Generalized coupled Markov chain model for characterizing categorical variables in soil mapping

We developed a general formulation of the Markovian transition probability model and the corresponding computational algorithm for characterizing heterogeneity in soil types. The generalized model is based on the previously developed coupled Markov chain (CMC) model in which spatial conditioning is done using transition probabilities that incorporate field observations. The generalized coupled Markov chain (GCMC) model is more flexible with respect to conditioning than the previous CMC model because there are no restrictions on the input data format, and a random sequence calculation algorithm is used. The GCMC model was compared with the sequential indicator simulation (SIS), and the results were quantitatively analyzed. When adequate soil sampling data are available, the GCMC model predicts the spatial distribution of soil types as well as or better than the SIS model. The GCMC model has the advantage of simple input variables (because preprocessing is not required) and faster computation time (by about 60%). The models were also tested with sparse data sets, and the GCMC model predicted the presence of soil types better than the SIS model, based on a metric derived from ensemble probabilities. Further studies are in progress to expand applications of the model to stationary and nonstationary soil type distributions, improve algorithm efficiency, address underestimation caused by undersampled lithology, and extend the model to three dimensions.