Detection of Overparameterization and Overfitting in an Automatic Calibration of SWAT

Abstract

Distributed hydrologic models based on small-scale physical processes tend to have a large number of parameters to represent spatial heterogeneity. This characteristic requires the use of a large number of parameters in model calibration. It is a common view that calibration with a large number parameters produces overparameterization and overfitting. Recent work using prior information, spatial information, and constraints on parameters for regularization of the calibration problem has improved model predictions using a few dozen parameters. We demonstrate that the Soil and Water Assessment Tool (SWAT) and the information associated with a SWAT watershed setup provide a regularized problem with many of recently published regularization techniques already utilized in SWAT. Our hypothesis is that the Soil and Water Assessment Tool (SWAT) regularizes the inverse problem so that a stable solution can be obtained for calibration of SWAT using a very large number of parameters, where very large means up to 10,000 calibration parameters. In this study, a two-objective calibration genetic algorithm based on a non-dominated sorting genetic algorithm (NSGA-II) was used to calibrate the Blue River basin in Oklahoma. We introduce the use of intermediate solutions found by the genetic algorithm to test identification of calibration parameters and diagnose model overfitting. Defining identification as the capability of a model to constrain the estimation of parameters, we introduced a method for statistically testing for changes from the initial uniform distribution of each parameter. We found that all 4,198 parameters used to calculate the Blue River SWAT model were identified. Diagnostic comparisons of goodness-of-fit measures for the calibration and validation periods provided strong evidence that the model was not overfitted.