In: Proceedings of the “8th International Workshop on the geological aspect of radon risk mapping”, pp. 88-97, I. Barnet, M.
Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
From Babel to the Round Table of Camelot:
on setting up a common language and objective for European
radon risk mapping.
Part I. Radon risk maps, different maps for different purposes.
G. Dubois, P. Bossew
European Commission – DG Joint Research Centre,
Institute for Environment and Sustainability, Ispra, Italy
Corresponding author: [email protected]
Abstract:
Radon is a naturally occurring radioactive gas known to be, by far, the main contributor to
exposure from natural background radiations received by the population. It is also considered
to be the leading cause of lung cancer, only second to smoking. This has stimulated most
European countries to adopt a number of regulations and launch surveys to identify radonprone areas. A recent report on the European efforts for delineating areas with increased radon
levels has shown a large variety of means and methods used to measure and report radon
levels.
Like all maps, Radon maps serve certain purposes, related to interests: displaying the actual
exposure will result in a different map from one which aims to predict the risk which results
from the geological structure of a region, or a map aimed at monitoring tectonic activity
through variations in Radon exhalation, etc. It is the purpose of this paper to explore the
variety of these maps and propose some definitions to make it easier to distinguish between
various radon-risk maps. The possibility of preparing some harmonised radon map at the
European level will also be discussed.
KEYWORDS: Radon mapping, mapping objective, risk map, terminology, natural radiations
atlas
1. Introduction
For the last 20 years, around 2 million radon-related measurements have been made all over
Europe and, in most cases, processed in the form of maps. A recent survey of these efforts
(Dubois 2005) has shown, however, that no two European countries have adopted comparable
approaches for choosing the measured variable and a method for presenting radon levels.
Although most of these studies refer to “radon risk maps” and their preparation as “radon risk
mapping”, a mosaic of all these maps (Figure 1) reveals a patchwork of very different-looking
maps, all of them showing some spatial fluctuation of radon levels, whichever way they are
defined. Generally, national maps either show some values averaged on grids or within
administrative areas or isolines derived from some spatial interpolation process. The spatial
resolution of these maps, that can range from local averages calculated over 1 km2 up to a
whole region, as well as the number of colour classes or isoline levels used to provide some
quantitative information on the radon concentrations also vary greatly. One may also imagine
that the choice of resolution and colours adopted to represent radon levels stems from a subtle
mixture of political and scientific decisions that are required to find the best balance between
information that is detailed enough to be useful to the map user but also sufficiently
generalized to facilitate the identification of general “radon patterns”.
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In: Proceedings of the “8th International Workshop on the geological aspect of radon risk mapping”, pp. 88-97, I. Barnet, M.
Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
Figure 1. “Collage” of the European radon maps published by the national authorities. Colours
and levels have not been harmonized in the figure. White areas do not mean that no surveys
were made but that no map was published (Dubois, 2005).
Many countries have adopted a monitoring strategy coordinated at the national level, thus
minimizing the heterogeneity of the tools and methods used to estimate radon levels. It is also
true that other countries have organised surveys at regional level, which complicates the
comparison of results collected by different surveys. It should be mentioned that Sweden
which has pioneered the field and made one of the largest radon surveys in Europe, has no
radon maps at country level, as the responsibility for monitoring and mapping radon lies in
the hands of each municipality.
Within the context of its institutional scientific support to the European Commission (DG
TREN H.04, Radioprotection Unit), the Radioactivity Environmental Monitoring (REM)
group at the Institute for Environment and Sustainability (IES, DG JRC) explores the
possibility of generating a European Radon risk map in the frame of a European Atlas of
Natural Radiation.
Clearly, not only do different maps serve different purposes, but, as is generally the case for
maps derived from environmental data, each map is proper to its authors given the many,
often arbitrary, decisions that are taken in the processing phase. In the following we aim to
identify the main differences in the approaches and definitions used and possibly find some
common ground for using a common language.
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In: Proceedings of the “8th International Workshop on the geological aspect of radon risk mapping”, pp. 88-97, I. Barnet, M.
Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
2. Radon: from rock to risk
We want to remind in Figure 2 the logical genesis of the health risk related to radon: while the
origin of radon progenies which are the agents which can cause lung cancer (Darby et al.,
2005), are U and Th minerals in soil and rock (building materials usually to a much lesser
extent), or their 226,228Ra content, the
risk
pathway from mineralogy / geology to
smoking
exposure, and finally to risk is surely not
habits
Dose (Sv)
straight.
Exposure
Figure 2.
Radon: from rock to risk
3
Conc. of Rn progenies (Bq/m )
equilibrium
fac tor
2.1. Risk definitions
Although risk is a very broad topic, we
want to recall three standard concepts used
to define the notion of “risk”. The term may
denote the hazard caused by Rn, in this case
(a and b below), but also, more technically,
the probability that a condition is met (c).
indoor atmosphere
3
indoor Radon concentration (Bq/m )
property of the building,
property of the room,
ventilation conditions,
......
meteorology:
pressure differences,
etc.
3
Rn potential (Bq/m )
(a) Individual risk
Given the variable “Rn progeny activity
concentration” in air at location (i), Ci, the
Conc. of Rn in soil gas (Bq/m )
risk of incidence of lung cancer of a person
water content
other
is
geological,
geophysical
conc. of Ra
r := f * ∑ Ci wi ,
parameters
in soil, rock (Bq/kg)
where wi is a weighting factor, accounting
for the time a person stays at location (i),
and f is the risk factor or odds ratio, expressed in (Bq/m3)-1, assuming a linear dose-riskrelationship. For mapping purposes, the variable r thus defined is referenced to the location
(x) where the person lives, or, more simplified, a risk value assigned to that very location:
r(x) := f * C(x).
Here C(x) is the indoor concentration of Rn, possibly normalized to standard conditions (see
part 2), or certain Rn / Rn progeny equilibrium factors and life habits assumed.
Transport in topsoil
permeability
3
(b) Collective risk
As a second approach, one may be interested in the distribution of the collective risk, R:=∑r,
summed over all persons, which can again be regionalized,
R(x) := r(x) * n(x),
where n(x) is the population density. R(x) represents the “population density-weighed Rn
risk”.
(c) Exceeding a regulatory threshold
A third approach to defining risk, ideally derived from the previous definitions, is one usually
chosen by regulators who need to translate the notion of risk into some quantity that is legally
binding. To this end thresholds of a variable are set and further used in regulations such as
Commission Recommendation 90/143/Euratom on the protection of the public against indoor
exposure to radon (EC, 1990) which recommends that new constructions not exceed an
effective dose equivalent of 10 mSv per annum. For practical purposes, this may be taken as
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Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
equivalent to an annual average radon gas concentration of 200 Bq/m3. Technically, the risk is
then the probability of exceeding a threshold T, prob(C>T).
2.2. Mapping
In geostatistical terms, risk-related variables such as the above can be considered as
realisations of random functions. If a function is spatially continuous and auto-correlated, i.e.
“the closer in space two observations the more alike they tend to be”, it can be interpolated,
i.e. its value estimated at unsampled locations. Various interpolation methods have been
developed: as two examples in Radon mapping, Kemski et al. (2001) have used an inverse
distance weighing function for mapping Rn in soil gas in Germany, whereas Bossew &
Lettner (2002, 2005) used kriging to produce Radon potential level and risk maps of Austria.
Ground floor, indoor radon concentrations (Austria)
Direction: 0.0 Tolerance: 90.0
Fig. 3: Variogram of indoor radon concentration
measured on ground floors of Austrian houses. Dashed
line: Variance of the data. Min. lag = 2000 m
120000
100000
Here we will not discuss advantages and drawbacks
of the many interpolators, but underline that
mapping based on spatial interpolation is only
justified if spatial correlation of the variable has been
identified, something that is less straightforward than
it may sound. Very few case studies that analyse this
spatial correlation have been published, in particular
studies that investigate indoor measurements as these
were usually available in a very large number. The
treatment of large amounts of measurements using
geostatistical software indeed became possible only
relatively late, in the mid 1990s, when new computers and algorithms were developed that
allowed the calculation of spatial covariance of datasets larger than a few hundreds of
measurements. Today it takes only a few minutes to process some 10,000 data points on an
ordinary PC, something inconceivable a few years ago in geostatistics. Figure 3 shows the
empirical semi-variogram (also called variogram), a function related to the spatial correlation,
of about 10,000 measurements of indoor radon concentrations made at ground floor level in
Austrian dwellings (see Friedmann et al., 2001).
Figure 3 shows that correlation clearly decreases with distance (the variogram increases). At
around 60 km, the function reaches saturation, indicating no spatial correlation over larger
distances. It also shows that a high fraction of the variability (ca. 70%) is still uncorrelated
within the minimum distance resolved by the analysis (i.e. 30% correlation within 2000 m;
details of the analysis and more discussion can be found in Dubois & Bossew, 2006).
Interestingly enough, almost identical results were found by Chaouch et al. (2003) for the
Valais region in Switzerland. Other recent studies show better correlation at short distances
(see Bertolo et al., 2006; Verdi & Pegoretti, 2006) but no cases have been found in which
local correlation was higher than about 40%. On the other hand, soil-gas data seem to show a
less “noisy” short-scale structure (see e.g. Badr et al., 1993).
This difficulty in finding a clear spatial structure over short distances has important
consequences: in the case of a deterministic exact interpolator, which honours the individual
sampling points, the map will appear so noisy because of local fluctuations that the final result
will be almost impossible to use. In the case of smoothing interpolators, taking into account
this lack of correlation at short distances will result in maps that are either so smooth that the
whole variability is hidden and the local uncertainties are very high or, in the case of
Variogram
80000
60000
40000
20000
0
0
20000
40000
60000
80000
100000
120000
140000
Lag Distance (m)
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Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
geostatistical simulations, each simulated map will appear very noisy again. In summary, if
geostatistical techniques provide essential information for the data analyst, one may wonder
about their potential use for mapping indoor radon levels, or predicting them at unsampled
locations, unless the data are somehow normalised or classified in order to reduce the very
high variability observed at short scale (see Dubois & Bossew, 2006).
In maps used to describe and make decisions, one can map the variable z itself, or the
probability z* that the variable exceeds a given threshold, z*(x):= [prob(z>T)](x). Table 1
gives a list of some candidates for variables that measure the risk from Rn. All these variables
are derived from the Rn concentration C; other options will be discussed in part 2.
Table 1.
Some possible variables which measure risk due to Radon. T: thresholds
z(x)
C(x)
r(x) = C(x) * f
R(x) = r(x) * n(x)
z*(x)
C*(x;TC):=[prob(C>TC)](x)
r*(x;Tr):=[prob(r>Tr)](x)
R*(x;TR):=[prob(R>TR)](x)
indoor Rn (progeny) concentration
individual risk
collective risk
While the traditional interpolation approach, z(xi) → z’(x) where z(xi) are the measured values
at sampling locations xi, which results in a level map of the estimates z’(x), may facilitate the
decision-making process, it is unrealistic as it does not account for uncertainties. Usually it
also smoothes away local fluctuations around the estimated local mean, which may be
significant, as experience with Rn data has shown. The alternative, so-called “probabilistic
risk mapping” approach often better represents the model uncertainties but it also frequently
renders the decision-making less straightforward. Possible regulatory consequences in using a
probabilistic approach is by cutting off peaks by, e.g., limiting the probability of exceeding a
threshold, r*(x,Tr) < Tp, where Tp is the probability threshold, 5% for example.
2.3. Calculating probabilities
Three important methods for estimating the probability that a variable exceeds a threshold are
discussed very shortly in the following.
Empirical probabilities
In this very popular approach, for the empirical data z(xi) within a region A (often an
administrative unit) the empirical probability is calculated as
prob[z>T](A) := (number of z(xi)>T: xi ∈ A) / (number of all z(xi) ∈ A)
A shortcoming of this method is that it sensitive to sampling design, i.e. clustering of data. An
unbalanced design may result in a biased estimate.
Indicator kriging
A common method used to estimate the spatial distribution of probabilities that a variable
exceeds a preset threshold at a given point (x), z*(x,T), is, as a first step to produce a set of
empirical probability values at the sampled locations, {z*(xi)}, and subject those to
geostatistical procedure with the aim of generating a continuous variable z*(x). Usually the
empirical probabilities are generated as z*: domain(z) → {0,1},
z* := ind(z,T) ≡ θ(z-T) ≡ {1 if z>T, 0 otherwise}.
However, while this choice is easy to implement, it is no natural choice. More generally,
“soft” indicator transforms have been suggested, sind: z → [0,1], for example (Goovaerts &
van Meirvenne 2001)
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Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
z*(xi;T) := erf((z(xi)-T)/sz(xi)),
where sz(xi) is the process standard deviation of z(xi), accounting for the uncertainty which is
inherent to z(xi) as a measured quantity. Indeed it has been shown (Bossew, Dubois &
Pebesma, 2005) that the result of the estimate, z*’(x), can depend critically on the chosen
“hardness” of the sind function (as well as on other more or less deliberate choices in the
estimation procedure).
Simulations
Conditional simulations have been extensively used over the past years as these can better
illustrate the local variability and uncertainty of the analysed variable. The underlying idea is
to add a random effect (noise) to the necessarily smoothed local estimates from traditional
interpolators, thus generating many simulated, equally probable maps. The method results in a
frequency distribution of simulated values at each grid point, out of which the local mean and
associated uncertainty can be estimated. As for other geostatistical functions, the results will
strongly depend on the modelling of spatial covariance, an issue that is a serious drawback for
indoor radon measurements as discussed above. As global estimates, simulations may not
account well for local anomalies, i.e. regions where the spatial behaviour of the field differs
strongly from its “mean” behaviour, typically in and around so-called hot spots. On the other
hand, the Conditional Sequential Gaussian Simulation (SGS) method uses the locally
estimated kriging variance as input for constructing the local pdf, out of which the simulated
value is sampled, thus re-introducing also locally anomalous behaviour to some degree, at
least. - As an overall result, simulations can become extremely noisy and their interpretation
difficult.
With the exception of a few countries, most maps of indoor radon levels published in
European countries have been obtained by averaging local measurements and by subsequently
classifying radon levels on an administrative basis according to various regulatory thresholds
(see method 1 below). This administrative 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.
2.4. Sources of the nugget effect
The intercept of the variogram with the y-axis (fig. 3), which measures the variability below
the spatial resolution of the variogram (about 60,000 (Bq/m³)² if a model is fitted to the
empirical variogram, fig. 3), also called noise, has two essentially different sources: (1) the
intrinsic
uncertainty
of
the
variability between physically identical rooms
measurements; and (2) the so-called
micro-variability, i.e. the variability
below
the
smallest
resolved
separation distance (lag) of the
1
variogram.
2a
2b
variability between
physically different rooms
=> RP
Figure 4: Sources of the nugget
variance
3
For indoor Rn concentration,
component (2) can further be split
into: (2a) variability between two
rooms located at the same position
(i.e. below the spatial resolution) but
with different physical properties;
4
variability within one room
"nugget area"
= area below variogram lag
counting uncertainty
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and (2b) variability between rooms with “identical” physical characteristics, as far as they can
be accurately quantified; in this case the variability can be the result of inaccuracy of
determining the physical characteristics and a variability of the Rn source between the rooms.
A simplified scheme of these various sources is given in figure 4.
In order to eliminate source (2a), the concept of the Radon potential has been developed, see
part 2 of this paper. – A more detailed discussion of the noise or nugget effect is given by
Dubois & Bossew (2006).
3. Different variables for different interests
While table 1 has given some candidates for variables that measure risk from Rn, the actual
choice of the working variable largely depends on the stakeholder’s interest. This is illustrated
in tables 2 and 3. In table 2, a (certainly incomplete) list of possible interests is given along
with their objects and the resulting variables. Evidently not all of these variables can be
mapped; and if they can be defined as spatial variable z(x), there is no guarantee that they
meet the mathematical requirements for mapping. In table 3 below, two particular interests are
selected, which belong to what is summarized under “public health” in table 2. The amount of
harm done by Rn, e.g. in terms of number of fatalities from lung cancer, is due to the
collective dose, while individual doses give rise to the chance of a person being harmed by
Rn. In most cases the collective dose results from many individual doses each of which may
be associated with a very small risk, whereas relatively few cases with individual high risk
contribute little to the collective dose.
Table 2.
interests and resulting variables
interest
public health
regulation
mapping
science:
geology
geophysics
tectonics
atmos. physics
object
incidents, fatalities of lung
cancer
legal framework
continuous, autocorrelated
variable as proxy to risk
variable
r(x), r*(x;Tr), R(x), R*(x;TR)
Rn emanation power,…
transport of Rn in soil,…
geological parameters
permeability, other
geophysical parameters
Rn emanation flux
Rn, Rn progeny concentrations
geostatistics
earthquake monitoring
circulation of air indoor, Rn as a
tracer of atmospheric processes
speciation of Rn progenies, RnTn
mapping, spatial structure
rad. biology
effect of radiation
aerosol physics
C*(x;TC)
Rn potential
Rn, Rn progenies
all variables which have
spatial structure
conc. of Rn+progenies, PAEC
Clearly, however, both individual and collective risks are subject to health politics, and the
public would certainly not accept excluding any one of them: cases of high individual risk
must be taken care of and possibly mitigated even if they contribute only little to the overall
consequences, while large scale mitigation is increasingly demanded by the public in spite of
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Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
small individual risks, as can be observed with many other environmental hazards. These two
interests may however result in quite different efforts from the technical point of view, as
statistics and mapping are concerned, as outlined in table 3.
Table 3.
Examples of relationships between working variables and stakeholders interests
interest / concern:
Objective:
Criterion:
Region identification
with:
Spatial modelling and
delineation:
Resulting map:
Working variables:
Implementation criteria:
individual dose
collective dose
cutting off extreme values
Tr (e.g. doubling of lung cancer risk),
TC (e.g. 400 Bq/m3)
high probability of high Rn
concentration
overall reduction
TR (e.g. additional number of lung
cancer cases)
identify & quantify hot spots
define, delineate regions
spatial distribution of probability of
occurrence of hot spots
r(x), r*(x;Tr), C(x), C*(x,TC)
r(x) < Tr; r*(x;Tr) < Tp; etc.
spatial distribution of collective
dose
R(x), R*(x;TR)
id.
high density of collective dose
4. Conclusions
Existing European Radon maps look very different in many aspects: in terms of the displayed
variable, the spatial resolution, the way to interpolate (or not), the selection of levels
displayed for the variables. More fundamental are even the differences between radon-prone
areas delineated by means of soil-gas radon surveys and those derived from indoor
measurements. Generating some common Rn risk map at the European level without undue
additional experimental effort may thus sound unreasonable at first sight.
We will nevertheless here advocate a concerted approach at the European level to allow the
comparison of data and maps. Such harmonisation should not only help everyone concerned,
citizens and decision-makers alike, better to assess this natural threat to our health, but also to
familiarize the population with the fact that their environment is naturally radioactive.
Considering this fundamental need for a European atlas of natural radiations one may give a
second thought to possible means of generating maps that can be compared between the
European countries. If we want to assess doses to the population, rather than to generate only
a descriptive work highlighting areas with increased radon levels, some mapping method for
indoor measurements need to be put in place as the mapping of radon-prone areas using only
soil-gas measurements or U content of soil and rock would probably not be sufficient. One
would certainly spare much effort in using an approach based on local averages based on
administrative boundaries, but these may not reflect the exposure of the population given the
heterogeneous distribution of the population density. Using a grid would probably be easier as
this can be used both to calculate local averages and the natural output of estimates obtained
from some interpolation technique. Raster data are much more flexible and useful for
subsequent maintenance and modelling. We have seen that handling data which present high
local variability is everything but straightforward. Reducing short-scale variability should be
possible, however, by combining geological information and radon measurements for
classification purposes (see e.g. Zhu et al., 2001; Miles & Appleton, 2005). Further
normalization levels of indoor measurements can probably be achieved by taking into account
various housing parameters (floors, window types, living habits) (see the discussion in part 2).
To achieve some progress in harmonizing data and maps at the European level, a condition
sine qua non for the preparing European maps, we will first need to agree on some common
definition of what a radon map is and then, even more importantly, on a common definition of
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Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
what our target variable is. This essential issue is further discussed, if not solved, in the
second part of this paper (Bossew & Dubois, 2006)
Acknowledgements: The authors would like to thank all members of the European forum on radon
mapping [http://radonmapping.jrc.it/], in particular R. Blaauboer, S. Darby, H. Friedmann, M.
Gruson, J. Miles, A. Siehl and F. Tondeur for their useful discussions on the harmonisation issue of
radon maps. Particular thanks to our colleague Tore Tollefsen for proofreading the paper.
REFERENCES
Badr, I., Oliver M.A., Hendry G.L. and Durrani S.A. (1993). Determining the spatial scale of
variation in soil radon values using a nested survey and analysis. Radiation Protection
Dosimetry (49), 433-442.
Bertolo A., Bigliotto C., Giovani C., Garavaglia M., Verdi L. and Pegoretti S. (2006)
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 2006, Biella, Italy. ARPA
Piemonte, ISBN-10: 88-7479-099-3.
Bossew P.& Dubois G. (2006). From Babel to the Round Table of Camelot: on setting up a
common language and objective for European radon risk mapping. Part II. Harmonization and
standardization of radon data and maps. This Volume
Bossew, P., Dubois, G. & Pebesma, E. (2006). Decision making and radiological maps:
understanding map uncertainties in emergencies. To appear in Proceedings of the Rio
Conference 21-25 November 2005, Rio de Janeiro. IAEA.
Bossew P. & Lettner H. (2002): Statistische Analyse von Radondaten. Report to the Austrian
Ministry of Social Affairs & Generations. Vienna, Feb. 2002
Bossew P. & Lettner H. (2005): Definition of the Radon potential, its spatial properties over
Austria and mapping of its levels and the related risk. Presentation, Radon workshop,
Lausanne, 4 March 2005
Chaouch, A., M. Kanevski, M. Maignan, J. Rodriguez and G. Piller (2003). 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, 7-12 September 2003.
Darby, S., Hill D., Auvinen A., Barros-Dios J. M., Baysson H., Bochicchio F., Deo H., Falk
R., Forastiere F., Hakama M., Heid I., Kreienbrock L., Kreuzer M., Lagarde F., Mäkeläinen
I., Muirhead C., Oberaigner W., Pershagen G., Ruano-Ravina A., Ruosteenoja E., Schaffrath
Rosario A., Tirmarche M., Tomásek L., Whitley E., Wichmann H-E. and Doll R. (2005):
Radon in homes and risk of lung cancer: collaborative analysis of individual data from 13
European case-control studies.BMJ, doi:10.1136/bmj.38308.477650.63
Dubois, G. &Bossew, P. (2006). The radon “noise” and its geostatistical implications: risk
mapping or mapping at risk? To appear in: Proceedings of the 11th International Congress of
the International Association of Mathematical Geology (IAMG 2006), 3-8 September 2006,
Liege, Belgium.
Dubois, G. (2005). An overview of Radon surveys in Europe. EUR 21892 EN, EC. 168 pp.
96
In: Proceedings of the “8th International Workshop on the geological aspect of radon risk mapping”, pp. 88-97, I. Barnet, M.
Neznal, P. Pacherova (Eds). 26-30 September 2006, Prague, Czech Republic.
EC (1990). Commission Recommendation of 21 February 1990 on the protection of the
public against indoor exposure to radon (90/143/Euratom). Official Journal of the European
Union, OJ L-80 of 27/03/90, page 26.
Kemski J., Siehl A., Stegemann R. & Valdivia-Manchego M. (2001). Mapping the geogenic
radon potential in Germany. The Science of The Total Environment, 272 (1-3): 217-30.
Friedmann, H., Atzmüller, C., Breitenhuber, L., Brunner, P., Fink, K., Fritsche, K., Hofmann,
W., Kaineder, H., Karacson, P., Karg, V., et al. (2001): The Austrian radon project. Science of
the Total Environment, 272 (1-3): 211-212
Goovaerts, P. & van Meirvenne, M. (2001) Accounting for measurement and interpolation
errors in soil contaminant mapping and decision-making. In: Proceedings of the 7th Annual
Conference of the International Associations for Mathematical Geology, Cancun, Mexico, pp.
1-12, September 2001.
Miles J.C.H. & Appleton J. D. (2005). Mapping variation in radon potential both between and
within geological units. Journal of Radiological Protection, 25: 257-276.
Verdi L. & Pegoretti, S. (2006). 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 2006, Biella,
Italy. ARPA Piemonte, ISBN-10: 88-7479-099-3.
Zhu, H. -C., Charlet J. M. and Poffijn A. (2001). Radon risk mapping in southern Belgium: an
application of geostatistical and GIS techniques. The Science of the Total Environment,
272(1-3): 203-210.
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