Kriging methods using non-linear trend functions from machine learning and its applications

Abstract

A accurate spatial interpolation of geostatistical data plays a crucial role in both climate risk assessment and adaptation. Kriging with external drift (KED) method emerges as a powerful tool for spatial interpolation. It specifically designs to incorporate auxiliary information in the estimations of target variable at unobserved points. However, the traditional KED methods relying on polynomial trend functions can exhibit limitations in certain scenarios. These limitations stem from their inability to fully capture the complicated and non-linear relationships that might exist between the target variable and the incorporated auxiliary variables. This dissertation introduces a novel trend function for the KED method that leverages the power of a machine learning algorithm, least squares support vector regression (LSSVR), to construct non-linear trend functions for enhanced spatial prediction accuracy. The polynomial trend functions were fitted using the generalized least squares (GLS) estimator to compare the effectiveness of the proposed trend prediction method. Additionally, the accuracy of both KED and regression kriging (RK) methods were evaluated through comparison with the ordinary kriging (OK) method for monthly mean temperature and pressure estimation across Thailand throughout the year 2017. The results indicated that KED with LSSVR exhibits demonstrably superior performance comparing to the other methods.