A process-based 222 Radon flux map for Europe and its 1 comparison to long-term observations

Abstract


Introduction
One of the limiting factors for applying atmospheric 222 Rn measurements for transport model validation is a reliable, high-resolution 222 Rn flux map for the global continents, but also on the regional scale for Europe.It has been shown earlier that the assumption of a constant exhalation rate of 1 atom cm −2 s −1 for continental areas, as was proposed by Jacob and Prather (1990) as an intermediate value from data reported by Wilkening et al. (1972) and Turekian et al. (1977), is an over-simplification of the true conditions, in particular for Europe (Dörr and Münnich, 1990;Schüßler, 1996;Conen and Robertson, 2002).Nevertheless, this assumption was used, for simplicity, in different transport model estimates and model inter-comparison studies (Rasch et al., 2000;Chevillard et al., 2002;Taguchi et al., 2011).Only in the last decade, a number of attempts have been made to develop high-resolution maps of the variability of 222 Rn exhalation from continental soils (Schery and Wasiolek, 1998;Sun et al., 2004;Zhuo et al., 2008;Szegvary et al., 2009;Griffiths et al., 2010;Hirao et al., 2010;López-Coto et al., 2013).We present here a high-resolution 222 Rn U. Karstens et al.: A process-based 222 radon flux map for Europe flux map for Europe, based on a parameterization of 222 Rn production and transport in the soil. 222Rn is a progeny of 238 uranium ( 238 U), a trace element in natural soils.Since 222 Rn is the first gaseous element in the 238 U decay chain that can escape from the soil, all daughter nuclides from 238 U up to 226 radium ( 226 Ra), the mother nuclide of 222 Rn, are often assumed to be in equilibrium in the soil.Besides the 226 Ra content, 222 Rn exhalation rates also strongly depend on soil properties (Nazaroff, 1992).Therefore, not only the 238 U content but also the parameters influencing diffusive transport characteristics of the soil need to be known to properly estimate the variability of 222 Rn exhalation rates (Schüßler, 1996).Taking these into account, Griffiths et al. ( 2010) developed a high-resolution 222 Rn flux map for Australian land surfaces.They used a transport model for the unsaturated upper soil layers, national γ -ray surveys, maps of soil properties, such as porosity and bulk density, as well as modelled soil moisture to estimate monthly 222 Rn exhalation rates at 0.05 • spatial resolution.Likewise, López-Coto et al. (2013) published a 222 Rn flux map for Europe that also uses numerical modelling of 222 Rn transport in the upper soil layers.Their input parameters were measured 238 U activity concentrations from the Geochemical Atlas of Europe (Salminen, 2005) and other soil properties as well as modelled soil temperature and moisture data.Based on these parameters, they estimated average monthly 222 Rn exhalation rates for the time period of 1957-2002 at a spatial resolution of 1 km.Szegvary et al. (2007b) found an empirical relation between 222 Rn exhalation rate and γ -dose rate.Following this finding, Szegvary et al. (2009) published a 222 Rn flux map for Europe that solely uses γ -dose rate as a proxy for 222 Rn exhalation rate.
In the present work, we use a similar approach as Griffith et al. (2010) for Australia and López-Coto et al. (2013) for Europe.We estimate the 222 Rn exhalation rate from European land surface based on the measured distribution of 238 U in the upper soil layers (Salminen, 2005), the soil texture class distribution (Reynolds et al., 2000) as well as model estimates of the soil moisture, which largely governs molecular diffusion in the unsaturated soil.For the period of 2006 to 2010, we test two different soil moisture reanalysis data sets: (1) from the Noah Land Surface Model in the Global Land Data Assimilation System (GLDAS Noah, Rodell et al., 2004), and (2) from the ERA-Interim/Land (ERA-I/L, respectively) reanalysis (Balsamo et al., 2015).Soil moisturedependent molecular diffusive transport in the upper metre of the soil is calculated based on the Millington and Quirk (1960) model.The validity of our diffusion model approach is tested at different soil moisture regimes, using systematic 222 Rn soil profile measurements at our observational site close to Heidelberg, Germany.The European flux maps are further compared to direct spot and long-term measurements of 222 Rn exhalation rates in different areas across Europe.

Basic equations for 222 Rn production, decay and diffusion in soils
The derivations below essentially follow those presented in Dörr and Münnich (1990), Born et al. (1990), Schüßler (1996), and Griffiths et al. (2010).They are valid for an infinitely deep unsaturated homogeneous soil, and we consider only changes of concentration c(z, t), flux j (z, t) as well as source Q(z, t) or sink strength S(z, t) in the vertical direction z (with the z coordinate defined as positive downwards and z = 0 at the soil-atmosphere interface).
In this case the equation of continuity in the soil air can be reduced to one spatial dimension, namely dc (z, t) dt + ∂j (z, t) ∂z = Q(z, t) + S(z, t). (1) We further assume that, at any depth in the soil, the only sink process is radioactive decay, which is described by with the decay constant λ( 222 Rn) = 2.0974 × 10 −6 s −1 .The source term Q, i.e. the production rate of 222 Rn gas in the soil, is calculated according to Schüßler (1996) from with ρ b the dry bulk density of the soil (kg m −3 ), c Ra the 226 Ra activity concentration in the soil material (Bq kg −1 ), and ε the 222 Rn emanation coefficient, which is defined as the probability that a 222 Rn atom produced in a soil grain can actually escape into the soil air.
If we consider steady state conditions, i.e. no explicit dependence on time, Eq. (1) simplifies to Taking into account only molecular diffusion of the trace gas in the soil air, we can apply Fick's first law where D e is the effective diffusion coefficient of the trace gas in the soil air (hereafter also named effective diffusivity or simply diffusivity).D e is assumed to be constant with depth.Note that in Eq. (5), j (z) is the flux per unit area of the bulk soil.This is not immediately obvious.In the respective Eq. (1) in Griffiths et al. (2010) and also in Sun et al. (2004), j (z) is multiplied with θ P , the porosity of the soil to yield the flux density per bulk unit area.However, they also use a different expression to calculate the source strength Q in the soil (Eq. 3 in Griffiths et al., 2010) where they divide our Eq.( 3) by θ P .Combining Eqs. ( 4) and (5) yields If we further assume that the 226 Ra activity concentration in the soil particles, the 222 Rn emanation coefficient, and the soil bulk density are constant with depth, we obtain a depthindependent source strength, i.e.Q(z) = Q, and Eq. ( 6) becomes

The 222 Rn soil air profile and its exhalation rate at the soil surface
The general solution of the inhomogeneous differential equation Eq. ( 6a) is where c ∞ is the asymptotic concentration at large depths and z the relaxation depth.
With the boundary conditions of (1) the 222 Rn concentration approaching zero at the soil-air interface and (2) zero concentration gradient, i.e. equilibrium between 222 Rn production and decay, at great depths c(z = 0) = 0 and dc dz (z = ∞) = 0 the solution of Eq. (6a) takes the following form: Introducing solution (7) into the diffusion Eq. ( 5), we can calculate the 222 Rn flux at the soil surface Note that the last term in Eq. ( 8), which allows calculating the 222 Rn flux density per unit bulk surface of the soil from "bottom-up" parameters and the effective diffusivity in the soil, is now identical to Eq. ( 4) in Griffiths et al. (2010).

Approximation of 222 Rn fluxes at sites with shallow water-table depth
The solution of the differential Eq. (6a) given by Eqs. ( 7 the solution of the differential Eq. ( 6) gives the modified flux at the surface according to The solution Eq. ( 8a) has the same form as Eq. ( 8) and for z G z it yields Eq. ( 8).

The role of snow cover and frost on the 222 Rn exhalation rate from continental soils
The role of snow cover on the 222 Rn exhalation rate is not yet fully understood.Robertson (2004) found in her measurements that a layer of snow had no significant influence on the 222 Rn exhalation rate.However, when the top layer of the snow melted and froze again, a smaller 222 Rn exhalation rate was measured.This finding suggests that the physical properties of the snow, such as a thin ice layer on its top, determine the magnitude of the 222 Rn flux.However, most of the studies cited in Robertson (2004) found no or merely a small effect of snow cover on 222 Rn exhalation rate.Thus, although a shielding effect of snow cover has been included in the López-Coto et al. ( 2013) flux map, this effect is not taken into account in our 222 Rn flux estimates.
Another point concerning the 222 Rn exhalation rate in winter months is the influence of frozen soils on 222 Rn exhalation rates.While different authors, e.g.cited by Robertson (2004) report a reduction in 222 Rn flux when the soil was frozen, Robertson (2004) found no evidence for a strong influence of frozen soils on 222 Rn emissions.However, particularly when soil moisture is high or when an ice layer forms on the ground, this might cause a substantial decrease in 222 Rn exhalation rates.Because no systematic analysis of the influence of soil freezing on the 222 Rn flux is available, our standard 222 Rn flux maps do not take into account any positive or negative effect of frozen soil on the exhalation rate.However, we will show one hypothetical scenario of the potential influence of frost on the exhalation rate with reduced fluxes, based on the number of ice days during winter months (Sect.4.3).

Estimating the effective diffusivity from soil properties
From Eq. ( 8) we see that the 222 Rn flux at the soil surface not only depends on the production rate Q in the soil (see Eq. 3), but also on the effective diffusivity D e of 222 Rn in the soil air.Estimating D e in soil air is, however, not a trivial task.This parameter depends mostly on the percentage of soil air volume available for gas diffusion, but also on the grain size distribution of the soil, i.e. its texture.The unit volume of soil consists of the soil material fraction θ m , the fraction that is filled with water θ w , and the air-filled fraction θ a so that The porosity θ p of the soil is defined as Different models were developed in the past to estimate D e depending on soil properties and soil moisture.While the more recent models by Moldrup et al. (1996Moldrup et al. ( , 1999) ) require as input detailed parameters of the soil texture, i.e. percentages of clay, coarse sand, and fine sand, the earlier models by Millington andQuirk (1960, 1961) and also the parameterization reported by Rogers and Nielson (1991) only require information on soil porosity and soil moisture.The latter parameterization by Rogers and Nielson (1991) has been used by Zhuo et al. (2008), Griffiths et al. (2010) and López-Coto et al. (2013) in their 222 Rn flux estimates.However, Jin and Jury (1996) could show that the original estimate of the effective diffusivity according to Millington and Quirk (1960), i.e.
where D a = 1.1 × 10 −5 m 2 s −1 is the diffusion coefficient of radon in air, yields excellent agreement with a large set of available observational data of the effective diffusivity D e for soils with different texture obtained from different studies in the literature (Jin and Jury, 1996, and references therein).Moreover, when comparing diffusivity calculated from the Millington and Quirk (1960) model with that of Moldrup et al. (1996), both agree very well (and for a hydraulic parameter b = 6, which corresponds to a typical soil with about 20 % clay, they yield identical values of D e (see Fig. S1 of the Supplement)).More importantly, when comparing measured 222 Rn profile-based diffusivity values calculated from Eq. (7a) (see Sect. 3, Table 1) with the modelestimated results, we find the best agreement with these two models (Millington and Quirk, 1960;Moldrup et al., 1996).The Rogers and Nielson (1991) model seems to overestimate diffusivity, particularly during dry conditions, and the Moldrup et al. (1999) model largely underestimates the measured diffusivity.Therefore, we decided to use the Millington and Quirk (1960) model (Eq. 11), which is solely based on soil porosity and soil moisture, to estimate effective diffusivity.
The temperature dependence of the diffusivity for the 222 Rn flux map has been estimated according to Schery and Wasiolek (1998): with T the mean soil temperature in Kelvin and D e0 the effective diffusivity at the reference temperature 273 K.  1).The ranges of the soil moisture classes resulted from a roughly equal distribution of all measured soil moistures (in the upper 20 cm of the soil) during the course of 1 year.By fitting a curve according to Eq. ( 7) to the mean profile data, one obtains the parameters z and c ∞ as well as values for the 222 Rn source strength Q and the effective diffusivity D e, exp (Table 1).The values for Q, which should be the same for all three moisture situations (wet, medium, dry), indeed agree rather well (i.e. to within ±25 %).The 222 Rn exhalation rate at the soil surface (j profile ) calculated according to Eq. ( 8) from the parameters fitted to the measured profiles as well as the mean exhalation rates j chamber independently measured using accumulation chambers are also listed in Table 1.They agree within a factor of 2 for all three soil moisture regimes and within 15 % for the annual mean flux.
For comparison with the measured profile-based diffusivity, we can calculate D e with the Millington and Quirk (1960) model D e, MQ from measured porosity (θ p = 0.368) and measured mean soil moistures according to Eq. ( 11).The Table 1.Parameters of the fit curves plotted in Fig. 1, mean exhalation rates estimated from the measured radon concentration profiles (j profile ) and directly measured with flux chambers (j chambers ) at the same site, as well as mean diffusivity as estimated from the experimental data (D e, exp ) from the Millington and Quirk (1960) model (D e, MQ ) and from the Rogers and Nielson (1991)   diffusivity was adjusted to the mean soil temperatures during the measurement dates for wet, medium and dry conditions according to Eq. ( 12).Likewise, we use the Rogers and Nielson (1991)  (7a).These profiles are plotted in Fig. 1 for comparison to the observations.Again the Millington and Quirk model fits the observations better than the Rogers and Nielson model.Hence, we favour the Millington and Quirk (1960) model (i.e. Eq. 11) for estimating moisture-dependent diffusivities for all European soils.

Evaluation of the concept to estimate flux restriction by water-table depth
As mentioned in Sect.2.3, water-table depth can be of huge importance limiting the 222 Rn exhalation when it rises to levels that are of the same order as z.These situations are quite frequent in coastal areas, e.g. of northern Germany or the Netherlands, or in wetland regions.Measurements of co-located 222 Rn exhalation rates and shallow water-table depths are available from a field site in Federovskoye, western Russia (Levin et al., 2002).Thus, we can test the validity of Eq. (8a) and compare the solution with the measurements from the Federovskoye transect measurements from Levin et al. (2002, their Fig. 3).The solid lines in Fig. 2

226 Ra content in the soil
The 226 Ra activity concentration in soils is the governing parameter for the 222 Rn flux at the soil surface.It scales linearly with the exhalation rate.The Geochemical Atlas of Europe (Salminen, 2005) summarises results of a European-wide effort within the FOREGS (Forum of European Geological Surveys) Geochemical Baseline Mapping Programme to provide high quality environmental geochemical baseline data for European stream waters, sediments and soils.Besides many other elements and trace constituents, the uranium content was also measured in regularly distributed topsoil and subsoil samples from 26 European countries.Topsoil samples were collected at 0-25 cm depth (with a potential overlying humus layer being removed), while subsoil samples were collected from another 25 cm layer located between 50 and 200 cm depth.Uranium content was measured on residual soil samples (from the < 2 mm grain fraction, with total organic matter (TOC) being removed from these samples) and is reported in mg uranium per kg residual soil.As total uranium in soil material consists of ca.99 % of 238 U, the values given in the Geochemical Atlas (Salminen, 2005) can be directly transferred into 226 Ra activity concentrations, when assuming secular equilibrium between 238 U and its daughter 226 Ra.The conversion factor from uranium concentration to 238 U activity concentration was taken from IAEA (1989), i.e. 12.35 Bq kg −1 per mg kg −1 uranium.The equally distributed 843 individual topsoil uranium measurements (median ± standard deviation: 2.03 ± 2.35 mg kg −1 ) and the 792 subsoil uranium measure-ments (median ± standard deviation: 2.00 ± 2.34 mg kg −1 ) were interpolated by ordinary kriging (e.g.Wackernagel, 2003) for both layers to the 0.083 • × 0.083 • grid of our map (see Fig. S2 of the Supplement).The resolution of our basic map is restricted in its spatial resolution by that of the global soil texture map of Reynolds et al. (2000), which we used to determine soil texture parameters (see Sect. 4.2).As the uranium content was measured on residual soil samples with total organic carbon being removed, we corrected the activity concentrations for "dilution" with organic carbon, using the TOC data that have also been reported in the Geochemical Atlas of Europe (Salminen, 2005).This correction is small with typical TOC values in topsoil between 0 and 6 % (median ± standard deviation: 1.73 ± 3.18 %) and in subsoil between 0 and 3 % (median ± standard deviation: 0.40 ± 2.86 %).
For calculating the 222 Rn exhalation rates for each pixel, we used the mean values of topsoil and subsoil from the TOC-corrected interpolated 226 Ra activity concentrations (i.e.c Ra of Eq. 3).Assuming a depth-constant c Ra seems to be well justified in view of the very good agreement between topsoil and subsoil uranium concentrations reported in the Geochemical Atlas of Europe (Salminen, 2005).
For those regions of our map, for which the uranium content was not available in the Geochemical Atlas (e.g.Belarus, Ukraine), we estimated the 226 Ra activity concentration based on geological information available from the highresolution global lithological map "GLiM" (Hartmann and Moosdorf, 2012).First, a median 226 Ra activity concentration was computed for each lithological class in GLiM using the measured uranium content at all sampling sites together with co-located GLiM data.The resulting relation was then used to extrapolate the 226 Ra activity concentration map to the regions not covered by the Geochemical Atlas.Due to this very indirect approach, the resulting 222 Rn exhalation rates will have a much higher uncertainty in these regions (hatched area in Fig. S2 of the Supplement).

Distribution of soil types and estimate of emanation coefficients
Soil texture, i.e. the percentages of sand (0.5-2 mm), silt (0.002-0.5 mm) and clay (< 0.002 mm) for our 222 Rn exhalation map have been taken from Reynolds et al. (2000), a soil database that is frequently used in modelling studies of similar problems.Porosity and soil bulk density were computed from soil texture according to Saxton et al. (1986).The data are given at a horizontal resolution of 0.083 • × 0.083 • and for two different depth intervals (from 0-30 cm and from 30-100 cm).Here we use weighted mean values for 0-100 cm depth for all parameters.As has been shown by Zhuo et al. (2006Zhuo et al. ( , 2008)), the emanation coefficient ε, i.e. the likelihood of a newly formed 222 Rn atom to escape the grain and reach the air-filled soil volume, depends on the soil type and on soil moisture.The soil moisture depen-dency is, however, only relevant at very small moisture content below 15 % water saturation (i.e. at θ w < 0.06 for a typical porosity of θ p = 0.4).Outside this range ε was shown to be largely constant (Zhuo et al., 2006).For simplicity and because water contents below 15 % saturation are very rare in European soils, we used constant (saturation) values for each texture class.We also neglected the temperature dependence of ε, as it changes by only a few percent within a temperature range of 0-20 • C (Iskandar et al., 2004).The numbers to calculate ε sat for sand, silt, and clay are given in Zhuo et al. (2008) in their Table 2.The values must, however, be exchanged, as was noted by Griffiths et al. (2010) and confirmed by W. Zhuo (personal communication, 2013).From this we estimated ε sat = 0.285 for sand, ε sat = 0.382 for silt, and ε sat = 0.455 for clay.These numbers are well in accordance with emanation coefficients determined by Schüßler (1996) from measured 222 Rn profiles and known 226 Ra contents in different soils of the surroundings of Heidelberg (M1-M5, see Sect.5.3 and Table 2).We used weighted mean values for the different texture classes to estimate the emanation coefficients for each pixel of our map.

Determination of variable soil parameters: soil
moisture, temperature, and frost influence

Soil moisture
Soil moisture has a strong impact on the effective diffusivity D e of the soil.Its high temporal and spatial variability makes it a crucial parameter for determining the 222 Rn exhalation rate at individual sites.As is illustrated in Fig. 1 and listed in Table 1, the measured mean 222 Rn flux from the loamy soil at the IUP sampling site changes by about a factor of 6 between wet (θ w ≈ 0.31) and dry (θ w ≈ 0.12) conditions.Systematic European-wide soil moisture measurements are still limited.Only few long-term in situ monitoring stations exist.Satellite-derived soil moisture, although providing relatively good spatial coverage, is only representative for the uppermost centimetres of the soil and hence not suited for our approach.Therefore, we use here soil moisture data simulated by soil models driven by numerical weather prediction models; i.e. these models have been specifically assimilated to determine soil moisture.Two estimates that provide data at high temporal resolution (3 or 6 h) have been used.
(1) Simulations were used from the Land Surface Model Noah (driven by NCEP-GDAS meteorological reanalysis), which are part of the Global Land Data Assimilation System GLDAS (Rodell et al., 2004).The spatial resolution of these estimates is 0.25 • × 0.25 • with depth intervals of 0-10, 10-40, 40-100, and 100-200 cm; data for the period of 2006-2012 were used.(2) Simulations from the ERA-Interim/Land reanalysis using the latest version of the ECMWF land surface model driven by ERA-Interim atmospheric reanalysis (Balsamo et al., 2015) were applied as alternative soil mois-ture model.From this model we used a data set with a horizontal resolution of 0.75 • × 0.75 • ; it has a depth resolution with simulated values for 0-7, 7-28, 28-100 and 100-289 cm and is available until 2010.From both soil moisture models, we calculated vertical means from 0-100 cm depth to cover the same depth interval as the other input parameters.Note that with a relaxation depth of the 222 Rn activity concentration profile in the soil of typically 20-100 cm (Table 1), soil parameters of the first 100 cm of the soil are most relevant to describe diffusive transport and the related flux at the soil surface.We further assume here that all parameters do not change with depth and are valid also below 100 cm.
Both soil moisture data sets were compared to observations from the International Soil Moisture Network (ISMN; http://ismn.geo.tuwien.ac.at/;Dorigo et al., 2011, and references therein).In addition, data from two German sites, Grenzhof near Heidelberg (Wollschläger et al., 2009) and Gebesee, located in north-eastern Germany (O.Kolle, personal communication, 2013), as well as soil moisture data from Binningen, Switzerland (Szegvary et al., 2007b) were used for comparison (see also Fig. 7).Soil moisture contents of the second and third model layer (10-40 and 40-100 cm for GLDAS Noah, 7-28 and 28-100 cm for ERA-I/L) were compared to measurements at corresponding depths.This preliminary model-observation comparison at European sites yielded an overall mean bias in volumetric soil moisture of GLDAS Noah observations = −0.01m 3 m −3 (relative bias = −5 %), while the bias between ERA-I/L and observations is +0.07 m 3 m −3 (relative bias = +32 %).This underlines that soil moisture simulated by land surface models is a highly model-specific quantity, which often represents the time variations much better than the absolute magnitude (Koster et al., 2009).The tendency of ERA-I/L to estimate relatively high soil moisture is also confirmed by the study of Balsamo et al. (2015), who found an overestimation of surface soil moisture at the European ISMN sites.

Spatial resolution and adjustment of soil moisture estimates to grid/pixel porosities
Soil moisture estimates are only available at lower spatial resolution than the other (constant) soil parameters described above.In order to apply internally consistent data sets for the flux estimates, based on the two different soil moisture models, we use the porosities originally applied in the respective land surface model to calculate effective diffusivity according to Eq. ( 11).Consequently, the different flux maps shown in Figs. 3 and 4 have different spatial resolutions.For flux estimates at higher spatial resolution, i.e. 0.083 • × 0.083 • , it will be necessary to make an adjustment of the modelestimated soil moisture (θ w(model) ) to the porosity of the pixel (θ p(pixel) ) to make sure the same free pore space is available for diffusion according to In Eq. ( 13) θ w(pixel) is the adjusted soil moisture, and θ p(model) is the original porosity used in the soil moisture model.However, in the present paper, we do not show any flux estimates at higher resolution than given by the soil moisture model estimates, but Eq. ( 13) is used here to adjust modelled soil moisture to the porosities measured at M1-M5 shown in Sect.5.3 and Fig. 6.

Soil temperature
Soil temperature estimates are available from both soil models that provide soil moisture for the different depths.For respective flux estimates, we thus used these values to calculate the temperature dependence of diffusivity according to Eq. ( 12).1), M1-M5 close to Heidelberg as well as Gebesee, northern Germany, and Gif-sur-Yvette, France.For M1-M5, the percentage of clay, silt, and sand have been estimated from the soil type description of Schüßler (1996), according to mean percentages reported by Cosby et al. (1984, Table 2); the 226 Ra activity concentrations have been reported by Schüßler (1996).For IUP, Gebesee and Gif-sur-Yvette, these parameters were measured by Schwingshackl (2013).For comparison with measurements, we also list the data for the respective pixels from the high-resolution map of soil parameters ("pixel") (ε: emanation coefficient, θ p : soil porosity, ρ b : dry bulk density).

Site
Location

Frost
While the reduction of the 222 Rn exhalation rate through snow cover is assumed as only minor according to Robertson (2004), the influence of frozen soil on the 222 Rn flux may not always be negligible.In order to test its potential impact, we introduced a restriction of the exhalation rate based on atmospheric temperature.A very simple parameterization was used here for comparison with our standard estimates without frost restriction: For each month we have summed up the number of days with maximum air temperature below 0 • C (ice days) and then reduced, for these days, the 222 Rn exhalation rate by 50 %.The monthly mean exhalation rate was then calculated as the weighted mean for all days during this month with and without frost.With this parameterization, we implicitly include also some potential effect of snow cover that may be present during ice days.The effect of frost restriction on the flux, compared to our standard estimates where no frost restriction is assumed, is shown in Fig. S3 in the Supplement.

Water-table depth
As in the case of soil moisture, systematic European-wide measurements of water-table depth that could be used as input for our 222 Rn exhalation map are not existing.Hence, we use data from a hydrological model simulation by Miguez-Macho et al. (2008).Supplementary Fig. S4 shows the influence of low water- For both soil moisture models, we find in many regions seasonal differences of the fluxes that are as large as a factor of 2. As mentioned before, these differences originate from the large changes of soil moisture and thus soil diffusivity between the drier summer and the, in general, wetter winter conditions.The frequency distribution of 222 Rn fluxes, displayed in the lower part of Fig. 3, is most confined during winter (January 2006) and when calculated with the ERA-Interim/Land soil moisture data; these fluxes also show a low median value of only 5.83 mBq m −2 s −1 (interquartile range (IQR) = 5.38 mBq m −2 s −1 ).This is about half of the median flux estimated with the GLDAS Noah soil moisture data set for January 2006 (12.08 mBq m −2 s −1 ).During summer (July 2006), both frequency distributions of fluxes are broader than during winter (IQR: ERA-I/L = 8.39 mBq m −2 s −1 and GLDAS Noah = 11.47 mBq m −2 s −1 ).The median values are much larger than in January 2006, i.e. in the case of the ERA-I/L soil moisture being more than a factor of 2 larger, while the difference of the medians in July 2006 between the two maps is much smaller than in winter (only about 30 %).
As both maps use the same 226 Ra distribution and also the same 222 Rn emanation coefficient (i.e. the same 222 Rn source term), differences of 222 Rn flux of the two maps are solely due to the differences of diffusivity, which we calculate from modelled soil moisture using the individual soil porosity data from the two models (according to Eq. 11).The right panels in Fig. 3 show the flux differences between the two maps for January and July 2006.In fact, the differences of fluxes between the two maps are not homogeneous all over Europe, but they show a distinct north to south gradient.While fluxes estimated with ERA-I/L soil moisture for January 2006 are slightly higher than those estimated based on GLDAS Noah in Sweden, Denmark and some parts of northern Germany and Poland, they are much smaller than GLDAS-Noah-based fluxes in central and southern Europe.The differences in soil porosity in the two models are only small (i.e.ERA-I/L uses about 10 % smaller porosity in northern than in central Europe, while porosity is pretty homogeneous all over Europe in GLDAS Noah and similar to ERA-I/L in central Europe) but very distinct differences are found in the soil moisture distributions.Soil moisture is much lower in the GLDAS Noah model estimates for central and southern Europe than in ERA-I/L.Only in some areas of Scandinavia and the northern coasts of central Europe, ERA-I/L estimates lower soil moisture than GLDAS Noah.This directly translates into higher 222 Rn fluxes in the mentioned regions of Scandinavia.
The mean 222 Rn flux for the period 2006-2010 is estimated to be 10 mBq m −2 s −1 (ERA I/L soil moisture) or 15 mBq m −2 s −1 (GLDAS Noah soil moisture) with mean seasonal variations ranging from 7 mBq m −2 s −1 in Febru-ary to 14 mBq m −2 s −1 in August (ERA I/L soil moisture) and from 11 mBq m −2 s −1 in March to 20 mBq m −2 s −1 in August (GLDAS Noah soil moisture).
The huge differences between the estimates with different soil moisture input data emphasize the importance of direct comparison of our process-based 222 Rn flux estimates with measured fluxes, in order to find out, which soil moisture model would better fit real ambient conditions.This comparison is shown below in Sect.5.4 and 5.5.(Szegvary et al., 2009;López-Coto et al., 2013).The upper four panels show the geographical distributions, while the lower four panels display the normalized frequency distributions of annual means from all pixels of the four maps.might, at least to some extent, be caused by the reduction of 222 Rn fluxes in snow-covered regions, which is included in the flux map of López-Coto et al. (2013) but not in our standard estimates.Including a restriction during frozen soil conditions in our flux estimates (orange and cyan lines in  2009) map has lower spatial resolution and less pronounced hotspots of exhalation rates, but the median of its annual mean exhalation rates lies between our GLDAS-Noah-and ERA-I/L-based estimates.However, as Szegvary et al. (2009) used γ -dose rate observations and an empirical correlation with measured 222 Rn fluxes, their fluxes are significantly different in certain areas of Europe.In particular, the pronounced maximum in the French Massif Central, where high 238 U concentrations are measured in the soils (Fig. S2), is only slightly visible in the Szegvary et al. (2009) map.A detailed picture of the differences between our maps and the Szegvary et al. (2009) estimate for 2006 is shown in the Supplement (Fig. S5).Largest differences are seen in central Europe, where our GLDAS-Noahbased estimates are in many places larger than the Szegvary et al. (2009) estimates by a factor of 2, while ERA-I/L-based estimates are often about 50 % smaller compared to the Szegvary et al. (2009) estimates.In northern Scandinavia our two estimates are higher than the Szegvary et al. (2009) map.The reason might be the shielding effect of snow cover on the observed γ -dose rate (Szegvary et al., 2007a).Including the frost restriction in our flux estimates reduces the difference of the annual mean in this region but leads to values lower than in the Szegvary et al. (2009) map in southern Scandinavia (Fig. 5).Millington and Quirk (1960).Soil moisture climatology is taken either from the GLDAS Noah LSM (red lines) or from the ERA-Interim/Land model (blue lines) for the respective pixels, averaged over the period of 2006-2010.Note that the monthly soil moisture values have been adjusted according to Eq. ( 13), i.e. taking into account the actual porosity at the measurement sites (see text).

Representativeness of local observations to validate the 222 Rn flux maps
A large number of systematic direct 222 Rn flux measurements using the accumulation chamber technique were carried out in the 1980s and 1990s at five sampling sites south of Heidelberg, Germany.Dörr and Münnich (1990) started these measurements in 1984 at a sandy soil site (M1) as well as at a clay-loam soil site (M4).Schüßler (1996), who sampled additional sites close to the earlier plots from Dörr and Münnich (1990), continued measurements on these plots.The soil parameters of the five sampling sites M1-M5 are listed in Table 2.For these sites we estimated the percentages of clay, silt, and sand according to Cosby et al. (1984, Table 2) from the soil type descriptions given by Schüßler (1996).The soil properties of other IUP sampling sites studied by Schell (2004;Gebesee), Schmithüsen (2012;IUP) and Schwingshackl (2013;Gif-sur-Yvette (Gif)) at locations in Germany and France are also listed in Table 2.
In addition, the soil parameter values of the 0.083 • × 0.083 • pixels from the high-resolution soil parameter map, in which the measurement sites are located, are listed.From comparison, we can assess the representativeness of the measurement sites for their corresponding pixel of the map.While the Sandhausen sites M1-M3 are not at all representative for the corresponding map pixel, the soil texture and 226 Ra activity concentration of the loamy sites M4 and M5 as well as the IUP site, discussed already above (Sect.3.1), are well comparable with the map pixel.The latter are thus suitable for validation of our maps and the transport model approach.For Gebesee in northern Germany, actual site parameters agree well with the soil parameters of the map.Only the 226 Ra content is about 20 % lower in the map than measured by Schwingshackl (2013).Contrary, for Gif-sur-Yvette in France porosity, bulk density and 226 Ra activity concentration are significantly different from the pixel values.This should be kept in mind when comparing our process-based maps with these observations.
Figure 6 shows the climatology of the monthly mean 222 Rn exhalation rates measured at the Heidelberg M1-M5 stations over the periods of 1987-1995 (M1, M2, M4) and 1987-1998 (M3, M5).Jutzi ( 2001) calculated these averages from the individual data of regular 1-2-weekly flux measurements reported by Schüßler (1996).The strong dependency of the mean exhalation rate on soil type is clearly visible.The clay or loamy soils (M4 and M5) show the highest fluxes with significant seasonal variations of the exhalation rate with up to a factor of 2 larger values in July/August compared to January/February.In contrast, the seasonality at M1 and M3 is only very weak, and fluxes at the sandy sites (M1-M3) are about 3 times lower than at M4 and M5.
Figure 6 also shows calculated exhalation rates (according to Eq. 8) based on the measured soil parameters listed in Table 2 and the climatology of soil moisture for the Heidelberg pixel as calculated from the two soil moisture models for the years 2006-2010.Note that for these process-based calculations the GLDAS Noah model used a porosity of θ p = 0.434 in the map pixels while the ERA-Interim/Land model used θ p = 0.439, i.e. both significantly different from measured porosities, in particular at the sites with sandy soils (M1 and M3, Table 2).For our calculations, we thus individually adjusted the soil moistures for all sites M1-M5 according to Eq. ( 13) to better approximate the pore volumes available for diffusion at the different sites.With these adjustments, the flux estimates based on GLDAS Noah soil moisture agree very well with observations for the sites M1-M3, but are about 30 % too high for the stations M4 and M5.When using modelled ERA-I/L soil moisture data, estimated mean seasonal 222 Rn fluxes are always lower than observations, by up to a factor of 3 at M1 and M3 and by about a factor of 2 at the loamy and clay sites M2, M4, and M5.Without adjustment of modelled soil moisture to the site porosities, for all sites and both soil moisture estimates, modelled 222 Rn fluxes would be up to a factor of 6 too low (results not shown in Fig. 6).From this comparison of process-based estimates with long-term observations, we can conclude that (1) the agreement between estimates and observations strongly depends on the validity of soil texture parameters used in the map; (2) modelled soil moisture values need to be adjusted to the local porosity according to Eq. ( 13), if reliable flux estimates shall be calculated; (3) in the Heidelberg pixels associated to M1-M5, GLDAS-Noah-based 222 Rn flux estimates agree rather well with existing observations, while ERA-I/Lbased estimates largely underestimate fluxes at all sites.This comparison also emphasizes that quantitative validation of our 222 Rn exhalation map can be misleading, if information on soil properties is missing at the measurement sites.

Comparison of model-based 222 Rn flux estimates with measured time series and other flux maps
As demonstrated in the previous section, proper validation of our 222 Rn flux estimates requires comparison with direct measurements carried out on soils representative for the respective pixel of the map.However, systematic 222 Rn flux measurements in Europe are very sparse so that we include in this section all sites (except for M1-M4 that have already been discussed before, see Sect.5.3), which have observations available to us over the course of at least 4 months.If the dotted red and blue lines can be distinguished, they show the effect of shallow water-table depth.Fluxes that are not restricted by the water table, contrary to those that are restricted, are then visible as dotted (red and blue) lines (relevant at Lutjewad and Gebesee where the water table is less than 2 m below the soil surface); otherwise, the solid and dotted lines fall onto each other.Figure 7 also shows the soil moisture estimates calculated by the two land surface models as well as direct soil moisture measurements in different depths, if available.
For most sites shown here, the ERA-Interim/Land-based 222 Rn fluxes (plotted in blue and cyan) are significantly lower (often by more than a factor of 2) than those estimated with the GLDAS Noah soil moisture data (plotted in red and orange).Accordingly, ERA-I/L soil moisture estimates are significantly higher than those estimated by GLDAS Noah at these sites; note that porosities do not differ very much in between models at these sites, with a maximum difference of 6 % at Gebesee.similar despite the high soil moisture in ERA-I/L; here also the porosity in the ERA-I/L model is by almost a factor of 2 higher than in GLDAS Noah.At all sites except for Gif-sur-Yvette and Lutjewad, ERA-I/L-based fluxes are significantly lower than observed fluxes.At Pallas station in northern Finland, no direct 222 Rn flux measurements are available.For this reason, we use flux estimates derived from summer observations in the atmosphere and atmospheric transport modelling (Lallo et al., 2009).For this time of the year, the GLDAS-Noah-based 222 Rn flux results compare best with the data.For the winter months, López-Coto et al. (2013) predict very low fluxes at Pallas, and here the effect of frost restriction on GLDAS-Noahand ERA-I/L-based estimates becomes visible (difference between red and orange as well as blue and cyan lines, respectively, in Fig. 7a).
A station with very shallow water table is Lutjewad, located at the Netherland's North Sea coast.Not taking into account ground water table restriction in the modelled 222 Rn exhalation rate (dotted lines in Fig. 7b) would largely overestimate the flux in both approaches by more than a factor of 4.Here the Szegvary et al. (2009) and the López-Coto et al. ( 2013) models overestimate observed fluxes by more than a factor of 2-3.Taking into account the restriction due to the shallow water table brings the modelled 222 Rn exhalation rate closer to the observations but also reduces the amplitude of the seasonal variations.Note that ERA-I/L-based and GLDAS-Noah-based fluxes are almost identical under water table restriction and therefore hardly distinguishable in Fig. 7b.
At Gebesee, co-located soil moisture measurements are available.They agree very well with the GLDAS-Noahbased model estimates (Fig. 7c); further, GLDAS-Noahbased 222 Rn fluxes fit the observations very well.Here again, the water-table depth flux restriction turns out to be important.Estimated GLDAS-Noah-based fluxes not restricted by water-table depth are significantly higher in early summer than observed fluxes (dotted red line in Fig. 7c), but those restricted by water table agree, on average, well with observations.At the end of the summer, local water-table depth may be deeper than in winter and spring, which is why observations then seem to fall on the unrestricted GLDAS-Noahbased model estimates.
As has been indicated already in Fig. 6, the GLDAS-Noahbased estimates for M5-Nußloch are slightly higher than observations, while the ERA-I/L-based estimates underestimate the observations by about a factor of 2 (Fig. 7d).Note, however, that in the current comparison, contrary to the results shown in Fig. 6, we use for both modelled fluxes all parameters, including 226 Ra activity concentration and soil porosity, from our map and not from observations.Although absolute fluxes are not perfectly reproduced, both of our models seem to capture the seasonal amplitude of observations much better than estimates by Szegvary et al. (2009) and López-Coto et al. (2013) models.The good agreement between GLDAS-Noah-based and observed 222 Rn fluxes at M5 is accompanied by good agreement of GLDAS-Noah-modelled soil moisture and respective observations.Soil moisture data plotted for M5 do not exactly stem from the M5 site but are taken from a soil monitoring station north of Heidelberg at Grenzhof (Wollschläger et al., 2009).Modelled soil moistures as well as soil properties in the grid cells corresponding to the location of M5 and Grenzhof are identical in GLDAS Noah and very similar in ERA-I/L.
At Gif-sur-Yvette, all models except for GLDAS Noah seem to reproduce well at least the annual mean observed fluxes (Fig. 7e).However, the seasonal amplitude seems to be best captured by the ERA-I/L-based and the GLDAS-Noahbased estimates, whereas the Szegvary et al. (2009) 2).From this difference alone, we would expect an underestimation of Gif-sur-Yvette flux observations by both of our flux estimates.On the other hand, the shallow water table at the measurement site (Campoy et al., 2013) might restrict the 222 Rn fluxes.This situation is not represented in our maps, where the water table is well below 10 m in this region.
At Binningen, Switzerland, which is the measurement station that Szegvary et al. (2009)  In summary, we conclude that at three out of six stations the (generally higher) GLDAS Noah soil-moisturebased 222 Rn exhalation rates are in good agreement with observations.At two of these sites, where we have data available, this correlates with good agreement of modelcalculated and observed soil moisture.Flux estimates based on ERA-Interim/Land soil moistures have the tendency to underestimate observed fluxes and only fit well at one of our comparison sites (Gif-sur-Yvette).The two published maps, in particular that developed by López-Coto et al. (2013), generally underestimate measured fluxes with the exception of the coastal site Lutjewad.There the shallow water-table depth is not taken into account in these models, which leads to large over-estimation.Concerning the seasonal amplitude of fluxes, the GLDAS-Noah-based estimates as well as those based on ERA-I/L soil moisture are in most cases very well in line with observations.Contrary, Szegvary et al. (2009) 2013) may be due to the use of an overly low emanation coefficient in their estimates.Based on available observations, the effect of frozen soils cannot be evaluated.However, restriction due to shallow water table turns out to be important, not only at the coastal site Lutjewad, but potentially also in river plains such as in the surroundings of the Gebesee site.S1).
order to better judge at least the reliability of the Europeanwide flux estimates, we have compiled here all published 222 Rn flux measurements available to us, even if they are only based on episodic field campaigns (see Table S1 in the Supplement).Larger short-term data sets from a single site have been averaged to monthly values and included in our modeldata comparison in ).This is in accordance with the earlier comparison based on the more systematic long-term results at fewer stations, discussed in Sect.5.4 and gives a strong hint that the GLDAS-Noah-based estimates on average provide the more accurate flux estimates than those based on ERA-I/L-soil moisture, which seem to be systematically too low.However, since IQR values of radon flux differences are large for both soil moisture models, a definitive decision, which soil moisture model to use is not yet possible.
The large IQR values are most probably caused by the nonrepresentativeness of many of our observations for the entire pixel and due to very similar uncertainties in the bottom-up information used for both flux estimates (see also Sect.5.6).

Soil moisture
Temporal and spatial variations of soil moisture have a huge influence on the effective diffusivity in the soil and thus on the 222 Rn exhalation rate.This can clearly be seen when comparing the GLDAS-Noah-based and the ERA-I/L-based 222 Rn flux maps.Using our observations at the Heidelberg IUP site we find that the diffusivity differences during dry and wet conditions are as large as a factor of 20, leading to differences in the fluxes up to a factor of 7 (Table 1).
When comparing model-estimated soil moisture values with respective observations it is not per se clear, if one or the other soil moisture model would generally provide more realistic values (see Fig. 7).Comparison of 222 Rn flux map results with point observations does also not always favour one soil moisture model.However, on average over Europe, annual mean fluxes are better reproduced with the GLDAS-Noah-based model.On the other hand, both models capture the seasonal amplitude of the fluxes very well.The same is true for the seasonal amplitudes of the soil moisture estimated by both models.And, most important, in cases where the soil moisture at a station is correctly captured by one of the models, we also find good agreement between the modelled and measured 222 Rn fluxes (e.g.GLDAS Noah at Gebesee and M5/Grenzhof).This underlines the importance of realistic soil moisture data for 222 Rn exhalation modelling.
With currently available and frequently used soil moisture models, biases in the mean European 222 Rn flux of 50 % can be introduced.

Diffusivity model
Even if we had good estimates of soil moisture, we need to keep in mind that the Millington-Quirk (1960) model used in this study does not necessarily describe effective diffusivity in the unsaturated soil zone correctly.Comparison of model-based diffusivity with diffusivity estimated from observed 222 Rn soil profiles (Fig. 1) shows differences as large as a factor of 2 at medium dry conditions.This may translate into differences of the fluxes of up to 40 % during these conditions.Therefore, also shortcomings in the parameterization of diffusivity may considerably contribute to the uncertainty of the 222 Rn flux.However, using different parameterizations as, e.g. that of Rogers and Nielson (1991), as done by Griffiths et al. (2010) and López-Coto et al. (2013), does not improve the situation (see Table 1).We estimate mean uncertainty of 222 Rn fluxes to be on the order of 30 % due to our choice of the diffusivity model.

226 Ra content
An important parameter determining the 222 Rn flux from soils is the 226 Ra content.In our study we have used an interpolated 238 U distribution based on systematic measurements published in the European Geochemical Atlas (Salminen, 2005).Uncertainties in the soil sample analysis (Sandström et al., 2005) and in the interpolation are both less than 10 %.From the interpolated 238 U distribution, we estimated 226 Ra activity concentration by assuming secular equilibrium between 238 U and its daughter 226 Ra.This assumption may not always be fulfilled at all sites due to preferential leaching of 234 U from the soil grains, so that our 238 U-based equilibrium estimate of 226 Ra must be seen as an upper limit of the true 226 Ra values.However, when comparing the 226 Ra values from the map with point measurements made at IUP Heidelberg, we find satisfactory agreement if other soil parameters, such as texture and bulk density, are similar, i.e. if the point measurement is representative for the pixel (data not shown).An example of obvious differences between the soil characteristics of our measurement site and the pixel of the map is Gif-sur-Yvette, France.Here we observe a factor of 2 higher 226 Ra activity concentration in our measurement than assumed for the map pixel, but also bulk density and porosity show a large difference.Therefore, the average uncertainty of our interpolated 226 Ra activity concentration data is most probably less than 15 %.

Emanation coefficient
Besides the 226 Ra activity concentration in the bulk soil material, the emanation coefficient is an essential parameter for correctly estimating the 222 Rn exhalation rate.Only few measurements of the emanation coefficients for different soil types and environmental conditions exist and reported values span a wide range of 0.05 to 0.7 (Nazaroff, 1992).The emanation coefficient estimates of our study compare well with the observation-based estimates by Schüßler (1996) around the Heidelberg site.The averaged value used in our study (0.35) is, however, 75 % higher than the constant emanation coefficient of 0.  2013) model at most sites indicates that an emanation coefficient of 0.2 is probably too small.More measurements of emanation coefficients and their dependence on soil texture would be helpful to reduce the uncertainty in this parameter.Still, the uncertainty of our assumption of the texture-specific emanation coefficient as used for our maps is probably smaller than 20 %.

Constancy of transport parameters with depth
One basic assumption in our estimate is homogeneity of soil parameters with depth up to 1m.While the differences of 238 U in the European Geochemical Atlas between upper and lower soil layers are only minor, other soil parameters such as porosity and texture may not be as homogeneous with depth.Porosity derived from the Reynolds et al. (2000) soil texture data set differs by ca. 3 % between the two soil layers, but this presumably underestimates vertical variability.The largest vertical inhomogeneity is most probably that of soil moisture.During summer months, at one of our sampling sites we observed that soil moisture differs by a factor of 2 between 30 and 90 cm depths (see Fig. 7 for M5 Nußloch).However, the differences between the two soil models, GLDAS Noah and ERA-I/L can be even larger.Therefore, with the current reliability of soil moisture input data from the models, our simplification assuming homogeneous parameters throughout the unsaturated soil seems justified.In any case, except for dry summer conditions, more than three-quarters of the total 222 Rn flux at the soil surface originate from the upper 50 cm of the soil; one should thus make sure that all parameters in this upper layer are determined to be as reliable as possible.

Soil texture
For consistency, we use in our European 222 Rn flux estimations the same porosity as applied in the soil moisture simulations of the respective land surface model.In both models, the soil properties were derived from the FAO Digital Soil Map of the World (FAO DSMW), though from different versions (Reynolds et al., 2000;FAO, 2003) As discussed above, the two largest uncertainties stem from the uncertainty to determine effective diffusivity based on soil texture/porosity and soil moisture (ca.30 %).The uncertainty contribution of modelled soil moisture is probably also of the order of 30 %, while the emanation coefficient is assumed to be known to about 25 %.Other parameters are uncertain to about 10-15 % on the pixel scale.Altogether, we therefore estimate the uncertainty of modelled fluxes for individual pixels to about 50 %.In atmospheric applications, footprints are often covering several pixels and the relatively large uncertainty on the pixel scale may be reduced through averaging.At this larger multi-pixel scale, the uncertainty of our 222 Rn fluxes is probably smaller than 20-30 %.Inspecting now our comparison between single measurements and modelled flux for the respective pixel (Fig. 8), the IQR of the differences were on the order of 11 mBq m −2 s −2 or about 70-100 % of the mean flux, depending on the soil moisture model.Standard deviations of these distributions are slightly larger than IQRs, in our case about 100 %.With an estimated uncertainty of the modelled flux of about 50 %, this would imply that the contribution from nonrepresentativeness and uncertainty of the measurements to the scatter is larger than 80 %.This emphasises the importance of auxiliary measurements of soil properties that need to be performed in future 222 Rn flux measurement campaigns if these data shall be useful for evaluation of bottom-up flux estimates.

Conclusions and perspectives
A high-resolution 222 Rn flux map for Europe was developed, based on a parameterization of 222 Rn production and transport in the soil.The approach includes a well-established parameterization of soil diffusivity (Millington and Quirk, 1960) and makes use of existing high-resolution data sets of soil properties, uranium content, model-derived soil moisture as well as model-derived water-table depth.Comparisons with direct 222 Rn flux measurements in different re-gions of Europe show that the observed seasonality is realistically reproduced by our approach, which was not achieved by earlier studies for Europe, and confirms the validity of estimating diffusivity in soil air based on the Millington and Quirk (1960)  15 mBq m −2 s −1 ), the ERA-I/L-based model underestimates mean fluxes by more than 60 %.The variability of modelmeasurement differences is, however, large for both maps.Besides model uncertainties, which are estimated to contribute about 50 % to the scatter of the differences, limited representativeness of single point measurements for the entire pixel of the map contributes most.
The spatial resolution of the soil moisture models used here restricts spatial resolution of the two realizations of our European 222 Rn exhalation map.In many applications, such as the Radon Tracer Method (e.g.Levin et al., 1999), local estimates of 222 Rn fluxes would also be useful.In such cases, our theoretical approach could easily be applied, e.g. by using local soil texture information and measured soil moisture data, which become more and more available at ecosystem sites in Europe or elsewhere (e.g.FLUXNET, Baldocchi et al., 2001).Also, in our study we restricted the temporal resolution to 1 month because (quasi-) continuous 222 Rn flux measurements were not available to us for comparison.However, extension of the temporal resolution to that of the soil moisture models (sub-daily) would be easily achievable.
Validation of our estimated 222 Rn fluxes was restricted in our study to relatively few not evenly distributed observational sites, most of them located in central Europe.Many climate zones and soil types such as subarctic regions, wetlands and dry areas of Europe, could not be validated with observations.This includes quantification of the influence of snow cover or frozen soils.Hence, additional systematic 222 Rn flux measurements that are accompanied with ancillary data of soil properties and soil moisture would facilitate and improve validation of the presented maps or may allow more reliable parameterizations, particularly for special regions and climatic situations.
It would also be interesting to apply our approach to other areas of the world, which would allow for comparison with maps developed for areas outside of Europe, using different methodologies, e.g. of diffusivity estimation.We decided to leave this effort to future work, also because of nonavailability of a systematic 238 U or 226 Ra survey in a number of important regions and continents of the world (e.g.Russia, the Americas, and Africa).Empirical correlations between 226 Ra activity concentrations and other soil parameters turned out to be only weak and do not allow for accurate evaluations of the 222 Rn source in these regions.
The presented 222 Rn flux maps for Europe are freely available, e.g. for atmospheric transport model evaluations or comparable studies.Feedback from such investigations that also integrate atmospheric observations could help to improve our flux map, e.g. during afternoon when atmospheric model transport is more reliable.
Although we currently favour the GLDAS-Noah-based 222 Rn flux estimates for Europe, we emphasise that in cases when soil moisture data or reliable model estimates are directly available in the transport model (as could be the case in most online transport models) our approach could also be applied using these measured or model-generated soil moistures.This may improve local or regional 222 Rn flux estimates.
Digital versions of the maps are available at doi:10.1594/PANGAEA.854715.
The Supplement related to this article is available online at doi:10.5194/acp-15-12845-2015-supplement.

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Karstens et al.: A process-based 222 radon flux map for Europe

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Figure 3. 222 Rn exhalation rate maps of European soils, their differences and frequency distributions for January and July 2006.The left panels show the flux maps and normalized frequency distributions calculated with the monthly mean soil moisture estimates from the GLDAS Noah LSM for January and July 2006, while the middle panels show respective estimates with the ERA-Interim/Land model.The mean values, median values and the interquartile range (IQR) of the normalized frequency distributions of January and July 2006 fluxes (in mBq m −2 s −1 ) are also given.The right panels show the differences between GLDAS-Noah-and ERA-Interim/Land-based fluxes.
222 Rn fluxes with those from other published maps Before comparing with observations at individual sites, we compare the distribution of annual mean fluxes calculated here based on the two soil moisture models for 2006-2010 with the other published European maps of Szegvary et al. (2009) for 2006 and of López-Coto et al. (2013).The latter is shown as climatology for the years 1957-2002.The maps and normalized frequency distributions are displayed in Fig. 4. Zonal averages of 1 • latitudinal bands are compared in Fig. 5.The general shape with higher 222 Rn exhalation rates in regions of high 238 U activity concentrations (e.g., on the Iberian Peninsula) is similar in all four maps.The difference between GLDAS-Noah-and ERA-I/L-based fluxes, with generally higher fluxes estimated based on the GLDAS Noah soil moisture model (except for some areas in northern Europe), was discussed before for January and July 2006 (Fig. 3) and is also visible in annual mean flux estimates.The annual median values for the 2006-2010 period differ by more than 50 % (Fig. 4, lower four panels).There is relatively good agreement in the spatial pattern, in the annual medians and IQRs between the ERA-I/L and the López-Coto et al. (2013) map.This is because the basis of the López-Coto et al. (2013) map is also the 238 U distribution from the Geochemical Atlas of Europe(Salminen, 2005), and López-Coto et al. (2013) use a similar process-based soil transport model as described here, but the parameterization for diffusivity developed byRogers and Nielson (1991).Soil moisture estimates in López-Coto et al. (2013) are from ERA-40 reanalyses, which are based on an earlier version of the land surface model than used in ERA-I/L.Soil moistures in ERA-40 show an overall smaller variability than the ERA-I/L model estimates(Balsamo et al., 2015) used in our study (compare also Sect.5.4, which discusses time profiles in comparison to observations).The maps of differences between our study and theLópez-Coto et al. (2013) climatology are displayed in Fig. S5 in the Supplement.While our GLDAS-Noah-based estimates are higher than López-Coto et al. (2013) throughout Europe (with the exception of northern Ireland and a few areas in Italy) the higher fluxes of our ERA-I/L-based estimates compared to López-Coto et al. (2013) are most prominent in Scandinavia.Differences in annual mean 222 Rn fluxes between these two maps are small in central Europe.The difference in annual fluxes in regions north of 60 • N (Fig. 5)

Figure 4 .
Figure 4. Annual mean 222 Rn exhalation rates for 2006-2010 from this study in comparison with published maps(Szegvary et al., 2009;López-Coto et al., 2013).The upper four panels show the geographical distributions, while the lower four panels display the normalized frequency distributions of annual means from all pixels of the four maps.

Fig. 5 )Figure 5 .
Fig.5) reduces the difference of the annual mean in this region, but they are still more than 50 % higher thanLópez- Coto et al. (2013).However, it is important to keep in mind that López-Coto et al. (2013) use a ca.40 % smaller emanation coefficient of 0.2 for all soils, compared to a median

Figure 6 .
Figure 6.Comparison of the observed climatology of monthly 222 Rn fluxes at the sampling sites M1-M5 (symbols with error bars representing monthly mean observational data and their standard error) with bottom-up estimates using the diffusivity estimate ofMillington and Quirk (1960).Soil moisture climatology is taken either from the GLDAS Noah LSM (red lines) or from the ERA-Interim/Land model (blue lines) for the respective pixels, averaged over the period of 2006-2010.Note that the monthly soil moisture values have been adjusted according to Eq. (13), i.e. taking into account the actual porosity at the measurement sites (see text).

Figure 7
compares estimates from our 222 Rn flux map based on the two soil moisture models GLDAS Noah (red lines: standard, orange: with frost restriction), ERA-I/L (blue lines: standard, cyan: with frost restriction) with those from Szegvary et al. (2009: dark green lines), from López-Coto et al. (2013: light yellow-green lines) and with observations (black dots).Note that in case the observations do not fall into the modelled time span of 2006-2008 displayed here, the data points have been repeated as climatology for all years.
model for 2006, if also valid for other years, and the López-Coto et al. (2013) model underestimate the seasonal amplitude.GLDAS-Noah-based fluxes are larger than observations by about a factor of 2. This is very surprising because 226 Ra ac-tivity concentration of the map pixel is a factor of 2 smaller than those measured by Schwingshackl (2013) (see Table also used for the empirical γdose rate-based estimates of their 222 Rn flux map for 2006, their measured data fall in between our GLDAS-Noah-and ERA-I/L-based fluxes (Fig. 7f).Only in spring 2007 both of our estimates are higher than the observed fluxes.Soil moisture estimates in both reanalyses are most of the time lower than the observations but capture the temporal variation rather well.In 3 summer months of 2006, the Szegvary et al. (2009) model estimates are slightly lower than the observations, while the López-Coto et al. (2013) model results are considerably lower than all other model estimates and lower than the observations by at least a factor of 2.
flux estimates largely underestimate seasonal amplitudes, at least in 2006.The same is true for the López-Coto et al. (2013) model estimates.As mentioned before, a large part of the general underestimation by López-Coto et al. (

5. 5 Figure 8 .
Figure 8. Map of episodic 222 Rn flux observations in Europe (upper panel) and frequency distribution of model-data differences at sites where co-located data exist (GLDAS-Noah-based fluxes: red histogram, ERA-I/L-based fluxes: blue histogram).All measurement data are provided in the Supplement (TableS1).

Fig. 8 .
The map in Fig. 8 (upper panel) shows the geographical distribution of these episodic observations and their individual values colour-coded.The frequency distributions of the differences between modelled and measured 222 Rn fluxes are shown in the lower part of Fig. 8.We find no geographical dependency of the differences (not shown) but a large mean bias between ERA-I/L-based and measured fluxes.While the GLDAS Noah differences yield a mean value close to zero (0.82 mBq m −2 s −1 with IQR = 11.29 mBq m −2 s −1 ), the ERA-I/L-based estimates are on average lower than observations by 5.73 Bq m −2 s −1 (IQR = 11.21mBq m −2 s −1 2 used by López-Coto et al. (2013) for all soils.The underestimation of the 222 Rn fluxes by the López-Coto et al. ( model.Using two different sets of soil moisture reanalyses underlines the strong dependence of 222 Rn flux estimates on realistic soil moisture values.Both model-based soil moisture estimates evaluated here, either from the GLDAS Noah or the ERA-Interim/Land model, realistically reproduce observed seasonality in soil moisture.This translates into a realistic seasonality of 222 Rn exhalation rates in both realizations of our flux map; however, the overall magnitude of the 222 Rn fluxes differs.Comparison of the two 222 Rn flux maps with European-wide point observations indicates better agreement of GLDAS-Noah-based flux estimates than of those calculated with ERA-I/L soil moisture.While at a monthly time resolution the overall mean 222 Rn flux values from the GLDAS-Noah-based map show almost no bias to the overall mean of point observations in Europe (ca. ) and (7a) is only valid if we can assume an infinitely deep unsaturated soil.This assumption is not always fulfilled.Particularly in northern Europe or in Siberian wetland areas, the water-table depth can be as close to the surface as 10 or 20 cm.In that case there is only a very shallow soil depth available for222Rn production and exhalation into the atmosphere (if we consider that the molecular diffusion coefficient of222Rn in water is lower by 2-3 orders of magnitude compared to air, and that there is only negligible222Rn flux from ground water into the unsaturated soil zone).With the boundary conditions of zero222Rn activity concentration at the soil-air interface and zero 222 Rn flux, i.e. zero concentration gradient, at water-table depth z G

3 Validation of the theoretical concepts to estimate 222 Rn fluxes 3.1 Evaluation of measured 222 Rn soil profiles and diffusivity estimates
model (D e, RN ).

U. Karstens et al.: A process-based 222 radon flux map for Europe
are estimates of the 222 Rn exhalation rate for a soil with a mean source strength Q = 12 mBq m −3 s −1 and relaxation depths z of 0.2,

4 Input data for estimation of the 222 Rn fluxes from soils in Europe
soil.Finally, (5) the water-table depth should be known, at least for areas where it is less than 2-3 m below surface.The respective input data used in our high-resolution 222 Rn exhalation map are described in the following sections.If available, we compare with independently measured data to have some quantitative evaluation of our input data fields (e.g. for soil moisture).

Table 2 .
Characteristics of the long-term 222 Rn flux sampling sites from IUP (compare Fig. 1 and Table

Distribution of European 222 Rn fluxes
table depth on 222 Rn fluxes for Europe.Large areas of the Netherlands, northern Italy, and Hungary with water table above 2 m are affected.For these areas, the 222 Rn exhalation rate was reduced according to our estimation described in Sect.2.3.July 2006 (middle panels).Both maps show some areas of very high 222 Rn exhalations rates, most pronounced in July, which coincide with the areas in Europe where the 226 Ra activity concentration in the upper soil layer is very high.These areas concern for example the Massif Central in southern www.atmos-chem-phys.net/15/12845/2015/Atmos.Chem.Phys., 15, 12845-12865,

2015 12854 U. Karstens et al.: A process-based 222 radon flux map for Europe
France, the Iberian Peninsula and areas in central Italy (compare226Ra distribution displayed in Fig.S2of the Supplement).

Karstens et al.: A process-based 222 radon flux map for Europe during
winter conditions, this parameterization could not be evaluated and can only give an estimate of the associated uncertainties.For more reliable estimations of 222 Rn fluxes in higher latitudes during winter, more investigations on the influence of frost and snow on 222 Rn exhalation is desirable.Uncertainties in annual mean222Rn fluxes mainly in northern Europe due to neglecting flux restriction by frozen soil may be of the order of 10-20 %.However, we do not include this uncertainty in our overall uncertainty estimate below.
In our sensitivity test with a very simple parameterization of frost and/or snow conditions,222Rn flux estimates in Scandinavia and eastern Europe are reduced by 30-40 % during winter and by 10 % for annual mean fluxes in this region.However, due to the lack of systematic flux measurements U.

8 Combined uncertainty of the 222 Rn flux map
The overall uncertainty of222Rn flux estimates for individual pixels, not taking into account systematic biases in the soil moisture models, can be roughly deduced from individual uncertainties of all parameters by error propagation.