Sensitivity analysis of the MCRF model to different transiogram joint modeling methods for simulating categorical spatial variables

Abstract

Markov chain geostatistics is a methodology for simulating categorical fields. Its fundamental model for conditional simulation is the Markov chain random field (MCRF) model, with the transiogram serving as its basic spatial correlation measure. There are different methods to obtain transiogram models for MCRF simulation based on sample data and expert knowledge: linear interpolation, mathematical model joint-fitting, and a mixed approach combining both. This study aims to explore the sensitivity of the MCRF model to different transiogram jointing modeling methods. Two case studies were conducted to examine how simulated results, including optimal prediction maps and simulated realization maps, vary with different sets of transiogram models. The results indicate that all three transiogram joint modeling methods are applicable, and the MCRF model exhibits a general insensitivity to transiogram models produced by different methods, particularly when sample data are sufficient to generate reliable experimental transiograms. The variations in overall simulation accuracies based on different sets of transiogram models are not significant. However, notable improvements in simulation accuracy for minor classes were observed when theoretical transiogram models (generated by mathematical model fitting with expert knowledge) were utilized. This study suggests that methods for deriving transiogram models from experimental transiograms perform well in conditional simulations of categorical soil variables when meaningful experimental transiograms can be estimated. Employing mathematical models for transiogram modeling of minor classes provides a way to incorporate expert knowledge and improve the simulation accuracy of minor classes.