Median Polish Kriging for space-time analysis of precipitation

According to Cressie (1991), the median polish kriging (MPK) is a hybrid method for predicting of spatial data in a two dimensional surface. It combines a kriging interpolator and an analysis of tables. As a result of the effect of a directional trend that models the orographic structure at a specific place, and the periodic temporal character associated with an atmospheric process, such as rainfall, an extension to the number of exploration dimensions is proposed by using median polish in an additive approach, for one temporal and three spatial dimensions (latitude, longitude and altitude). In this sense, after applying an outlier resistant and robust prediction method as the MPK, the stationary on residuals was ideal to estimate the structure covariance function, which was obtained fitting a sum-product model with a spatial exponential effect and a hole-effect without dampening in time. The spatio-temporal modified MPK was used for mapping of monthly precipitation, based on 102 irregularly spaced weather stations from Colombia, for the period 2000-2010. The functional form was adapted to spatial-temporal kriging to create monthly precipitations maps for wettest and driest periods, and a forecast for the rainiest period in the year 2010. Finally, the accuracy of the method was assessed through a cross validation analysis.