Estimating Spatial Distribution of Rainfall by Fuzzy Set Theory

One of the important inputs for a water resources study is rainfall. Choosing improper interpolation methods may result in extensive errors. Geostatistical methods may also fail to be used, in case of insufficient data. However, generated data has small errors that produce unequivalency in data. Using fuzzy set theory, every data (observed, generated value and obtained from an expert or imprecise) valuated by membership function. Kriging, Weighted Moving Average (WMA), Thin Plate Smoothing Splines (TPSS) and Fuzzy Kriging Interpolation is executed for annual rainfall in eastern and southeastern Iran. Two cases were studied. The first case generated the data for some of the points and fuzzified these points. In the second case, the number of the generated points are increased. Variogram analysis demonstrated spatial correlation between the runoff and the annual rainfall in the study area. Also, fuzzy variogram showed spatial correlation with larger ranges. The results show that the fuzzy kriging method is an accurate method in estimating monthly and annual rainfall. Increasing the number of generating points would however increase the estimating error.