Estimating soil properties from thematic soil maps: the Bayesian maximum entropy approach

Current soil process models require the most accurate values for each of their input parameters at the finest spatial scale. Traditionally, soil property values are obtained either from soil maps or from geostatistical methods using exact laboratory measurements. Both data types convey substantial information: soil maps provide exhaustive but soft (,,ague) information, whereas laboratory analyses provide hard (accurate) but scarce measurements. Ideally, they should be combined. This objective can be reached using a recently developed method, namely the Bayesian maximum entropy (BME) approach, that allows the user to incorporate hard and soft data in a spatial estimation context. In this work, both the regular BME algorithm and a new variant of it using a Monte Carlo procedure (BME/MC) are proposed for obtaining an estimated map for the textural (sand, silt, and clay) fractions from a limited number of accurate measurements and a spatially exhaustive soil map. Compared with popular geostatistical methods like ordinary kriging (OK), this approach has the advantage of using soft information on a sound theoretical basis. The entire probability distribution function can be estimated at each estimation location, allowing the computation of confidence intervals, probability of exceeding a threshold, etc. Using expectation properties in a Monte Carlo procedure, the BME/MC algorithm takes additionally into account the fundamental constraints on the textural fractions (they are summing to one and belong to the [0, 1] interval). As illustrated with a real data set from Belgium,using BME results in much more accurate textural fractions estimates and more realistic maps than those obtained with regular geostatistical algorithm.