A Distance-based Method for Spatial Prediction in the Presence of Trend

Abstract

A new method based on distances for modeling continuous random data in Gaussian random fields is presented. In non-stationary cases in which a trend or drift is present, dealing with information in regionalized mixed variables (including categorical, discrete and continuous variables) is common in geosciences and environmental sciences. The proposed distance-based method is used in a geostatistical model to estimate the trend and the covariance structure, which are key features in interpolation and monitoring problems. This strategy takes full advantage of the information at hand due to the relationship between observations, by using a spectral decomposition of a selected distance and the corresponding principal coordinates. Unconditional simulations are performed to validate the efficiency of the proposed method under a variety of scenarios, and the results show a statistical gain when compared with a more traditional detrending method. Finally, our method is illustrated with two applications: earth’s average daily temperatures in Croatia, and calcium concentration measured at a depth of 0–20 cm in Brazil. Supplementary materials accompanying this paper appear online.