Long-term rainfall monthly shortage in Spain: Spatial patterns, statistical models and time trends

摘要

Several patterns of the monthly rainfall shortage in Spain are investigated by using long-term series of monthly rain amounts, which were recorded at 34 observatories and compiled by the Agencia Estatal de Meteorolo?i{dotless}a, AEMET (Spanish Ministry of Environment). Owing to the strong variability of the pluviometric regime along the year, the median of the empirical monthly rain amounts is estimated for every month of the year. A monthly shortage is then defined as the difference between the corresponding monthly median and the monthly rain amount. A spell of monthly shortage is a set of consecutive months with amounts below the corresponding monthly medians. Five magnitudes are defined to characterize the rainfall shortage: (1) the spell length, L (months); (2) the average monthly shortage of a spell, (mm); (3) the largest monthly shortage in a spell, S_M (mm); (4) the total rainfall shortage for every spell, CS (mm) and (5) the rainfall amount for every shortage spell, CR. The whole number of spells, N, and the number of spells as a function of shortage lengths, N(L), are compared with those deduced from the distribution theory of runs (TR). Instead of a geometric distribution, a Markov chain of first order with two states becomes a better option for the probability density function of L. Although the empirical distributions of , S_M and CS are well fitted by a Pearson-type III model for most gauges, the generalized Pareto (GP) distribution is sometimes a better choice. The distribution of CR is well fitted by gamma and especially Poisson-gamma models. Besides these statistical analyses, an interpretation of the rainfall shortage is attempted by looking for links between the distributions of cumulative monthly shortage (CMS), and cumulative number of months (CNM) with rainfall deficit. Both distributions generate normalized shortage curves (NSC), which follow similar laws to the normalized rainfall curves (NRC), used, for instance, in the study of daily rainfall amounts. Finally, statistical significance of local and field time trends of , S_M and CS are evaluated.