Efficient nonlinear modeling of rainfall-runoff process using wavelet compression

Summary This investigation proposes the wavelet-based efficient modeling of nonlinear rainfall-runoff processes and its application to flood forecasting in a river basin. Inspired by the theory of wavelet transforms and Kalman filters, based on the excellent capacity of the Volterra model, a time-varying nonlinear hydrological model is presented to approximate arbitrary nonlinear rainfall-runoff processes. A discrete wavelet transform (DWT) is used to decompose and compress the Volterra kernels, generating smooth reparametrizations of the Volterra kernels, reducing the number of coefficients to be estimated. Kalman filters were then utilized to on-line estimate compressed wavelet coefficients of the Volterra kernels and thus model the time-varying nonlinear rainfall-runoff processes. Kalman filters and the Volterra model that had been used over recent decades in the nonlinear modeling of rainfall-runoff processes, typhoon or storm events over Wu–Tu and Li–Ling watersheds are chosen as case studies were used herein to verify the suitability of a combination of wavelet transforms. The validation results indicated that the proposed approach is effective because of the multi-resolution capacity of the wavelet transform, the adaptation of the time-varying Kalman filters and the characteristics of the Volterra model. Validation results also reveal that the resulting method improves the accuracy of the estimate of runoff for small watersheds in Taiwan.