Bayesian Data Fusion Applied to Soil Drainage Classes Spatial Mapping

Soil drainage classes spatial mapping is of great interest since drainage has direct effects on crop productivity and hydrological modelling. However, the prediction of this categorical variable often requires a laborious and expensive sampling over large areas. There is thus a need for a methodology that is able to combine several sources of information to improve the prediction. Bayesian maximum entropy (BME) has become a complete framework in the context of space-time prediction. This method proposes solutions to combine several sources of data no matter what the nature of information is. However, the various attempts that were made for adapting the BME methodology to categorical variables and mixed random fields faced some limitations, as a high computational burden. The main objective of this paper is to overcome this limitation by generalizing the Bayesian data fusion (BDF) theoretical framework to categorical variables, which is a simplification of the BME method through the conditional independence hypothesis. The BDF methodology for categorical variables is first described and then applied to a practical case study: the estimation of soil drainage classes using a soil map and point observations around Mechelen (Belgium). The BDF approach is compared to BME along with more classical approaches, as indicator cokriging (ICK) and logistic regression. Estimators are compared using various indicators, namely the percentage of correctly classified locations and the average highest probability. Although BDF methodology for categorical variables is a simplification of BME approach, both methods lead to very close results and have strong advantages compared to ICK and logistic regression.