Errors and uncertainty in physically-based rainfall-runoff modelling of catchment change effects

The error in physically-based rainfall-runoff modelling is broken into components, and these components are assigned to three groups: (1) model structure error, associated with the model’s equations; (2) parameter error, associated with the parameter values used in the equations; and (3) run time error, associated with rainfall and other forcing data. The error components all contribute to “integrated” errors, such as the difference between simulated and observed runoff, but their individual contributions cannot usually be isolated because the modelling process is complex and there is a lack of knowledge about the catchment and its hydrological responses. A simple model of the Slapton Wood Catchment is developed within a theoretical framework in which the catchment and its responses are assumed to be known perfectly. This makes it possible to analyse the contributions of the error components when predicting the effects of a physical change in the catchment. The standard approach to predicting change effects involves: (1) running “unchanged” simulations using current parameter sets; (2) making adjustments to the sets to allow for physical change; and (3) running “changed” simulations. Calibration or uncertainty-handling methods such as GLUE are used to obtain the current sets based on forcing and runoff data for a calibration period, by minimising or creating statistical bounds for the “integrated” errors in simulations of runoff. It is shown that current parameter sets derived in this fashion are unreliable for predicting change effects, because of model structure error and its interaction with parameter error, so caution is needed if the standard approach is to be used when making management decisions about change in catchments.