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Two-dimensional Markov Chain Simulation of Soil Type Spatial Distribution

^a Dep. of Geography, Univ. of Wisconsin, Madison, WI 53706
^b Dep. of Geography and Geology, Univ. of Wisconsin, Whitewater, WI 53190
^c State Key Lab. of Resources and Environmental Information Systems, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Science, Beijing 100101, China
^d Institute for Land and Water Management, Catholic Univ. of Leuven, B-3000 Leuven, Belgium

View larger version (75K): [in a new window]   Fig. 1. A triplex Markov chain is applied to each window (light gray cells) of a two-dimensional domain. Simulation is conditioned on window boundaries, that is, survey lines (dark gray cells).

View larger version (31K): [in a new window]   Fig. 2. A simplified soil map with seven soil types. This map is discretized into a 160 x 34 grid with a cell size of 50 m. Note: The length should be multiplied by 50 to obtain the correct length values.

View larger version (79K): [in a new window]   Fig. 3. Simulated results of the soil type distribution in the study area of Fig. 2 under different conditioning schemes. Labels 1000m, 500m, and 250m represent conditioning schemes used, that is, survey line intervals. R1 means the first simulated realization based on the corresponding survey line interval. S6 means Soil Type 6. The bottom row gives the estimated soil map based on maximum occurrence probabilities.

View larger version (108K): [in a new window]   Fig. 4. Simulated results of the soil type distribution in the left half of the study area under different conditioning schemes. Labels 1000m, 500m, and 250m represent conditioning schemes used, that is, survey line intervals. R1 means the first simulated realization based on the corresponding survey line interval. S6 means Soil Type 6. The bottom row gives the estimated soil map based on maximum occurrence probabilities.

View larger version (27K): [in a new window]   Fig. 5. Indicator variograms and cross-variograms calculated from the original map and one realization (500m-R1) in Figure 4. Graphs (a) to (g) are indicator variograms of individual soil types and Graphs (h) to (j) are indicator cross-variograms between soil types. Graph legends represent the related maps and soil types; for example, R1-3 means Soil Type 3 in the simulated realization map R1, and Original-1 x 6 means Soil Type 1 vs. Type 6 in the original soil map. Note: The length should be multiplied by 50 to obtain the correct length values.

View larger version (80K): [in a new window]   Fig. 6. Simulated results of the soil type distribution in the study area under different conditioning schemes. Labels 1000m, 500m, and 250m represent conditioning schemes used, that is, survey line intervals. R1 means the first simulated realization based on the corresponding survey line interval. S6 means Soil Type 6. The bottom row gives the estimated soil map based on maximum occurrence probabilities. Parameters (i.e., one-step transition probability matrices) for each simulation are directly estimated from the survey lines used in the simulation.

View larger version (116K): [in a new window]   Fig. 7. Simulated results of the soil type distribution in the left half of the study area under different conditioning schemes. Labels 1000m, 500m, and 250m represent conditioning schemes used, that is, survey line intervals. R1 means the first simulated realization based on the corresponding survey line interval. S6 means Soil Type 6. The bottom row gives the estimated soil map based on maximum occurrence probabilities. Parameters for each simulation are directly estimated from the survey lines used in the simulation.