Modeling of geogenic radon in Switzerland based on ordered logistic
regression
Georg Kropat
a,*, François Bochud
a, Christophe Murith
b, Martha Palacios (Gruson)
b,
Sebastien Baechler
baInstitute of Radiation Physics, Lausanne University Hospital, Rue du Grand-Pre 1, 1007 Lausanne, Switzerland bSwiss Federal Office of Public Health, Schwarzenburgstrasse 157, 3003 Berne, Switzerland
a r t i c l e i n f o
Article history:
Received 9 November 2015 Received in revised form 20 April 2016
Accepted 6 June 2016 Available online 22 June 2016
Keywords: Geogenic radon
European atlas of natural radiation Ordered logistic regression Terrestrial gamma dose rate Fault lines
Soil permeability
a b s t r a c t
Purpose: The estimation of the radon hazard of a future construction site should ideally be based on the geogenic radon potential (GRP), since this estimate is free of anthropogenic influences and building characteristics. The goal of this study was to evaluate terrestrial gamma dose rate (TGD), geology, fault lines and topsoil permeability as predictors for the creation of a GRP map based on logistic regression. Method: Soil gas radon measurements (SRC) are more suited for the estimation of GRP than indoor radon measurements (IRC) since the former do not depend on ventilation and heating habits or building characteristics. However, SRC have only been measured at a few locations in Switzerland. In former studies a good correlation between spatial aggregates of IRC and SRC has been observed. That’s why we used IRC measurements aggregated on a 10 km 10 km grid to calibrate an ordered logistic regression model for geogenic radon potential (GRP). As predictors we took into account terrestrial gamma dos-erate, regrouped geological units, fault line density and the permeability of the soil.
Results: The classification success rate of the model results to 56% in case of the inclusion of all 4 pre-dictor variables. Our results suggest that terrestrial gamma doserate and regrouped geological units are more suited to model GRP than fault line density and soil permeability.
Conclusion: Ordered logistic regression is a promising tool for the modeling of GRP maps due to its simplicity and fast computation time. Future studies should account for additional variables to improve the modeling of high radon hazard in the Jura Mountains of Switzerland.
© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Radon is a radioactive gas that is known to be the second leading cause of lung cancer after smoking (Zeeb and Shannoun, 2009). As a daughter product of Uranium, radon appears everywhere in nature and occurs in substantial concentrations especially in buildings. Hence, the major exposure of the population to radon takes place at home. In order to manage this health risk, many countries have developed maps based on indoor radon measurements (Dubois, 2005). The drawback of maps based on indoor radon measure-ments is that they are dependent on building characteristics and anthropogenic influences. This limits the generalizability of the
resulting estimates. In order to get rid of the anthropogenic in-fluences on potential estimates of radon, the Radioactivity Envi-ronmental Monitoring group at the Joint Research Center of the European Commission is working on the development of a Europe-wide map of Geogenic Radon Potential (GRP). Geogenic radon re-fers to“what the earth delivers” in terms of radon. A GRP map is very important when making decisions for the construction of new buildings. Since each house has a unique characteristic of radon entry, an initial radon estimate used to determine radon preventive measures should be free of building related influences. The goal of this study was to evaluate the following variables as predictors for the creation of a GRP map based on logistic regression: terrestrial gamma dose rate (TGD), geology, fault lines and topsoil permeability.
* Corresponding author. Institute of Radiation Physics, Lausanne University Hospital, Rue du Grand-Pre 1, 1007 Lausanne, Switzerland.
E-mail address:georg.kropat@chuv.ch(G. Kropat).
Contents lists available atScienceDirect
Journal of Environmental Radioactivity
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j e n v r a dhttp://dx.doi.org/10.1016/j.jenvrad.2016.06.007
2. Material and methods 2.1. The radon data
The GRP can be described as the geogenic source of the radon hazard at a location or over an area (Szabo et al., 2014). Several studies proposed different definitions of a geogenic radon potential (Kemski et al., 2001; Neznal et al., 2004; Szabo et al., 2014). Ideally a GRP estimation is derived from radon soil gas concentration (SRC) measurements. However, in Switzerland nearly no SRC measure-ments are available. SRC and indoor radon concentrations (IRC) often show only a weak correlation for single buildings. Never-theless, spatial aggregation results in a stronger association be-tween both quantities (Chen and Ford, 2016; Kemski et al., 2009). The Europe-wide GRP map is planned to be based on a spatial support of a 10 km 10 km grid. On this spatial resolution we expect a considerable correlation between aggregated SRC and IRC. Therefore, we used IRC mean values on a spatial grid of 10 km 10 km in order to calibrate our GRP model.
The WHO proposes an indoor radon concentration of 100 Bq/m3 as a reference level to minimize health hazards (Zeeb and Shannoun, 2009). For countries for which this reference level is not feasible, the WHO recommends not to exceed a reference level of 300 Bq/m3, which corresponds to a dose of 10 mSv per year at an equilibrium factor of 0.4 and an annual occupancy rate of 7000 h (IAEA, 2014). Therefore, we assigned the GRP classes to the grid cells based on the following scheme: Low< 100 Bq/m3, Medium 100e300 Bq/m3, High> 300 Bq/m3After sub-setting of the IRC data from the Swiss radon survey to inhabited rooms at the groundfloor and removal of missing data, 72,638 IRC measurements remained for analysis. For each building we calculated the average mean of all measurements taken in inhabited rooms on the groundfloor of one house.
2.2. The predictor variables
As predictor variables for the GRP model we considered the terrestrial gamma dose rate, geology, fault line density and the permeability of the soil.
2.3. Terrestrial gamma dose rate
Under the assumption, that terrestrial gamma dose rate (TGD) is proportional to the uranium content in the ground, we included this variable into our model. The TGD data observations are based on a method to extract the terrestrial component of ambient dose equivalent rate from EURDEP routine monitoring data (Cinelli et al., 2014). In order to interpolate the data, we used support vector regression using the coordinates as predictors. Support vector regression is an approach to determine a function fð x!Þ for the estimation of a dependent variable y (in our case the TGD) in dependence of a set of predictor variables x! ¼ x1; …; xk. The opti-mization problem is to find the optimum between flatness and over-fitting of f ð x!Þ. This tradeoff is described by the cost parameter C. A small C represents under-fitting of the data and a high C over-fitting. The interested reader will find more detail about support vector regression in (Cherkassky and Mulier, 2007; Smola and Sch€olkopf, 2004). We performed training and validation of the support vectors in R using the package e1071 (Meyer et al., 2014). The cost parameters were determined via 5-fold-cross validation.
The aggregation of the TGD estimations on a 10 km 10 km grid was performed by predicting the TGD on a 100 m 100 m grid and then calculating the average per 10 km 10 km grid cell. We used this method to obtain a more representative estimate for the average TGD in a 10 km 10 km cell instead of just predicting the
TGD at the center of a 10 km 10 km cell. 2.4. Grouping of geological units
Numerous studies on radon hazard mentioned the association between IRC or SRC and geology (Appleton and Miles, 2010; Appleton et al., 2011; Drolet et al., 2014; Friedmann and Gr€oller, 2010; Kemski et al. 2006, 2009; Smethurst et al., 2008). To take advantage of this predictor in our model we grouped geological units into 6 classes based on a data driven approach that considers the similarity of IRC distributions between geological units. This method basically performs k-medoids clustering based on the pair-wise Kolmogorov distances between the IRC distributions of the geological units. A detailed description of this method can be found in (Kropat et al., 2015). We used Swiss geological data that can be obtained from the OneGeology project (Federal Office of Topography swisstopo, 2013). To take account of the lithological properties as well as the age of the rock, we classified the geology by thefields “description” and “urn_litho1”. Only geological classes that covered more than 30 IRC measurements were included in the analysis to provide a stable estimate. This resulted in 58 combined classes of both geological age and lithology.
The conversion of the polygon data to the 10 km 10 km grid was performed by sampling the regrouped geological units on a 1 km 1 km grid all over Switzerland. Then the most prevalent regrouped geological unit of the 1 km 1 km grid within a 10 km 10 km grid cell was assigned to the corresponding 10 km 10 km grid cell.
2.5. Fault lines
The Jura Mountains in Switzerland are known to be subject to high IRC. Former studies suggested that the abundant karstification of the Jura Mountains could explain the higher IRCs measured in this region (Savoy et al., 2011). To get an estimate of local kar-stification in the Jura Mountains we analyzed the tectonic accidents (fault lines) using a geological map of Switzerland on a scale of 1:500,000 (swisstopo, 2005).
To obtain an aggregated estimate of the density of fault lines within a 10 km 10 km cell, we calculated the total length of lines within a cell and divided it by the surface area of the cell. 2.6. Soil permeability
Many studies include soil permeability as predictor for GRP, since this variable is supposed to influence flux of radon in the soil (Neznal et al., 2004; Szabo et al., 2014; Kemski et al., 2001). Following the Czech approach it is possible to derive a rough esti-mation of the permeability very easily from the weight percentage offine fraction (<63
m
m) (Barnet et al., 2008). Soils with the weight percentage of the fine fraction <15% were designed as high permeable soils, in the range 15e65% as medium permeable and in the case of thefine fraction above 65% as low permeable ones. The soil erodibility, k-factor parameter, was used as proxy of the weight percentage of fine fraction (Panagos et al., 2014). The great advantage of this parameter is the fact that it has already been modelled by soil experts for all Europe (with a grid size of 500 m) using LUCAS data (Toth et al., 2013). We used an extrapolated dataset for Switzerland. The correlation between k-factor value and weight percentage offine fraction have been calculated using data of LUCAS samples. Hence the value of k-factor corresponding to high, median and low permeability have been estimated and the permeability class assigned to each cell. Similar to the geological data we aggregated the permeability classes by assigning the most prevalent permeability within a 10 km 10 km cell to thecorresponding cell. 2.7. The model
We classified the GRP, i.e. our outcome variable, into the following classes: Low, Medium, and High. Consequently, our study aims to model an ordered categorical outcome variable. Logistic regression is one of the most common and also simplest statistical approaches to model a categorical outcome variable in dependence of a set of predictor variables. Our GRP classification consists of three classes that have an intrinsic order (“Low”, “Medium” and “High”). Ordinary logistic regression can only account for two classes. To overcome this limitation, we took advantage of ordered logistic regression to model the GRP (also called proportional odds model).
Given a vector z!of observations zi2f1; …; Jg with J2N of a categorical response variable, ordered logistic regression aims at modeling the probability for z to take a certain value inf1; …; Jg in dependence of a set of predictor variables xk k2f1; …; kg. The probability
p
ij¼ Pðzi¼ j
X!¼ x!iÞ can be observed by the variable yijwhich is the number of successes to take the value j at the ith combination of x!. Since in this study we suppose the outcome variable as being ordered, the model can be defined by making use of the cumulative probability.
P zi j X!¼ x!i ¼
p
i1þ … þp
ij j2f1; …; Jg (1)This leads to the following logit function
logit P zi j X!¼ x!i ¼ P zi j X!¼ x!i 1 P zi jX!¼ x!i ¼
p
i1þ … þp
ijp
ijþ1þ … þp
iJ (2)With this definition the logit model can be expressed as:
logit P zi j X!¼ x!i ¼
a
jþb
! x ! j2f1; …; J 1g (3)The probability of zito take a value in f1; …; Jg results conse-quently to P zi¼ jX!¼ x!i ¼ P zi jX!¼ x!i P zi j 1X! ¼ x!i (4)
The likelihood function can be calculated as being proportional to YN i¼1 0 @YJ j¼1
p
yij ij 1 A ¼YN i¼1 YJ j¼1 P zi j X!¼ x!i P zi j 1 X!¼ x!i yij (5)Finally the coefficients !
b
can be found by maximizing the likelihood by means of a Newton-Raphson algorithm.This model can deal with outcome variables consisting of more than 2 ordered classes. For theoretical details we refer to (Agresti, 2013). The model is readily implemented in the open source sta-tistical programming language R (R Core Team, 2014) and can be found in the software package“MASS” (Venables and Ripley, 2002)
under the function“polr”. 3. Results
Fig. 1shows the IRC measurements that we considered for the spatial aggregation andFig. 2 the spatial aggregation of the IRC measurements on a 10 km 10 km grid. Grid cells with no mea-surements are indicated as whitefields.Fig. 3illustrates the results of the dose rate spatial modeling as well as the dose rate mea-surements used for the model. A 5-fold cross validation yielded an R2of 36% based only on the geographical coordinates as predictors. Taking altitude into account as an additional predictor, results in an R2of 49%. The spatial clustering of dose rate measurements in the north of Switzerland are due to a higher monitoring network around nuclear power plants.Fig. 4shows the results of the clus-tering of geological units. The results of the spatial aggregation of the fault lines is shown inFig. 5. The unit of the aggregation is length per area. Fig. 6 shows the spatial aggregation of the permeability class. Cells where no permeability class was assigned are cells that are predominantly covered by lakes or glaciers.Fig. 7 illustrates the result of the radon modeling based on ordered lo-gistic regression. As predictors we took into account the dose rate, the clustered geology, the fault lines and the permeability. A five-fold cross validation resulted in a classification success rate of 56%. Random guessing would have resulted in 33% on average, since this corresponds to the rate tofind the right class out of three classes just by chance.Table 1shows the classification success rate after the exclusion of each variable and the corresponding decrease of the classification success rate.
4. Discussion
The goal of this study was to evaluate the potential of the following variables to create a GRP map based on logistic regres-sion: terrestrial gamma dose rate (TGD), geology, fault lines and topsoil permeability.
The spatial aggregation of IRC measurements on a 10 km 10 km grid inFig. 2shows a clear and well-known pattern of higher IRC measurements in the Jura Mountains (north-west Switzerland) and in the Alps. The Swiss Plateau is characterized by lower IRC. This regional tendency is well-reflected in the map of the regrouped geological units inFig. 4. The grouping clearly differ-entiates between areas that are abundant in karstified limestone (Jura Mountains), quaternary deposits (Swiss Plateau) and different
Fig. 1. Spatial distribution of indoor radon measurements that were used in this study. One observation corresponds to the arithmetic mean of all radon measurements that were taken in inhabited rooms on the groundfloor of a building.
metamorphic rocks (Canton of Ticino) and granites (Alps).Fig. 3 shows a clear trend of higher TGDs in the south of Switzerland compared to the north. This can be explained by the higher
occurrence of uranium in the Alps with certain types of granites and gneisses. Taking altitude into account as a predictor variable considerably increases the explained variance of the TGD model from 36% to 49%. This is also reflected in the mapping results (not Fig. 2. Indoor radon classes per grid cell. The classes were determined by the
arith-metic mean of all radon measurements in one grid cell with the following rules: Low< 100 Bq/m3, Medium 100e300 Bq/m3, High> 300 Bq/m3.
Fig. 3. Dose rate measurements and spatial modeling. The modeling was carried out via support vector regression using coordinates as predictor variables.
Fig. 4. Results of geological unit grouping based on k-medoids clustering.
Fig. 5. Fault lines and length of fault lines per area of grid cell.
Fig. 6. Permeability of top soil layer. The class of a cell is determined by the most prevalent permeability class within a grid cell.
Fig. 7. Determination of GRP classes. The classification of the GRP is in terms of the IRC classes since we calibrated our models on this data.
shown here). Using altitude as an additional predictor variable leads to a strong appearance of topography in the TGD mapping. However, taking altitude into account can be problematic for two reasons. First of all, the increase of the explained variance by ac-counting for the altitude may be due to the fact that the cosmic gamma dose rate was not entirely eliminated from the data. Sec-ondly, even if altitude has a real association with TGD in Switzerland, this may not be the case in other countries. To yield a better generalizability of the approach we excluded altitude from thefinal mapping. The mapping of the fault line density distin-guishes between areas of thick quaternary layers in the Swiss Plateau and mountainous regions like the Alps and the Jura Mountains. The reader has to bear in mind that a fault line in the Alps may have different radon characteristics than a fault in the Jura Mountains.
Backward elimination yields that the TGD and the regrouped geology are the variables with the strongest influence. When excluded the classification success rate drops from 56% to 28%. Theoretically, 33% is the lowest obtainable success rate since this represents the case of random guessing for a 3-class problem. Nevertheless, the output of our classifier is a random variable, which explains the appearance of the lower classification rates (28%) after exclusion of TGD or regrouped geology. We observed that fault lines and permeability were the least important variables in the model. For fault lines this may be explained by the fact that not all fault lines have the same radon characteristics. We suppose that soil permeability only plays a role for radon exhalation that is measured at the very surface of the soil. However, the entry point of radon in houses is generally several meters below the soil surface. This may explain the low influence of permeability into the model. A variable that describes the rock permeability instead of the soil permeability may lead to better estimates in future studies. This is a clear limitation of using IRC measurements to calibrate a GRP model. Furthermore, this leads to the fundamental question of whether GRP is in terms of radon measured at the surface of the ground or below the topsoil layer.
The classification success rate of 56% of the final GRP model performs better than random guessing. Nevertheless, thefinal GRP map does not sufficiently point out the areas of high radon con-centrations in Switzerland. Notably, the Jura Mountains are not represented. This is probably due to the fact that the included variables do not appropriately represent the trends of the GRP in Switzerland. Indeed, our model is mainly driven by the variables of TGD and regrouped geology. However, TGD cannot explain the elevated GRP in the Jura Mountains since here TGD is rather low. This is apparently not sufficiently compensated by the regrouped geology. The limestone of the Jura Mountains is clearly visible in the map of the regrouped geology. However, since limestone in the Alps have lower GRP, the model considers areas of limestone as intermediate GRP.
We suggest that future approaches have to focus mainly on the exploration of other variables that may better explain the regional trends of GRP.
5. Conclusion
We implemented a method to model Geogenic Radon Potential based on four variables: terrestrial gamma dose rate, regrouped geological units, fault line density and soil permeability. For this purpose, we used an ordered logistic regression model. We ob-tained a classification success rate of 56% for the model when including all 4 variables. Our results suggest that terrestrial gamma dose rate and regrouped geological units are better predictors of GRP than fault line density and soil permeability.
Acknowledgements
We want to thank the Swiss Federal Office of Public Health for financial support.
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Classification success rate after exclusion of each variable. The inclusion of all 4 variables resulted in a classification success rate of 56%. In the third column the decrease of the success rate is shown when excluding the corresponding variable from the model.
Predictor variable Success rate of model after exclusion of variable (in %) Decrease of success rate (in %)
TGD 28 28
Regrouped geology 28 28
Fault lines 52 4
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