Incorporating Information from a Digital Elevation Model for Improving the Areal Estimation of Rainfall

Abstract

Rainfall areal estimation is a common problem that appears in many fields such as meteorology, hydrology or agronomy. Rainfall is an intermittent phenomenon in both space and time and it displays large spatio- temporal variability. Raingage networks collect point estimates of rainfall that can be spatially interpolated to provide an estimate of the rain spatial distribution within a catchment area. In general, these interpolations provide good estimates of the total amount of rainfall but they do not model accurately its complex spatio-temporal structure.

Better descriptions of rainfall spatial variability should be obtained by incorporating indirect information as such obtained from a digital elevation model. The application of some geostatistical techniques to improve rainfall estimation by integrating elevation data in a catchment area located in Asturias region of Spain is discussed. The algorithms used are kriging with an external drift, traditional cokriging and collocated cokriging. The results are compared with methods that do not account for the digital elevation model data, such as ordinary kriging, and the two most common techniques applied by hydrologists: the Thiessen polygons (or nearest-neighbor estimator) and inverse squared-distance weighting.

The data set used in this exercise corresponds to the Asturias region (North of Spain) and consists of annual rainfall data from 69 pluviographs and a digital elevation model on a grid of 198 by 75 square cells of 1 km by 1 km size covering an area of 14850 km².

The different algorithms are quantitatively evaluated using cross-vali-dation and analyzing the histogram of the cross-validation errors (for global unbiasedness), the scatterplot of errors versus estimated values (for conditional unbiasedness) and the variogram of the errors (for lack of spatial correlation). The results, while in the line of similar applications in other fields, favor the geostatistical methods including the secondary information; however, the scores of the different methods are very similar making difficult to justify complex geostatistical analysis in this specific case study. Reasons for this performance should be found in the weak spatial correlation of the rainfall and between the rainfall and elevation.