ABSTRACT
The assessment of uncertainty in a model output requires the propagation of different sources of uncertainty through the model . The probability theory-based uncertainty assessment methods involve either the propagation of probability distributions or the moments of distributions (means and variances). Various methods exist both for the propagation of distributions and propagation of moments of distributions. These methods of uncertainty propagation can be broadly classified into three categories:
2. Sampling methods
Although various analytical solutions exist (e.g central limit theorem and transformation of variables) for the propagation of uncertainty through a model, they are limited to very simple problems and will not be detailed here. For problems with nonlinear functions of multiple variables, such solutions become complicated and are impracticable to use. Therefore, sampling methods, such as Monte Carlo (MC) and Latin hypercube simulations, or approximation methods, such as the First-Order Second Moment (FOSM) and Rosenblueth' s point estimation (Rosenblueth, 1 975) are preferred for practical applications. The sampling methods provide the estimation of the probability distribution of an output (propagation of distribution), while the approximate (or point estimate) methods provide only the moments of the distribution (propagation of moments) . Comparative applications of different sampling methods and approximate or point estimate methods to a distributed rainfall-runoff model are reported by Yu et al. (200 I ) . The MC simulation and FOSM are the broadly used methods for uncertainty assessment (Guinot, 1 998) in a number of fields of engineering, including water resources. The present study also uses these two methods for the probabilistic assessment of uncertainty. Subsection 3 . 1 . 1 presents the principle of the Monte Carlo simulation and Subsection 3 . 1 .2 outlines the principle of the FOSM method.
