Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology

Abstract

It may be endemic to mechanistic modelling of complex environmental systems that there are many different model structures and many different parameter sets within a chosen model structure that may be behavioural or acceptable in reproducing the observed behaviour of that system. This has been called the equifinality concept. The generalised likelihood uncertainty estimation (GLUE) methodology for model identification allowing for equifinality is described. Prediction within this methodology is a process of ensemble forecasting using a sample of parameter sets from the behavioural model space, with each sample weighted according to its likelihood measure to estimate prediction quantiles. This allows that different models may contribute to the ensemble prediction interval at different time steps and that the distributional form of the predictions may change over time. Any effects of model nonlinearity, covariation of parameter values and errors in model structure, input data or observed variables, with which the simulations are compared, are handled implicitly within this procedure. GLUE involves a number of choices that must be made explicit and can be therefore subjected to scrutiny and discussion. These include ways of combining information from different types of model evaluation or from different periods in a data assimilation context. An example application to rainfall-runoff modelling is used to illustrate the methodology, including the updating of likelihood measures.