Optimal Interpolation of Daily Rainfall Equations with Fuzzy Theory and Genetic Algorithms in Mashhad Plain Basin

Regional analysis، estimating missing values، areal rainfall، estimating PMP and rainfall- runoff models in daily scale are essential in water resources and climatological researches. Modified inverse distance interpolation method based on Fuzzy Mathematics (MIDW-F) is a new، efficient method and independent of complex preconceptions hypothesis. The purpose of this paper is applying the new interpolation equation for above essential needs by calibration the daily rainfall of Mashhad Plain catchment. Screening and normalizing distances and elevations were done، then effects of fuzzy operations (Max، Min، Sum، Multiplication and SQRT) are Checked out and optimizing the parameters of MIDW-F by Genetic algorithms. The 215 daily precipitations (49 rain gauge stations) were analyzed and were calibrated. The results showed that the best operators are Minimum (Share58%)، multiplying (Share35%) and total contribution rate of others are 6%. The MIDW-F was compared with the three others conventional methods (the Arithmetic mean، Thiessen polygon and IDW) and results showed that the errors of MIDW-F method were reduced noticeably. Largest Regional Mean Square errors (RMSE) is for Arithmetic mean (Max. 90. 45، Min. 5. 76، variance 686. 8 and 70% Cv) and smallest RMSE belong to MIDW-F (Max. 56. 67، Min. 4. 6، variance 340. 92 and 57% Cv). Zoning of daily rainfall at 22/3/2009 and 23/2/2010 and with MIDW-F and IDW methods were conducted and evaluated. The results showed that the zoning by MIDW-F proposed more details. So this method\ is proposed for the interpolation of daily precipitation in a homogeneous region.