C = concentration of radon in water, pCi/L.
F = fraction of radon remaining in water at time of ingestion.
V = volume of water ingested, L/d.
RF = ingestion risk factor for radon gas (cancer-death risk per person per picocurie ingested).
Table F.1 summarizes the probability distributions used to represent value ranges for the parameters of this model. Each parameter has a variability distribution that is defined by two parameters, such as the mean and standard deviation. The two parameters are drawn from two distributions that represent their uncertainty. The concentration of radon in water, C, was derived by EPA from the National Inorganics and Radionuclides survey (Longtin 1990). A population-weighted population density function (PDF) was developed that was fitted to a lognormal distribution having a geometric mean of 200 pCi/L and a GSD of 1.85. The uncertainty in this distribution was obtained by using the Student t-distribution and the inverse chi-squared distribution to simulate the resampling of mean values and standard deviations. A sample size of 10 was used to resample from the Student t and inverse chi-squared distributions. Even though some 1,000 water systems are represented in the survey set, the assumed small sample size was selected to reflect the fact that the population-weighted concentration distribution was dominated by a small number of large water supplies for which there were a limited number of measurements. The variability of F, the fraction of radon remaining in water, was modeled as a beta distribution in the interval 0.1–0.3 with an uncertain mean and mode. The uncertainty of the mean was modeled as a uniform distribution in the range 0.7-0.9, and the uncertainty in the mode was modeled as a uniform distribution between 0.5 and the sampled mean value.
In the EPA uncertainty analysis, the basic equation used to calculate inhalation uptake of radon gas is based on both the uncertainty and the variability of the unit dose factor, but the risk factor per unit dose is based on a single value. The unit dose factor for gas released from water includes three factors:
UD = unit dose (pCi inhaled per year per pCi/L of radon in water).
TF = transfer factor, which is the increase in radon concentration in indoor air per unit radon concentration in water (pCi/L[air] per pCi/L[water]).
BR = breathing rate (L/d).
OF = occupancy factor (fraction of time person spends indoors).