Nonlinear Stochastic Model of Rainfall Runoff Process

A nonlinear stochastic model is proposed to model the rainfall runoff process in which higher order derivatives of rainfall are used in addition to the magnitude of rainfall as inputs. The rainfall, runoff, and derivatives of rainfall are considered as stochastic. The model consists of several subsystems in parallel. The first subsystem utilizes the observed rainfall and runoff as input and output, respectively. The subsequent subsystems use higher order derivatives of rainfall as input and forecast error from the previous subsystems as output. The subsystems improve the performance of the overall model by using higher order derivatives of input. The error in forecasting the runoff is progressively reduced by each subsystem. The method of analysis and parameter estimation of each of the subsystems are the same except that different inputs and outputs are used to characterize the subsystems. The optimal output of each of the subsystems is computed by minimizing the corresponding mean square error, and the estimation procedure is based on the statistical theory of filters involving the marginal and joint probability density functions of rainfall, runoff, and rainfall derivative sequences. The model is tested using daily rainfall runoff data from the Rough River basin in Kentucky, and its prediction performance is discussed. Testing the residuals of the model for whiteness is emphasized in order to improve the prediction performance of the model.