Improved First‐Order Uncertainty Method for Water‐Quality Modeling

Uncertainties are unavoidable in water‐quality modeling and subsequent management decisions. Monte Carlo simulation and first‐order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water‐quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first‐order analysis' are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first‐order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first‐order method is tested on the Streeter‐Phelps equation to estimate the probability distribution of critical dissolved‐oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first‐order method provides a close approximation of the exceedance probability for the Streeter‐Phelps model output estimated by Monte Carlo simulation using less computer time—by two orders of magnitude—regardless of the probability distributions assumed for the uncertain model parameters.