CALCULATING SITE-SPECIFIC SELENIUM WATER QUALITY STANDARDS FOR PROTECTING FISH AND BIRDS

We have developed a method for determining site-specific water quality standards for substances regulated based on tissue residues.  The method uses a multi-site regression model to solve for the conditional prior probability density function (PDF) on water concentration, given that tissue concentration equals a tissue residue threshold.  It then uses site-specific water and tissue concentration data to update the probabilities on a Monte Carlo sample of the prior PDF using Bayesian Monte Carlo analysis.  The resultant posterior PDF identifies the water concentration that, if met at the site, would provide a desired level of confidence of meeting the tissue residue threshold contingent on model assumptions.  This allows for derivation of a site-specific water quality standard.  The method is fully reproducible, statistically rigorous and easily implemented.  A useful property of the method is that the model is sensitive to the amount of site-specific data available, i.e., a more conservative or protective number (water concentration) is derived when the data set is small or the variance is large.  Likewise, as the site water concentration increases above the water quality standard, more site-specific information is needed to demonstrate a safe concentration at the site. 

The methodology is applied to selenium as an example.  Models were developed to describe selenium bioaccumulation in aquatic-dependent bird eggs and whole fish.  A simple log-linear model best described selenium accumulation in bird eggs (r² = 0.50).  For fish, separate hockey stick regressions were developed for lentic (r² = 0.65) and lotic environments (r² = 0.37).  The low r² value for the lotic fish model precludes its reliable use at this time.  Corresponding tissue residue criteria (i.e., tissue thresholds) for bird eggs and whole fish were also identified and example model predictions made.  The models were able to predict SSWQS over a wide range of water:tissue combinations that might be encountered in the environment.  The models were also shown to be sensitive to variability in measured tissue residues with relatively small changes in variability (as characterized by the standard error) resulting in relatively large differences in SSWQS.