Integrating Many Data Types into Optimized Inverse Modeling: An Example from Hydrology

Abstract:

Integrating different data types into inverse modeling and uncertainty quantification is important in all types of environmental systems. One integration method is to use a single objective function with weighting to accommodate quantities with different units, which would otherwise not be validly additive. Another is multi-objective functions. This talk uses a saltwater intrusion example to examine the use of three data types in model development with a weighted single objective function. The data types involved are water age, salinity, and hydraulic heads. Water age is simulated with MODPATH, salinity and heads are simulated with the transport and flow equations in SEAWAT. Initial efforts to weight the data were intended to diminish the effect of the age dates because they were thought to be less accurate. However, the sensitivity analysis measure leverage showed that the age dates dominated the head and concentration observations. Stacked CSS graphs showed that nearly all parameters considered in the optimization were dominated by the age dates. How could this be? The age dates were assigned weights of 0.00449, while the concentrations were assigned weights of 3.80. To compare the imposed weights, error-based weighting theory was used. Error-based weighting is the only weighting that can be shown theoretically to produce unbiased parameter estimates. Results showed that the imposed weighting actually overemphasized the age dates relative to the concentration and head data. The age dates ranged from 2,932 to 11,837 days. The weighting was consistent with coefficients of variation on the age dates that were all less than 10%, and most were less than 1%. This was a much greater level of accuracy than intended by the modelers. In contrast, the concentrations ranged from 0.0 to 35 g/l. The weights on the non-zero chloride concentrations were consistent with coefficients of variation that were between 1% and 15%. The 15% was consistent with expected data errors. Smaller coefficients of variation produce larger weights for a given observation. Thus, while the intent was to deemphasize the age dates, the result of the weighting was the opposite. This example illustrates the insight provided by evaluating weights from an error-based perspective. Implications for multi-objective function methods are discussed.