RADON RISK MAPPING IN IRELAND

Transcription

1 Radon in the Living Environment, 137 RADON RISK MAPPING IN IRELAND S.G. Fennell 1, Y. Pawitan 2, G.M. Mackin 1, J.S. Madden 1 and A.T. McGarry 1 1 Radiological Protection Institute of Ireland, 3 Clonskeagh Sq., Dublin 14, Ireland 2 Department of Statistics, University College Dublin, Dublin 4, Ireland The work described in this paper is based upon the results of the recently completed National Survey of Radon in Dwellings [1] carried out by the Radiological Protection Institute of Ireland (RPII). Measurements were carried out in 11,054 dwellings, located in km grid squares across the country. The main objective of the survey was to identify High Radon Areas throughout the country; a High Radon Area is a grid square in which 10% or more of the houses are predicted to have radon concentrations in excess of 200 Bq/m 3, the national Reference Level. It is generally accepted that the distribution of indoor radon levels in houses follows a log-normal distribution. Based upon this assumption the percentage of houses exceeding the Reference Level in a grid square, was predicted using the Geometric Mean (GM) and Geometric Standard Deviation (GSD) for the data obtained. An improvement to this prediction can be made by examining the distribution of the radon concentrations measured and applying a corrected log transform to achieve normality. For grid squares in which fewer than five measurements were obtained, a smoothing algorithm based upon data in neighbouring squares was used to obtain values for the GM and GSD and a prediction made using these interpolated results. Keywords: Radon, linear model, smoothing INTRODUCTION Radon risk maps have been produced in many countries and serve to identify the areas most at risk from indoor radon levels. These maps are based on the results of indoor radon measurements carried out in houses selected at random. Ideally the designation of radon areas should be based upon the actual number of houses with indoor levels exceeding a reference level. However, it is often the case that only a small number of measurements are available making it difficult to map the fraction of the housing stock which exceeds the reference level with any degree of confidence. However, through the use of data modelling this fraction can be predicted accurately. METHODS It has been shown that the distribution of radon levels in dwellings approximates a log-normal distribution [2] and that such a log-normal approximation appears to hold whether a whole country, or a smaller area unit, is considered [3]. Modelling the distribution of indoor radon concentrations therefore allows the percentage of dwellings exceeding a reference concentration to be estimated [4]. To produce a radon risk map, the standard methodology is to estimate the proportion of houses exceeding the reference level for a small area unit. The geometric mean (GM) and geometric standard deviation (GSD) are computed for each area unit and these values are used to estimate the proportion of houses exceeding a radon concentration (X Bq/m 3 ) using the formula 1125

2 137 Radon in the Living Environment, ( X ) ln( GM ) ln( GSD) ln kˆ =. kˆ is a transformed threshold for use with the standard normal distribution, and can be calculated for any area unit once the GM and GSD for the data within the area have been obtained. Once the kˆ value is known, the proportion of houses in excess of the concentration X Bq/m 3 can be read from statistical tables of the area under the standardised curve. In this survey the area unit chosen was the 10 km grid square of the National Grid. The statistical procedure is described by Daly [5] and is based on the approach of Liberman and Resnikoff [6]. The main difficulty with this method is that for squares with less than 5 data points it is not possible to accurately determine the GM or GSD for the data. In order to obtain representative values for the GM and GSD, a smoothing procedure using the available data within the square and data in surrounding squares was carried out on the data set. As part of the smoothing procedure a weighting matrix was generated which was applied to the radon measurements in the surrounding grid squares. A unique weighting matrix was generated for each grid square and took into account the amount of data in the surrounding squares and the variance in that data. For grid squares along the sea coast the weighting matrix was adjusted to take account of no data being available for neighbouring squares which cover the sea. A full description of this model is given by Pawitan and Fennell [7] and Breslow and Clayton [8]. RESULTS Upon completion of the National Survey of Radon in Dwellings, valid results for 11,054 houses in km grid squares were obtained. The number of valid measurements ranged from 1 to 67 houses per grid square. For grid squares in which there were data for less than five houses, the percentage of houses exceeding 200 Bq/m 3, the Reference Level, was not calculated as insufficient data were available to accurately calculate the GM and GSD. Figure 1 shows the Radon in Irish Dwellings map for the predictions based upon the actual radon measurements. The predictions are represented by 5 percentage bands i.e. <1%, 1-5%, 5-10%, 10-20% and >20%. The two percentage bands 10-20% and >20% delimit the High Radon Areas. For a number of the grid squares as many as 49% of dwellings are predicted to have radon levels greater than 200 Bq/m 3. To test the data set for log-normality 20 grid squares were selected with between 32 and 67 houses measured per square. Figure 2a and b show the normal quantile plots for the measured and standardised radon concentration data respectively. If the overall distribution was log-normal then the plotted data would appear as a straight line. As can be seen from the plots there is a deviation from linearity in the data in the upper tail of the distribution, indicating a slight departure from log normality. Gunby et al. [9] describe the UK data set as being composed of a base radon level due to the outdoor air radon concentration and an additional log-normal distribution of radon in domestic dwellings. The Irish data set was examined for evidence of a similar contribution from outdoor air. Following subtraction of different constants from the data set, the resulting distributions were examined to see if 1126

3 Radon in the Living Environment, 137 the log-normality of the distribution was improved. From Figure 2c it can be seen that by subtracting a value of 6 Bq/m 3 from the data the resulting distribution has excellent correlation with log-normality. Although the value of the mean radon concentration in outdoor air in Ireland is not known, a value of 6 Bq/m 3 appears to be consistent with measurements obtained throughout Europe. Once this corrected log transformation has been carried out on the data, a prediction can be made as to the percentage of houses exceeding the reference level. It is important to note that the reference level, for which we are making the prediction, must also undergo the same log transformation. For squares in which there were fewer than 5 houses the GM and GSD were estimated from data in the surrounding squares. A smoothing algorithm, optimised on the Irish data set using the cp-criterion, was used. This algorithm is best illustrated by an example. Figure 3 represents a five by five section of the Irish National 10 km grid. The 26 counties in the Republic of Ireland are covered by 832 squares. The grey shaded square in Figure 3a represents a typical grid square for which we wish to estimate the GM and GSD. The number of houses in each of the 25 squares is shown in Figure 3b. A weighting matrix was generated (Figure 3c) which takes into account the number of houses in each square and the variability of the data. This was then applied to the data, which in this example is the log of geometric means (Figure 3d), and the resultant matrix summed to give the interpolated GM for the square in question. The GM and GSD were determined separately in this manner for all squares with fewer than 5 measurements and the results were used to calculate the percentage of houses exceeding the reference level in the manner described above. The revised prediction map, generated using the normal transformed data and the smoothing procedure, is illustrated in Figure 4. CONCLUSIONS The original prediction map for Ireland was based on the actual radon measurements on the assumption that the distribution of radon levels in homes is log-normal. Although the data approximates a lognormal distribution this can be further improved by carrying out a log transform on the data. It is possible that this transformation removes the contribution from radon in outdoor air, however without further measurements this assumption cannot be proved. For squares in which insufficient data is available the GM and GSD were estimated from the surrounding squares. Using this refined data set a new prediction map was produced. Although the radon designation (percentage band) has changed for a number of squares, in several of these squares this is due to the fact that the original prediction was at or close to the upper or lower boundary. REFERENCES [1] Fennell, S.G. et al., The National Radon Survey in Ireland. 136, Radon in the Living Environment, April 1999, Athens, Greece. [2] Commission of the European Communities, Exposure to natural radiation in dwellings of the European Communities. Luxembourg: Commission of the European Communities. [3] National Radiological Protection Board, Radon affected areas: Cornwall and Devon. Documents of the NRPB, 1,(4), p

4 137 Radon in the Living Environment, [4] Miles, J.C.H., Mapping the proportion of the housing stock exceeding a radon reference level. Radiation Protection Dosimetry, 56,(1/4), p [5] Daly, L., Personal communication. [6] Liberman, G.J. and Resnikoff, G.J., Sampling plans for inspection by variables. American Statistical Association Journal, June 1955, p [7] Pawitan, Y and Fennell, S Mapping of indoor radon concentrations. To be presented at the Applied Statistics in Ireland Conference, Belfast, May 1999 [8] Breslow, N.E. and Clayton, D.G Approxinmate Inference in Generalized Linear Mixed Models. American Statistics Association Journal, 1993, p9-25. [9] Gunby, J.A. et al Factors Affecting Indoor Radon Concentrations in the UK. Health Phys. 64, p

5 Radon in the Living Environment, 137 Normal :48 >20% 10-20% 5-10% 1-5% <1% Insufficient Data Figure 1: Radon in Irish Dwellings 1129

6 137 Radon in the Living Environment, (a) Raw residuals (b) Standardized residuals Sample Quantiles Sample Quantiles Theoretical Quantiles Theoretical Quantiles (c) Std-residuals, data-6 Sample Quantiles Theoretical Quantiles Figure

7 Radon in the Living Environment, (a) Grid (b) Number of Houses (c) Weighting Factors (d) ln(gm) Figure

8 137 Radon in the Living Environment, > 20% 10-20% 5-10% 1-5% < 1% Figure 4: Radon in Irish Dwellings 1132