Modelling soil variation: past, present, and future

The soil mantles the land, except where there is bare rock or ice, and it varies more or less continuously. Many of its properties change continuously in time, too. We can measure the soil at only a finite number of places and times on small supports, and any statement concerning the soil at other places or times involves prediction. Variation in soil is also complex, so complex that no description of it can be complete, and so prediction is inevitably uncertain. Soil scientists should be able to quantify this uncertainty, and manage it. This means representing the variation by models that may be in part deterministic, but cannot be wholly so; they must have some random element to represent the unpredictable variation. Here we review three families of statistically based models of soil variation that are currently in use and trace their development since the mid-1960s. In particular, we consider classification and geostatistics for modelling the spatial variation, time series analysis and physically based approaches for modelling temporal variation, and space–time Kalman filtering for predicting soil conditions in space and time simultaneously. Each of these attaches to its predictions quantitative estimates of the prediction errors. Past, present and future research has been, is, and will be directed to the development of models that diminish these errors. A challenge for the future is to investigate approaches that merge process knowledge with measurements. For soil survey, this would be achieved by integration of pedogenetic knowledge and field observations through the use of data assimilation techniques, such as the space–time Kalman filter.