Representing the precipitation regime by means of Fourier series

摘要

We propose the use of Fourier series for representing the precipitation regime in a certain location and predicting it in ungauged locations, allowing for map production. We analyse monthly average precipitation data of 2043 gauging stations covering the Italian territory. The Fourier series allows to represent a curve as a sum of different sinusoidal components characterized by their period, amplitude and phase. Being the different harmonics not correlated, it is possible to fit them with stepwise multiple linear regressions. The Fourier series allows for a parsimonious representation of the regime, being usually the 12- and 6-month harmonics able to reproduce the observed values with little residuals [in this exercise the fitting gave an average monthly root mean square error (RMSE) of 9.21 mm and a correlation coefficient of 0.979]. Once the at-station harmonics parameters are obtained, it is possible to map them for predicting the regime in ungauged locations. Here we use ordinary kriging and the leave-one-out validation scheme for evaluating the amplitudes and phases of the harmonics of the 12- and 6-month periods and reconstructing the precipitation regime. We use the same scheme for the interpolation of the station data on a month-by-month basis, whose results are used as a benchmark. The analyses provide similar results, with overall RMSEs of 17.53 and 15.97 mm and correlation coefficients of 0.909 and 0.921, respectively. The spatial patterns of the reconstruction error are similar for the two cases. The stations having higher RMSE are clustered in the areas presenting high precipitation gradients, such as in the Appennines, or where major precipitation regime changes occur. For demonstrating that the Fourier series approach is more suitable for regionalization purposes, a k-means cluster analysis on the Fourier parameters was performed and the effect of such stratification on the mapping of the precipitation regime by applying regression kriging was assessed.