Parameterization Impacts on Linear Uncertainty Calculation

Efficient linear calculation of model prediction uncertainty can be an insightful diagnostic metric for decision-making. Specifically, the contributions of parameter uncertainty or the location and type of data to prediction uncertainty can be used to evaluate which types of information are most valuable. Information that most significantly reduces prediction uncertainty can be considered to have greater worth. Prediction uncertainty is commonly calculated including or excluding specific information and compared to a base scenario. The quantitative difference in uncertainty with or without the information is indicative of that information's worth in the decision-making process. These results can be calculated at many hypothetical locations to guide network design (i.e., where to install new wells/stream gages/etc.) or used to indicate which parameters are the most important to understand thus likely candidates for future characterization work. We examine a hypothetical case in which an inset model is created from a large regional model in order to better represent a surface stream network and make predictions of head near and flux in a stream due to installation and pumping of a large well near a stream headwater. Parameterization and edge boundary conditions are inherited from the regional model, the simple act of refining discretization and stream geometry shows improvement in the representation of the streams. Even visual inspection of the simulated head field highlights the need to recalibrate and potentially re-parametrize the inset model. A network of potential head observations is evaluated and contoured in the shallowest two layers of the six-layer model to assess their worth in both predicting flux at a specific gage, and head at a specific location near the stream. Three hydraulic conductivity parameterization scenarios are evaluated: using a single multiplier on hydraulic conductivity acting on the inherited hydraulic conductivity zonation using; the inherited zonation which results in a five-by-five network of homogeneous zones in each layer; a single multiplier on hydraulic conductivity acting on the inherited hydraulic conductivity zonation; and a 20-by-20 network of pilot points in each laye. The robustness of the network analysis in all three scenarios is compared, and significant impact of the parameterization decision is illustrated. Two tools are freely available to perform this analysis: OPR-PPR, designed to interact with UCODE_2005, and PREDUNC, designed to interact with PEST. The mathematical derivation and assumptions of the two methods differs, but under special circumstances where certain restrictions in the problem design are met, the results are shown to be equivalent. Results from this inset modeling suggest that the OPR-PPR approach is more appropriate for sparsely parameterized problems, while PREDUNC is better suited for highly parameterized problems.