Optimal biased Kriging: Homeogram tapering and applications to geoid undulations in Korea

This article studies the Optimal Biased Kriging (OBK) approach which is an alternative geostatistical method that gives up the unbiasedness condition of Ordinary Kriging (OK) to gain an improved Mean Squared Prediction Error (MSPE). The system of equations for the optimal linear biased Kriging predictor is derived and itsMSPE is compared with that of Ordinary Kriging. A major impediment in implementing this system of equations and performing Kriging interpolation with massive datasets is the inversion of the spatial coherency matrix. This problem is investigated and a novel method, called "homeogram tapering", which exploits spatial sorting techniques to create sparse matrices for efficient matrix inversion, is described. Finally, as an application, results from experiments performed on a geoid undulation dataset from Korea are presented. A precise geoid is usually the indispensable basis for meaningful hydrological studies over wide areas. These experiments use the theory presented here along with a relatively new spatial coherency measure, called the homeogram, also known as the non-centered covariance function.