Data-based mechanistic modelling of stochastic rainfall-flow processes by state dependent parameter estimation

Due to the inherent nonlinearity in the process of transformation of rainfall into river flow, a simple direct input-output transfer function (TF) model may not sufficiently capture the catchment's hydrological dynamics. This paper presents an application of state dependent parameter (SDP) models for nonlinear, stochastic dynamic system to identify the location and form of the nonlinearity in the rainfall-effective rainfall dynamics. The objective was to develop an effective rainfall input time series that was then used to improve the performance of an originally developed direct input-output TF model of daily rainfall-flow relationship. The CAPTAIN Toolbox in the MATLAB® environment was used in the model identification in which the recursive filtering and smoothing procedures formulated within a stochastic state space setting were applied to the time series data in order to identify the location and form of nonlinearities within a generic TF model. The nonparametric estimation as well as the parametric optimisation of the resulting nonlinear models was done using the Curve Fitting Toolbox in MATLAB®. The results showed an improved and more parsimonious TF model. The model improved from explaining only 13% of the data to 56% presenting an improvement of 43% in the model fit. The study demonstrates that simple stochastic but robust tools can be successfully applied to develop and improve applicable hydrological models.