Model complexity control for hydrologic prediction

A common concern in hydrologic modeling is overparameterization of complex models given limited and noisy data. This leads to problems of parameter nonuniqueness and equifinality, which may negatively affect prediction uncertainties. A systematic way of controlling model complexity is therefore needed. We compare three model complexity control methods for hydrologic prediction, namely, cross validation (CV), Akaike's information criterion (AIC), and structural risk minimization (SRM). Results show that simulation of water flow using non‐physically‐based models (polynomials in this case) leads to increasingly better calibration fits as the model complexity (polynomial order) increases. However, prediction uncertainty worsens for complex non‐physically‐based models because of overfitting of noisy data. Incorporation of physically based constraints into the model (e.g., storage‐discharge relationship) effectively bounds prediction uncertainty, even as the number of parameters increases. The conclusion is that overparameterization and equifinality do not lead to a continued increase in prediction uncertainty, as long as models are constrained by such physical principles. Complexity control of hydrologic models reduces parameter equifinality and identifies the simplest model that adequately explains the data, thereby providing a means of hydrologic generalization and classification. SRM is a promising technique for this purpose, as it (1) provides analytic upper bounds on prediction uncertainty, hence avoiding the computational burden of CV, and (2) extends the applicability of classic methods such as AIC to finite data. The main hurdle in applying SRM is the need for an a priori estimation of the complexity of the hydrologic model, as measured by its Vapnik‐Chernovenkis (VC) dimension. Further research is needed in this area.