Mapping potassium and thorium concentrations in Belgian soils

Abstract

The European Atlas of Natural Radiation developed by the Joint Research Centre (JRC) of the European Commission includes maps of potassium K and thorium Th. With several different databases available, including data (albeit not calibrated) from an airborne survey, Belgium is a favourable case for exploring the methodology of mapping for these natural radionuclides. Harmonized databases of potassium and thorium in soil were built by radiological (not airborne) and geochemical data. Using this harmonized database it was possible to calibrate the data from the airborne survey. Several methods were used to perform spatial interpolation and to smooth the data: moving average (MA) without constraint, or constrained by soil class and by geological unit. Overall, there was a reasonable agreement between the maps on a 1 × 1 km² grid obtained with the two datasets (airborne data and harmonized soil data) with all the methods. The agreement was better when the maps are reduced to a 10 km × 10 km grid used for the European Atlas of Natural Radiation. The best agreement was observed with the MA constrained by geological unit.

Highlights

• •Harmonization of soil K and Th radiological and geochemical data.
• •Calibration of airborne K and Th survey.
• •Analysis of variance of soil K and Th data.
• •Mapping: moving average without constraint, by soil class and by geological unit.
• •Influence of mapping method and resolution.

1. Introduction

Terrestrial radioactivity is mostly caused by uranium (²³⁸U, ²³⁵U) and thorium (²³²Th) radioactive families together with potassium (⁴⁰K) (UNSCEAR, 2008). U mapping in Belgian soils was considered in a previous paper (Cinelli et al., 2017). The present contribution is devoted to K and Th, following similar methods. Maps of K and Th concentrations in soil are included in the European Atlas of Natural Radiation (EANR) developed by the Joint Research Centre (JRC) of the European Commission. The EANR is a collection of maps of Europe displaying the levels of natural radioactivity caused by different sources of radiation. The digital version is now available online at: https://remon.jrc.ec.europa.eu/About/Atlas-of-Natural-Radiation.

⁴⁰K and ²³²Th contents in soil could be estimated through geochemical or radiological analysis. The isotopic abundances of ⁴⁰K (0.0117%) and ²³²Th (100%) being very stable, the elemental concentrations can be directly deduced from the activity concentrations. In radiological analysis, ⁴⁰K is measured by gamma spectrometry, whereas ²³²Th could be measured directly (through alpha spectrometry) or indirectly by considering its progenies (by gamma spectrometry) (Knoll, 2000, Gilmore, 2008). Gamma spectrometry could be performed in situ, on an airborne platform or in the laboratory. ²⁰⁸Tl is mostly used in gamma spectrometry for measuring ²³²Th assuming the secular equilibrium in its decay chain. In the environment, this condition may not be perfectly achieved due to the mobilization of the radionuclides. However, disequilibrium is expected to be less marked than in the uranium decay chain, due to the lack of long-lived progeny.

Geochemical K and Th data in soil were collected for all of Europe through the Geochemical Atlas of Europe (FOREGS) and Geochemical Mapping of Agricultural and Grazing Land Soil (GEMAS) projects (Reimann et al., 2014a, Reimann et al., 2014b). Radiological data are available at national to regional scale. In many European countries, these data were not collected with a density high enough to perform local statistics on the 10 × 10 km² square grid used for the EANR, and some kind of interpolation and smoothing is necessary.

It is reasonable to assume that K and Th concentrations in the soil are correlated to other soil properties (Ferreira et al., 2018). This makes it possible to use European soil maps (ESDB, 2004) as a framework in which K-Th mapping could be inserted. The relation with geology is a bit less direct, but many soil types are expected to include material derived from the alteration of the local bedrock.

Belgium is a favourable case for testing various possible mapping options, because of the availability of detailed airborne radiological surveys that could be used as the reference map. We present a study of different options to map K-Th concentrations in soil in Belgium using geochemical and radiological data. While the results have intrinsic interest for Belgium, this work can also be considered as a contribution for the development of the EANR, i.e. at the European level.

This paper is structured as follows: In Section 2, we present the data available on K and Th in soil and the soil and geological classifications applicable in Belgium, as well as the software packages used in the present work. Then, three important methodological aspects will be examined. First, in Section 3, we examine harmonization of the input data, as they stem from different studies, each with its own methods. Second, statistical tools, such as analysis of variance (ANOVA) and variograms, will be used to select the mapping methods in section 4. Finally, in Section 5, the different mapping methods are applied to K and Th data: (a) interpolation/smoothing/averaging of measured data, without considering any other factor; or (b) mapping separately the data belonging to distinct classes, such as soil or geological classes. The impact of the mapping resolution is examined, and the method giving the best agreement between the maps of harmonized data and of airborne data is determined.

2. Input data and software

This section is limited to a synthetic presentation, because the databases and methods used in the present paper are very similar to those used in our previous work devoted to U mapping (Cinelli et al., 2017), to which the reader should refer for more detail.

Belgium may be divided into three regions of progressive elevation: in the North, a low-altitude plain with Cenozoic grounds; in the Centre, a low Meso-Cenozoic plateau often covered with quaternary loess; in the South, higher Paleozoic massifs, except a small Mesozoic area in the extreme South.

2.1. Databases of K and Th in Belgian soils

The positions of the measurement sites are plotted in Fig. 1, and the main features of the different datasets are summarized in Table 1.

Fig. 1.

Map showing sampling points for the datasets used in the present work. The areas covered by forest are displayed (source: CORINE Land Cover map, Silva and Lavalle, 2011).

Table 1.

Summary of the datasets used in the present work. G = geochemical, R = radiological, S = soil sampling, IS = in situ. ICP-MS = inductively coupled plasma mass spectrometry, AR = aqua regia extraction, HR γ = high resolution gamma spectrometry.

Dataset	Number of data	Type	Mode	Depth (m)	Technique	Measured nuclide or element	Land use
FOREGS	4	G	S	0.5–2	ICP-MS, AR	(K & Th)	any
GEMAS	26	G	S	0–0.2	XRF ICP-MS, AR (*)	(K) (Th)	Culture, grazing
SCK-IHE	35	R	S	0.3	HR γ	40K, 208Tl	any
GENT	62	R	IS	–	HR γ	40K,232Th progeny	grassland
ISIB	18	R	S	1	HR γ	208Tl	any

(*) Th concentrations measured by ICP-MS with aqua regia extraction and corrected for extractability, based on XRF measurements.

2.1.1. Geochemical data

FOREGS is a European database developed for the Geochemical Atlas of Europe. Topsoil and subsoil samples were taken at the same sites (http://weppi.gtk.fi/publ/foregsatlas/index.php).

The GEMAS European database (Reimann et al., 2014a, Reimann et al., 2014b; http://gemas.geolba.ac.at/) includes samples of agricultural soil (Ap, 0–20 cm) and of grazing land (Gr, 0–10 cm).

2.1.2. Radiological data

The Study Centre for Nuclear Energy (SCK-CEN) and the Institute of Public Health (IHE) (Gillard et al., 1988, Deworm et al., 1988) collected soil samples and measured their activity by gamma spectrometry. Similar measurements were done by the Institut Supérieur Industriel de Bruxelles (ISIB), for ²³²Th in soil samples taken at a few sites close to Brussels.

The University of Ghent (GENT), collected data by in-situ gamma spectrometry in air, at 1 m height (Uyttenhove et al., 2000).

2.1.3. Airborne measurements of K and Th progeny

The Belgian Geological Survey organised an airborne campaign of radiometric measurements (BGS, 1995), using a multi-crystal NaI detector and a 256-channel spectrometer, considering three energy windows for gamma rays, corresponding to lines of ⁴⁰K (1.35–1.59 MeV), ²¹⁴Bi (²³⁸U/²²²Rn progeny, 1.63–1.89 MeV) and ²⁰⁸Tl (²³²Th progeny, 2.42–2.81 MeV). The results were reported as counts per second (cps), without calibrating concentrations of the elements considered. Data were acquired along parallel lines at 1 km from each other at 120 m altitude. The data were interpolated at the nodes of a 100 × 100 m² grid. We only used these data on a kilometric grid. For each node of our grid, we linearly interpolated the 4 nearest values of the 100 × 100 m² grid. It is important to realize that the airborne spectrometer “saw”, from the altitude of 120 m, an area of about 1 km², and thus reducing the dataset from the 100 × 100 m² grid to the 1 × 1 km² grid does not imply a real loss of information.

2.2. Soil and geological classifications

2.2.1. European soil maps

The European Soil Database – ESDB (ESDB, 2004, Panagos, 2006) provides EU-wide data for 73 soil attributes. The datasets used in the current work were: (a) WRBLV1 containing the soil reference group code of the Soil Typological Units (STU) from the World Reference Base (WRB) for Soil Resources, (b) TXSRFDO contains the dominant surface textural class of the STU. The corresponding maps are available to be downloaded at ESDAC (ESDAC: https://esdac.jrc.ec.europa.eu/content/european-soil-database-v20-vector-and-attribute-data.

2.2.2. Geological maps

An old set of 1:40,000 geological maps (BGS, 2015), still the only set of geological maps to cover the entire territory of Belgium, is available in numerical version, and was used in the present work. The presence of quaternary sand and loess deposits, indicated on the image version, is not accessible in the vectorized version, but was evaluated visually on the maps. Lithological information is not included in a standardised way and is therefore almost impossible to treat digitally. Simplified versions of the geological map are available online, e.g. http://www.lave.be/main/Perso/Belgium_geol.jpg.

The OneGeology-Europe project brings together a web-accessible, interoperable geological spatial dataset for the whole of Europe at 1:1 M scale based on data held by the pan-European Geological Surveys (OneGeology-Europe,, Baker and Jackson, 2010). As for the Belgian maps, the presence of quaternary sand and loess deposits is not reported.

2.2.3. Geological units

The same sets of geological units (GUs) were used as for the U map (Cinelli et al., 2017). The “extended” set (EGU) consists of 37 units adequate for indoor radon mapping in Belgium. A “reduced” set of 12 geological units (RGU, Table 2) was also defined, because the scarcity of data, (except airborne) does not allow good statistics when they are distributed over a large number of classes. RGU is compatible with the stratigraphic scale of the OneGeology map, except for loess and sand covers. Finally, a schematic set of 4 geological units (SGU) was combined with soil classes (Table 2).

Table 2.

Codes of the reduced geological units (RGU) and schematic geological units (SGU).

Name	Code	SGU code
Cambrian	CAM	PAL
Ordovician & Silurian	ORS	PAL
Lower Devonian	LDV	PAL
Middle Devonian	MDV	PAL
Upper Devonian	UDV	PAL
Lower Carboniferous	LCA	PAL
Upper Carboniferous	UCA	PAL
Permian and Mesozoic	MES	MES
Cenozoic clay	CLA	CEN
Cenozoic sand	SAN	CEN
Quaternary loess	QLO	QLO

2.3. Software used for statistical analysis and geostatistical mapping

The data were analysed using tools of descriptive statistics and inferential statistics such as ANOVA. ANOVA was used to calculate the proportion of the variation of K and Th concentration in soil explained by geology and soil properties of the sampling/measurement site. STATISTICA software was used to perform ANOVA analysis (STATISTICA 7).

Variograms were calculated using SURFER software to check the spatial correlation of the data. Several software programs were used to perform geostatistical analysis and map the data: ArcGIS^® (ESRI, 2010), SURFER^® 11 (Golden Software, LLC) and MAVERN (Tondeur and Cinelli, 2014) which calculates the moving average (MA) of N nearest neighbours in the same class as the local position. The classes used here will be the soil classes and the geological classes.

3. Harmonization of input data

The datasets described in Section 2.1 measure different quantities with different methods. We assumed that all these reported quantities were proportional respectively to the K and Th concentrations in the soil, and we neglected the possible disequilibrium in the Th decay chain. Because of the very different origins of the data, it is necessary to determine that they were compatible and, if necessary, to perform the corrections needed to achieve this compatibility. This will be done in two steps: first, by harmonizing calibrations of the scattered data from FOREGS,, GEMAS,, SCK-IHE, GENT and ISIB, and then by using the harmonized data to calibrate the results of the airborne survey.

3.1. Harmonization of geochemical and radiological data

3.1.1. Analysis of the data

Simple statistics revealed some differences between the five datasets, which might have several reasons, like (a) the number of data too small for a good estimation of the true population statistics; (b) the lack of representativity, especially for FOREGS and ISIB; and most importantly, the methodological differences between sampling and measurement techniques.

We renormalized each dataset by comparing it to SCK-IHE data taken as reference. The harmonization factor HF to which we refer hereafter is the factor by which respectively GENT, GEMAS,, FOREGS, and ISIB data had to be multiplied to harmonize them with SCK-IHE.

3.1.2. Harmonization methodology

A discussion of harmonization methods was given for U data in (Cinelli et al., 2017). The following methods were considered here for harmonizing GENT and GEMAS with SCK-IHE, assuming that all 3 databases are geographically representative:

Method 1: The harmonization factor (HF) is the ratio of arithmetic mean (AM) values (1.1) or medians (1.2) <SCK-IHE>/<GENT> and <SCK-IHE>/<GEMAS>

Method 2: data were first mapped with the moving average method, on a 10 × 10 km² grid, taking the 4 nearest data (SCK, GEMAS) or the 8 nearest data (GENT).

• (2.1)HF is the mean ratio < SCK-IHE/GENT> and <SCK-IHE/GEMAS> (AM and geometrical mean GM were considered)
• (2.2)HF is the slope of the trendline in the graphs SCK-IHE vs. GENT and SCK-IHE vs. GEMAS.

Method 3: data were grouped by schematic GU, HF is calculated for each GU and the average factor (AM) is determined.

Because ISIB data are spatially concentrated, methods 1 and 2 cannot be applied. Method 3 was applied for 3 GUs: loess, sand, alluvia, and the AM ratio <SCK-IHE>/<ISIB> was taken for the HF.

For the scarce FOREGS data, method 2 was modified by mapping harmonized (SCK-IHE + GENT + GEMAS) data at the coordinates of FOREGS data, taking the AM ratio HF = <harmonized>/<FOREGS>.

HF values evaluated with the different methods for K data, rounded to the nearest second digit, are consistent for GENT (HF = 1.4) and for GEMAS (HF = 1.0 or 1.1) except GEMAS with method 3 (HF = 1.2), an anomaly related to a discrepancy between the few K data on Mesozoic. The correlation between SCK-IHE and GENT averaged data in method 2 is good (correlation coefficient CC = 0.82), an indication that harmonization of GENT with SCK-IHE is actually meaningful, whereas the correlation is worse between SCK-IHE and GEMAS (CC = 0.52).

Altogether, the results suggested HF = 1.4 for GENT, the same as for U (Cinelli et al., 2017), and HF = 1.0 for GEMAS. As for FOREGS, HF = 0.9 (subsoil) or 1.0 (topsoil).

The harmonization factors with respect to SCK-IHE determined for Th data are quite similar: HF = 1.3 to 1.5 for GENT, rounded to 1.4, HF = 1.0 for GEMAS (except HF = 1.3 with method 1.2, an anomaly related to the particular bimodal character of the distribution of SCK-IHE Th data). As for ISIB data, HF was rounded to 1.0, like in the case of U (Cinelli et al., 2017). For FOREGS, HF is 0.9 (subsoil) and 1.0 (topsoil), the same as for K.

The correlation between SCK-IHE and GENT data in method 2 is good (CC = 0.90), an indication that harmonization of UGent with SCK is actually meaningful, whereas the correlation is much worse between SCK-IHE and GEMAS (CC = 0.49).

Thus, within a few percent accuracy, the calibration of SCK-IHE, FOREGS topsoil, GEMAS and ISIB were found to be compatible. The harmonization factor 1.4 consistently obtained for GENT data suggests a systematic calibration difference with the other datasets, independent of the nuclide or element. Whereas the calibration of SCK-IHE is simple and sound (comparison with a sample of calibrated activity in the same geometry), the calibration of in situ GENT data was not described in detail in their report and is inherently more questionable, relying on a complex calculation based on a model of uniform distribution of the radionuclide in the soil.

The two types of FOREGS data are quite similar after harmonization, but only one data could be kept per site. Subsoil data were kept to be consistent with our work on U mapping (Cinelli et al., 2017), this choice having almost no impact on the results, due to the similarity and small number of these data.

3.2. Calibration of airborne data

Unlike airborne U data, airborne K and Th data are not very noisy, and no preliminary smoothing was necessary. The airborne counting was evaluated at the coordinates of the harmonized soil data by interpolating the 4 nearest airborne data from the 100 × 100 m² grid.

3.2.1. K data

Airborne counts (in mcps) were plotted against the harmonized data (in g/kg) for each point. The correlation coefficient between airborne and harmonized K data is satisfactory (CC = 0.66).

The linear fit in Fig. 2 (R² = 0.92) includes a shift of −1000 mcps for zero K concentration, based on the average value of airborne data above the North Sea. The conversion slope is approximately 5.3 cps/(g/kg). On this basis, the airborne data were converted into g/kg:

airborne K (g/kg) = (airborne K (cps) + 1)/5.3.

Fig. 2.

Airborne counts (vertical, mcps) vs.harmonized K concentration (g/kg) at the coordinates of the sampling points.

The corresponding map is given in Fig. 3.

Fig. 3.

Map of K concentration in soil (%), from calibrated airborne data. In blank the area not included in the airborne survey.

3.2.2. Th data

The same methodology was applied for calibration the airborne Th map. The airborne counting was evaluated at the coordinates of the 145 harmonized data by interpolating the 4 nearest airborne data. Airborne counts (in mcps) were plotted against the harmonized data (in mg/kg) for each point, excluding an outlier. The correlation coefficient is satisfactory (CC = 0.69).

The linear fit (R² = 0.92) in Fig. 4 includes a shift of airborne Th data by −900 mcps for zero Th concentration, based on the average value of airborne data above the North sea. The conversion slope is approximately 3.2 cps/(mg/kg). On this basis, the airborne data are converted into mg/kg:

airborne Th (mg/kg) = (airborne Th (cps) +0.9)/3.2.

Fig. 4.

Airborne counts (mcps) vs. harmonized Th concentration (mg/kg) at the coordinates of the sampling points.

The corresponding map is given in Fig. 5.

Fig. 5.

Map of calibrated airborne Th concentration in the soil. In blank the area not included in the airborne survey.

3.2.3. Short analysis of airborne maps

The area near Brussels, in the centre of the map, was not included in the airborne survey. The general trends of the maps are the following:

• -Low K and Th concentrations in the North, mostly associated with sandy soils on Cenozoic background, with a few scattered spots, associated with industrial and coal mining residues.
• -Medium concentrations associated to the Quaternary loess cover in Middle Belgium. Low-K Cretaceous and Cenozoic areas appear in the discontinuities of loess.
• -Higher K and Th concentrations in Condroz and Famenne, associated with Middle Devonian to Lower Carboniferous K-bearing rocks like psammites and arkose.
• -A variable landscape in the old Ardenne-Stavelot massifs (Cambrian to lower Devonian), which include zones with low concentrations as well as zones with higher K and Th content.
• -In the “far South”, the Mesozoic area of Gaume is mainly a low to medium-K region. The highest Th values, up to 25 mg/kg, are observed there, along the French border, on Jurassic grounds (upper Virtonian, Toarcian, Bajocian, in strong contrast with the neighbouring older Jurassic formations which have a low Th content).

3.2.4. Impact of the forest cover

The shielding effect due to the presence of forest could affect the airborne data. Land cover data - the Corine Land Cover 2006 (Silva and Lavalle, 2011) - have been used to check the impact of the forest cover in our calibration. In Fig. 1 areas covered by forest are reported. Because GEMAS and GENT excluded forest areas (Table 1), only few measurements were performed under the forest cover. The corresponding data were excluded and the resulting change in the calibration factor is about 1% for Th, less than 1% for K. Hence the impact of the forest could be considered negligible and it was not included in the calibration.

The evaluation of the shielding by the forest would need more data measured under the forest cover, to be compared to the calibrated airborne data, but this is not feasible due to the scarcity of such data. A trend towards lower values can be observed visually in the airborne maps (Fig. 3, Fig. 5) for forest-covered areas, but it cannot be automatically attributed to the shielding effect. Indeed, the forest cover is often strongly correlated with the soil properties. In particular, as K is one of the main elements of fertility, K-rich soils are often more devoted to agriculture than to the forest.

4. Statistical analysis

4.1. Statistics of harmonized and airborne soil K data

The histogram of 127 harmonized K data is slightly asymmetrical, showing a “fat tail” for low K, with values ranging from 2.6 g/kg to 33.7 g/kg, the mean value being 14.8 g/kg. The histogram of airborne data taken on a 1 × 1 km² grid, i.e. 30,582 data, has similar characteristics, with a slightly higher mean of 15.6 g/kg, probably more realistic because of the dense sampling over the whole country. The variogram of harmonized K is very noisy (Fig. 6), especially at short distance where no firm conclusion can be drawn about the presence of spatial correlation. The variogram of airborne data is much better (Fig. 6). The airborne measurement by itself includes a spatial smoothing, and short-range variations of the K concentration, which are present in the harmonized soil K dataset, are washed out in the airborne dataset, which we may therefore expect to have a lower variance, to be less noisy. The absence of the short-range variability is well seen in the variogram.

Fig. 6.

Variograms of harmonized (left) and airborne (right) K data.

The geological unit and the soil class were determined for harmonized and airborne data. The Analysis of Variance (Table 3) showed that an important part of the variance of the global sampling can be explained by the variability of soil classes or geological units. Considering the number of classes, the WRB soil classification in the ESDB (§2.2.1) and the reduced set of geological units RGU (Table 2) show the best performance in explaining the variance of soil K data. The geological classification is slightly better than the soil classification for harmonized soil data, but the opposite is true for airborne data. The good result with the extended set of geological units EGU (§2.2.4) for harmonized data and with the combined WRB/SGU classification cannot be considered as conclusive because of the very low number of data in a majority of the classes. The still good result of RGU is certainly more robust.

Table 3.

ANOVA analysis of K data.

Classification	Number of classes harmonized	Percentage of the variation	Number of classes airborne	Percentage of the variation
SGU* (Table 2)	4	39%	4	28%
RGU* (Table 1)	12	48%	12	40%
EGU (§2.2.4)	17	55%	38	42%
WRBLV1*(§2.2.1)	8	41%	10	45%
TXSRFDO*(§2.2.1)	5	38%	6	39%
WRB/SGU*	15	52.98%	31	50.76%

(*) Available at European scale.

Discarding classes with very few data, the distribution of soil K data according to the underlying geological unit (RGU set) in Table 4 shows K concentrations higher than the average from Ordovician to Carboniferous, culminating with Upper Devonian. Soils above Meso-Cenozoic have less K than the average, with the noticeable exception of Quaternary loess.

Table 4.

Statistics of K data according to geological units.

GU	Number of harmonized data	Mean concentration (g/kg)	Number of airborne data	Mean concentration (g/kg)
CAM	1	15.2	671	13.6
ORS	1	13.6	421	21.9
LDV	17	17.8	4444	17.9
MDV	7	21.2	483	20.2
UDV	10	22.2	2099	23.6
LCA	3	21.2	888	18.4
UCA	5	18.1	498	16.7
MES	12	11.7	1353	13.1
SAN	31	9.8	9146	11.3
CLA	12	13.6	2507	15.3
QLO	18	15.8	5155	18.1
ALM	10	13.6	2470	14.5

Similarly, higher K concentrations are found (Table 5) in Cambisol (corresponding to the thin stony loam which is common in Paleozoic areas), and in Luvisol (mostly developed above loess) and values less than the average are found in other soil classes.

Table 5.

Statistics of K data according to the soil class.

Soil class	Number of harmonized data	Mean concentration (g/kg)	Number of airborne data	Mean concentration (g/kg)
CM - Cambisol	37	19.0	8075	18.9
LV - Luvisol	45	15.3	9196	18.0
AB - Albeluvisol	7	13.0	3516	13.9
FL - Fluvisol	15	14.4	3193	13.5
HS - Histosol	1	15.2	92	8.9
AR - Arenosol	1	10.7	154	8.9
PZ - Podzol	21	7.6	5481	8.7
RG - Regosol	–	–	116	7.3
1 (built area)	–	–	271	10.6

In Table 4, Table 5, the arithmetic mean is used, like in the European Atlas. This choice is supported by the limited asymmetry of the histograms of most classes, and the limited deviations of their q-q plots from the normal trend, the exceptions mostly concerning the low-K tail of classes with a low mean.

4.2. Statistics of harmonized and airborne soil Th data

The mean value of 145 harmonized soil Th data is 8.2 mg/kg, the minimum (in sand) being 0.6 mg/kg and the maximum (on a Jurassic ground) 23.1 mg/kg. The histogram of the data is not symmetric, showing a strong departure from a normal distribution. However, the data also clearly depart from a lognormal trend. The histogram of airborne data shows the same kind of asymmetry, with the mean value 8.3 mg/kg.

The variogram of the harmonized soil Th data shows no indication of spatial correlation (Fig. 7). The low-distance trend is associated to the central region of Belgium where ISIB data are concentrated, creating more low-distance pairs in an area characterised by a discontinuous loess cover (∼10 mg/kg Th) above tertiary sand (∼4 mg/kg), thus with many contrasted loess-sand pairs (this point and its impact on the variogram was discussed in Cinelli et al. (2017) in relation with U data). The variograms of separated soil classes or geological units are very noisy and inconclusive, due to the too small number of data. As for the variogram of airborne data (Fig. 7), it is similar to that of airborne K data (Fig. 6) with a low variability at short distance, the explanation given for K being also valid for Th.

Fig. 7.

Variograms of harmonized (left) and airborne (right) Th data.

The Analysis of Variance (Table 6) shows that an important part of the variance of the global sampling can be explained by the variability of soil classes or geological units. Considering the number of classes, the WRB soil classification in the ESDB (§2.2.1) shows the best performance in explaining the variance of harmonized and airborne soil Th data. As for geological classifications, the reduced set RGU (Table 1) will be considered as the best choice. The good result obtained with the extended set EGU (§2.2.3) or the combined classification WRB/SGU (Table 2) for harmonized data is not conclusive, because of the very low number of data in a majority of the units. For airborne data, the gain associated to EGU (compared to RGU) and WRB/SGU (compared to WRB) is marginal.

Table 6.

ANOVA analysis of Th data.

Classification	Number of classes harmonized	Percentage of the variation	Number of classes airborne	Percentage of the variation
SGU*	4	33%	4	39%
RGU*	12	45%	12	47%
EGU	17	53%	38	48%
WRBLV1*	7	43%	10	65%
TXSRFDO*	5	25%	6	47%
WRB/SGU*	16	53%	31	68%

(*) Available at European scale.

We shall only consider hereunder the two master-choices: the WRB soil classification, and the reduced RGU geological classification. Their statistics are given in Table 7, Table 8. The statistics per soil class or geological unit show contrasted situations, mainly between the low concentrations in Podzol (3 mg/kg) or above Sand (4 mg/kg), and a majority of data in classes or units with a mean value close to 10 mg/kg, with a few intermediate cases (Abluvisol, Fluvisol, Clay, Alluvia, Cretaceous). One must be cautious with the strong contrast between Jurassic and Cretaceous, based on a small number of harmonized data, which is not found with airborne data. As noted above, Jurassic is very inhomogeneous for Th, and an excess of high data may easily occur in a small sampling.

Table 7.

Statistics of Th data according to geological units.

GU	Number of harmonized data	Mean concentration (mg/kg)	Number of airborne data	Mean concentration (mg/kg)
QLO	24	10.07	5155	10.05
ALM	15	8.57	2470	7.82
CLA	12	6.96	2507	7.71
SAN	38	4.48	9146	5.16
MES	12	9.69	1353	9.49
JUR	6	12.84	690	9.64
CRE	6	6.54	570	9.32
UCA	5	10.85	498	10.48
LCA	3	12.15	888	10.74
UDV	10	10.79	2099	11.59
MDV	7	10.15	483	10.89
LDV	17	9.24	4444	10.24
ORS	1	8.25	421	11.88
CAM	1	11.54	671	8.08

In italics two major periods of Mesozoic, Jurassic (JUR) and Cretaceous (CRE), are reported.

Table 8.

Statistics of Th data according to the soil class.

Soil class	Number of harmonized data	Mean concentration (mg/kg)	Number of airborne data	Mean concentration (mg/kg)
LV - Luvisol	59	9.60	9196	10.55
CM - Cambisol	37	9.63	8075	10.44
FL - Fluvisol	17	7.51	3193	6.86
AB - Albeluvisol	9	6.44	3516	6.83
HS - Histosol	1	11.54	92	5.34
AR - Arenosol	–	–	154	4.50
PZ - Podzol	21	3.02	5481	3.55
RG - Regosol	–	–	116	2.92
Built area	–	–	271	8.82

Considering separately the histograms of the most abundant soil classes and geological units generally shows distributions more symmetrical than the global one, with rather small dispersion (LV, CM, QLO), for which the normal distribution would be a reasonable approximation, with the noticeable exception of sand, which probably reveals a lack of homogeneity of the soils above sand, a bimodal distribution being not excluded. A similar conclusion applies to the distribution of airborne data by soil class or geological unit, a majority being reasonably well described by a normal distribution, except classes/units with a low mean value, and a few other exceptions.

5. Mapping methods

Because of the relative scarcity of the data, the harmonized dataset cannot be directly used for producing maps, even at a 10 km scale, because many 10 × 10 km² squares include no data or only a single one. For this dataset, a stage of interpolation and/or smoothing is necessary before producing a map. For this purpose, kriging would generally be the most adequate method.

However, the variograms of harmonized data given Fig. 6, Fig. 7 show no spatial correlation. Therefore the simple moving average (MA) was used. As for the airborne data, the variogram is not meaningful because the data were subjected to regularization/smoothing stages that increase the spatial correlation. For comparison with harmonized data, airborne data will also be mapped with the MA.

The high percentages of the variance that can be explained by organizing the data in geological units or soil classes means that a more accurate average can be obtained by applying the Moving average-MA separately for each GU or soil class. Therefore three options were considered:

• (a)Mapping with the MA with all data together,
• (b)MA separately for each geological unit of the RGU set (MA-RGU),
• (c)MA separately for each WRB soil class (MA-WRB).

Methods (b) and (c) introduce discontinuities at the limits of the mapping units.

The number of data to be averaged around each point of the considered grid is a compromise between the wish to keep information about the local situation, and the statistical accuracy of this information. For example, with the simple MA (a), assuming a normal distribution, the standard error on the mean of 8 harmonized Th data is approximately 1.2 mg/kg, the 8 nearest data occupying on the average a circle with a radius of 23 km (except close to the border). Thanks to the lower variance of data in soil classes, the standard error for 8 Th data could be reduced to 0.8 mg/kg on the average with MA-WRB, 0.9 mg/kg with MA-RGU. The circle contains on the average 7 harmonized K data and about 1500 airborne data. When these numbers of data are not available in the considered GU or soil class, the global mean of the GU or soil class was taken.

5.1. Smoothed maps of K concentration on the 1 km × 1 km grid

Maps were produced with the moving average of the nearest 7 harmonized data or the nearest 1500 airborne data. The simple MA gives maps (Fig. 8) with similar trends for both datasets, the main difference being seen in central Hainaut (Mons basin, middle of the SW border), with a low-K area seen in harmonized data, not in smoothed airborne data. However this structure was seen in the airborne map of Fig. 3, before smoothing. A similar situation is seen in the centre of the country, around Brussels, an area with no airborne data (Fig. 3), here filled by interpolation/smoothing based on the neighbouring areas. This procedure clearly misses the local situation associated with sandy soils. Thus, some interesting information can be lost with the moving average on a radius of ∼23 km.

Fig. 8.

MA maps of harmonized K data (left) and airborne K data (right).

MA-RGU maps are quite similar (Fig. 9). The difference observed for the Stavelot massif (middle of E border) corresponds to the difference between CAM and ORS in Table 6, a case for which the number of harmonized data is clearly too low. In these maps, the main area with higher K concentration is associated to middle- and upper Devonian in Condroz and Fagne-Famenne. The area with lower concentration in the NE corresponds to Cenozoic sand.

Fig. 9.

MA-RGU maps of harmonized K data (left) and airborne K data (right).

In the extreme South, both the simple MA and MA-RGU show a clear contrast between Ardenne (lower Devonian) and Gaume (Jurassic), and this contrast still appears with harmonized data for MA-WRB, but not with airborne data (Fig. 10).

Fig. 10.

MA-WRB maps of harmonized (left) and airborne (right) K data. Blanked areas: too few data.

Table 9 gives the percentage of pixels differing in K concentration by more than 3 g/kg (∼20% of the mean value) between two maps. If we consider the airborne dataset as the reference, because of its dense sampling, the best way of mapping harmonized data seems to be MA-RGU.MA-RGU maps are also seen to be quite different from MA and MA-WRB, which are closer to each other.

Table 9.

Percentage of pixels in the maps with strong difference in K concentration.

Maps compared	% of pixels differing by more than 3 g/kg
Airborne vs. harmonized
MA	19.6%
MA-RGU	15.2%
MA-WRB	23.3%
Harmonized
MA vs MA-RGU	22.6%
MA vs. MA-WRB	12.9%
MA-RGU vs. MA-WRB	23.2%
Airborne
MA vs MA-RGU	19.5%
MA vs. MA-WRB	11.5%
MA-RGU vs. MA-WRB	27.9%

5.2. Smoothed maps of Th concentration on the 1 km × 1 km grid

Fig. 11 shows the map of harmonized Th data (left) and airborne Th data (right) obtained on a 1 × 1 km² grid by the moving average of 8 and 1500 data respectively, corresponding approximately to the same radius as for the K maps.

Fig. 11.

MA maps of harmonized Th data (left) and airborne K data (right).

Several differences can be noticed between the two maps. The low-Th area in the centre does not appear in airborne data, because data are missing there (region of Brussels) and the MA simply interpolates from the neighbouring area. The somewhat higher “Midwest” area in the map of harmonized data, and the high-Th area in the South, is associated with a few GEMAS data.These structures do not appear in SCK-IHE data and UGent data.

In Fig. 12 are shown the MA-RGU maps for harmonized data (left) and airborne data (right). The areas with higher Th and lower Th are very similar to those with higher K (Condroz-Fagne-Famenne) and lower K (NE border) discussed above, but the NW also appears depleted in Th.

Fig. 12.

MA-RGU maps of harmonized Th data (left) and airborne Th data (right).

Finally, Fig. 13 gives the MA-WRB maps for harmonized data (left) and airborne data (right).

Fig. 13.

MA-WRB maps of harmonized (left) and airborne (right) Th data. Blanked areas: too few data.

Table 10 shows the percentage of pixels differing by more than 2 mg/kg (∼24% of the mean value) between two maps. The agreement between the maps of harmonized data and the corresponding maps of airborne data is quite independent of the mapping method. However, like for K, the MA-RGU maps are quite different from MA and MA-WRB, which are closer to each other.

Table 10.

Percentage of pixels in the maps with strong difference in Th concentration.

Maps compared	% of pixels differing by more than 2 mg/kg
Airborne vs. harmonized
MA	13.4%
MA-RGU	12.2%
MA-WRB	12.5%
Harmonized
MA vs MA-RGU	27.4%
MA vs. MA-WRB	15.8%
MA-RGU vs. MA-WRB	26.7%
Airborne
MA vs MA-RGU	13.9%
MA vs. MA-WRB	9.5%
MA-RGU vs. MA-WRB	19.8%

5.3. Averaging MA, MA-WRB and MA-RGU maps on 10 × 10 km² squares

Whatever mapping method is chosen, the last stage in preparing the results for the European Atlas should be to reduce the maps to 10 × 10 km² pixels. In this operation, a lot of detail will be lost. Therefore, the usefulness of RGU mapping, and even WRB mapping, could be questioned. We compare the different maps in Fig. 14, Fig. 15.

Fig. 14.

Same maps as in Fig. 8, Fig. 9, Fig. 10, averaged on a 10 km × 10 km grid. Top: MA harmonized K (left), MA airborne K (right). Middle: RGU harmonized K (left), RGU airborne K (right). Bottom: WRB harmonized K (left), WRB airborne K (right).

Fig. 15.

Same maps as in Fig. 11, Fig. 12, Fig. 13, averaged on a 10 km × 10 km grid. Top: MA harmonized Th (left), MA airborne Th (right). Middle: RGU harmonized Th (left), RGU airborne Th (right). Bottom: WRB harmonized Th (left), WRB airborne Th (right).

Fig. 14, Fig. 15 show a better agreement between harmonized and airborne maps of K and Th than the maps at 1 × 1 km², for all mapping methods. This is confirmed by the values of the percentage of pixels differing by more than 3 g/kg for K and 2 mg/kg for Th between two maps reported in Table 11.

Table 11.

Percentage of pixels differing by more than 3 g/kg (K) or 2 mg/kg (Th) when comparing maps of Fig. 14, Fig. 15.

Maps compared	K	Th
% of pixels differing	by more than 3 g/kg	by more than 2 mg/kg
Airborne vs. harmonized
MA	17.7%	13.0%
MA-RGU	6.0%	6.5%
MA –WRB	20.1%	10.1%
Harmonized
MA vs. MA-RGU	11.1%	7.6%
MA vs. MA-WRB	6.5%	8.2%
MA-WRB vs. MA-RGU	8.2%	5.2%
Airborne
MA vs. MA-RGU	3.3%	1.1%
MA vs. MA-WRB	4.6%	1.4%

As expected, like for 1 × 1 km² maps, if we consider the airborne dataset as the reference, the best way of mapping the harmonized data seems to be the MA-RGU approach.

6. Conclusion

Belgium is a favourable case for exploring the methodology of soil K and Th mapping thanks to the different available datasets, including an airborne survey, albeit not calibrated. The necessity to harmonize in-situ radiometric data and other radiological and geochemical data was shown. Harmonized soil K and Th databases were built merging radiological (no airborne) and geochemical data. Thanks to this harmonized soil database it was possible to calibrate the airborne survey.

Several methods were used to perform spatial interpolation and smoothing of the harmonized data: moving average without constraint (MA), by soil class (MA-WRB) and by geological unit (MA-RGU). This step is necessary to evaluate the K and Th concentration in areas without data or with an insufficient number of data in the harmonized database.

The maps based on soil classes do not give fine details, but would be adequate for mapping at European scale. The finer resolution possible with a map based on geological units can be very useful at national and regional level, but the full information is only available with a sampling density higher than that of our Belgian harmonized soil databases, which only contains 4 to 5 data per 1000 km².

Globally, there is a reasonable agreement between the maps on a 1 × 1 km² grid obtained with the two datasets (airborne and harmonized soil concentrations) with all the methods. The agreement is better when the maps are reduced to a 10 × 10 km² grid used for the European Atlas. The best agreement between maps based on harmonized and airborne data is observed for the MA-RGU method, i.e. mapping within geological units, which could thus be recommended for the European Atlas.