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A Markov Chain-Based Probability Vector Approach for Modeling Spatial Uncertainties of Soil Classes

^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 System, Inst. of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China and Dep. of Geography, Univ. of Wisconsin, Madison, WI 53706

View larger version (77K): [in a new window]   Fig. 1. Illustration of the simulation algorithm of the TMC model. The state of the current cell (i,j) depends on its four nearest known neighbors in four axis directions (west, east, south, and north), that is, grid cells (i,j – 1), (i – 1,j), (Nx,j), and (i,Ny), their states being denoted as m, l, p, and o, respectively. The dark gray cells stand for observed data (i.e., parts of survey lines, survey lines may be regular or irregular). The light gray cells stand for cells already visited. The thick arrows illustrate the alternate proceeding directions of the TMC model. The dashed arrows illustrate the interactions between the current unknown cell and its four nearest known neighbors in axis directions.

View larger version (103K): [in a new window]   Fig. 2. The maximum occurrence probability map of soil classes and the occurrence probability maps of individual soil classes visualized from the calculated PVs using the probability vector approach.

View larger version (103K): [in a new window]   Fig. 3. The maximum occurrence probability map of soil classes and the occurrence probability maps of individual soil classes visualized from the PVs estimated from 100 TP-realizations.

View larger version (103K): [in a new window]   Fig. 4. The maximum occurrence probability map of soil classes and the occurrence probability maps of individual soil classes visualized from the PVs estimated from 10 TP-realizations.

View larger version (132K): [in a new window]   Fig. 5. Prediction maps and single realizations using the probability vector approach and the simulation approach of the TMC model. (a) The reference soil map. (b) The prediction map from the probability vector approach. (c) The first PV-realization. (d) The second PV-realization. (e) The prediction map estimated from 100 TP-realizations. (f) The first TP-realization. (g) The second TP-realization.

View larger version (34K): [in a new window]   Fig. 6. Indicator (direct and cross) variograms of soil classes in the original soil map and realization maps. The first four are direct variograms. The last four are cross variograms. Or–The original soil map (corresponds to Fig. 5a). PV1–The first PV-realization (corresponds to Fig. 5c). TP1–The first TP-realizations (corresponds to Fig. 5f).