Effect of seasonal adjustment on empirical rainfall distributions

Summary The empirical rainfall distributions of 42 monthly time series in Spain, for both raw data and for residual series, after removing the seasonal component, were fitted with six theoretical distribution functions (d f's). The distributions were fitted with 2, 3, and 4 parameters, which had been used previously with meteorological variables. The parameters of the probability density functions were calculated using maximum likelihood estimation procedures, and six statistics were examined to identify the bestd f to fit each series.The observations {X _t},t = 1,,N were assumed to consist of a seasonal componentS _t described by an harmonic process model, whose frequencies, number of terms, amplitudes and phases are unknown constants, plus a residualY _t which is a general linear process (for example, an autoregressive, moving-average, or mixed autoregressive/movingaverage process).The frequencies and number of terms in the harmonic process were chosen via a periodicity test, the Siegel test (1980). This is essentially a uniparametric family of periodicity tests which contains the Fisher test as a special case, which improves the results of the latter in cases of simultaneous periodicity at several frequencies. The remaining unknown parameters were determined by regression analysis.It is well known that precipitation has a positively skewed, non-Gaussian distribution. However, the results obtained here show that while the statistical techniques used to eliminate the seasonal component do not require the original data normal distribution, when they are normally distributed the quality of the estimates is better.With 7 Figures