Smoothing the seasonal means of rainfall and runoff in the linear perturbation model (LPM) using the kernel estimator

As many natural catchments exhibit a significant or even marked degree of seasonality in their rainfall and runoff data, the means of identification of the seasonality structure and the determination of a quantitative expression or index of seasonality are topics of considerable interest to hydrologists. In a rainfall–runoff model such as the linear perturbation model (LPM), which explicitly takes into account the seasonality of daily data by identifying, smoothing, and subsequently abstracting the smoothed seasonal means of daily rainfall and runoff data, it is also of interest to examine how its efficiency in simulating the rainfall–runoff relationship of a catchment is affected by the smoothing method used. In the standard version of the LPM, the discrete Fourier smoothing method is employed to remove the high-frequency fluctuations of the seasonal means obtained from records of observed daily rainfall and runoff data of necessarily limited length. In the present study, the kernel estimator, which is a widely used non-parametric regression method, is employed as a simpler alternative to Fourier smoothing. Testing the LPM, using both smoothing methods, on three catchments and comparing its results, it is found that both smoothing methods achieve virtually the same results in terms of the Nash–Sutcliffe model efficiency index R2. To quantify the relative significance of the seasonal component in the simulated runoff series, a seasonality index (SI) is proposed. It is observed that the performance of the LPM is influenced much more by the seasonal characteristics of the rainfall and runoff processes in a catchment, as expressed by the proposed seasonality index SI, than by the methods used to smoothen the seasonal means. Clearly, for those catchments characterized by strong seasonality, thereby satisfying the design assumption of the model, the LPM can be expected to perform satisfactorily, much better than on catchments having weak seasonality.