Parameter and predictive outcomes of model simplification

Abstract

Simplification is an unavoidable aspect of model usage. Even complex, physically based models are simplifications of reality. More profound simplification is required to construct the “lumped parameter” models of semiphysical basis that are often employed for simulation of large‐scale processes operative over one or many watersheds. Simplification can lead to model predictive error beyond that which would be expected on the basis of study‐area information deficits alone. Building on a recently developed mathematical description of the model simplification process, this work employs linear subspace methods to analyze in detail the nature and ramifications of that process when applied to a 1‐D, Richards equation‐based unsaturated zone model used to predict recharge to a groundwater system. Two simplified versions of this model are examined. The first achieves simplification through assuming vertical parameter uniformity. The second achieves simplification through use of a lumped parameter model in place of the Richards equation‐based model. Relationships between parameters employed by the complex model and those used by each of the simplified models are analyzed. The nature of predictive errors incurred through simplification is explored. Also explored is the ability of the calibration process to decrease the propensity for model error in making some predictions, while increasing the propensity for model error in the making of others (an outcome that may be considered counterintuitive from a Bayesian perspective, but which is a natural consequence of suboptimal simplification).