Geostatistical Methods for Up- and Downscaling of Soil Properties and Crop Responses in Space and Time.

The variation of soil properties and crop responses in space and time provides challenges to agronomists and farmers who need to take this variation into account to optimize land management. Modern geostatistical approaches represent the variation as a sum of a deterministic component that is expressed as a function of environmental explanatory variables and a stochastic residual that represents the remaining variation that cannot be explained by the explanatory information. This presentation first reviews the basic geostatistical approach, which makes use of the regression kriging model. Regression kriging is frequently adopted in 2D space but its extension to 3D space and space-time are also discussed. The latter is particularly interesting because it allows a merge of geostatistical and mechanistic, dynamic modelling approaches. Next we address geostatistical methods for up- and downscaling. Upscaling refers to the prediction of averages over larger areas or time intervals from observations at points. This has since long been solved with block-kriging. Downscaling has the opposite objective in which predictions at points are made from observed averages over blocks. This problem has recently been solved using area-to-point kriging. The main difficulty with this method is that block observations do not completely reveal the variation at point support, and for this expert elicitation combined with Bayesian statistics offers solutions. Special attention is paid to how uncertainties about predicted soil properties and crop responses vary under a change of scale, and how users can benefit from uncertainty information to improve decision making. Methods are illustrated with real world case studies on space-time interpolation of biomass in a Dutch potato field, block kriging of soil properties in the Allier river valley in France, and area-to-point kriging of satellite-based crop growth indices.