Spectral analysis of temporal non-stationary rainfall-runoff processes

This study treats the catchment as a block box system with considering the rainfall input and runoff output being a stochastic process. The temporal rainfall-runoff relationship at the catchment scale is described by a convolution integral on a continuous time scale. Using the Fourier-Stieltjes representation approach, a frequency domain solution to the convolution integral is developed to the spectral analysis of runoff processes generated by temporal non-stationary rainfall events. It is shown that the characteristic time scale of rainfall process increases the runoff discharge variability, while the catchment mean travel time constant plays the role in reducing the variability of runoff discharge. Similar to the behavior of groundwater aquifers, catchments act as a low-pass filter in the frequency domain for the rainfall input signal.