COMPARISON OF INDOOR RADON MAPS OBTAINED WITH DIFFERENT SOFTWARES AND METHODS

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1 Radon in the Living Environment, 039 COMPARISON OF INDOOR RADON MAPS OBTAINED WITH DIFFERENT SOFTWARES AND METHODS François Tondeur (2), Antoine Kies (1), André Robinet (1), Huichao Zhu (3) (1) Centre Universitaire de Luxembourg (CUNLUX) avenue de la faïencerie 162a, L1511 Luxembourg; (2) Institut Supérieur Industriel de Bruxelles (ISIB) rue Royale 150, B0 Bruxelles, Belgium; (3) Faculté Polytechnique de Mons (FPMs) rue de Houdain 9, B7000 Mons, Belgium; Corresponding author: F. Tondeur, Tel: , Fax: , tondeur@isib.be The use of two mapping methods, kriging and moving average, in mapping the indoor radon risk, is investigated. Both methods are applied to three databases: simulated radon data, data collected in Southern Belgium with low sampling density, and data collected in Luxembourg. We use commercial software (SURFER R 6) for kriging, as well as softwares developed by the authors, especially for the radon case, for kriging and for moving average. Simulated data prove to be very useful in this context. We conclude that kriging as implemented in SURFER R 6 may not be well adapted to radon mapping. It seems easier to obtain reasonable maps with the moving average, though it may be difficult to find the good compromise between showing only significant features, and showing all of them. Key words: indoor radon, risk mapping, software, method INTRODUCTION Indoor radon concentrations may be considered as a stochastic function of spatial or spatio-temporal coordinates. This function is characterised by a combination of deterministic and stochastic factors, including an important local noise. Following Cressie (1993), we may write the concentration measured in a house of coordinates (x,y) as the decomposition: C(x,y) = µ(x,y) + ω(x,y) + η(x,y) + ε(x,y) where µ is the deterministic long-range mean structure, ω is a stochastic function reflecting smooth small-scale variations, η is a stochastic function reflecting microscale variations (i.e. variations whose range is smaller than the typical sampling interval) and ε a measurement noise. Usually, η and ε cannot be distinguished in practice and we shall consider η+ε globally as the noise, unless otherwise specified. Radon mapping always consists in trying to smooth out the noise, in order to extract some kind of average trend of risk. Whether the factors controlling the variations of this average trend are of deterministic or stochastic nature, or a mixture of both, is often not discussed. However, the statistical methods to use in the averaging procedure could be more adapted to one case than to the other. The first aim of the present contribution is to present and discuss the application of two mapping methods to different radon databases: kriging and weighted moving average (Cressie,1993). Kriging 373

2 039 Radon in the Living Environment, assumes that all variations, except the noise, are contained in the stochastic function ω; it gives the best prediction of µ + ω(x,y). The moving average instead is a way to evaluate the variable deterministic mean µ(x,y). The second aim of this paper is to test the possibility to use a commercial software (SURFER R 6, Keckler 1994) in radon mapping. Its results will be compared to those of homemade codes specially designed for the radon problem. Our goal at this stage is not to select a method that can be appropriate to obtain one specified kind of radon risk map. We rather want to make a first evaluation of the behaviour of the two considered methods when applied to the radon risk problems, in order to determine the options and factors that are most important in this context. THE DATABASES Maps are generated for different databases that include a spatial location of the data. We first consider simulated data with medium density (2 data per km 2 ) generated by assuming a specified mean value depending on the co-ordinates and a typical lognormal noise with a GSD of 2.5. Three patterns were generated on km x km squares: (a) a constant average of Bq/m 3, (b) an average with a constant slope from to 200 Bq/m 3 ; (c) a cross-shaped area with an average 200 Bq/m 3 within it and Bq/m 3 out of it. We are grateful to J. Miles (NRPB) who generated these data and kindly enabled us to use them in the present work. Using these data to test the mapping methods and softwares proved to be very enlightening. In the present paper, we only present results obtained for the cross pattern, from which the most important conclusions can be drawn. However the sole discussion on simulated data could be unrealistic if the conclusions were not confirmed when applying the same methods to real indoor data. Therefore we also consider here the indoor radon database of the Ministry of Health of Luxembourg, obtained with alpha-track measurements, which has a medium sampling density (1 to 2 data per km 2 ). This database presently only contains the geometrical mean of data grouped by village. This can be considered as a kind of preliminary smoothing. Luxembourg is quite simple from the geological point of view, being divided into two roughly equivalent areas: Oesling in the North and Gutland in the South. Oesling is a part of the Palaeozoic Ardenne-Eifel Massif, where Lower Devonian is dominant. Gutland is mostly constituted of Mesozoic formations. Radon levels are significantly higher in Oesling (Kies, 1996). For Southern Belgium (the Walloon region), the indoor radon database was collected by ISIB with charcoal canister detectors exposed for 3-4 days. This database was presented earlier (Tondeur and Gerardy, 1994) but has been extended by new measurements. However, it still has a quite low sampling density (0.1 data per km 2 ) except for a few small well-sampled areas. It also has a somewhat larger noise due to the short sampling time associated with charcoal detectors. Southern Belgium is also divided into two main parts. The NNW part is made of Mesozoic and Cenozoic grounds. The Palaeozoic dominates the SSE part. None of the two parts is homogenous, as a few localised Palaeozoic 374

3 Radon in the Living Environment, 039 outcrops are found in the NNW part, whereas Mesozoic formations, connected to Gutland, are found in the extreme South. MAPPING METHODS In most of this paper, we shall consider that radon concentrations are, at least approximately, lognormally distributed, and that it is more adequate to take the natural logarithm of C(x,y) as the data to be mapped. Kriging Kriging is a widely used geostatistical method that assumes the stationarity of the expectation value µ of the stochastic variable ln(c) (or at least its stationarity within the area implied by the kriging prediction for each coordinate) but takes into account the correlations between the data that are contained in the short-range ω(x,y). Any global trend in the data is assumed to be the effect of these correlations. The key of kriging is the variogram model. The variogram is defined as: 2 γ(h) = var(ln C(s+h) ln C(s)) where the vector s=(x,y). The variogram of radon data usually show different features: (a) a non-zero value at zero distance (nugget effect) due to the local stochastic noise ε+η (important in radon data); it can be formally separated into two contributions c ME from measurement errors and c MS from microscale variations related respectively to ε and η. (b) a rapid variation related to short-range correlations; (c) a constant trend (sill) at large distance, that indicates the absence of correlations at that distance. Kriging requires that some mathematical function is used to model the variogram. Without nugget effect, kriging acts as an interpolator that gives the best prediction of the stochastic variable, taking the correlations into account through the variogram model. Including a nugget effect transforms kriging into a smoothing interpolator. Moving average The moving average calculates the mean value of all data within a circle (or any other type of neighbourhood), and takes it as the predicted value at the centre. It implicitly assumes that no correlations are present, but accepts a linear trend within that area (a variant allowing for a quadratic trend is also examined here). This trend is understood as a deterministic variation of the mean. The data can be weighted according to their distance d to the centre. With an inverse-square weight (d - 2 ), the method acts as a pure interpolator. We rather use it here as a smoother, with a quadratic weight decreasing with increasing distance (a - b.d 2 ). 375

4 039 Radon in the Living Environment, The mapping softwares Three mapping softwares are used. The first one is a commercial software: SURFER R 6 [5]. It is a grid-base contour program giving the possibility to generate a grid from the data using several gridding methods. We use here the kriging method, that is proposed as the default method. Additional smoothing is possible after gridding. The factors to be specified in the kriging method are the variogram model and the nugget effect. Different variogram models were tested, finally the linear and Gaussian model are retained. Results presented here use the isotropic linear model γ(h)=g.h limited to h<14 km and G=2/14. A satisfactory treatment of radon data with SURFER proved to be impossible without using high values of the nugget parameters (c ME =1, c MS =0.1), that cause kriging to become a smoothing interpolator. But even the nugget smoothing proved to be insufficient for the high variability of radon data. We had to proceed through a further smoothing to eliminate remaining spikes and better approach the general trends. The smoothing consists in an average of 25 values on the kilometric grid, with double weight for the central value. The same kriging and smoothing parameters are used throughout the present work. A few results obtained with lognormal kriging for the Luxembourg database will be presented, using a software developed for radon mapping at FPMs, with a model fitted to the variogram deduced from the data (Zhu, 1996). Finally, we use a weighted moving geometrical mean software with weight decreasing with the distance w(d)=a-bd 2, developed for radon mapping at ISIB. This software also applies a preliminary weighting of the data that is inversely proportional to the local density of data, in order to avoid the excessive weight that could be attributed to well-sampled areas. The geometrical mean at each selected point is calculated within a circle of radius R containing a fixed number N of data, in order to get the same accuracy at each point. The distance-dependent weight is maximum at the centre and vanishes on the circumference of the circle: w(d)=1-(d/r) 2. This was found to be essential to improve the continuity of the calculated µ(x,y). In a variant of the moving average program, we tried to improve the results by performing a quadratic least-squares fit to the data within the circle, keeping the same weights, the fitted value at the center being retained as the predicted µ(x,y). Only minute variations were observed in the maps, and this option will not be applied in the following paragraphs. RESULTS AND DISCUSSION Cross Figure 1 shows results obtained for the cross-like pattern with the moving average method (with N=50 and with N=200), and with SURFER R 6 (kriging alone, and kriging followed by smoothing). Both the kriging map and the N=50 moving average map show strong remaining spurious fluctuations that are only due to the stochastic clustering of high or low values or to outliers, as by construction the 376

5 Radon in the Living Environment, 039 data do not include short-range variations within the two areas of the map. The moving average with N=50 however gives a slightly less fluctuating map than the kriging map. Increasing N to 200 allows to reproduce reasonably the constant mean expected in each of these two areas. The same result is obtained by adding the smoothing step after kriging. Both maps are now strikingly similar. In this context, the usefulness of kriging is not obvious. Clearly, the nugget smoothing alone is not able to smooth out the noise included in simulated data. On the other hand, it seems that the choice of the method is not really crucial, as two calculations based on quite different approaches finally lead to similar results. Southern Belgium (Walloon region) The maps obtained with the moving average method (N=50 and N=200) and with kriging (SURFER R ) for the Walloon region are given in figure 2. Again pure kriging (not shown) is insufficient for smoothing out the noise. After smoothing on 25 km 2, details that are probably not significant (not related to local geology or housing types) still appear. This is due, of course, to the low density of sampling in this database. As smoothing in SURFER R inactivates a band of territory along the border, further smoothing rapidly reduces the area in which predictions are made. Thus, no satisfactory map is obtained with SURFER R for this database. Better maps are obtained with the moving average method. The map obtained with N=50 seems more regular than with simulated data. However, some of the small structures it displays are probably not significant. Taking instead N=200 largely smoothes out many structures that are probably significant, because they are clearly related to geology (e.g. the hot spot in the middle of the NNW part). This drawback is again clearly due to the low sampling density of the database. It is not possible in this case to display all significant structures and simultaneously to avoid the nonsignificant ones. Luxembourg Here better-looking maps are much easier to obtain, because the sampling density is higher, and because of the preliminary smoothing of the data that are grouped by village. They are given in figure 3. The average number of data per village is 6.6. The moving average maps are now given for 8 and 32 villages respectively, which is roughly equivalent on the average to the 50 and 200 data used above (this explains the labels Lux50 and Lux200 used in the figures). Small but probably significant features are lost when going from 8 to 32 villages with the moving average method. Though the sampling density is here much better, the situation is thus similar to the one observed in the previous section: it is not obvious to find the compromise between only displaying significant structures present in the data and displaying all of them. Pure kriging map without nugget with SURFER R 6 is given in figure 3 for the purpose of comparison with a map (figure 5) obtained by lognormal kriging (Rendu,1979) and a fitted variogram model. The variogram is fitted, without nugget, to the experimental variogram (figure 4). For figures 4 and 5, Luxembourg has been divided into Oesling and Gutland, with two different variogram models. The experimental variograms are isotropic in each region. They are fitted by the model function: 377

6 039 Radon in the Living Environment, where γ(h) = c 1 γ 1 (h) + c 2 γ 2 (h) γ i (h) = 1.5 h/a i h 3 3 /a i, h<a i γ i (h) = 1, h>a i. For zone A (Oesling) c 1 = ,a 1 =5516,c 2 = ,a 2 =19456, and for zone B(Gutland) c 1 = ,a 1 =1624,c 2 = ,a 2 =31064, wit c i in units ln(bq.m-3) and a i in m. Without nugget, kriging is an exact interpolator. This would not be reasonable to use for radon mapping if the data were not grouped into villages. When using kriging in SURFER R with the same nugget as above, a map is obtained that is quite similar to the N=32 moving average map (Lux200). No additional smoothing is necessary, because of the preliminary smoothing made by grouping the data. CONCLUSIONS SURFER R 6 with kriging is not well-adapted to radon mapping. Reasonable results were only obtained with pure kriging for the Luxembourg database, with the data grouped into villages, and with a quite good sampling density. Additional smoothing after kriging strongly improves the results when the sampling density is good, as for simulated data, but it was not possible to obtain a reasonable map with SURFER R for the low-density ISIB database of Southern Belgium. In general, map it is easier and more transparent to obtain a satisfactory with the moving average method. However, when the sampling density is too low, it is hard to find the good compromise between displaying the significant features, and not displaying features that are not significant. Any structure in the data, like local hot spots (or cold spots, but they generally deserve less attention) should be, wherever possible, represented by enough data, the number of 200 data being suggested by this work. When both methods (kriging/smoothing and moving average) give acceptable results, the maps are very similar. Thus the choice of one method rather than the other does not seem to be the crucial point, despite their different statistical basic assumptions. Simulated data may be of great interest in testing mapping methods and softwares for the radon problem, and we strongly recommend their systematic use. Of course the results will be more interesting if all authors use the same set of simulated data. The cross data set provided by Jon Miles is quite well adapted. We believe that it would be even more interesting after including a few smaller local structures (hot and cold spots). REFERENCES [1] Cressie N.A.C., Statistics for spatial data, Wiley,

7 Radon in the Living Environment, 039 [2] Keckler D., SURFER R for Windows, User Guide, Golden Software, 1994 [3] Kies A., Biell A., Rowlinson L., Feider M., Radon survey in the Grand Duchy of Luxembourg- Indoor measurements related to house features, soil, geology and environment, Envir.Int. 1996; 22:S5-8 [4] Rendu J.M., Normal and lognormal estimation, J.INT.Assoc.Math.geol.,1979;11: [5] Tondeur F., Gerardy I., Geographic and Geologic Distribution of the Indoor Radon Risk in Southern Belgium, IRPA regional congress on radiological protection, W. Nimmo-Scott, D.J.Golding editors, Nuclear Technology Publishing, 1994, [6] Zhu H.C., Charlet J.M., Doremus P., Kriging radon concentrations og groundwaters in western Ardennes, Environmetrics, 1996;7:

8 039 Radon in the Living Environment, Cross 50 Cross Krigging + nugget Krigging + nugget + smoothing Figure1: Maps obtained for the simulated data with cross-like pattern. The four maps are obtained respectively with the moving average method with N=50 (cross50) and N=200 (cross200), with kriging in SURFER R 6, and with kriging + smoothing. The variable is the natural logarithm of the radon concentration measured in Bq/m 3. 3

9 Radon in the Living Environment, Wallonie 50 Wallonie Krigging + nugget + smoothing Krigging + nugget + heavy smoothing Figure 2: Maps obtained for the Walloon region, with the moving average method with N=50 and N=200, with kriging + smoothing in SURFER R 6, and with kriging + heavier smoothing. The variable is the natural logarithm of the radon concentration measured in Bq/m

10 039 Radon in the Living Environment, Lux 50 Lux Lux krigging Lux krigging + nugget Figure 3: Maps obtained for Luxembourg, with the moving average method with N=8 (Lux50) and N=32 (Lux200), with kriging without nugget in SURFER R 6, and with kriging with nugget. The variable is the natural logarithm of the radon concentration measured in Bq/m

11 Radon in the Living Environment, 039 Figure 4: Isotropic variograms deduced from experimental data and fitted variogram models for Luxembourg: zone A = Oesling, zone B = Gutland. 383

12 039 Radon in the Living Environment, (m) Figure 5: Map obtained for Luxembourg with lognormal kriging without nugget, the variogram model being fitted to the experimental variogram. The variable is the predicted concentration. 384

INDOOR RADON ON LOESS DEPOSITS IN WALLONIA

INDOOR RADON ON LOESS DEPOSITS IN WALLONIA François TONDEUR, Isabelle GERARDY, Nathalie GERARDY Institut supérieur industriel de Bruxelles, 150 rue Royale, B1000 BRUSSELS, BELGIUM ABSTRACT Pleistocene