A Development of Two-Dimensional Generalized Coupled Markov Chain Model and Its Applications on a Soil Map Reconstruction

The conceptual model of under-sampled study area will include a great amount of uncertainty. In this study, we investigate the applicability of coupled Markov chain model in a two-dimensional (2D) spatial domain as a tool for minimizing the uncertainty arose from the lack of data. A new formulation of conditional probability equation is developed to generalize the previous 2D coupled Markov chain (CMC) model, which has more versatility to fit any computational sequence. Furthermore, the computational algorithm is improved to utilize more conditioning information and reduce the existing artifacts in previous CMC, such as the artificial parcel inclination and step-like parcel boundary change. A developed model of generalized 2D CMC (GCMC) is tested through applying a hypothetical soil map to evaluate the appropriateness as an alternative model for conventional geostatistics. Comparing to sequential indicator simulation (SIS) algorithm, the simulated single realization results from GCMC show lower entropy at the boundaries of indicator parcels. Presented correlation decay versus distance matrices show sound prediction on the indicator structures of reconstructed map simulated by GCMC in case of adequate numbers of conditioning information. For under-sampled indicators, however, GCMC under-estimates the presence of the indicators, which is a common aspect of geostatistical models. To improve this under-estimation, further study on data assimilation inclusion in the GCMC or improved field data sampling maneuver is required. The applicability of 2D GCMC can be various map reconstructions from sparse data such as soil or geologic map. Integration the developed model into geographic information system (GIS) is under development for the purposes.