percentages of the PMF. Taking the 100,000

PAR, assuming the worse case of complete dam failure at 100% PMF, a value of 50,000

lives lost was estimated for the status quo. From there, the values were scaled back as

the percentage of PMF scaled back. In the modification design, the 100% PMF can now

pass. For this case, assuming no warning time also, a value of 1000 lives lost was

assigned. As for the status quo, the values were scaled back as the percentage of PMF

scaled back. Refer to Appendix C for the full data set, the regression plots, and the

derived line equations. This set the constants mPARs, bPARs, mPARm, and bPARm.

The Economic Damages were compiled for both the status quo and the

modification plan. They were annualized in order to allow for easy comparison, and

compiled in Table 2 of Mr. Graham�s article (Graham, 2000). The Annualized Damages

for the modification plan followed a decreasing trend that is expected. The damages in


higher magnitude floods are larger, but occur less frequently. For the status quo, the

damages start downward, but then drastically increase in the 75-100 PMF range. The

cause of this is not explained, but one can infer dam failure must be involved. In order to

demonstrate the linear program, a linear downward trend was assumed to simplify the

issue. For future work, two equations would need to be developed: 1. Damages with

dam intact, and 2. Damages with dam failure.

Additional minimal conditions were needed in order to limit the percentage of

PMF for this test example. The damages begin to incur at certain percentages of the

PMF; therefore, a minimum value for XS and XM was needed. This tailors the

generalized linear program to the realistic data. Otherwise the linear program would

most likely optimize the modification plan at zero percent of the PMF. The whole

purpose for the analysis is consistent in that the status quo dam is not in compliance

with current dam regulations, and the modification must reach some percentage of the

PMF being passed. Refer to Appendix 3 for the data set, plots, and the linear regression

equations for the Economic Damages. This data set the values for the constants mS,

bS, mM, and bM.

The final data part needed was the construction cost data. The annualized

yearly construction costs were $1.55 million. An annualized fixed cost of 500,000 was

assumed. This represents a fixed cost that must be overcome to make any modification.

Data points were then generated for the other percentages of PMFs such that the 100%

PMF equaled the total cost of $1.55 million. Refer to Appendix C for the data set, plots,

and the linear regression equations for the Construction Costs. This data set the values

for the constants mCM and bCM.

With the test example set up, the model was then entered into Excel Solver to

run the Model. A total of six different runs were completed in order to demonstrate the


capabilities of the linear program, as well as test different conditions. The next section

explains the results.

6.3.3 Results from Simulation Runs

The linear program formulated above for the test example was inputted into

Excel Solver. Refer to Appendix C for the original model, and the model outputs. Six

different runs are summarized in Table 6.6:

Table 6.6: Summary of Results Eb Lb Xs/Xm Feasible

Run # ($) (+ or 0) (%) Solution 1 N/A N/A N/A Not Feasible 2 N/A N/A N/A Not Feasible 3 239750 + (11) 0 Feasible 4 239750 + (39) 25 Feasible 5 239750 + (39) 25 Feasible 6 239750 0 25 Feasible

The first run was the first set of derived conditions loosely based up the test

example from Graham (2000). As expected, there was not a feasible solution found for

the model. This follows Graham�s purpose that completing modifications to dam

spillways are usually not practical. The second run simply switched the Economic

Damages from the two conditions, thus creating a situation where the Damages from the

modification are much less then the status quo. This run also proved to be infeasible as

the construction costs were much too large to overcome.

The third run eliminated the construction costs, thus pushing the model to select

the modification course of action. For this case, the Economic Damages are better

under the Modification Plan, and the cost of the Modification Plan is zero. As expected,

a feasible solution was found. The Economic Value was maximized, Life Benefits were

positive, but the Flood magnitude was zero. To account for the fact that a minimum


value for the flood is required, Xs was set at 25%. The model was rerun, and a feasible

solution was found. Interestingly, the magnitude of the Life Benefits increased.

To further test the sensitivity of the model, the fifth and sixth runs set the People

at Risk for the modification plan to zero, and then both PARs at zero. This creates a

situation where the modification plan produces less economic damages and does not

increase the PAR parameter. As expected feasible solutions were found for both of

these runs, and this concluded the sensitivity analysis performed on the new model.

6.3.4 Discussion of New Linear Program Technique

The formulated linear program is an expansion of Graham�s work. The model

was an attempt to apply his technique to more realistic conditions. The model is more

complicated then Graham�s, however simplifying assumptions may prove to be

ineffective when applied to a real case study. The damage curves could be more

complicated, and thus assuming a linear regression equation may introduce

unacceptable error. Also, the uncertainty at arriving at the values for the Flood

Damages and People at Risk creates new areas where this model may not be effective,

or at least may need to be adjusted. These complexities were overcome by making

assumptions in order to create a test example for the model. However since every dam

situation is different, specific analysis must be performed anyways that arguable would

lead to results similar to the assumptions that we made.

The overall goal for the linear program was met in that the economic benefit (EB)

was maximized. The new model was applied to a test situation in which data was

generated from Mr. Graham�s example. Varying the warning time should cause the

model to yield different results, and so becomes a key value that must be selected.

Using the BUREC�s method for estimating the PAR relies heavily on the warning time

prior to the catastrophic event. A modification plan that included a highly reliable warning


detection system, coupled with a systematic notification process can drastically

decrease the loss of life caused by major flooding or even dam failure. With warning

system in place the PAR parameter would be reduced, which will increase the

possibilities of achieving positive life benefits (LB).

6.4 Summary

This chapter brings forth two alternative analyses for dam rehabilitation: Mr.

Graham�s economic analysis and linear programming techniques. Both analyses are

meant to be used as supplemental tools that would augment the traditional rehabilitation

analysis presented in Chapter 4. Graham�s analysis, although founded upon criticism of

the PMF design standard, proved to be effective when applied to the South River dams.

Results from the applied analysis showed that the recommended dam rehabilitations of

the three South River dams should not be completed, and the NRCS economic analyses

yielded benefit-cost ratios of less then one. Yet the fact that NRCS went forward with

the recommendation to complete the rehabilitation demonstrates that other

circumstances can factor into the decision to proceed with a project, and that these

analyses are only decision making tools.

The extension of Graham�s analysis through the use of linear programming is a

new concept that needs further testing for real situations. The South River case study

was not a good match for the initial conditions. All three of the dams are classified as

high risk, and so the NRCS design and economic analysis was never intended to reach

a lower design standard than passing the PMF. Consequently, the available economic

data was limited to the 500 year flood, and the breach failure. If we assume the breach

failure occurs at the known percentage of the PMF for the dams (55%, 60%, & 50% for

Robinson Hollow, Toms Branch, and Inch Branch respectively), then we could fit a trend

line from the 500 damages to the damages at the dam failure. This linear function might


sufficiently represent the damages, but the best result would be to route the flood waves

for percentages of the PMF and calculate the expected damages.

A similar discussion could be repeated for the expected lives lost from the same

flood waves. Hence, based upon the available data from the South River dams,

significant assumptions would have to have been made in order for the proposed

extension analysis to be applied. These broad assumptions would be similar to the ones

made for Graham�s test example, and so would still remain as a theoretical approach.

The next logical step to validate the extended analysis would be to apply the approach to

a real case study of a �significant� classified dam in need of dam rehabilitation.

Chapter 7: Summary, Conclusions, and Recommendations 107

Chapter 7: Summary, Conclusions, and Recommendations

7.1 Summary

In order to comment on the completion of this thesis, the following original goals

were presented in Chapter 1 as a desired end state:

1. Develop a standard protocol to assist dam owners in performing decision

analysis for dam rehabilitation for dams that are out of safety compliance.

2. Develop a method to prioritize courses of actions for dam remediation.

The 12 step traditional approach discussed in Chapter 4 is the recommended standard

protocol that will assist dam owners in performing decision analysis. This method is by

no means easy or rapid. In fact, it is usually quite the opposite. Even though the process

introduces some �art� in an otherwise scientific approach, the method produces credible

results that can be weighted significantly in making an informed decision.

The continual advancement in GIS and mathematically based simulation models

in analysis areas of hydrology, hydraulics, economics, and optimization has opened the

way for automation in assessing the feasibility of dam rehabilitation. However, as shown

in Chapter 5, the existing programs have many limitations and are concluded to be

inferior to the traditional approach. There certainly is potential gain from employing

existing analysis programs, but at this time these should only augment the traditional

approach.

As for the second goal, the traditional approach to economic analysis also sets

the priority for courses of action. The incremental economic analysis by definition

analyzes the incremental gain or loss between two courses of action. Thus, the courses

of action can easily be ranked based upon the incremental analysis. Linear

programming as shown in Chapter 6 can also be an effective way to prioritize courses of

action. An additional feature of linear programming is that sensitivity analyses can be


performed on the recommended course of action by adjusting the constraints for the

given problem.

The Chapter 3 HEC-HMS modeling work performed on the South River

watershed represents the necessary hydrologic analysis that is critical to the economic

assessment of dam rehabilitation. The model work was performed to establish the

impact of the flood control dams on the city of Waynesboro, Virginia. This separate goal

was also achieved, in that the local impacts as well as the down stream impacts were

represented in the modeling results. These results were acknowledged by the

Headwaters Soil & Water Conservation District as being extremely effective in

demonstrating the importance of the flood control dams for the city of Waynesboro.

The HEC-HMS model could be further refined as a future project. The large

scale averaging on certain model input parameters made during the calibration of the

model may prove to be grossly inaccurate at sub-watershed level. For example, the

variations in observed rainfall depth in comparison to location were not well addressed.

Applying a rainfall distribution to the rainfall gage data, and checking against recorded

NEXRAD imagery could enhance the calibration of the model. Additionally, the

watershed parameters can also be spatially distributed using GIS applications. An

interesting question might arise: �By distributing the watershed parameters, are the

model results closer to the observed flows then what was created by the current model?�

Finally, the proposed extension of Graham�s economic analysis through linear

programming is at best a theoretical approach. The application needs further testing on

real examples where dam rehabilitation is being looked at for significant classified dams.

The data requirements may not be attainable without personally performing data

calculations. This problem arises because the economic analyses might not always be

incremented by percentages of the PMF. This might force unwanted assumptions to be


made in order for the analysis approach to work, which could detract from the credibility

of the method.

7.2 Conclusions

The following compiled comments represent sequential conclusions presented in

earlier chapters:

• The 12 agricultural flood control dams in the South River watershed effectively

reduce flood events in the immediate localized area below the dams.

• The flood reduction effects of the dams diminish significantly with distance down

stream, and therefore partially impact flooding in Waynesboro, Virginia.

• The upper South River dams effectively meet the original SCS intent of

protecting agricultural lands in the watershed.

• The traditional step-by-step economic process to perform a dam rehabilitation

analysis is one way of completing the necessary economic analysis for a project

proposal.

• The traditional economic analysis is time and resource intensive, and

incorporates several professional disciplines such as engineering and economics.

• The HAZUS-MH model was demonstrated as not versatile enough to perform

dam rehabilitation analysis, nor was the model ever meant to perform such an

analysis.

• The HAZUS-MH model is a GIS application, and therefore does have potential to

assist with defining an initial flood inundation zone as a starting point.

• The HAZUS-MH model achieves semi-automation at the expense of accuracy in

results.


• The application of linear programming has demonstrated that linear programming

can be used to enhance a dam rehabilitation analysis through establishing an

optimal solution.

• The expanded Graham�s analysis potentially could assist a rehabilitation analysis

to establish an optimal solution that is less then full PMF, and thus reduce

construction costs.

7.3 Recommendations

The passage of the PMF versus a percentage of the PMF as a dam safety

standard discussion remains a critical issue for a large portion of existing dams. In the

situation of Significant and Low risk classified dams, the passage of the full PMF is not

always required. However, what is required in most cases is an engineering/economic

analysis demonstrating that passage of the percentage of the PMF meets established

safety criteria, and that increasing to the full PMF does not decrease flood damages. A

way of solving such a problem is through an iterative method of designing the structure,

routing the flood wave, and calculating damages for each percentage of PMF increment.

This approach, like the presented traditional economic analysis in Chapter 4 is time and

resource intensive.

The alternative linear programming technique potentially could reduce the time

and effort of the rigorous iterative approach. The solution of the linear program

immediately arrives at the optimal solution, assuming the established constraints

accurately represent the real situation. Validation of the linear program method might

prove to be a very useful technique for dam owners. To accomplish the validation,

several case study dams would be required, preferably not in the same watershed. The

case study dams would need to be Significant or Low risk dams that must be

rehabilitated to meet a certain PMF passage standard.


Validation of the linear program could be accomplished using the case study

dams by first completing the rehabilitation analysis through the rigorous iterative

approach. While completing the more traditional approach, the required economic data

will be gathered that could then be used for the alternative linear programming method.

The linear program parameters discussed in Chapter 6 will be obtained from the reduced

economic data. Finally, a comparison of the results from the traditional method versus

the linear programming technique could be made.

Assuming the alternative linear programming technique proved valid for the case

study dams classified as Significant and Low risk, then the question arises: �Are there

High risk dams where a percentage of the PMF may prove to be the optimal solution?�

This question remains the essential one in the argument put forth in Graham (2000).

The new approach may prove to be a justification for requesting an exception to the full

PMF passage requirement on certain qualified dams. Such an exception would reduce

the rehabilitation costs of certain dams, and potentially allow for other aging dams to

also be rehabilitated.

Bibliography 112

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Appendix A: HEC-HMS Data

Appendix A: HEC-HMS Data 115

Table A.1: South River Watershed Sub-Area Data

South River Watershed

Sub Area

Drainage Area

SCS Curve #


Reach Length

Elev Drop

Reach

Reach Channel

Slope (#) (Sq Mi) (#) (in) (hr) (ft) (ft) (ft/ft) 1 3.41 66 1.030 1.51 - - - 2 2.72 66 1.030 1.41 - - - 3 0.42 66 1.030 0.55 4050 48 0.012 4 3.61 66 1.030 1.54 - - - 5 1.67 68 0.941 0.91 14200 66 0.005 6 3.14 65 1.077 1.40 - - - 7 0.66 66 1.030 1.20 10000 66 0.007 8 0.71 67 0.985 0.99 6400 55 0.009 9 0.99 66 1.030 1.63 - - - 10 2.91 65 1.077 0.98 - - - 11 0.52 65 1.077 1.10 5200 40 0.008 12 2.61 65 1.077 1.77 14000 160 0.011 13 4.23 65 1.077 1.35 - - - 14 0.77 65 1.077 1.17 5200 120 0.023 15 0.68 66 1.030 0.89 5300 36 0.007 16 0.67 67 0.985 0.81 6400 24 0.004 17 2.27 61 1.279 1.27 - - - 18 0.30 66 1.030 0.80 2100 60 0.029 19 0.45 66 1.030 0.49 3400 14 0.004 20 3.43 65 1.077 1.81 - - -

21a 2.70 68 0.941 1.51 10700 39 0.004 21b 3000 8 0.003 22 2.85 65 1.077 1.66 - - - 23 2.79 65 1.077 1.16 - - - 24 1.65 65 1.077 2.02 - - - 25 1.04 66 1.030 1.34 5100 61 0.012 26 0.10 66 1.030 0.53 4500 17.5 0.004 27 0.97 68 0.941 1.36 - - - 28 1.29 69 0.899 0.91 1000 0.5 0.001

29a 3.61 69 0.899 1.26 7000 4.8 0.001 29b 1400 0.2 0.0001 30 3.30 65 1.077 1.75 - - - 31 0.94 65 1.077 0.71 - - - 32 1.15 66 1.030 1.39 12100 239 0.020 33 2.48 65 1.077 1.07 - - - 34 3.66 67 0.985 1.57 20500 438.8 0.021 35 0.82 67 0.985 0.83 4400 2 0.0005 36 1.42 65 1.077 1.16 - - - 37 1.03 66 1.030 1.46 7900 121 0.015 38 0.74 67 0.985 0.77 4800 6 0.001 39 2.85 65 1.077 1.90 - - - 40 0.76 67 0.985 1.08 4200 47 0.011



Table A.1 (cont.): South River Watershed Sub-Area Data

South River Watershed

Sub Area

Drainage Area

SCS Curve #


Reach Length

Elev Drop

Reach

Reach Channel

Slope (#) (Sq Mi) (#) (in) (hr) (ft) (ft) (ft/ft) 41 1.60 67 0.985 1.15 7300 7 0.001 42 1.17 67 0.985 0.82 - - - 43 2.46 67 0.985 1.73 13200 10 0.001 44 2.03 67 0.985 0.91 - - - 45 0.52 67 0.985 0.89 7700 11 0.001 46 2.76 65 1.077 1.04 - - - 47 2.20 65 1.077 0.88 10000 180 0.018 48 2.85 61 1.279 1.63 - - - 49 1.31 65 1.077 0.56 6000 71 0.012 50 1.16 65 1.077 0.76 9100 99 0.011 51 4.40 65 1.077 1.28 16600 238 0.014 52 2.19 65 1.077 1.16 - - - 53 4.56 61 1.279 1.31 - - - 54 1.16 65 1.077 0.88 1900 78 0.041 55 0.83 66 1.030 1.19 8100 56 0.007 56 1.58 65 1.077 1.04 - - - 57 3.70 65 1.077 1.45 - - - 58 1.10 65 1.077 1.25 18900 416 0.022 59 1.64 67 0.985 2.04 10600 65 0.006 60 1.13 65 1.077 0.58 - - - 61 0.69 66 1.030 0.53 5900 159 0.027 62 1.60 66 1.030 1.20 4900 25 0.005 63 2.35 66 1.030 0.97 - - - 64 0.54 66 1.030 0.39 4600 70 0.015 65 2.38 67 0.985 1.04 - - - 66 0.07 67 0.985 0.28 1600 23 0.014 67 0.56 66 1.030 0.47 3900 44 0.011 68 1.42 69 0.899 2.05 7800 31 0.004 69 3.59 68 0.941 1.25 12600 27 0.002

Totals 125.87 65.85507



Table A.2: South River Manning's n Values

South River Manning's n Values

Section Description

Main Channel

n

Left Bank

n

Right Bank

n 419 Right after Canada Run SA38 0.069 0.053 0.053 420 Before RR in SA 38 0.069 0.078 0.060 421 After RR in SA 38 0.069 0.078 0.060 422 SA 38 0.076 0.050 0.050 430 SA 45, Right Before SR 664 0.072 0.103 0.090 431 SA 45, Right After SR 664 0.072 0.103 0.090 432 SA 45, Just beyond SR 664 0.072 0.103 0.102 433 SA 45, 2000 feet beyond SR 664 0.072 0.087 0.078 434 SA 69, Just Beyond Back Creek 0.076 0.050 0.052 435 SA 69, Just Before SR 650 0.070 0.075 0.078 436 SA 69, Middle of SR 650 0.070 0.075 0.078 437 SA 69, After SR 650 0.070 0.075 0.078 438 SA 69, Near TBM 18 0.073 0.078 0.063

Averages 0.072 0.078 0.072

Table A.3: Back Creek Manning's n Values

Back Creek Manning's n Values

Section Description Main

Channel n Left

Bank n Right

Bank n 310 SA 51 0.068 0.075 0.078 311 SA 55 0.070 0.078 0.070 312 SA 55, SR 610 0.066 0.070 0.078 313 SA 59, Near TBM 213 0.066 0.050 0.060 314 SA 59, Further Down 0.066 0.078 0.050 315 SA 59, Before End 0.066 0.050 0.075 316 SA 61, Beginning 0.066 0.050 0.050 317 SA 61, 0.066 0.050 0.050 318 SA 67 0.066 0.052 0.083 320 SA 68 at SR 624 0.066 0.060 0.063 323 SA 68 at RR 0.073 0.070 0.070

Averages 0.067 0.062 0.066



Table A.4: South River Cross Section Data Reach Number: 1 Reach Number: 2 Reach Number: 3 Streambed Elevation: 1633 Streambed Elevation: 1585 Streambed Elevation: 1585 Bottom Width: 5 Bottom Width: 5 Bottom Width: 5 Dist Elevation Dist Elevation Dist Elevation Station 1 0 1644 Station 1 0 1596 Station 1 0 1596 Station 2 50 1639 Station 2 50 1591 Station 2 50 1591 Station 3 150 1638 Station 3 150 1590 Station 3 150 1590 Station 4 152 1633 Station 4 152 1585 Station 4 152 1585 Station 5 157 1633 Station 5 157 1585 Station 5 157 1585 Station 6 159 1638 Station 6 159 1590 Station 6 159 1590 Station 7 259 1639 Station 7 259 1591 Station 7 259 1591 Station 8 309 1644 Station 8 309 1596 Station 8 309 1596

Reach Number: 4 Reach Number: 5 Reach Number: 6 Streambed Elevation: 1519 Streambed Elevation: 1700 Streambed Elevation: 1660 Bottom Width: 7 Bottom Width: 5 Bottom Width: 6 Dist Elevation Dist Elevation Dist Elevation Station 1 0 1530 Station 1 0 1711 Station 1 0 1671 Station 2 50 1525 Station 2 50 1706 Station 2 50 1666 Station 3 150 1524 Station 3 150 1705 Station 3 150 1665 Station 4 152 1519 Station 4 152 1700 Station 4 152 1660 Station 5 159 1519 Station 5 157 1700 Station 5 158 1660 Station 6 161 1524 Station 6 159 1705 Station 6 160 1665 Station 7 261 1525 Station 7 259 1706 Station 7 260 1666 Station 8 311 1530 Station 8 309 1711 Station 8 310 1671





Table A.4 (cont.): South River Cross Section Data Reach Number: 13 Reach Number: 14 Reach Number: 15 Streambed Elevation: 1387 Streambed Elevation: 1440 Streambed Elevation: 1379 Bottom Width: 11 Bottom Width: 7 Bottom Width: 12 Dist Elevation Dist Elevation Dist Elevation Station 1 0 1398 Station 1 0 1451 Station 1 0 1390 Station 2 50 1393 Station 2 50 1446 Station 2 50 1385 Station 3 150 1392 Station 3 150 1445 Station 3 150 1384 Station 4 152 1387 Station 4 152 1440 Station 4 152 1379 Station 5 163 1387 Station 5 159 1440 Station 5 164 1379 Station 6 165 1392 Station 6 161 1445 Station 6 166 1384 Station 7 265 1393 Station 7 261 1446 Station 7 266 1385 Station 8 315 1398 Station 8 311 1451 Station 8 316 1390






Table A.5: Rating Table Data

Poor Creek Rating Table

Lofton Lake Rating Table



Table A.5 (Cont.): Rating Table Data

Stoney Creek Rating Table

Lake Wilda Rating Table



Table A.5 (Cont.:) Rating Table Data

Canada Run Rating Table

Waynesboro Nursery Rating Table




Inch Branch Rating Table

Toms Branch Rating Table




Robinson Hollow Rating Table

Happy Hollow Rating Table




Mills Creek Rating Table

Upper Sherando Rating Table

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

12

8

Ta

ble

A.6:

IFL

OW

S R

ainf

all D

ata

Hur

rican

e Is

abel

, Sep

tem

ber,

2003

ID #

10

:00

10:1

5 10

:30

10:4

5 11

:00

11:1

5 11

:30

11:4

5 12

:00

12:1

5 12

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12:4

5 13

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13:1

5 13

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13:4

5

Tota

l To

ms

Bra

nch

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0

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0

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04

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0

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eran

do

1201

0

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04

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0

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Rob

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n H

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w

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0

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St

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48

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28

ID

#

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0 14

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14:3

0 14

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15:0

0 15

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15:3

0 15

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16:0

0 16

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16:3

0 16

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17:0

0 17

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To

tal

Tom

s B

ranc

h 12

00

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08

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16

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16

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16

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08

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12

Sher

ando

12

01

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24

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52

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ollo

w

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12

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24

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U

pper

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rand

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24

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24

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0.

35

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87

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28

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16

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5.82

M

ills

Cre

ek

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24

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0

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12

0.12

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3

ID

#

18:0

0 18

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18:3

0 18

:45

19:0

0 19

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19:3

0 19

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20:0

0 20

:15

20:3

0 20

:45

21:0

0 21

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0 21

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To

tal

Tom

s B

ranc

h 12

00

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12

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12

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3.

96

Sher

ando

12

01

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16

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18

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low

12

02

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24

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16

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64

Ston

ey C

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12

07

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08

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08

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pper

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rand

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55

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3 M

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ek

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04

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25

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3 0.

25

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0.

16

0.16

6.24

ID #

22

:00

22:1

5 22

:30

22:4

5 23

:00

23:1

5 23

:30

23:4

5 0:

00

0:15

0:

30

0:45

1:

00

1:15

1:

30

1:45

Tota

l To

ms

Bra

nch

1200

0.

34

0.34

0.

24

0.2

0.2

0.2

0.08

0.

08

0.27

0.

25

0.24

0.

12

0.16

0.

16

0.08

0

6.

92

Sher

ando

12

01

0.32

0.

4 0.

16

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0.

12

0.16

0.

16

0.23

0.

25

0.16

0.

08

0.2

0.16

0.

12

0

7.68

R

obin

son

Hol

low

12

02

0.4

0.4

0.28

0.

16

0.04

0.

12

0.12

0.

08

0.08

0.

2 0.

12

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14

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04

0

7.08

St

oney

Cre

ek

1207

0.

3 0.

3 0.

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27

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08

0.08

0.

06

0.06

0

0

6.59

U

pper

She

rand

o 12

40

0.9

0.9

0.56

0.

55

0.34

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36

0.14

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14

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0.

47

0.24

0.

04

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0.

14

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0

20

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Mill

s C

reek

12

48

0.31

0.

37

0.44

0.

16

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0.2

0.08

0.

08

0.26

0.

26

0.12

0.

08

0.1

0.1

0.04

0

9.

04

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

12

9

Tabl

e A.

6 (c

ont.)

: IF

LOW

S R

ainf

all D

ata

H

urric

ane

Isab

el, S

epte

mbe

r, 20

03 (c

ont.)

ID #

2:

00

2:15

2:

30

2:45

3:

00

3:15

3:

30

3:45

4:

00

Tota

l Sh

eran

do

1201

0.

24

0.12

0.

12

0.12

0.

08

0.08

0

0 0

0 0

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0 0

0

8.44

ID #

11

:00

12:0

0 13

:00

14:0

0 15

:00

16:0

0 17

:00

18:0

0 19

:00

20:0

0 21

:00

22:0

0 23

:00

0:00

1:

00

2:00

3:

00

To

ms

Bra

nch

1200

0.

04

0.16

0.

04

0.04

0.

24

0.44

0.

56

0.32

0.

2 0.

44

0.36

0.

6 0.

92

0.56

0.

72

0.32

0

Sh

eran

do

1201

0

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0

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0.

24

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0.

84

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0.

52

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52

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0.

84

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44

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Rob

inso

n H

ollo

w

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0.

04

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0

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24

0.6

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44

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76

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36

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Ston

ey C

reek

12

07

0 0.

12

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0

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44

0.6

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76

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36

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0

U

pper

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rand

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40

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16

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83

2.09

1.

19

1.84

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81

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05

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0.

98

0.8

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0

M

ills

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ek

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0

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32

0.52

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96

0.56

0.

72

0.56

0.

72

0.84

1

0.56

0.

52

0.2

0.04

ID

#

4:00

5:

00

Tota

l

Tom

s B

ranc

h 12

00

0 0.

08

6.04

Sher

ando

12

01

0.16

0

7.6

R

obin

son

Hol

low

12

02

0.04

0

6.32

Ston

ey C

reek

12

07

0.04

0

5.79

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er S

hera

ndo

1240

0.

08

0 17

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M

ills

Cre

ek

1248

0.

04

0 7.

8

M

ean

6.71

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

0

Ta

ble

A.6

(con

t.): I

FLO

WS

Rai

nfal

l Dat

a

Hur

rican

e Je

anne

, Sep

tem

ber,

2004

ID #

14

:00

14:1

5 14

:30

14:4

5 15

:00

15:1

5 15

:30

15:4

5 16

:00

16:1

5 16

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16:4

5 17

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17:1

5 17

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17:4

5

Tota

l To

ms

Bra

nch

1200

0

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01

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01

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eran

do

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0

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obin

son

Hol

low

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02

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07

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ills

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ek

1248

0

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02

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02

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0

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ID #

18

:00

18:1

5 18

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18:4

5 19

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19:1

5 19

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19:4

5 20

:00

20:1

5 20

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20:4

5 21

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21:1

5 21

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21:4

5

Tota

l To

ms

Bra

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1200

0

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02

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low

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02

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32

Mill

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reek

12

48

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02

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02

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16

ID

#

22:0

0 22

:15

22:3

0 22

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23:0

0 23

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23:3

0 23

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0:00

0:

15

0:30

0:

45

1:00

1:

15

1:30

1:

45

To

tal

Tom

s B

ranc

h 12

00

0 0

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0.

02

0 0

0 0

0 0

0 0

0 0

0.

12

Sher

ando

12

01

0 0

0 0

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02

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0

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02

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0.

24

Rob

inso

n H

ollo

w

1202

0

0 0.

02

0.02

0

0 0

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02

0.02

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04

0.04

0

0

0.36

St

oney

Cre

ek

1207

0

0 0

0 0

0 0

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02

0.02

0

0 0

0 0

0

0.2

Upp

er S

hera

ndo

1240

0

0 0

0 0

0 0

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04

0.04

0

0 0

0 0.

02

0.02

0.44

M

ills

Cre

ek

1248

0

0 0

0 0.

02

0.02

0

0 0

0 0

0 0.

02

0.02

0

0

0.24

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

1

Tabl

e A.

6 (c

ont.)

: IFL

OW

S R

ainf

all D

ata

Hur

rican

e Je

anne

, Sep

tem

ber,

2004

(Con

t.)

ID

#

2:00

2:

15

2:30

2:

45

3:00

3:

15

3:30

3:

45

4:00

4:

15

4:30

4:

45

5:00

5:

15

5:30

5:

45

To

tal

Tom

s B

ranc

h 12

00

0.02

0.

02

0 0

0.16

0.

1 0.

1 0.

04

0 0

0 0

0.04

0.

08

0.08

0.

04

0.

8 Sh

eran

do

1201

0

0 0

0 0.

12

0.04

0.

04

0.08

0

0 0

0 0.

02

0.06

0.

12

0.08

0.8

Rob

inso

n H

ollo

w

1202

0.

06

0.06

0.

04

0 0.

08

0.1

0.1

0.08

0.

04

0.02

0.

02

0 0

0.08

0.

08

0.04

1.16

St

oney

Cre

ek

1207

0.

02

0.02

0

0 0.

1 0.

1 0

0 0

0 0

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08

0.08

0.

04

0

0.64

U

pper

She

rand

o 12

40

0 0

0 0.

1 0.

14

0.02

0.

02

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0 0.

18

0.15

0.

15

0.04

1.24

M

ills

Cre

ek

1248

0

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0.

02

0.06

0.

06

0.04

0.

04

0.04

0

0 0

0 0.

04

0.06

0.

06

0.04

0.72

ID #

6:

00

6:15

6:

30

6:45

7:

00

7:15

7:

30

7:45

8:

00

8:15

8:

30

8:45

9:

00

9:15

9:

30

9:45

Tota

l To

ms

Bra

nch

1200

0.

08

0.08

0.

04

0 0.

16

0.2

0.08

0.

38

0.41

0.

16

0.16

0.

04

0.06

0.

1 0.

04

0

2.79

Sh

eran

do

1201

0.

04

0.04

0.

04

0 0.

18

0.2

0.06

0.

21

0.15

0.

15

0.28

0.

12

0.04

0.

04

0.08

0.

08

2.

51

Rob

inso

n H

ollo

w

1202

0.

04

0.04

0.

08

0.08

0.

2 0.

3 0.

06

0.18

0.

29

0.28

0.

28

0.08

0.

14

0.18

0.

04

0

3.43

St

oney

Cre

ek

1207

0.

04

0.04

0

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08

0.08

0.

08

0.1

0.18

0.

1 0.

14

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0

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0

1.56

U

pper

She

rand

o 12

40

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08

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0.

04

0.16

0.

2 0.

11

0.4

0.4

0.4

0.28

0.

04

0.04

0.

08

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0

3.

71

Mill

s C

reek

12

48

0.06

0.

06

0.04

0

0.08

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08

0.08

0.

1 0.

06

0.06

0.

06

0.04

0.

06

0.02

0.

04

0

1.56

ID #

10

:00

10:1

5 10

:30

10:4

5 11

:00

11:1

5 11

:30

11:4

5 12

:00

12:1

5 12

:30

12:4

5 13

:00

13:1

5 13

:30

13:4

5

Tota

l To

ms

Bra

nch

1200

0.

02

0.02

0.

02

0.02

0.

57

0.41

0.

41

0.35

0.

37

0.33

0.

33

0.04

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08

0.04

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04

0

5.84

Sh

eran

do

1201

0

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57

0.37

0.

37

0.39

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4 0.

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04

0.1

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0

5.

79

Rob

inso

n H

ollo

w

1202

0.

04

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04

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33

0.43

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43

0.47

0.

34

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0.4

0.08

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08

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0

0

6.63

St

oney

Cre

ek

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06

0.25

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25

0.08

0.

02

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04

0

2.84

U

pper

She

rand

o 12

40

0.06

0.

06

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0.

06

0.28

0.

35

0.36

0.

55

0.41

0.

35

0.35

0.

12

0.04

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02

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0

6.

8 M

ills

Cre

ek

1248

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01

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01

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24

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06

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16

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0.

08

0.04

0.

1 0.

08

0.06

0

2.

64

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

2

Tabl

e A.

6 (c

ont.)

: IF

LOW

S R

ainf

all D

ata

Hur

rican

e Fr

ance

s, S

epte

mbe

r, 20

04

ID

#

5:00

5:

15

5:30

5:

45

6:00

6:

15

6:30

6:

45

7:00

7:

15

7:30

7:

45

8:00

8:

15

8:30

8:

45

To

tal

Tom

s B

ranc

h 12

00

0.08

0.

04

0.04

0.

08

0.04

0.

02

0.02

0.

04

0.08

0.

04

0.04

0.

16

0.28

0.

2 0.

2 0.

12

1.

48

Sher

ando

12

01

0

Rob

inso

n H

ollo

w

1202

0.

04

0.02

0.

02

0.1

0.1

0.1

0.1

0.12

0.

18

0.18

0.

2 0.

08

0.57

0.

5 0.

47

0.35

3.13

St

oney

Cre

ek

1207

0

0 0

0.06

0.

06

0.06

0.

06

0.08

0.

06

0.06

0.

08

0 0.

22

0.22

0.

32

0.2

1.

48

Upp

er S

hera

ndo

1240

0.

06

0.06

0.

04

0.12

0.

12

0.08

0.

08

0.04

0.

3 0.

3 0.

24

0 0.

7 0.

84

1.1

0.71

4.79

M

ills

Cre

ek

1248

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04

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02

0.04

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04

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0.

04

0.04

0.

14

0.14

0.

16

0 0.

32

0.32

0.

44

0.32

2.12

ID #

9:

00

9:15

9:

30

9:45

10

:00

10:1

5 10

:30

10:4

5 11

:00

11:1

5 11

:30

11:4

5 12

:00

12:1

5 12

:30

12:4

5

Tota

l To

ms

Bra

nch

1200

0.

2 0.

32

0.24

0.

12

0.06

0.

06

0 0

0.24

0.

24

0.12

0.

04

0.02

0.

02

0 0

3.

16

Sher

ando

12

01

0

Rob

inso

n H

ollo

w

1202

0.

3 0.

29

0.08

0

0.06

0.

06

0 0

0.3

0.3

0.28

0.

04

0.06

0.

06

0 0

4.

96

Ston

ey C

reek

12

07

0.1

0.1

0.04

0

0.04

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04

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02

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02

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1.

88

Upp

er S

hera

ndo

1240

0.

3 0.

42

0.24

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12

0.12

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12

0.12

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0.08

0.

08

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6.

59

Mill

s C

reek

12

48

0.3

0.26

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04

0 0.

04

0.04

0.

04

0 0.

2 0.

2 0.

2 0.

04

0 0

0 0

3.

48

ID

#

13:0

0 13

:15

13:3

0 13

:45

14:0

0 14

:15

14:3

0 14

:45

15:0

0 15

:15

15:3

0 15

:45

16:0

0 16

:15

16:3

0 16

:45

To

tal

Tom

s B

ranc

h 12

00

0.02

0.

02

0 0

0 0

0 0.

04

0.04

0.

04

0.04

0

0.16

0.

16

0.28

0.

12

4.

08

Sher

ando

12

01

0

Rob

inso

n H

ollo

w

1202

0.

06

0.06

0

0 0.

04

0.04

0

0.18

0.

18

0.12

0.

12

0 0.

2 0.

2 0.

4 0.

28

6.

84

Ston

ey C

reek

12

07

0.02

0.

02

0 0

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0.

02

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0.16

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16

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16

0.16

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16

2.

92

Upp

er S

hera

ndo

1240

0

0 0

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08

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04

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44

0.5

0.86

0.

39

8.

98

Mill

s C

reek

12

48

0 0

0 0

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04

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0.

27

0.28

0.

2

4.56

ID #

17

:00

17:1

5 17

:30

17:4

5 18

:00

18:1

5 18

:30

18:4

5 19

:00

19:1

5 19

:30

19:4

5 20

:00

20:1

5 20

:30

20:4

5

Tota

l To

ms

Bra

nch

1200

0.

1 0.

1 0

0 0.

04

0.04

0.

08

0.08

0.

2 0.

2 0

0 0

0 0

0

4.92

Sh

eran

do

1201

0 R

obin

son

Hol

low

12

02

0.18

0.

17

0 0

0 0

0.2

0.2

0.2

0.11

0.

08

0 0

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0

7.98

St

oney

Cre

ek

1207

0

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24

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48

0.2

0.4

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4.48

U

pper

She

rand

o 12

40

0 0

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0.14

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14

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28

0.04

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04

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9.

9 M

ills

Cre

ek

1248

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02

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06

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02

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0

5

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

3

Tabl

e A.

6 (c

ont.)

: IF

LOW

S R

ainf

all D

ata

N

ovem

ber 2

9, 2

005

Stor

m

ID

#

18:0

0 19

:00

20:0

0 21

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22:0

0 23

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0:00

1:

00

2:00

3:

00

4:00

5:

00

6:00

7:

00

8:00

9:

00

To

tal

Tom

s B

ranc

h 12

00

0 0.

04

0 0

0.04

0.

12

0.24

0.

2 0.

4 0.

2 0.

28

0.12

0.

08

0.04

0.

2 0.

4

2.36

Sh

eran

do

1201

0

0 0.

08

0 0.

04

0.08

0.

16

0.08

0.

24

0.12

0.

16

0.12

0.

16

0.08

0.

24

0.4

1.

96

Rob

inso

n H

ollo

w

1202

0

0.04

0.

04

0 0

0.04

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12

0.12

0.

32

0.16

0.

16

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0.

08

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12

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1.64

St

oney

Cre

ek

1207

0

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04

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04

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04

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04

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04

0.04

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U

pper

She

rand

o 12

40

0 0

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04

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0.

28

0.36

0.

32

0.84

0.

48

0.28

0.

36

0.24

0.

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52

0.56

4.56

M

ills

Cre

ek

1248

0

0.08

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04

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04

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0.

16

0.16

0.

28

0.16

0.

24

0.12

0.

16

0.08

0.

24

0.4

2.

24

ID

#

10:0

0 11

:00

12:0

0 13

:00

14:0

0 15

:00

16:0

0 17

:00

18:0

0 19

:00

20:0

0

To

tal

Tom

s B

ranc

h 12

00

0.28

0.

24

0.24

0.

36

0.68

0.

12

0.08

0.

12

0.12

0

0

4.

6 Sh

eran

do

1201

0.

32

0.4

0.28

0.

24

1.1

0.12

0.

08

0.12

0.

16

0.04

0

4.82

R

obin

son

Hol

low

12

02

0.28

0.

2 0.

12

0.24

0.

79

0.2

0.12

0.

04

0.16

0

0

3.

79

Ston

ey C

reek

12

07

0.04

0

0.08

0.

04

0.44

0.

08

0 0.

04

0.16

0

0

1.

12

Upp

er S

hera

ndo

1240

0.

24

0.04

0.

16

0.08

0.

16

0.12

0.

08

0.24

0

0 0

5.68

M

ills

Cre

ek

1248

0.

4 0.

36

0.36

0.

36

0.91

0.

04

0.16

0.

36

0.12

0

0

5.

31

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

4

Ta

ble

A.7:

Hur

rican

e Is

abel

Hig

h W

ater

Mar

ks

App

endi

x A

: HEC

-HM

S D

ata

Appe

ndix

A: H

EC-H

MS

Dat

a

13

5

Tabl

e A.

7 (C

ont.)

Hur

rican

e Is

abel

Hig

h W

ater

Mar

ks

App

endi

x B

: Sou

th R

iver

Mod

el O

utpu

t Dat

a

Appe

ndix

B: S

outh

Riv

er M

odel

Out

put D

ata

136

Tabl

e B

.1:

Sim

ulat

ion

Out

put,

CN

= 6

5

C

N =

65

Dis

char

ge in

cfs

; Dam

s Pr

esen

t D

isch

arge

in c

fs; w

ith o

ut D

ams

Pres

ent

# D

ata

Poin

t Q

2 Q

10

Q50

Q

100

Q50

0 Q

2 Q

10

Q50

Q

100

Q50

0 1

Poo

r Cre

ek D

am

42

52

59

62

520

247

748

1521

19

34

3095

2

Junc

tion

3 86

2 25

25

5177

66

05

1075

0 10

64

3210

66

12

8420

13

754

3 Lo

fton

Lake

Dam

52

60

67

70

40

1 28

7 88

7 18

10

2302

36

73

4 S

tone

y C

reek

Dam

49

59

67

70

57

7 33

3 10

07

2049

26

06

4169

5

Junc

tion

4 12

85

3442

69

26

9140

15

109

1682

58

23

1221

6 15

740

2589

8 6

Wild

a La

ke D

am

48

57

65

68

427

188

565

1162

14

81

2376

7

Junc

tion

9 13

21

3541

70

89

9290

15

444

1756

61

08

1291

2 16

555

2775

5 8

Junc

tion

14

1599

47

43

1044

3 13

825

2408

6 20

80

7287

16

522

2159

7 36

832

9 C

anad

a R

un D

am

43

48

59

176

772

124

377

769

978

1562

10

W

ayne

sbor

o N

urse

ry D

am

39

48

57

60

398

186

547

1115

14

20

2273

11

Ju

nctio

n 23

17

97

5683

13

257

1774

1 32

327

2265

80

19

1896

0 25

272

4459

0 12

Ju

nctio

n 26

18

59

5956

13

778

1849

4 33

672

2314

81

44

1918

2 25

727

4513

0 13

U

pper

She

rand

o D

am

84

99

115

121

537

200

617

1253

15

94

2565

14

Ju

nctio

n 29

67

6 20

34

4498

59

16

9731

71

3 21

48

4647

60

98

1025

5 15

To

ms

Cre

ek D

am

46

55

63

66

470

378

1134

23

33

2975

47

73

16

Mills

Cre

ek D

am

79

83

89

92

1021

28

0 83

7 17

16

2187

35

05

17

Hap

py H

ollo

w D

am

33

55

61

64

73

152

484

992

1262

20

16

18

Junc

tion

36

1445

42

33

9929

13

117

2181

4 18

85

5651

13

743

1816

2 30

178

19

Rob

inso

n H

ollo

w

44

51

58

60

262

234

721

1469

18

67

2978

20

In

ch B

ranc

h 44

51

57

60

14

6 23

2 71

7 14

67

1867

29

81

21

Junc

tion

38

1564

45

48

1059

2 13

695

2296

2 21

45

6540

16

050

2098

8 35

572

22

Junc

tion

42

2651

80

77

1887

9 25

653

4684

7 31

30

1119

5 27

022

3639

6 66

305

App

endi

x B

: Sou

th R

iver

Mod

el O

utpu

t Dat

a

Appe

ndix

B: S

outh

Riv

er M

odel

Out

put D

ata

137

Tabl

e B

.2:

Sim

ulat

ion

Out

put,

CN

= 6

0

C

N =

60

Dis

char

ge in

cfs

; Dam

s Pr

esen

t D

isch

arge

in c

fs; w

ith o

ut D

ams

Pres

ent

# D

ata

Poin

t Q

2 Q

10

Q50

Q

100

Q50

0 Q

2 Q

10

Q50

Q

100

Q50

0 1

Poo

r Cre

ek D

am

40

49

57

60

298

157

561

1247

16

27

2712

2

Junc

tion

3 55

3 19

12

4209

55

37

9424

64

7 24

07

5386

70

73

1206

2 3

Lofto

n La

ke D

am

50

58

65

68

219

177

662

1483

19

35

3226

4

Sto

ney

Cre

ek D

am

46

56

65

68

320

211

755

1680

21

91

3653

5

Junc

tion

4 82

1 27

33

5681

74

18

1319

4 11

13

4312

99

04

1306

9 22

652

6 W

ilda

Lake

Dam

46

54

63

66

24

2 11

8 42

4 94

7 12

40

2081

7

Junc

tion

9 86

4 28

02

5806

76

05

1342

5 11

22

4427

10

434

1385

7 24

125

8 Ju

nctio

n 14

10

65

3686

83

66

1127

8 20

717

1318

52

86

1321

0 17

786

3182

9 9

Can

ada

Run

Dam

38

46

54

80

55

8 78

28

2 63

0 82

2 13

72

10

Way

nesb

oro

Nur

sery

Dam

37

46

54

58

24

7 11

9 41

2 91

3 11

92

1993

11

Ju

nctio

n 23

12

24

4254

10

484

1438

2 27

221

1484

57

81

1509

3 20

525

3826

0 12

Ju

nctio

n 26

12

76

4419

10

908

1499

4 28

392

1526

58

98

1524

4 20

918

3870

8 13

U

pper

She

rand

o D

am

81

95

111

117

299

132

464

1028

13

40

2241

14

Ju

nctio

n 29

42

3 14

30

3673

48

72

8490

46

8 15

15

3794

49

98

8882

15

To

ms

Cre

ek D

am

44

53

61

64

259

236

850

1903

24

91

4179

16

M

ills C

reek

Dam

78

82

87

90

61

9 17

7 62

7 14

02

1833

30

70

17

Hap

py H

ollo

w D

am

20

53

59

62

70

90

358

811

1060

17

70

18

Junc

tion

36

951

3107

78

58

1073

6 18

946

1335

40

93

1101

0 14

805

2688

8 19

R

obin

son

Hol

low

42

49

56

58

15

2 14

4 53

8 12

04

1570

26

16

20

Inch

Bra

nch

43

49

55

58

63

144

534

1200

15

68

2616

21

Ju

nctio

n 38

10

82

3345

84

34

1147

4 20

195

1491

47

83

1266

3 17

245

3065

0 22

Ju

nctio

n 42

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2036

80

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6

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endi

x B

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th R

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a

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ndix

B: S

outh

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odel

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put D

ata

138

Tabl

e B

.3:

Sim

ulat

ion

Res

ults

, CN

= 5

5

C

N =

55

Dis

char

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cfs

; Dam

s Pr

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376

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0

Appendix C: Linear Programming Test Example Data

Appendix C: Linear Programming Test Example Data 139

Flood Plain PAR= 100000Ls Max = 50000 Lm Max 1000

% PMF PAR w/o Mod PAR w Mod 0 0 0 15 0 0 25 0 50 50 30,000 200 75 40,000 400

100 50,000 1,000

People at Risk (PAR) Regression

y = 577.65x - 5512.9

y = 9.404x - 140.34

-10,0000

10,00020,00030,00040,00050,00060,000

0 50 100 150

% PMF

Peop

le a

t Ris

k PAR w /o Mod

PAR w Mod

Linear (PAR w /oMod)

Linear (PAR wMod)

Figure C.1: Regression Plot for People at Risk Parameter



Table C.2: Flood Damage Regressions

Annualized

% PMF Flood Q (cfs)

Existing Damage

Post Construction

Damage 0 0 0 0

15 99000 0 0 25 166000 0 240000 50 331000 18000 229000 75 497000 14000 26700 100 662700 11,200 6600

Flood Damage Without Modification

y = -136x + 24600

05000

100001500020000

0 50 100 150

% PMF

Ann

ualiz

ed

Dam

age

($)

Status Quo

Linear (Status Quo)

Figure C.2: Regression Plot for Damage without Modification

Flood Damage With Modificationy = -3610x + 351200

-100000

0

100000

200000

300000

0 50 100 150

% PMF

Ann

ualiz

ed D

amag

e ($

) Series1

Linear (Series1)

Figure C.3: Regression Plot for Damage with Modification



Table C.3: Construction Cost Regression

Total $ 31,000 Fixed $ 500,000Annualized 1,550,000 Variable $ 1,050,000

% PMF Cost

Annualized 0 0 15 600,000 25 750,000 50 900,000 75 1,250,000

100 1,550,000

Modification Cost vs % PMF

y = 10923x + 431085

0

500,000

1,000,000

1,500,000

2,000,000

0 50 100 150

% PMF

Ann

ualiz

ed C

ost (

$)

Series1

Linear (Series1)

Figure C.4: Regression Plot for Modification Cost v. % PMF



Table C.4: Run #1: Original Data; Not Feasible

Max Z: Eb 239750 Variables Constraints Ls 11.0258 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0.28068 Es-Em-Eb = 0 Con2 0Lc 10.74512 Ls-Wt*PARs = 0 Con3 0Lb 0 Lm-Wt*PARm = 0 Con4 0Es 24600 Lc-Cl*Cm = 0 Con5 0Em 24600 -Es+mS*Xs+bS = 0 Con6 0Eb 0 -Em+mM*Xm+bM = 0 Con7 0

Cm 76.75086 -PARs+mPARs*Xs+bPARs = 0 Con8 0

Xs 0

-PARm+mPARm*Xm+bPARm = 0 Con9 0

Xm 0 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 5512.9 Xs-Xm = 0 Con11 0PARm 140.34 All variables are non-negative Constants Wt 0.002 CL 0.14 mS -136 bS 24600 mM -3610 bM 351200 mPARs 577.65 bPARs 5512.9 mPARm 9.404 bPARm 140.34 mCm 10923 bCm 431085



Table C.5: Run #2: Flood Damage Switched; Not Feasible Max Z: Eb 239750 Variables Constraints Ls 11.0258 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0.28068 Es-Em-Eb = 0 Con2 0Lc 10.74512 Ls-Wt*PARs = 0 Con3 0Lb 0 Lm-Wt*PARm = 0 Con4 0Es 351200 Lc-Cl*Cm = 0 Con5 0Em 24600 -Es+mS*Xs+bS = 0 Con6 0Eb 326600 -Em+mM*Xm+bM = 0 Con7 0

Cm 76.75086 -PARs+mPARs*Xs+bPARs = 0 Con8 0

Xs 0


Xm 0 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 5512.9 Xs-Xm = 0 Con11 0PARm 140.34 All variables are non-negative Constants Wt 0.002 CL 0.14 mS -3610 bS 351200 mM -136 bM 24600 mPARs 577.65 bPARs 5512.9 mPARm 9.404 bPARm 140.34 mCm 10923 bCm 431085



Table C.6: Run #3: Flood Damage Switched, no construction costs; Feasible Solution Max Z: Eb 239750 Variables Constraints Ls 11.0258 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0.28068 Es-Em-Eb = 0 Con2 0Lc 0 Ls-Wt*PARs = 0 Con3 0Lb 10.74512 Lm-Wt*PARm = 0 Con4 0Es 351200 Lc-Cl*Cm = 0 Con5 0Em 24600 -Es+mS*Xs+bS = 0 Con6 0Eb 326600 -Em+mM*Xm+bM = 0 Con7 0

Cm 0 -PARs+mPARs*Xs+bPARs = 0 Con8 0

Xs 2.71E-20


Xm 0 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 5512.9 Xs-Xm = 0 Con11 0PARm 140.34

All variables are non-negative

Constants Wt 0.002 CL 0.14 mS -3610 bS 351200 mM -136 bM 24600 mPARs 577.65 bPARs 5512.9 mPARm 9.404 bPARm 140.34 mCm 0 bCm 0



Table C.7: Run #4 Additional Condition Xs > 25; Feasible Solution Max Z: Eb 239750 Variables Constraints Ls 39.9083 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0.75088 Es-Em-Eb = 0 Con2 0Lc 0 Ls-Wt*PARs = 0 Con3 0Lb 39.15742 Lm-Wt*PARm = 0 Con4 0Es 260950 Lc-Cl*Cm = 0 Con5 0Em 21200 -Es+mS*Xs+bS = 0 Con6 0Eb 239750 -Em+mM*Xm+bM = 0 Con7 0


Xs 25


Xm 25 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 19954.15 Xs-Xm = 0 Con11 0PARm 375.44 All variables are non-negative Xs > 25 Constants Wt 0.002 CL 0.14 mS -3610 bS 351200 mM -136 bM 24600 mPARs 577.65 bPARs 5512.9 mPARm 9.404 bPARm 140.34 mCm 0 bCm 0



Table C.8: Run #5: PARM is reduced to zero to check impact on LB; Feasible Solution Max Z: Eb 239750 Variables Constraints Ls 39.9083 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0 Es-Em-Eb = 0 Con2 0Lc 0 Ls-Wt*PARs = 0 Con3 0Lb 39.9083 Lm-Wt*PARm = 0 Con4 0Es 260950 Lc-Cl*Cm = 0 Con5 0Em 21200 -Es+mS*Xs+bS = 0 Con6 0Eb 239750 -Em+mM*Xm+bM = 0 Con7 0


Xs 25


Xm 25 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 19954.15 Xs-Xm = 0 Con11 0PARm 0 All variables are non-negative Xs > 25 Constants Wt 0.002 CL 0.14 mS -3610 bS 351200 mM -136 bM 24600 mPARs 577.65 bPARs 5512.9 mPARm 0 bPARm 0 mCm 0 bCm 0



Table C.9: Run #6: Take PAR out of equation, Economic Only; Feasible Solution Max Z: Eb 239750 Variables Constraints Ls 0 Ls-Lm-Lc-Lb = 0 Con1 0Lm 0 Es-Em-Eb = 0 Con2 0Lc 0 Ls-Wt*PARs = 0 Con3 0Lb 0 Lm-Wt*PARm = 0 Con4 0Es 260950 Lc-Cl*Cm = 0 Con5 0Em 21200 -Es+mS*Xs+bS = 0 Con6 0Eb 239750 -Em+mM*Xm+bM = 0 Con7 0


Xs 25


Xm 25 -Cm+mCm*Xm+bCm = 0 Con10 0PARs 0 Xs-Xm = 0 Con11 0PARm 0 All variables are non-negative Xs > 25 Constants Wt 0.002 CL 0.14 mS -3610 bS 351200 mM -136 bM 24600 mPARs 0 bPARs 0 mPARm 0 bPARm 0 mCm 0 bCm 0

Vita 148

Vita

Major Michael Bliss, U.S. Army, hails originally from Massena, New York. He is

married to Cheria Bliss, and they have three children Cheyennee, Tiyler, and Brandon.

Mike is stationed here in Blacksburg, VA for educational training as part of a utilization in

the U.S. Army Corps of Engineers (USACE). His follow on assignment is Fort Riley,

Kansas in USACE resident office as a project engineer.

Michael�s educational background started at Clarkson University, Potsdam, New

York. He earned a Bachelor of Science in Chemical Engineering in May, 1996. While

stationed at Ft. Leonard Wood Missouri in 2000, Mike earned a Master of Science in

Engineering Management from the University of Missouri at Rolla, Rolla, Missouri.

Major Bliss� army career began when he enlisted in the U.S. Army Reserves in

1992. Completing Army Basic and Advanced Individual Training by the end of 1992, he

accepted an ROTC Scholarship in May of 1993. Mike was commissioned in May 1996,

as a 2nd Lieutenant as an Engineer Officer. His career assignments include various

Company, Battalion, and Brigade level positions.

Michael�s operational deployments include tours in Bosnia-Herzegovina, Kosovo,

and most recently Iraq. Mike deployed his 105 soldier, combat engineer company, B

Company, 11th Engineer Battalion to Kuwait in January 2003 as part of the 3rd Infantry

Division�s preparations for Operation Iraqi Freedom. B Company executed initial

breaches on two lanes into Iraq as part of the 3rd Infantry Division�s assault into Iraq. His

company also executed combat operations in support of Task Force 2-7 Infantry,

culminating with assistance in the seizure of the Baghdad International Airport in April

2003. Mike�s most notable awards include the Bronze Star with �Valor� Device and the

Meritorious Service Medal.

procedures to perform dam rehabilitation analysis in aging

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