Analyse quantitative du phénomène de pluie ponctuelle maximale sur une surface Coefficient d'épicentrage des averses de 1 h à 24 h

Quantitative analysis of the phenomenon of maximum spot rainfall over an area - Epicentric coefficient of showers from 1 h to 24 h

Division Hydrologie-Hydraulique Fluviale, CEMAGREF, Paris-Antony

Abstract

The problem of estimating extraordinary rainfall usually arises in connection with a given location. In practice, meteorologists are very often confronted with the problem of estimating heavy rainfall, not in a given place, but over a whole section of space. For these practitioners, the problem is posed in the following terms : What is the probability of rainfall exceeding R over a zone within a region of Area A ? Consider a region whose area is S covered by p rainfall recorders (thus defining p sub-zones of average area S/p). Assume that rain for t hours follows the same statistical law at all points of the region. The investigation covers the maximum rainfall recorded by the p rainfall recorders for each time interval t. The problem consists of assessing the theoretical distribution of this rain. Denote by PL (T) local rainfall over a return period of T years and by PX (T) maximum rainfall (recorded on the p rainfall recorders) with the same return period. The coefficient (KX) is the ratio of the two quantiles. KX(T) =PX(T)/PL(T) Knowledge of KX(T) thus provides an estimate of PX(T) when local rainfall by site is known. A priori, KX(T) depends on the four variables listed below : - area S of the region under study (km2) ; - the number of rainfall recorders (or sub-zones) : p ; - the duration of rainy spells to (hours) ; - the return period T (years). We have proposed the following analytical expression for KX, taking account of limit conditions, based on rainfall data portraying the Orgeval area. KX = 1+[ln (S+1)/S+1/P][0.03+0.26 lnT +0,32e-t/20] This formula has been drawn up within the following limits: 7 ≤ S ≤ 104 (km2) 0.2 ≤ T ≤ 10 (year) 2 ≤ t ≤ 24 (hour) 5 ≤ p ≤ 21 Climatic conditions of the Paris basin The formula can reasonably be extrapolated beyond these limits, expecially for p. when the functions used make it possible to have p tend to infinity. The formula can be used to assess likely risks in a given small region : hydrical erosion in a sensitive agricultural zone, local overflow of a city sewage system, etc.