Geostatistical analysis of spatial variability of rainfall and optimal design of a rain gauge network

Kriging is a geostatistical estimation technique for regionalized variables that exhibit an autocorrelation structure. Such a structure can be described by a semivariogram of the observed data. The punctual-kriging estimate at any point is a weighted average of the data, where the weights are determined by using the semivariogram and an assumed drift, or lack of drift, in the data. The kriging algorithm, based on unbiased and minimum-variance estimates, involves a linear system of equations to calculate the weights. Kriging is applied in an attempt to describe the spatial variability of rainfall data over a geographical region in northern Greece. Monthly rainfall data of January and June 1987 have been taken from 20 measurement stations throughout the above area. The rainfall data are used to compute semivariograms for each month. The resulting semivariograms are anisotropic and fitted by linear and spherical models. Kriging estimates of rainfall and standard deviation were made at 90 locations covering the study area in a rectangular grid and the results used to plot contour maps of rainfall and contour maps of kriging standard deviation. Verification of the kriging estimates of rainfall are made by removing known data points and kriging an estimate at the same location. This verification is known as the jacknifing technique. Kriging errors, a by-product of the calculations, can then be used to give confidence intervals of the resulting estimates. The acceptable results of the verification procedure demonstrated that geostatistics can be used to describe the spatial variability of rainfall. Finally, it is shown how the property of kriging variance depends on the structure and the geometric configuration of the data points and the point to be estimated can also be used for the optimal design of the rain gauge network in an area.