A Method for Estimating Mean Areal Rainfall Using Moving Trend Functions of the Intensities

Abstract

This paper investigates the internal spatial distribution of rain rates inside the rain areas. Moving trend functions are defined for different thresholds τ. They are obtained as conditional mathematical expectations of the rain rates above τ, and depend on the distance between the considered point with rain rate higher than τ and the boundary of the τ-thresholded area, which is the area where the intensity is above τ. These functions are linked to the dynamics of rainfall patterns and are thus named moving trend functions. Such functions are calculated on a dataset of hourly rainfall fields recorded in 1989 and 1990 in the framework of the Epsat-Niger project. The study area is about 12 000 km2 and is instrumented with a dense gauge network. The shape of the moving trend functions show that, on average, the rain intensity increases from the edge to the center of the τ-thresholded areas. Thus, the spatial distribution of the rain rates depends on the shape of the τ-thresholded areas. An estimation algorithm for mean areal rainfall is then proposed using the moving trend functions. This estimation implicitly depends on the shape of the τ-thresholded area. The algorithm is applied to two subareas of 400 and 3600 km2 of the Niger dataset. The method is also compared with the threshold method on these two subareas. The two techniques give equivalent results on the 3600-km2 area and some small improvements can be observed on the 400-km2 area, especially for low thresholds. However, problems encountered in the estimation of the moving trend functions discussed in the paper and due to the finite size of the study area prevent the moving trend function technique to demonstrate its potentiality clearly.