Setting cleanup targets in a probabilistic assessment

Risks from environmental contaminants in water are estimated with a risk equation involving contaminant concentration and other factors. Because the intent of environmental remediation is to ensure that these risks are not intolerably large, some way is needed to backcalculate from tolerance limits on risk mandated by regulators to the allowable environmental concentration for the contaminant. It is now well known that the approach used in deterministic assessments of simply inverting the risk equation to compute the cleanup goal does not work in a probabilistic assessment. We introduce simple and efficient methods for computing cleanup goals satisfying multiple simultaneous criteria in the context of a probabilistic assessment. This approach uses probability bounds analysis to characterize the concentration distributions and can be used with multiple receptors with arbitrarily many constraints on percentiles of the target risk distribution. The calculations yield two kinds of bounds on concentration: a 'kernel' and 'shell'. If the concentration distribution is entirely inside the kernel, then the result surely obeys the prescribed constraints. If the concentration distribution is anywhere outside the shell, then the result certainly fails to comply with the prescribed constraints. If the concentration distribution is outside the kernel but inside the shell, then compliance must be determined by a forward calculation.