Normalised monthly shortage curves: a contribution for a better understanding of monthly rain deficit in Western Europe

Abstract

A new approach to the statistics of rainfall shortage at monthly scale in Western Europe is obtained from precipitation records of 115 gauges over the twentieth century. In this paper, a month is considered to have rainfall deficit when its rain amount is below the 50th percentile of the respective calendar month. The monthly shortage, MS, for every month with deficit is then computed as the absolute value of the difference between its monthly amount and the corresponding truncation level. The cumulative distributions of monthly shortage, CMS, and number of shortage months, CNM, constitute a new description of the monthly rainfall deficit. Both CMS and CNM distributions fit well to a Weibull model. Using the analogy to the normalised daily rainfall curves formulation, NRC, the relationship between CMS and CNM, named as normalised shortage curve, NSC, is modelled by the same function applied to NRCs. Similarly to NRCs, the behaviour of the NSCs strongly depends on the coefficient of variation of the monthly shortage, CVMS. Four coordinates characterising every NSC are then introduced: the CMS percentile associated with the median of CNM; the CNM percentile related to the median of CMS; and the percentiles of CMS and CNM for the average monthly shortage. In this way, the degree of asymmetric distribution of the monthly deficit is quantified. With the aim of performing a clustering process based on these four coordinates, a principal component analysis, is previously applied to remove redundancies, being obtained two uncorrelated principal components, PCs, characterising every NSC. An average linkage algorithm is then applied to these two PCs, leading to obtain spatially coherent groups of gauges with very similar NSC patterns. This clustering process permits to discard latitude and vicinity to the Atlantic Ocean or the Mediterranean Sea as main factors conditioning the monthly shortage regime.