The paper proposes a strategy for model uncertainty propagation analysis. As an example, parameter uncertainty propagation analysis in the runoff block of the HYSTEM-EXTRAN model is carried out. The model is a modification of the well-known SWMM (Storm Water Management Model). Uncertainty propagation methods such as first-order analysis, sensitivity analysis, statistical linearization and Monte-Carlo analysis are discussed and applied. A pathway of parameter uncertainty propagation analysis is given based on validity, simplicity, and computational requirements. The pathway starts with sensitivity analysis which may help to reduce the dimensions of a multidimensional model by discarding insensitive parameters. This is to obtain a mathematically tractable uncertainty propagation problem for a complicated model. Then, the nonlinearity of the model must be quantified to check the validity of first-order analysis. If first-order analysis is not valid, and if components of model output uncertainty need to be known, the application of statistical linearization is the only analytical alternative. Monte-carlo analysis can always be applied and taken as a reference as long as the components of the model output uncertainty are not of interest. The parameter sensitivity is characterized by its sensitivity coefficient which is defined as the ratio of the coefficient of variance of a model output to the coefficient of variance of the model parameter itself. A nonlinear rainfall runoff model usually results in a variable parameter sensitivity. Hence, recommendations about parameter sensitivity cannot be generalized for a given rainfall-runoff model, but depend on the type and the range of the model output variable. It is shown that the type of probability density function describing the parameter uncertainty with known mean and variance has only a small effect on the results of the model output uncertainty.

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