Second-order Monte Carlo uncertainty/variability analysis using correlated model parameters: application to salmonid embryo survival risk assessment

This paper presents a Monte Carlo uncertainty/variability analysis applied to assessment of salmonid embryo survival affected by the deposition of fine sand in the spawning gravel riverbed. For the system being modeled, the uncertainty originates from the lack of perfect knowledge about the spawning habitat, while the variability arises from the natural diversity in the amount of sand deposit. A second-order Monte Carlo simulation (MCS) procedure consisting of multiple realizations of model parameters and full-range iterations of input variable is used to separately propagate the knowledge uncertainty and natural variability of the system. Given that the three parameters of the present model are highly correlated (correlation coefficients >0.8), we use four multivariate methods (Iman–Conover method, standard normal transformation method, normal copula method, and maximum-entropy copula method) to generate correlated model parameters. The scatter plots of the correlated parameters generated with various methods demonstrate different correlation patterns. An important finding of the present uncertainty/variability analyses and risk assessments is that the outcomes resulting from the four correlated scenarios are very similar, regardless of the diverse correlation patterns. The output of the second-order MCS is a collection of cause–effect relations (spaghetti plot) that can facilitate the analyses of survival-rate uncertainty/variability. The favorable habitat conditions are also defined on the basis of the spaghetti plot. It is revealed that significant values of information are associated with the parameter correlations, especially when higher levels of embryo survival are targeted. The results further indicate that the outcomes of the independent (less realistic) scenario substantially differ from those of the correlated ones, indicating that the effect of parameter correlations should be incorporated into the MCS whenever possible. This work provides a useful paradigm for the systematic uncertainty/variability analyses in the context of ecological risk assessments.