KEYWORDS : Indoor radon mapping, radon risk map, nugget effect, radon potential

Transcription

1 The radon noise and its geostatistical implications: risk mapping or mapping at risk? G. Dubois and P. Bossew European Commission DG Joint Research Centre, Institute for Environment and Sustainability, Ispra, Italy Corresponding author: ABSTRACT: Maps of indoor radon levels are frequently generated by averaging measurements on an administrative basis and subsequently classifying radon levels according to various regulatory thresholds. Such classification of risk areas certainly facilitates decision-making as local average values are usually not put into question as long as the number of measurements made is considered sufficient. One would still be tempted to further apply geostatistical techniques for producing maps showing local probabilities to exceed a given threshold as the information obtained should be more useful for a cost effective remediation strategy. An apparent obstacle to the use of geostatistics here is the very high level of fluctuations found between measurements made in neighbouring dwellings. It is the purpose of this paper to discuss the use of geostatistics for the mapping of indoor radon levels using a set of around 11 measurements made on the ground floors of Austrian dwellings. The further normalisation of the data using Friedmann s radon potential is further discussed. KEYWORDS : Indoor radon mapping, radon risk map, nugget effect, radon potential 1. Introduction In the last 2 years, around 2 million radon (Rn) measurements have been made all over Europe and the collected information was generally summarized by means of maps. A recent survey (Dubois, 25) has shown that no two European countries followed a common methodology allowing the comparison of these maps. Main fundamental differences reside in the diversity of the original objectives, the measurement techniques, the sampling strategies, the data handling and even in the nature and definitions of the original variable that was investigated. On the other hand, all maps had some common aspiration, which is to delineate and classify areas into hazardous and non-hazardous zones. Using geostatistics for probabilistic risk mapping of indoor radon levels is obviously very tempting as it potentially would provide much additional information on local uncertainties and on the spatial variability of the monitored variable. Still, the few case studies published so far have usually shown that measurements are poorly correlated in space, a serious drawback obviously for any statistical mapping method relying on a model of the spatial covariance. 2. Contribution of geostatistics to radon mapping Geostatistics is based on regionalized variables that describe natural phenomena as a combination of a smooth global structure with random local variations (see e.g. Chiles and Delfiner, 1999). It is thus very naturally that this collection of methods and tools was applied to analyse the spatial structure of soil-gas radon concentrations (see e.g. Badr et al., 1993, 1996). Indoor radon concentration levels have been investigated only later on and recent studies have explored possibilities to combine some geological information with the measurements made indoor (see Zhu et al, 21; Miles and Appleton, 25) as this would help to extract from the data the global trend due to the geological bedrock. The geological Liège September, 3 rd - 8 th 26 S2-2

2 origin of the radon gas found indoor does, however, not explain in most cases the spatial variability between measurements made in two neighbouring rooms that can be of a factor 1. Overall, the difficulty in modelling the spatial distribution of indoor radon levels explains why most countries rely on very large surveys involving techniques like track-etch detectors left in the dwellings for several months. For what concerns the literature on geostatistics applied to indoor radon measurements, it is worthwhile to recall the reader that the treatment of large amounts of measurements using geostatistical software became possible only in the mid 9 s, when new computers and algorithms were developed allowing the calculation of the spatial covariance of datasets larger than a few hundreds of measurements. It takes today a few minutes to process thousands of measurements and one may thus expect to see more an more researchers in the near future to give a try to their large sets of radon data. Yet, many will encounter the same difficulties that have been encountered by authors like Zhu et al., 1996, 21; Chaouch et al., 23; Verdi and Pegoretti 26; Bertolo et al 26: the data are heavily skewed and considered approximately log-normally distributed (log-normal kriging is a possible solution but the back-transform is complex issue), the spatial correlation can be difficult to identify, and the sample support can vary in many ways, both in time and space. 3. Normalization of the data using the radon potential Senso stricto, the raw indoor Rn concentration level C(x) determined at a location x can not be considered as a regionalized variable as x usually points to the building in which measurements have been made in different rooms. Because these neighbouring rooms will often show very different Rn concentrations, Friedmann (21, 25) proposed the construction of a new variable, called radon potential (RP), that is corresponding to an expected radon level in a standard situation. The RP characterizes thus the radon risk after having eliminated the different living habits and situations. Using RP, C n (x) can be considered as different realisations of the same random process and the variability between the n realisations would so define most of the nugget effect. From the many non-geological factors that affect indoor radon concentration levels, Friedmann identified a set of independent (to a high degree) factors explaining most of the variability of C(x). Among these factors are the floor of the building in which the room is located where C has been measured, the basement type, the season of the measurement, etc. 4. Case study: Indoor radon measurements in Austria Looking at a the set of 11 3 measurements (Figure 1) made on the ground floors in Austria (Friedmann et al., 21), one will find many similarities with the observations made by Chaouch et al. (23) who analysed data from the Valais region in Switzerland. First, the statistical distributions of the raw data are almost identical between both neighbouring countries; the mean and median values are 15 and 13 Bq/m 3, and 59 and 61 Bq/m 3, for Switzerland and Austria, respectively. For what concerns the standardisation of the raw data using some RP, we adopted here the version of Bossew and Lettner (22) which is slightly different from the one proposed by Friedmann. Figure 2 summarizes the relationship between the raw measurements and the transformed values into the RP. Liège September, 3 rd - 8 th 26 S2-2

3 Society for Mathematical Geology XIth International Congress 55 Rn concentrations (Bq/m3) to 1 1 to 2 2 to 3 3 to 4 4 to Fig. 1. Classed post map of indoor radon measurements made in the ground floors of Austria. Data Statistics (N = 11 3) 3 Rn potential, ground floor (Bq/m ) 1 8 Min January April+October July Rn concentration, ground floor (Bq/m ) 1 Mean Std. Dev. Max Rn Rn Pot In summer the Rn concentrations are lower in tendency than in winter, because ventilation rates tend to be higher (open windows etc.). This seasonal effect is removed when using the RP. Fig. 2. Plot and statistics of Austrian indoor Rn measurements on the ground floors against their counterpart of Rn potential (RP.). From the analysis of the spatial correlation of the measurements and of the RP (Figure 3), one can observe that both variables behave almost identically although the RP should reflect, in the ideal case, the geological variability only. Spatial autocorrelation is clear but up to 25 km only and the nugget effect is high (7-8%). The nugget effects as well as the total variance (dashed lines in Fig. 3) are a bit lower for the RP. The difficulty in further reducing the short scale variability by means of the RP comes from the intrinsic uncertainties of the correction factors used for the standardisation that, partially, re-enter into the nugget effect. Using some regularization effect to reduce the impact of the many outliers, one will find in the spatial structures shown by the rodograms and the variograms of the nscore transform much smoother structures (Figure 3, middle and bottom). While the impact of the RP correction was almost non- apparent so far, the nscore transform does reveal notable changes: a linear component appears clearly within the spatial structure of the nscore transform of the raw data, showing some underlying trend, while the transform applied to RP shows a clear stationarity. Liège September, 3rd - 8th 26 S2-2

4 5 Society for Mathematical Geology Variogram : Rn Variogram : Rn Variogram : Rn pot Variogram : Rn pot Rodogram : Rn Rodogram : Rn Rodogram : Rn pot Rodogram : Rn pot Variogram : nscore Rn Variogram : nscore Rn Variogram : nscore Rn pot Variogram : nscore Rn pot Fig. 3. Spatial correlation of Austrian indoor radon concentration levels (left) and of the radon potential RP (right). Top= experimental variograms. Middle = Rodograms. Bottom = variograms (experimental = red, model = black) of the nscore transformed data. Lag distance = 3 km. Liège September, 3 rd - 8 th 26 S2-2

5 5. Discussion: Risk mapping and mapping at risk If there is no doubt about the existence of a spatial structure between indoor measurements which authorizes some interpolation process, the short scale variability of the measurements is very high. Such noise of what ever source (micro-scale variability, measurement uncertainty, uncertainties in the definition of the RP) is not without consequences on the estimation process and on the uncertainties of the resulting maps: the higher the nugget effect, the similar become the sample weights and the estimation process tends towards a simple averaging of the measurements. Visually, kriged maps will appear too smooth and simulation results too erratic to be of any use to the decision makers. Figure 4 shows local probabilities to exceed 2 Bq/m 3 calculated by means of conditional simulations applied to the nscore transformed data. As one could expect from the similar variograms found for both variables (Rn and RP), the radon risk maps appear very similar with some differences regarding the distribution of the higher probabilities: RP shows higher probabilities to exceed 2 Bq/m 3 in the South when compared to the raw Rn measurements Rn Rn pot Prob > 2 Bq/m N/A Fig. 4. Probabilities to exceed 2 Bq/m 3 for Rn (above) and Rn potential RP (below) calculated using the models shown in Figure 3 and conditional simulations (1 simulations each with 1 turning bands). Map resolution = 2 km.. N/A Prob. > 2 Bq/m Liège September, 3 rd - 8 th 26 S2-2

6 If geostatistics offer without any doubts many useful tools and methods for investigating indoor radon measurements, the mathematical elegance of the approach will not suffice to render the information useful for the decision-makers. In particular, the very high nugget effect will remain a serious obstacle to the production of maps with uncertainties that can be efficiently used for remediation and risk assessment. Hence, when disregarding the benefit of better understanding the spatial behaviour of our variable, one may wonder at this stage if these methods can ever compete with simple local averaging for mapping purposes. The use of a standardised variable like Friedmann s radon potential may, in theory, contribute to reduce the nugget effect and help regularizing the variograms but this case study has shown that the impact of this standardisation on the spatial structure as measured by the experimental variograms was very small. In addition to a more detailed investigation of the various components contributing to the nugget effect, future research will involve some factorial kriging approach to further explore the contribution of each variogram model as Friedmann s radon potential seems to have extracted some hidden trend within the data. Further research will also target the key issue of the sampling support of the radon measurements which can affect estimates considerably by averaging away local hot spots. REFERENCES Badr, I., M.A. Oliver and S.A. Durrani (1996). Statistical evidence of the geological control over radon soil gas concentrations and its implications for mapping radon potential. Radiation Protection Dosimetry (63): Badr, I., M.A. Oliver, G.L. Hendry and S.A. Durrani (1993). Determining the spatial scale of variation in soil radon values using a nested survey and analysis. Radiation Protection Dosimetry (49), Bertolo A., Bigliotto C., Giovani C., Garavaglia M., Verdi L. and Pegoretti S. (26) Distribuzione territoriale del radon indoor nel Triveneto: un approccio di tipo geostatistico. In Proceedings of the "Terzo Convegnio Nazionale. Controllo ambientale degli agenti fisici: dal monitoraggio alle azioni di risanamento e bonifica", 7-9 June 26, Biella, Italy. (ed. by ARPA Piemonte), ISBN-1: Bossew, P. and H. Lettner (22): Statistische Analyse von Radondaten. Endbericht zum Projekt: Statistische Detailanalyse von ÖNRAP-Daten (Final Report to the Austrian Ministry of Social Affairs and Generations). February 22 (in German) Chaouch, A., M. Kanevski, M. Maignan, J. Rodriguez and G. Piller (23). Indoor radon data mining with geostatistical tools: case study with a highly clustered and variable dataset. In: Proceedings of the Annual Meeting of the International Association for Mathematical Geology, Portsmouth, UK September Dubois, G. (25). An overview of radon surveys in Europe. EUR EN, EC. 168 pp. Friedmann, H. (25) Final results of the Austrian Radon Project. Health Physics (89): Friedmann, H., Atzmüller, C., Breitenhuber, L., Brunner, P., Fink, K., Fritsche, K., Hofmann, W., Kaineder, H., Karacson, P., Karg, V., et al. (21): The Austrian radon project. Science of the Total Environment (272): Chiles, J-P and P. Delfiner (1999). Geostatistics: Modeling Spatial Uncertainty. John Wiley & Sons Miles, J. C. H. and J. D. Appleton (25). Mapping variation in radon potential both between and within geological units. Radiological Protection (25): Verdi L. and Pegoretti, S. (26). Mappatura del Radon in Alto Adige: un analisi di tipo geostatistico. In Proceedings of the "Terzo Convegnio Nazionale. Controllo ambientale degli agenti fisici: dal monitoraggio alle azioni di risanamento e bonifica", 7-9 June 26, Biella, Italy. (ed. by ARPA Piemonte), ISBN-1: Zhu H.-C., Charlet J.M., Tondeur F.. Mapping indoor radon using geostatistical approach. In: Barnet I, Neznal M, editors. Proc. Radon Investigations in the Czech Republic VI and 3rd Int. Workshop on Geological Aspects of Radon Risk Mapping. Czech Geological Survey & Radon corp., 1996b:51_61. Zhu, H. -C., J. M. Charlet and A. Poffijn (21). Radon risk mapping in southern Belgium: an application of geostatistical and GIS techniques. The Science of The Total Environment (272): Liège September, 3 rd - 8 th 26 S2-2