Applying fuzzy theory and genetic algorithm to interpolate precipitation

Abstract

A watershed management program is usually based on the results of watershed modeling. Accurate modeling results are decided by the appropriate parameters and input data. Rainfall is the most important input for watershed modeling. Precipitation characteristics, such as rainfall intensity and duration, usually exhibit significant spatial variation, even within small watersheds. Therefore, properly describing the spatial variation of rainfall is essential for predicting the water movement in a watershed. Varied circumstances require a variety of suitable methods for interpolating and estimating precipitation. In this study, a modified method, combining the inverse distance method and fuzzy theory, was applied to precipitation interpolation. Meanwhile, genetic algorithm (GA) was used to determine the parameters of fuzzy membership functions, which represent the relationship between the location without rainfall records and its surrounding rainfall gauges. The objective in the optimization process is to minimize the estimated error of precipitation. The results show that the estimated error is usually reduced by this method. Particularly, when there are large and irregular elevation differences between the interpolated area and its vicinal rainfall gauging stations, it is important to consider the effect of elevation differences, in addition to the effect of horizontal distances. Reliable modeling results can substantially lower the cost for the watershed management strategy.