The effects of simple perturbations of a process model on the spatial variability of its output

The predictions of a spatially distributed model will not exactly match a corresponding set of observations, due either to an inadequacy in the model (e.g. an inappropriate expression in a subprocess of the model), or an inadequacy in the data used as input to the model (e.g. through measurement error). In previous studies it has been found that the relation between an observed soil variable and a corresponding set of model predictions depends on scale, and may not be spatially uniform. We hypothesize that various kinds of model error will give rise to such scale-dependent and statistically non-stationary effects when predictions are compared with observations. If so, then this underlines the importance of a spatial analysis of model error.We investigated this hypothesis by using a process model to simulate the leaching of bromide through hypothetical soil profiles on a regularly spaced transect. This model was then perturbed in different ways so that its predictions reflected different causes of model failure, in this case a failure to reproduce the predictions of the unperturbed model. We quantified the effects of the perturbations with non-spatial statistics and also by a method of spatial analysis, the wavelet transform. Analysis with wavelet transforms revealed that our hypothesis was justified generally: at different spatial scales and/or locations, the variance of the model output, and the correlation of the output with the observations, were affected differently by the various causes of model failure. At fine spatial scales adverse effects on the variance and correlation were seen clearly when the data used as input to the model had been interpolated from spatially sparse measurements, or when the input data were affected by large measurement errors. Also, when there is a non-linear failure in a subprocess of the model, the correlation of the model output with the observations at some scales and locations may be better than at others (i.e. non-stationary). The effects of other types of model failure – i.e. an inadequacy in a model subprocess, a missing subprocess, or the use of input data that are themselves predictions from another model – were demonstrated with less success. Non-spatial statistics were generally inadequate for validating the performance of a spatially distributed model because they could not represent variation as a function of spatial scale and/or location. In summary, the different causes of model failure affect the spatial relations between model output and the target observed variable; however, while there is generally a predictable effect of model failure on the spatial variation of the model errors, it does not seem possible to deduce the source of the former from spatial analysis of the latter.