Effects of Model Simplification: Insights from a Synthetic Vadose Zone Example

The issue of model simplification is central to model-based environmental management. Simplification is unavoidable, as even the most complex models are inherently simplifications of reality. The demands of model calibration and calibration-constrained uncertainty analysis often demand further simplification in order to attain reduced model run times and numerical stability.

Theoretical analysis shows that calibration of a simplified model can introduce bias to some predictions but not to others, this depending on the degree of predictive dependency on solution and null space parameter combinations. It also provides a means for quantification of simplification induced bias, and possibly its amelioration through adoption of certain calibration strategies and/or through the use of paired simple/complex models as demonstrated by Doherty and Christensen (in press).  In this study, we apply this method and theoretical analysis to a synthetic case involving an unsaturated flow model that is used to predict recharge to a groundwater model. Two levels of simplification are undertaken; one in order to achieve a parsimonious parameter set, and the other in order to replace this model with a lumped parameter “bucket” model.

Briefly, our findings are as follows:

• where a model has defects, the link between minimum error variance parameters and minimum error variance predictions is broken;
• a large degree of “parameter surrogacy” can result from only modest simplification, even where the simplification process appears to preserve the physical meaning of parameters. This suggests that transfer of inversion results to alternative sites is a tenuous undertaking;
• parameters of a simplified model may require more variability to fit a given calibration dataset than their “physical basis” would suggest. This questions the role of prior information and parameter bounds in the simple model calibration process;
• Paired simple and complex model usage provides a computationally efficient methodology for bias reduction and uncertainty computation in this context.