Calibration Guidelines

1. Start simple, add complexity carefully2. Use a broad range of information3. Be well-posed & be comprehensive4. Include diverse observation data for

‘best fit’5. Use prior information carefully6. Assign weights that reflect ‘observation’

error7. Encourage convergence by making the

model more accurate 8. Consider alternative models

9. Evaluate model fit 10. Evaluate optimal

parameter values

11.11. Identify new data to improve parameter estimates

12.12. Identify new data to improve predictions

13. Use deterministic methods14. Use statistical methods

Model development Model testing

Potential new dataPotential new data

Prediction uncertainty

Guideline 11: Identify New Data to Improve Model Parameter Estimates and Evaluate Potential for

Additional Estimated ParametersHere we consider measurements related to observations because the

connection between hydrologic and hydrogeologic data is direct and needs no special statistics.

Hydrologic and hydrogeologic dataRelate to model inputs

Dependent variable ObservationsRelate to model outputs

Ground-Water Model -- Parameters

Predictions

Prediction uncertainty

Societal decisions

Potential new observations to improveparameter estimates

• Goal: evaluate worth of the type and location of potential observations. No observed value yet, so need statistics that don’t depend on this value. Use fit-independent statistics

• In the context of reducing parameter uncertainty and increasing uniqueness, use the statistics:A. Dimensionless scaled sensitivities. B. One-percent scaled sensitivities. Often plotted in map form.C. Parameter correlation coefficientsD. Leverage statisticsE. Influence statistics (not discussed here)

A. Dimensionless scaled sensitivities (dss): • Can be calculated for any potential observation type or location• Account for the expected accuracy of the measurements because dss

include the observation weight. • Larger values identify observations that are likely to reduce parameter

uncertainty.

B. Maps of one-percent scaled sensitivities

• Conveniently shows spatial relations.

• One map for each parameter, for each model layer, for each time step: potentially a huge number of maps!.

• Inconvenient because can not determine the effect on the entire set of parameters.

• Does not reflect the expected accuracy of observations in the different locations.

Parameter pair for each correlation coefficient

0.5

0.6

0.7

0.8

0.9

1.0

1 (Heads) 2 (+Flow) 3 (+ADV)

Observation set

Abs

olut

e va

lue

of th

e co

rrel

atio

n co

effi

cien

t

K-RCH K-Qn

K-Qb K-GHB

RCH-Qn RCH-Qb

RCH-GHB Qn-Qb

Qn-GHB Qb-GHB

• Clearly illustrates that collecting flow and advective transport data can radically reduce the extreme parameter correlations that occur when only head are used.

Example from Cape Cod (Anderman and others

1996; Anderman and Hill 2001)

C. Parameter correlation coefficientsCalculate without and with the potential new data. If correlations with absolute values close to 1.00 become smaller, the new data will help attain unique parameter estimates.

D. Leverage StatisticsIndicate potential effect of an observation on a set of parameter estimates. Do not indicate the particular parameter(s) to which an observation is important

Dimensionless scaled sensitivities (dss) for each parameter. Leverage

HK_2 VK_CB K_RB RCH_2

Potential head observation

-3.5 8.010-3 -0.105 54.8 0.988

Potential flow observation

-3.210-

5 1.110-6 -0.3510-

5 -4.50 0.491

css for existing observations

3.1 0.22 0.20 25.3

Table 13.1, p. 331

0

2

4

6

8

10

12

K1

K2

K3

K4

K5

K6

(el)

K7

(Nw

flt)

K8

(dr)

K9

(fm

tn)

AN

IV1

AN

IV3

RC

H0

RC

H1

RC

H2

RC

H3

ET

M

GH

Ba

m

GH

Bg

s

GH

Bo

GH

Bfc

GH

Bt Q Q

Po

ros

Parameter label

Com

posi

te s

cale

d se

nsiti

vity

0

50

100

150

200

250

K1

K2

K3

K4

AN

IV3

AN

IV1

RC

H

ET

M

P arameter names

Com

posi

te s

cale

d se

nsit

ivit

y

First model

Final model

What parameters could be supported in more detail, given the information in the observations? Use css

Evaluation of possible additional estimated parameters

Calibration Guidelines

1. Start simple, add complexity carefully2. Use a broad range of information3. Be well-posed & be comprehensive4. Include diverse observation data for

‘best fit’5. Use prior information carefully6. Assign weights that reflect ‘observation’

error7. Encourage convergence by making the

model more accurate 8. Consider alternative models

9. Evaluate model fit 10. Evaluate optimal

parameter values

11.11. Identify new data to improve parameter estimates

12.12. Identify new data to improve predictions

13. Use deterministic methods14. Use statistical methods

Model development Model testing

Potential new dataPotential new data

Prediction uncertainty

Guideline 12: Identify New Data to Improve Model Predictions

Two categories of potential new data: Measurements related to observations and hydrology and hydrogeology

Hydrologic and hydrogeologic dataRelate to model inputs

Dependent variable ObservationsRelate to model outputs

Ground-Water Model -- Parameters

Predictions

Prediction uncertainty

Societal decisions

Potential new data to improve predictions

– What existing or new observations are important to predictions?• Observation-Prediction Statistic (opr)

– Which parameters are important to predictions? Infer important hydrologic and hydrogeologic data• Prediction scaled sensitivities (pss) with

composite scaled sensitivies (css) and parameter correlation coefficients (pcc)

• Parameter-Prediction Statistic (ppr)

Potential new observations to improve predictions

Hydrologic and hydrogeologic dataRelate to model inputs

Dependent variable ObservationsRelate to model outputs

Ground-Water Model -- Parameters

Predictions

Prediction uncertainty

Societal decisions

Approach: OPR

Potential new observations to improve predictions

Observation-Prediction (opr) Statistic

• Which existing observations are important to predictions?

– opr indicates the percent increase in prediction uncertainty caused by omitting an existing observation

• What new observations would be most valuable to predictions?

– opr indicates the percent decrease in prediction uncertainty caused by adding a new observation

• Advantages:– Combines dssdss, csscss,, and psspss into one statistic that also accounts

for parameter correlation– is independent of model fit – is computationally manageable

Predictions of Interest in the Death Valley Model

• Resource managers are interested in long-term, regional transport from selected sites, including all processes – advection, dispersion, reactions, adsorption and desorption

• The regional model can be used to address advection.

• Advective transport considered -- consistent with regional-scale model

• Track movement in 3 coordinate directions – here, north-south, east-west, and vertical

Which existing observations are important(or not) to predictions?

Use opr(-1) to rank the 501 existing observation locations by their importance to predictions

• Averaged values of opr(-1) for all the predictions are used, to obtain a measure indicating the importance of a single observation to all the predictions of interest.

• Calculate opr(-100) by removing the 100 least important observations

• opr(-100) = mean prediction uncertainty increase = 0.6%

Consider potential new head observations in layer 1.

Calculate opr(+1) for each cell in the layer.

What new observations would be important(or not) to predictions?

Potential new data to improve predictions

– What existing or new observations are important to predictions?• Observation-Prediction Statistic (opr)

– Which parameters are important to predictions? Infer important hydrologic and hydrogeologic data• Prediction scaled sensitivities (pss) with

composite scaled sensitivies (css) and parameter correlation coefficients (pcc)

• Parameter-Prediction Statistic (ppr)

Potential new system property information to improve predictions

Two approaches:

A. Prediction scaled sensitivities (pss) together with composite scaled sensitivities (css) and parameter correlations (pcc)

B. Parameter-prediction (ppr) statistic

Hydrologic and hydrogeologic dataRelate to model inputs

Dependent variable ObservationsRelate to model outputs

Ground-Water Model -- Parameters

Predictions

Prediction uncertainty

Societal decisions

A. Prediction Scaled Sensitivities (pss): What parameters are important to predictions?

Vertical advective-transport distance

0.0001

0.001

0.01

0.1

1

10

100

1000

K1 K2 K3 K4 K5

K6(el)

K7(Nwflt)

K8(dr)

K9(fmtn)

ANIV1

ANIV3

RCH0

RCH1

RCH2

RCH3

ETM

GHBam

GHBgs

GHBo

GHBfc

GHBt Q1

Q2

POROS

Parameter label

Per

cen

t ch

ang

e

pss-desired model

complexity

Here, pss are scaled to equal percent change in prediction

caused by 1% change in parameter value

0

2

4

6

8

10

12

K1

K2

K3

K4

K5

K6(

el)

K7(

Nw

flt)

K8(

dr)

K9(

fmtn

)

AN

IV1

AN

IV3

RC

H0

RC

H1

RC

H2

RC

H3

ET

M

GH

Bam

GH

Bgs

GH

Bo

GH

Bfc

GH

Bt Q Q

Por

os

Parameter label

Com

posi

te s

cale

d se

nsiti

vity

Vertical advective-transport distance

0.0001

0.001

0.01

0.1

1

10

100

1000

K1 K2 K3 K4 K5

K6(el)

K7(Nwflt)

K8(dr)

K9(fmtn)

ANIV1

ANIV3

RCH0

RCH1

RCH2

RCH3

ETM

GHBam

GHBgs

GHBo

GHBfc

GHBt Q1

Q2

POROS

Parameter label

Per

cen

t ch

ang

ecss – css –

supported supported model model

complexity complexity

pss – pss – desired desired model model

complexity complexity

B. Parameter-Prediction (ppr) Statistic

• Which parameters are important to predictions?

– ppr indicates percent decrease in prediction uncertainty caused by a decrease in parameter uncertainty.

• The decrease in parameter uncertainty is implemented by increasing the weight on prior information for the parameter(s).

• This increase in weight represents the increased certainty that would result from collection of additional field data about the parameter or associated system property.

Predictions of Interest in the Death Valley Model(simulations from the 3-layer model of D’Agnese +, 1998)

Apply ppr statistic to

one prediction on

Yucca Flat

East-WestR4K2

K1K3

0

5

Vertical R1

0

6

12

North-SouthR4K2

K1

K3

0

5

Parameter with Improved Information

Hydraulic Conductivity Recharge

Which individual parameters (and associated system features) would be most beneficial to further

characterize in the field?

Ppr statistic(percent

decrease in prediction

uncertainty)

A. Prediction scaled sensitivities (pss) together with composite scaled sensitivities (css) and parameter correlations (pcc)

– PRO: pss, css, and pcc are each conceptually easy to understand and convey to others

– PRO: independent of model fit and computationally manageable– CON: Can be cumbersome to evaluate the three measures to

determine the value of new system property data

B. Parameter-prediction (ppr) statistic – PRO: Combines csscss, pss, pss, andand pcc pcc into one statistic– PRO: independent of model fit and computationally manageable– CON: More conceptually difficult to understand and explain to

others. Best so far -- express in terms of percent changes in prediction uncertainty

Pros and cons of A (pss+) and B (ppr)