Comparison of univariate and bivariate approaches to map precipitation using geostatistics and the kalman filter

Abstract

Measured rainfall data are very important in agriculture and environmental science. However, in many cases, the information gathered by existing rain gauges is insufficient for characterizing climatic variation within a study area. Thus, the use of interpolation techniques is necessary to predict values to unsampled sites. In this work, the performances of geostatistical algorithms, such as ordinary kriging and ordinary cokriging, and a proposed Kalman filter method were compared for mapping rainfall. The analysis was performed using both univariate and bivariate approaches. Natural terrain elevation was taken as the auxiliary variable for the bivariate case. The analysis was conducted for specific months of the dry and wet seasons in the Santiago River basin in Mexico. After comparison of the statistical errors, it was established that the geostatistical methods provided excellent results (especially cokriging) for the wet season months, with good correlation of 0.7 or above between rainfall and e evation, but not for the dry season months. Nevertheless, good results were achieved for the dry season months using the proposed Kalman filter methodology, due to the high normality and spatial dependence of the sample in this period.