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Due to our imperfect knowledge of soil distributions acquired from field surveys, spatial uncertainties inevitably arise in mapping soils at unobserved locations. Providing spatial uncertainty information along with survey maps is crucial for risk assessment and decision-making. This paper introduces a novel probability vector approach for spatial uncertainty modeling of soil classes based on an existing two-dimensional Markov chain model for conditional simulation. The objective is to find an accurate and efficient way to represent spatial uncertainties that arise in mapping soil classes. Joint conditional probability distribution (JCPD) represented by a set of occurrence probability vectors (PVs) of soil classes is directly calculated from conditional Markov transition probabilities, rather than the conventional approximate estimation from a limited number of simulated realizations. By visualizing the calculated PVs, information reflecting spatial uncertainly of soil distribution can be quickly assessed. We hypothesize that these directly calculated PVs are equivalent to the PVs estimated from an infinite number of realizations and thus realizations visualized from the calculated PVs represent the spatial variation of soil distribution. This hypothesis is supported by simulation results showing that: (i) with increasing the number of realizations generated by the Markov chain model from 10 to 100 and to 1000, PVs estimated from these realizations gradually approach the calculated PVs; (ii) similar to simulated realizations, realizations visualized from calculated PVs also can reflect the spatial patterns of soil classes and approximately reproduce the complex indicator variograms of soil classes of the original soil map.

Soils typically exhibit complex spatial variation of multi-categorical variables such as soil types and soil textural classes. Quantifying and assessing soil spatial variation is necessary for land management and environmental research, especially for accurately assessing the water and solute transport processes in watershed scales. This study describes an efficient Markov chain model for two-dimensional modeling and simulation of spatial distribution of soil types (or classes). The model is tested through simulations of a simplified soil map. The application of the model for predictive soil mapping with parameters estimated from survey lines is explored. Analyses of both simulated maps and associated semi-variograms show that the model can effectively reproduce observed spatial patterns of soil types and their spatial autoeorrelation given an adequate number of survey lines. This indicates that the model is a feasible method for modeling spatial distributions of soil types (or classes) and the transition probability matrices of soil types in different directions can adequately capture the spatial interdependency relationship of soil types. The model is highly efficient in terms of computer time and storage. The model also provides an approach for assessing the uncertainty of soil type spatial distribution in areas where detailed survey data are lacking. The major constraint on applications of the model at this stage is that the minor soil types are relatively underestimated when survey lines are too sparse.

Some problems in traditional soil mapping--high cost, high subjectivity, poor documentation, and low accuracy and precision--have motivated the development of a knowledge-based fuzzy soil mapping system, named SoLIM (Soil Land Inference Model). The rule-based method of the current SoLIM has its limitations. It requires explicit knowledge of the details of soil-environment relationships and it assumes that the environmental variables are independent from each other. This paper presents a case-based reasoning (CBR) approach as an alternative to the rule-based method. Case-based reasoning uses knowledge in the form of specific cases to solve a new problem, and the solution is based on the similarities between the new problem and the available cases. With the CBR method, soil scientists express their knowledge by providing locations (cases) indicating the association between a soil and a landscape or environmental configuration. In this way, the soil scientists avoid the difficulties associated with depicting the details of a soil-environment relationship and assuming the independence of environmental variables. The CBR inference engine computes the similarity between the environmental configuration at a given location and that associated with each case representing a soil type, and then uses these similarity values to approximate the similarity of the local soil at the given location to the given soil type. A case study in southwestern Wisconsin demonstrates that CBR can be an easy and effective way for soil scientists to express their knowledge. For the study area, the result from the CBR inference engine is more accurate than that from the traditional soil mapping process. Case-based reasoning can be a good solution for a knowledge-based fuzzy soil mapping system.