A Non-Linear Trend Function for Kriging with External Drift Using Least Squares Support Vector Regression

Abstract

Spatial interpolation of meteorological data can have immense implications on risk management and climate change planning. Kriging with external drift (KED) is a spatial interpolation variant that uses auxiliary information in the estimation of target variables at unobserved locations. However, traditional KED methods with linear trend functions may not be able to capture the complex and non-linear interdependence between target and auxiliary variables, which can lead to an inaccurate estimation. In this work, a novel KED method using least squares support vector regression (LSSVR) is proposed. This machine learning algorithm is employed to construct trend functions regardless of the type of variable interrelations being considered. To evaluate the efficiency of the proposed method (KED with LSSVR) relative to the traditional method (KED with a linear trend function), a systematic simulation study for estimating the monthly mean temperature and pressure in Thailand in 2017 was conducted. The KED with LSSVR is shown to have superior performance over the KED with the linear trend function.

Keywords

• geostatistics
• spatial interpolation
• kriging with external drift
• least squares support vector regression
• trend function