Spatial aggregation and soil process modelling

Nonlinear soil process models that are defined and calibrated at the point support cannot at the same time be valid at the block support. This means that in the situation where model input is available at point support and where model output is required at block support, spatial aggregation should take place after the model is run. Although block kriging does both in one pass, it is sensible to separate spatial aggregation from spatial interpolation. Contrary to aggregation, interpolation should better take place before the model is run because this enables a more efficient use of the spatial distribution characteristics of individual inputs. When a model is run with interpolated inputs, it is important not to ignore the interpolation error. Substituting conditional expectations in place of probability distributions into a nonlinear model leads to bias, essentially for the same reason that aggregating inputs prior to running a model is not the same as aggregating the output after the model is run. Running a model with inputs that are probability distributions will usually call for a Monte Carlo simulation approach. This causes a substantial increase in the numerical load, but apart from eliminating bias, an important advantage is that it shows how uncertainties in model inputs propagate to the model output. Many models used in soil science suffer not only from input error but also from model error, which is support- and case-dependent. Case dependency implies that model error can only be assessed realistically through validation. A major problem in validation is that the validation data are often collected at a much smaller support than the aggregated model predictions.