Wavelet–Volterra coupled model for monthly stream flow forecasting

Natural stream flow dynamics is an outcome of complex nonlinear and multiscale phenomena, integrated together in some coherent manner and this paper is an attempt to model them by combining wavelet decomposition with Volterra models. This paper describes a methodology that yields a 1 month ahead forecast of stream flow using wavelets based multiscale nonlinear models. The method uses the multi resolution decomposition capability of wavelets to obtain corresponding scale specific features of the underlying generating system and the reconstruction of the given time series is accomplished by linking together the derived decompositions using second order Volterra kernels which are estimated in an on-line mode using the well known Kalman filter formulation. The model has been applied to two case studies from Cauvery River Basin, India. Results also indicate presence of discernable nonlinear characteristics in the stream flow data as evidenced by the results of the BDS non-linearity test. The proposed model performed well for both the stations when compared to the Wavelet based Linear models, the linear regression models and other nonlinear approaches such as the coupled Wavelets-Artificial Neural Networks based models.