Use of Gene Expression Programming for Multimodel Combination of Rainfall-Runoff Models

Abstract

This paper deals with the application of an innovative method for combining estimated outputs from a number of rainfall-runoff models using gene expression programming (GEP) to perform symbolic regression. The GEP multimodel combination method uses the synchronous simulated river flows from four conventional rainfall-runoff models to produce a set of combined river flow estimates for four different catchments. The four selected models for the multimodel combinations are the linear perturbation model (LPM), the linearly varying gain factor model (LVGFM), the soil moisture accounting and routing (SMAR) model, and the probability-distributed interacting storage capacity (PDISC) model. The first two of these models are black-box models, the LPM exploiting seasonality and the LVGFM employing a storage-based coefficient of runoff. The remaining two are conceptual models. The data of four catchments with different geographical locations and hydrological and climatic conditions are used to test the performance of the GEP combination method. The results of the model using the GEP method are compared with the original forecasts obtained from the individual models that contributed to the development of the combined model by means of a few global statistics. The findings show that a GEP approach can successfully be used as a multimodel combination method. In addition, the GEP combination method has the benefit over other hitherto tested approaches such as an artificial neural network combination method in that its formulation is transparent, can be expressed as a simple mathematical function, and therefore is useable by people who are unfamiliar with such advanced techniques. The GEP combination method is able to combine model outcomes from less accurate individual models and produce a superior river flow forecast.