Rainfall Estimation in the Sahel. Part I: Error Function

Abstract

Rainfall estimation in semiarid regions remains a challenging issue because it displays great spatial and temporal variability and networks available for monitoring are often of low density. This is especially the case in the Sahel, a region of 3 million km2 where the life of populations is still heavily dependent on rain for agriculture. Whatever the data and sensors available for rainfall estimation?including satellite IR and microwave data and possibly weather radar systems?it is necessary to define objective error functions to be used in comparing various rainfall products. This first of two papers presents a theoretical framework for the development of such an error function and the optimization of its parameters for the Sahel. A range of time scales?from rain event to annual?are considered, using two datasets covering two different spatial scales. The mesoscale [Estimation des Pluies par Satellite (EPSAT)-Niger (E-N)] is documented over a period of 13 yr (1990?2002) on an area of 16 000 km2 covered by 30 recording rain gauges; the regional scale is documented by the Centre Regional Agrometeorologie?Hydrologie?Meteorologie (AGRHYMET) (CRA) dataset, with an annual average of between 600 and 650 rain gauges available over a period of 8 yr. The data analysis showed that the spatial structure of the Sahelian rain fields is markedly anisotropic, nonstationary, and dominated by the nesting of two elementary structures. A cross-validation procedure on point rainfall values leads to the identification of an optimal interpolation algorithm. Using the error variances computed from this algorithm on 1° ? 1° and 2.5° ? 2.5° cells, an error function is derived, allowing the calculation of standard errors of estimation for the region. Typical standard errors for monthly rainfall estimation are 11% (10%) for a 10-station network on a 2.5° ? 2.5° (1° ? 1°) grid, and 40% (30%) for a single station on a 2.5° ? 2.5° (1° ? 1°) grid. In a companion paper, this error function is used to investigate the differences between satellite rainfall products and how they compare with ground-based estimates.