Invariance in the Spatial Structure of Sahelian Rain Fields at Climatological Scales

Abstract

The occurrence of rainfall in the semiarid regions is notoriously unreliable and characterized by great spatial variability over a large spectrum of timescales. Based on analytical considerations, an integrated approach is presented here in order to describe the spatial structure of rain fields for timescales used in climatological studies, that is from the daily to the seasonal scales and beyond to the interannual scale. At the scale of the rain event, two factors determine the spatial structure of rain fields. One is the spatial variability of the conditional rainfall H* (H > 0), represented by its variogram ?*e. The other is the intermittency, its spatial structure being described by the indicator variogram ?1. It is shown that the spatial structure of rain fields for time steps larger than the event may be analytically derived from ?*e and ?1, taking into account the anisotropy and nonstationarity that may affect either of these two functions, which are thus two timescale invariants of the rainfall process. The upscaling factor used to obtain the structure at large timescales is the number of rain events recorded over the period under consideration. An application using a large dataset of 450 Sahelian rain events observed with the Estimation des Précipitations par Satellite (EPSAT)?Niger monitoring network is presented. The theoretical model provides a good representation of the spatial variability observed in the data. The validation of the model confirms that knowledge of the average event rain field structure and the number of events N is sufficient to determine the structure of the N-event rain fields.