On the concept of model structural error

Abstract

A consideration of model structural error leads to some particularly interesting tensions in the model calibration/conditioning process. In applying models we can usually only assess the total error on some output variable for which we have observations. This total error may arise due to input and boundary condition errors, model structural errors and error on the output observation itself (not only measurement error but also as a result of differences in meaning between what is modelled and what is measured). Statistical approaches to model uncertainty generally assume that the errors can be treated as an additive term on the (possibly transformed) model output. This allows for compensation of all the sources of error, as if the model predictions are correct and the total error can be treated as “measurement error.” Model structural error is not easily evaluated within this framework. An alternative approach to put more emphasis on model evaluation and rejection is suggested. It is recognised that model success or failure within this framework will depend heavily on an assessment of both input data errors (the “perfect” model will not produce acceptable results if driven with poor input data) and effective observation error (including a consideration of the meaning of observed variables relative to those predicted by a model).