Sensitivity Analysis of the MCRF Model to Different Transiogram Joint Modeling Methods for Simulating Categorical Spatial Variables
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Markov chain geostatistics is a methodology for simulating categorical fields. Its fundamental model for conditional simulation is the Markov chain random field (MCRF) model, and its basic spatial correlation measure is the transiogram. There are different ways to get transiogram models (i.e., continuous-lag transiograms) for MCRF simulation based on sample data and expert knowledge: linear interpolation method, mathematical model joint-fitting method, and a mixed method of the former two. Two case studies were conducted to show how simulated results, including optimal prediction maps and simulated realization maps, would respond to different sets of transiogram models generated by the three different transiogram jointing modeling methods. Results show that the three transiogram joint modeling methods are applicable; the MCRF model is generally not very sensitive to the transiogram models produced by different methods, especially when sample data are sufficient to generate reliable experimental transiograms; and the differences between overall simulation accuracies based on different sets of transiogram models are not significant. However, some minor classes show obvious improvement in simulation accuracy when theoretical transiogram models (generated by mathematical model fitting with expert knowledge) are used for minor classes. In general, this study indicates that the methods for deriving transiogram models from experimental transiograms can 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.
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