It is proposed that a numerical environmental model cannot be justified for predictive tasks without an implicit uncertainty analysis which uses reliable and transparent methods. Various methods of uncertainty-based model calibration are reviewed and demonstrated. Monte Carlo simulation of data, Generalised Likelihood Uncertainty Estimation (GLUE), the Metropolis algorithm and a set-based approach are compared using the Streeter–Phelps model of dissolved oxygen in a stream. Using idealised data, the first three of these calibration methods are shown to converge the parameter distributions to the same end result. However, in practice, when the properties of the data and model structural errors are less well defined, GLUE and the set-based approach are proposed as more versatile for the robust estimation of parametric uncertainty. Methods of propagation of parametric uncertainty are also reviewed. Rosenblueth's two-point method, first-order variance propagation, Monte Carlo sampling and set theory are applied to the Streeter–Phelps example. The methods are then shown to be equally successful in application to the example, and their relative merits for more complex modelling problems are discussed.
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