Applying multi-resolution analysis to differential hydrological grey models with dual series

This investigation proposes a new approach for modeling rainfall–runoff processes by wavelet-based multi-resolution analysis. Firstly, a redundant wavelet transform is used to decompose the observed effective rainfall and direct runoff time series to obtain wavelet coefficients at each resolution level. Then, these wavelet coefficients are applied to model rainfall–runoff processes using differential hydrological grey models with dual series at each resolution level. The average of the estimated grey parameters at each resolution level not only provides information for validating the proposed approach, but also represents the average system characteristics at each resolution level. The summation of the forecast results at various resolution levels yields the overall forecast and reveals that this procedure is suitable for modeling the rainfall–runoff process.