The behaviour of soil process models of ammonia volatilization at contrasting spatial scales

Process models are commonly used in soil science to obtain predictions at a spatial scale that is different from the scale at which the model was developed, or the scale at which information on model inputs is available. When this happens, the model and its inputs require aggregation or disaggregation to the application scale, and this is a complex problem. Furthermore, the validity of the aggregated model predictions depends on whether the model describes the key processes that determine the process outcome at the target scale. Different models may therefore be required at different spatial scales. In this paper we develop a diagnostic framework which allows us to judge whether a model is appropriate for use at one or more spatial scales both with respect to the prediction of variations at those scale and in the requirement for disaggregation of the inputs. We show that spatially nested analysis of the covariance of predictions with measured process outcomes is an efficient way to do this. This is applied to models of the processes that lead to ammonia volatilization from soil after the application of urea. We identify the component correlations at different scales of a nested scheme as the diagnostic with which to evaluate model behaviour. These correlations show how well the model emulates components of spatial variation of the target process at the scales of the sampling scheme. Aggregate correlations were identified as the most pertinent to evaluate models for prediction at particular scales since they measure how well aggregated predictions at some scale correlate with aggregated values of the measured outcome. There are two circumstances under which models are used to make predictions. In the first case only the model is used to predict, and the most useful diagnostic is the concordance aggregate correlation. In the second case model predictions are assimilated with observations which should correct bias in the prediction, and errors in the variance; the aggregate correlations would be the most suitable diagnostic.