Using Ground-Water Model Predictions and the ppr and opr Statistics to Guide Data Collection

Motivation Parameter Distribution Parameter Uncertainty Prediction 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.

Approach Collect hydrogeologic data: ­Parameter values ­Flow system characteristics Incorporate these data into model to reduce parameter and prediction uncertainty. Use calibrated model to identify parameters important to predictions.

Parameter-Prediction Statistic (PPR) 1.Calculate prediction uncertainty (s Z ) using the calibrated model. 2. Assume improved information on one or more parameters, and recalculate s Z. 3. PPR statistic equals the percent decrease in s Z from step 1 to step 2. Prediction Uncertainty (standard deviations s Z ) Parameter Uncertainty Prediction Sensitivities Observation Sensitivities

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 Advective path

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 Advective path

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 s Z. Repeat for all model parameters.

Parameter with Improved Information Hydraulic Conductivity Recharge PPR: Individual Parameters PPR

Parameter with Improved Information Hydraulic Conductivity Recharge PPR: Individual Parameters PPR

PPR: Multiple Parameters Specify improved information on three parameters. Calculate PPR statistic (decrease in prediction standard deviation s Z ). Repeat for all possible sets of three model parameters.

PPR: Multiple Parameters VOII on Individual Parameters VOII on 3 Parameters PPR

VOII: Multiple Parameters VOII on Individual Parameters VOII on 3 Parameters PPR

Advective Path from Yucca Flat Site K zones, layer 1 Recharge zones K1 K5 R1 10 km R4 K3 layer 2

Using the PPR Results 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 (s Z ) using the calibrated model and all 517 observations. 2. Add or omit one or more observations, and recalculate s Z. 3. opr statistic equals the change in s Z from step 1 to step 2. Prediction Uncertainty (standard deviations s Z ) Parameter Uncertainty Prediction Sensitivities Observation Sensitivities

Predictions evaluated for assessing observations Hill and Tiedeman, 2007, fig p. 366

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% Hill and Tiedeman, 2007, fig p. 368

Consider one potential new head observation in each cell of model layer 1. Determine weights for the potential observations. Here, same weighting strategy used as for weighting existing observations – weights smaller for heads in high-gradient areas. Calculate opr (+1) for each cell in the layer, even those with an existing observation, so that opr (+1) is continuous over the whole map. What new observations would be important (or not) to predictions? Hill and Tiedeman, 2007, fig p. 369

Improve Model & Parameters Recalibrate Model Hydrologic and Hydrogeologic Data Collect additional observation data Improved Predictions, Reduced Uncertainty Societal decisions Using the OPR results for potential new observations

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!