Rainfall estimation in the Sahel. Part I: Error function

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 km(2) 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 degrees x 1 degrees and 2.5 degrees x 2.5 degrees 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 degrees x 2.5 degrees (1 degrees x 1 degrees) grid, and 40% (30%) for a single station on a 2.5 degrees x 2.5 degrees (1 degrees x 1 degrees) 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.