Uncertainty analysis in environmental modelling under a change of spatial scale

Although environmental processes at large scales are to a great degree the resultant of processes at smaller scales, models representing these processes can vary considerably from scale to scale. There are three main reasons for this. Firstly, different processes dominate at different scales, and so different processes are ignored in the simplification step of the model development. Secondly, input data are often absent or of a much lower quality at larger scales, which results in a tendency to use simpler, empirical models at the larger scale. Third, the support of the inputs and outputs of a model changes with change of scale, and this affects the relationships between them. Given these reasons for using different models at different scales, application of a model developed at a specific scale to a larger scale should be treated with care. Instead, models should be modified to suit the larger scale, and for this purpose uncertainty analyses can be extremely helpful. If upscaling disturbed the balance between the contributions of input and model error to the output error, then an uncertainty analysis will show this. Uncertainty analysis will also show how to restore the balance. In practice, application of uncertainty analysis is severely hampered by difficulties in the assessment of input and model error. Knowledge of the short distance spatial variability is of paramount importance to input error assessment with a change of support, but current geographical databases rarely convey this type of information. Model error can only be estimated reliably by validation, but this is not easy because the support of model predictions and validation measurements is usually not the same.