Using Ground-Water Model

Predictions and the ppr and opr

Statistics to Guide Data Collection

Motivation

Parameter Distribution

Parameter

UncertaintyPrediction Uncertainty

Hydrogeologic Data

Calibrated Model & Predictions

Incomplete Data

• Ground-water model predictions are always uncertain.

• What hydrogeologic data could be collected to reduce this prediction uncertainty most effectively?

Motivation

Parameter Distribution

Reduced Parameter

Uncertainty Reduced Prediction Uncertainty

Hydrogeologic Data

Calibrated Model & Predictions

Additional Data

Approach

Use calibrated model to identify parameters important to predictions.

Parameter Distribution

Calibrated Model & Predictions

Approach

Collect hydrogeologic data: ­ Parameter values­ Flow system characteristics

Use calibrated model to identify parameters important to predictions.

Hydrogeologic Data

Parameter Distribution

Calibrated Model & Predictions

Approach

Collect hydrogeologic data: ­ Parameter values­ Flow system characteristics

Incorporate these data into the model to reduce parameter and prediction uncertainty.

Use calibrated model to identify parameters important to predictions.

Parameter-Prediction Statistic (PPR)

1. Calculate prediction uncertainty (sZ) using the calibrated model.

2. Assume improved information on one or more parameters, and recalculate sZ.

3. PPR statistic equals the percent decrease in sZ from step 1 to step 2.

Prediction

Uncertainty(standard­deviations­sZ­)­

Parameter­Uncertainty

Prediction­Sensitivities

Observation­Sensitivities

DVRFS Model Parameters

9 Hydraulic Conductivities

4 Recharge Parameters

Predictions: Advective-Transport Paths

• Advective transport used as a surrogate for regional contaminant transport.

• Advective transport paths are 10 km.

• Predictions are the distances traveled in the N-S, E-W, and vertical directions.

Black bars: Prediction standard deviations calculated using calibrated model.

Uncertainty in Path Position

Advective­path

Black bars: Prediction standard deviations calculated using calibrated model.

Red bars: Prediction standard deviations calculated with improved information on a parameter.

Uncertainty in Path Position

Advective­path

PPR Statistic:Individual Parameters

• Specify improved information on one parameter, so that its uncertainty decreases by 10 percent.

• Calculate resulting decrease in prediction standard deviations sZ.

• Repeat for all model parameters.

Parameter with Improved Information

Hydraulic­Conductivity Recharge

PPR: Individual Parameters

East-WestR4K2

K1K3

0

5VOII (percentdecrease

in sZ)

PPR

East-WestR4K2

K1K3

0

5VOII (percentdecrease

in sZ)

Vertical R1

0

6

12

North-SouthR4K2

K1

K3

0

5

Parameter with Improved Information

Hydraulic­Conductivity Recharge

PPR: Individual Parameters

PPR

PPR:Multiple Parameters

• Specify improved information on three parameters.

• Calculate PPR statistic (decrease in prediction standard deviation sZ).

• Repeat for all possible sets of three model parameters.

PPR: Multiple Parameters

East-West

K5

K1,K3,K5

R4K2K1 K3

0

10

Percentdecrease

in sZ

VOII on Individual Parameters VOII on 3 Parameters

PPR PPR

VOII: Multiple Parameters

East-West

K5

K1,K3,K5

R4K2K1 K3

0

10

Percentdecrease

in sZ

VOII on Individual Parameters VOII on 3 Parameters

Vertical

K4

R1R1,K4,A3

0

13

PPRPPR

Advective Path from Yucca Flat Site

K zones, layer 1 Recharge zones

K1

K5

R1

10 km

R4K3

layer 2

Using­the­PPR­Results

Collect hydrogeologic data related to important

parameters

System State Observations

Improved Predictions, Reduced Uncertainty

Societal decisions

Improve Model & Parameters

Recalibrate Model

Observation-Prediction (opr) Statistic

1. Calculate prediction uncertainty (sZ) using the calibrated model and all 517 observations.

2. Add or omit one or more observations, and recalculate sZ.

3. opr statistic equals the change in sZ from step 1 to step 2.

Prediction

Uncertainty(standard­deviations­sZ­)­

Parameter­Uncertainty

Prediction­Sensitivities

Observation­Sensitivities

Predictions­evaluated­for­assessing­observations

Hill and Tiedeman, 2007, fig. 15.7. p. 366

Which­existing­observations­are­important(or­not)­to­predictions?

Use­opr(-1)­to­rank­the­501­existing­observation­locations­by­their­importance­to­predictions

• Averaged­values­of­opr(-1)­for­all­the­predictions­are­used,­to­obtain­a­measure­indicating­the­importance­of­a­single­observation­to­all­the­predictions­of­interest.­

• Calculate­opr(-100) by­removing­the­100­least­important­observations

• opr(-100) =­mean­prediction­­uncertainty­increase­=­0.6%

Hill and Tiedeman, 2007, fig. 15.9. p. 368

Consider­one­potential­new­head­observation­in­each­cell­of­model­layer­1.

Determine­weights­for­the­potential­observations.­

Here,­same­weighting­strategy­used­as­for­weighting­existing­observations­–­weights­smaller­for­heads­in­high-gradient­areas.­

Calculate­opr(+1)­for­each­cell­in­the­layer,­even­those­with­an­existing­observation,­so­that­opr(+1)­is­continuous­over­the­whole­map.

What­new­observations­would­be­important(or­not)­to­predictions?

Hill and Tiedeman, 2007, fig. 15.10. p. 369

Improve Model & Parameters

Recalibrate Model

Hydrologic and Hydrogeologic Data

Collect additional observation data

Improved Predictions, Reduced Uncertainty

Societal decisions

Using­the­OPR­results­for­potential­new­observations

Summary

• Parameters and observations most important to the predicted advective-transport paths do not necessarily lie near the paths themselves.

• Best to not use ppr and opr results alone for making decisions about future data collection – consider other criteria such as geologic insight about important subsurface units to investigate, maintaining good geographic and depth coverage of monitoring network, etc.

• The ppr and opr results are only as good as the model itself!