A Mathematical Approach for Predicting Long-term Indoor Radon Concentrations from Short-term Measurements

Assessment of long-term indoor radon concentrations from short-term testing results are of significant importance when radon risk assessment and liability issues are considered. These issues are based on the figure of annual exposure to indoor radon while radon measurement practices are mainly followed the EPA short-term testing protocols. A mathematical framework has been developed that facilitates non-statistical approach to construct the relationship between the short-term indoor radon measurements and the long-term annual indoor radon levels. This approach was based on the application of the timedependent indoor radon concentrations calculated from the corresponding contributions of indoor radon driving forces for different time periods having a reference starting time. The approach utilizes an analytical procedure that is based on the solutions of the mass balance equation for the radon gas in the indoor environment. The solutions are applied through semi-analytical modeling of timedependent indoor radon concentrations. This treatment provides a powerful tool and procedure to assess long-term indoor radon concentrations from short-term testing results. INTRODUCTION Prediction of long-term indoor radon concentrations has been a major source of disagreement when some issues of the indoor radon problem are considered. The conflict arises from what is considered practical for testing and the health hazards and liability issues. On one hand, obtaining a long-term measurement of the average indoor radon concentration in a structure by continuous testing for possibly several years (a minimum of one year) is not practical (although it is possible). On the other hand, health and some legal-related actions are based on the annual exposure to indoor radon concentration. Many of the radon testing utilized commercially are performed over a very short period of time, typically 48 hours, following the US Environmental Protection Agency short-term testing protocols. Although such testing may be sufficient for determining the need for mitigation action for some cases, using these results to represent the annual indoor radon concentration in the structure can create major debate for marginal cases, estimation of health hazards, and liability related issues. The problem is particularly complex given the known fluctuations of indoor radon concentrations. Several studies have addressed the issue of predicting annual indoor radon concentration from short-term testing results. Such studies utilized two basic methodologies in approaching the problem. The first methodology uses specific research structures and develops correlations between indoor radon concentrations and other environmental parameters that are simultaneously monitored for a long period of time (a minimum of one year). Then researchers experimentally fit the data and obtain the best representation of indoor radon concentration based on the particular set of data (Hull and Reddy 1990; Reddy et. al. 1990). The second methodology analyzes large data bases (survey data) related to indoor radon measurement, although they are not particularly designed for this purpose, and tries to obtain general correlations relating indoor radon concentrations to the available parameters in the survey data set (White et. al 1994, White et. al. 1992; Cohen 1990, Roessler et. al. 1990, Steck 1990; ). The second approach covers a large number of houses, but there is 1995 International Radon Symposium IVP 3.1 uncertainty in the results and a lack of experimental control parameters. However, this type of study may provide an indication of the relationship between parameters based on statistical evaluation. The first approach has the advantages of design and control of the experiments and better measurement uncertainty, however, it is restricted to the experimental fit of data of the particular structure. Neither of these approaches provides a means to explicitly predict the average annual indoor radon concentration from the short term-testing results, but rather each provides indications of the trends of annual indoor radon concentrations when other parameters are considered. An approach that provides an explicit relationship between the short-term testing and the actual annual indoor radon concentration has not been developed. In this section, an analytical method will be utilized to relate the annual indoor radon concentration to the short-term testing results. A mathematical framework is developed, based on the mass balance equation of radon in the indoor environment which facilitates semi-analytical predictions of annual indoor radon levels. This treatment can serve as a tool to establish the general relationship, based on the actual physical processes of entry and removal, between the time-averaged annual level of indoor radon concentration and the short-term testing of the indoor radon concentration.