Use of universal function approximation in variance-dependent surface interpolation method: An application in hydrology

Variance dependent stochastic interpolation approaches such as kriging are widely recognized as standard stochastic methods for interpolation of geophysical and hydrologic variables. Deterministic weighting and stochastic interpolation methods are the most frequently used methods for estimating missing rainfall values at a gage based on values recorded at all other available recording gages. Traditional kriging has a major limitation due to the need for an a priori definition of a mathematical function for a semivariogram that might fit the surface to be interpolated. Use of the universal function approximator, artificial neural network (ANN), as a replacement to fitted authorized semivariogram model within ordinary kriging is investigated in the current study. The revised ordinary kriging is used for estimation of missing precipitation data at a rainfall gaging station based on data recorded at all other available gaging stations. Historical daily precipitation data obtained from 15 rain gaging stations from a temperate climatic region, Kentucky, USA, is used to test the improvised method and derive conclusions about the efficacy of this method. Results suggest that use of universal function approximator such as ANN within a kriging has several advantages over ordinary kriging.