Symbolic Regression for the Estimation of Transfer Functions of Hydrological Models

Current concepts for parameter regionalization of spatially distributed rainfall-runoff models rely on the a priori definition of transfer functions that globally map land surface characteristics (such as soil texture, land use, and digital elevation) into the model parameter space. However, these transfer functions are often chosen ad hoc or derived from small-scale experiments. This study proposes and tests an approach for inferring the structure and parametrization of possible transfer functions from runoff data to potentially circumvent these difficulties. The concept uses context-free grammars to generate possible proposition for transfer functions. The resulting structure can then be parametrized with classical optimization techniques. Several virtual experiments are performed to examine the potential for an appropriate estimation of transfer function, all of them using a very simple conceptual rainfall-runoff model with data from the Austrian Mur catchment. The results suggest that a priori defined transfer functions are in general well identifiable by the method. However, the deduction process might be inhibited, e.g., by noise in the runoff observation data, often leading to transfer function estimates of lower structural complexity.