Uncertainty in exposure estimates made by modeling versus monitoring

To conduct an initial exposure assessment for an airborne toxicant, industrial hygienists usually prefer air monitoring to mathematical modeling, even if only one exposure value is to be measured. This article argues that mathematical modeling may provide a more accurate (less uncertain) exposure estimate than monitoring if only a few air samples are to be collected, if anticipated exposure variability is high, and if information on exposure determinants is not too uncertain. To explore this idea, a hypothetical "true" distribution of 8-hour time-weighted average airborne exposure values, C, is posited based on an NF exposure model. The C distribution is approximately lognormal. Estimation of the mean value, microC (the long-term average exposure level), is considered. Based on simple random sampling of workdays and use of the sample mean C to estimate microC, accuracy (uncertainty) in the estimate is measured by the mean square error, MSE(C). In the alternative, a modeling estimate can be made using estimates of the mean chemical emission rate microG, the mean room dilution supply air rate microQ, and the mean dilution ventilation rate in the NF of the source mu beta. By positing uniform distributions for the estimates microG, microQ, and mu beta, an equation for the modeling mean square error MSE(microC) is presented. It is shown that for a sample size of three or fewer workdays, mathematical modeling rather than air monitoring should provide a more accurate estimate of microC if the anticipated geometric standard deviation for the C distribution exceeds 2.3.