Model uncertainty analysis by variance decomposition

Errors and uncertainties in hydrological, hydraulic and environmental models are often substantial. In good modelling practice, they are quantified in order to supply decision-makers with important additional information on model limitations and sources of uncertainty. Several uncertainty analysis methods exist, often with various underlying assumptions. One of these methods is based on variance decomposition. The method allows splitting the variance of the total error in the model results (as estimated after comparing model results with observations) in its major contributing uncertainty sources. This paper discusses an advanced version of that method where error distributions for rainfall, other inputs and parameters are propagated in the model and the “rest” uncertainties considered as model structural errors for different parts of the model. By expert knowledge, the iid assumption that is often made in model error analysis is addressed upfront. The method also addresses the problems of heteroscedasticity and serial dependence of the errors involved. The method has been applied by the author to modelling applications of sewer water quantity and quality, river water quality and river flooding.

► Model uncertainty sources are compared by splitting the variance of the total error in the model results in its major contributing uncertainty sources.
► Model structural errors are estimated as “rest uncertainties” after subtracting contributions of input and parameter uncertainties from total model errors.
► Correlations and non-linear interactions between different model inputs and parameters are addressed, as well as heteroscedasticity and serial dependence of the errors involved.
► Results of three applications are shown: sewer water quantity and quality, river water quality and river flood modeling.