Spectral analysis of temporal variability of nonlinear and nonstationary rainfall-runoff processes

This study deals with the time-dependent nonlinear response of catchments to the variations in rainfall. Both the rainfall and runoff discharge fields are treated to be nonstationary in time. A functional series representation, a generalization of the linear convolution integral, is employed to quantify the nonlinear relation between the input and output. The Fourier-Stieltjes representation approach is used to evaluate the variance of runoff discharge in the spectral frequency domain. The analysis based on the spectral solution for the runoff discharge variance clearly demonstrates that larger values of rainfall characteristic time scale or catchment size parameter lead to larger variability of the runoff discharge, while a larger catchment scale parameter leads to smaller variability of the runoff discharge.