4 - The distribution of the l-day total precipitation amount

Summary

ABSTRACT On the two-dimensional domain of the time (discrete variable) and the cumulative daily rainfalls (continuous one) an alternating rainfall process is constructed. Methods of renewal theory are used to define the process and to calculate its properties. The fundamental assumption used to derive results of this paper is: the total precipitation amount of the wet days sequence is dependent on the length of this sequence. The independence of the successive dry and wet sequences is assumed too. Based on the above assumptions we finally derive the theoretical distribution of the l-day total precipitation.

INTRODUCTION

Hydrology, from its beginnings, is concerned with rainfall modelling. The importance of precipitation for other hydrological processes caused a stormy development of various models. For a detailed review see for instance the work of Waymire & Gupta (1981). More recent investigations about the properties of daily rainfalls can be divided into three parts:

1. (a) the seasonal variation of the stochastic model parameters (Woolhiser & Pegram, 1979; Valdes, Rodriguez-Iturbe & Gupta 1985; Yevjevich & Dyer, 1983; Woolhiser & Roldan, 1986);

2. (b) the description of precipitation occurrence and intensity (Buishand, 1979; Woolhiser & Roldan, 1982);

3. (c) the construction of models of wet and dry sequences occurrence (Roldan & Woolhiser, 1982; Mimikou, 1983; Jakubowski, 1988).

Unfortunately, though the obtained results are generally more useful than raw observations, they can rarely be applied as an input for simulation models. They do not even give a precise description of the precipitation climatology of a region.