Adaptive window size selection for Kriging method and its applications

Abstract

Ordinary kriging (OK) has attained widespread popularity within spatial interpolation due to its ability to minimize error variance and deliver statistically optimal estimations that the expectation of error equals zero. This dissertation proposes the selection of window sizes using four distinct methodologies for spatial interpolation via the moving window ordinary kriging method. These approaches encompass the application of the K-means clustering algorithm, the nearest neighbor search using the Voronoi diagram, the employment of similarity measure with distinct distance functions, and the determination of adaptive neighborhood sizes based on the computation of expected probability at individual sample points. Our proposed methodologies are designed to specifically address the challenge of selecting appropriate windows for estimation points, which can lead to more efficiency and accurate spatial interpolation. We compared four window selection methods with OK and a fixed window size-based implementation of the moving window kriging method with 30 points (MWK) to estimate the annual average pressure and humidity in Thailand for the year 2018. The results illustrate the superior estimation capabilities of our approaches when compared to OK, as evidenced by a range of quantitative performance metrics, including the mean absolute percentage error (MAPE), root mean square error (RMSE), percentage average estimation error (PAEE), normalized mean squared error (NMSE), and relative improvement (RI). The effectiveness of our window selection methods for spatial interpolation can be attributed to their capacity for automatically adjusting window sizes at any given estimation point, which is a rather important feature.