A Random-Path Markov Chain Algorithm for Simulating Categorical Soil Variables from Random Point Samples

Abstract

Quantitative prediction and simulation of categorical soil variables from limited samples are crucial for cost-effectively acquiring exhaustive area-class maps. Conventional methods, however, usually cannot meet all of the requirements for class simulation in incorporating interclass relationships and generating polygon features. We developed a random-path sequential simulation algorithm based on the Markov chain random field theory. Our objective was to find a suitable method for predictive area-class soil mapping from irregularly distributed point samples, and thus extend Markov chains into practical nonlinear geostatistics. The algorithm was used to simulate soil type maps conditioned on three different sample data sets, and was compared with the widely used indicator kriging simulation algorithm-sequential indicator simulation with ordinary indicator kriging (SISoik). Results show that the algorithm works well with both dense and sparse random samples in reproducing all classes and input statistics. Compared with SISoik, the algorithm has the following advantages: (i) it more effectively captures complex patterns of soil classes and obeys their interclass relationships; (ii) it generates lower spatial uncertainty and more accurate realizations-for example, the relative increases in average percentage of correctly classified locations of realizations for the sparse, medium, and dense data sets are 5.0, 9.9, and 8.5%, respectively; (iii) it generates polygon features in realizations in accordance with the style of area-class soil maps; and (iv) it can generate classes missed in sampling but confirmed by experts. We concluded that the algorithm provides a practical spatial statistical tool for prediction and simulation of categorical soil spatial variables.