Thursday, November 8, 2007 - 9:30 AM
341-5

On Effective Linearity of Soil Process Models during Spatial Aggregation.

Ronald Corstanje and Murray Lark. Rothamsted Research, Hertfordshire, England

Soil process models are often developed at a scale finer than that at which the output is needed and the inputs are available. If the model is linear with respect to its inputs, then predictions at the coarser scale can be obtained with the aggregated inputs. If the model is nonlinear, then this procedure gives biased estimates of the aggregate output variable. Most soil models will not be strictly linear. The practical question is whether this nonlinear behaviour is important, given other sources of uncertainty. We quantify model linearity by computing the weighted mean-squared deviations of the model output from a linear approximation. We can consider a model nonlinear if this number is in excess of the analytical variability for our measured model outputs. So for a model deemed effectively linear, nonlinearity introduces no more uncertainty than the measurement error. We also use as a weighting function the probability density function (pdf) for the model inputs. What we obtain is an assessment of model effective linearity that depends on location (i.e. where we are in parameter space) and the variability within the units over which we are aggregating. The model may be linear with respect to one parameter or variable but nonlinear with respect to another. We assess the contribution of any single input parameter to model nonlinearity by computing a lack of fit from a postulated linear response to this parameter given a mean (non linear) response to all other parameters. This allows us to identify parameters or groups of parameters for which the model is linear at a given scale. We have applied this method to two case studies. The first consists of a model of ammonia volatilization in soil after urea application and the second is a functional model of leaching from soil (SLIM model).