Assessment of ¹³⁷Cs and ^239,240Pu Distribution in Forest Soils of the Opole Anomaly

Abstract

Distribution of ¹³⁷Cs and ^239,240Pu in the forest soils horizons of the Opole Anomaly was established. Gamma and alpha spectrometry was used for determination of these isotopes. It was found that the ¹³⁷Cs activity was approx. 1,000 times higher than that of ^239,240Pu. The highest activities of both radioisotopes were found close to the boundary region in soil profile where the organic horizon turns into the inorganic one. Cluster analysis did not clearly indicate the group’s existence in data in respect to ¹³⁷Cs and ^239,240Pu activities and organic matter content. Distributions of ¹³⁷Cs and ^239,240Pu in soil horizons were non-normal but similar to each other. These distributions were substantially different from that one for organic matter content. The data were separated into two groups, for organic and inorganic soil horizons, respectively. Data transformation using Box–Cox formula was performed following by standardization. Mutual relationships between variables were investigated using ordinary and robust regression methods. Good correlation between ¹³⁷Cs and ^239,240Pu was found. No significant relationship between organic matter content and radioisotopes activity was asserted.

1 Introduction

Starting from the 1950s and 1960s of the twentieth century, radioactive dust, originating from nuclear weapon tested in the atmosphere, gave rise to the increased interest in radioactive isotope study in the environment. Radioactive fallout contained a number of radionuclides, among them ¹³⁷Cs and ^239,240Pu. Studies focused generally on the permissible dose for men and its influence on human health (UNSCEAR 2000a, 2006).

During the Chernobyl nuclear power plant breakdown in April 26th 1986, a large amount of radioactive matter was exhausted to the atmosphere, among them ¹³⁷Cs, ²³⁹Pu, and ²⁴⁰Pu, which are the most interesting ones as the long-life isotopes (UNSCEAR 2000b). Estimated initial ¹³⁷Cs activity in the damaged reactor core ranged from 2.6 × 10¹⁷ to 3.0 × 10¹⁷ Bq. About 33 ± 10% of this amount was released to the atmosphere. Estimated activities of ²³⁹Pu and ²⁴⁰Pu in the reactor core were 8.5 × 10¹⁴–9.5 × 10¹⁴ Bq ²³⁹Pu and 1.2 × 10¹⁵–1.8 × 10¹⁴ Bq ²⁴⁰Pu. About 1.4 ± 0.5% of plutonium isotopes were released, mainly to the reactor surroundings (Kashparov et al. 2003).

The isotopes introduced to the environment as radioactive fallout have started, depending on their chemical nature, circulation between various alive and abiotic components of natural environment. In forest, the intercepted radioactive dust was relocated to the forest floor by the processes of leaf fall or by rain leaching the material from the canopy (throughfall). Migration of radionuclides in soil depends on numerous and various parameters, among others, on soil type, physicochemical properties of soil horizons or chemical properties of soil solution (Odintsov et al. 2005). The distribution of deposited element in soil in a given area is influenced by amount of initial fallout, its physicochemical properties as well as horizontal and vertical migration rate in soil. Determination of radioisotope activity in vertical profile layers enable to calculate a migration rate. The factors that determine changes of radionuclide activity in soil are, among others: weather conditions, moisture content in soil, duration of radioactive fallout, soil structure, and water infiltration rate (Block and Pimpl 1990; Bunzl and Schimmack 1989; Nimis 1996).

The ¹³⁷Cs accumulation in soil is mainly caused by chemisorption processes and usually follows the general principles of metals sorption in natural or artificial ion exchangers (Berg and Shuman 1995) and depends mainly on the charge of an ion and its size, including hydration sphere (Janusz et al. 1997). Numerous experiments proved that the size of ¹³⁷Cs ion exchange depends upon the mineral particle size, structure, the ionic strength in the soil solution or the presence of the competing ions, especially K⁺ and NH ⁺₄ (for example: Korobova et al. 2008). It was found that clay components of the organic horizons in forests soils caused decreasing in the available ¹³⁷Cs fraction (e.g., de Brouwer et al. 1994). Though organic soil horizons do not contain enough clay minerals to immobilize cesium, many authors (Beli et al. 1994; Takenaka et al. 1998; Nakamaru et al. 2007; El Samad et al. 2007; El-Reefy et al. 2006; Zhiyanski et al. 2008; Wacławek et al. 2004; Dołhańczuk-Śródka et al. 2006a, 2006b, 2006c) reported the highest ¹³⁷Cs activities just in upper horizons, rich in organic matter. A reason of Cs⁺ retention in organic horizons could be explained by formation of certain complexes between cesium ions and humic acids (Macášek 1999). There is a hypothesis which suggested that organic matter modifies the adsorption properties of clay minerals in soil (El-Reefy 2006). It was found that low pH values improve cesium uptake from soil by plants (Kruyts and Delvaux 2002; Squire and Middleton 1966; Schuller et al. 1988) but decreases velocity of the Cs⁺ cation transfer (Schuller et al. 1988). Type of clay and a sand content in mineral horizons may also influence the Cs transport parameters (Rogowski and Tamura 1970; Cremers et al. 1988; Giannakopoulou et al. 2007).

Plutonium behavior in environment is much more complicated than that for cesium. The most stable oxidation state for Pu ions in solution is +4, although some amounts of plutonium in its +3, +5, and +6 oxidation states can also exist simultaneously. The Pu chemistry in water is further complicated by the successive hydrolysis of Pu⁴⁺ compounds to form polymers of colloidal dimensions. It was found that the behavior of Pu cations in the soil–water system depends on the speciation and soil type (Skipperud 2000). In forest soils, both soluble and insoluble plutonium compounds remain in top layers (Bunzl 1998; Druteikienė 1999; Lujanienė 2002). The main reason of plutonium compounds retention in organic soil horizons are associations between humic substances and Pu ions (Fujikawa 1999; Macášek 1999; Sokolik 2003). It was found that besides organic matter Pu was also bound with Fe/Mn oxides (e.g., Komosa 2002). Transport of Pu in soil is influenced by physicochemical properties of soil and soil solution. The negative correlation between the exchangeable pH of soil and plutonium concentration in forest soils was found (Komosa 1999). It was also found that both oxidation and reduction mechanisms can play an important role in Pu transport through the vadose zone (Kaplan 2004).

One of the most important transport mechanisms of elements in the environment involves their uptake by living organisms. A considerably simplified description of this process includes transport of elements from abiotic components to autotrophic organisms and then to the heterotropic consumers within the food network system. Further transport occurs between successive higher trophic levels, e.g., from herbivores to carnivores. The presence of both ¹³⁷Cs and ^239,240Pu was confirmed in plants, for example in mushrooms (e.g., Kirchner 1998; Strandberg 2004; Kuwahara 2005; Baeza 2006), lichen and mosses (e.g., Testa et al. 1998; Mietelski et al. 2000; Kłos et al. 2006), and green plants (Frissel et al. 2002; Dushenkov 2003; Sokolik et al. 2004). These radioisotopes were also found in animal organisms. Presence of ¹³⁷Cs and ^239,240Pu in different insects species was affirmed (Copplestone et al. 1999; Mietelski et al. 2004) as well as in small mammals (Copplestone et al. 1999; Mietelski 2003) and carnivores (Mietelski et al. 2006, 2008).

In Poland, some areas of increased radiocesium activity resulting from the Chernobyl fallout were observed. The highest activities were noted in south-western Poland, in the eastern part of the Silesian and Foreland Lowland. In this zone, several smaller areas were distinguished, among which the most important is the so-called Opole Anomaly (Communique 1996; Jagielak 1996). In February and in March 1986, the mean beta activity in total fallout in this region was 13 Bq/m². On April 29^th, the beta activity reached 100 Bq/m² and on May 1st the activity exceeded 10⁵ Bq/m² (VSES 2008). In 2007, there were still areas of ¹³⁷Cs surface activities exceeding 70 kBq/m² in some forests on the region of the Opole Anomaly (Dołhańczuk-Śródka et al. 2007).

Determination of elements concentrations in particular constituents of environment is a crucial issue for description of their translocation mechanisms. However, information about other parameters of the system is indispensable. Among others, climate type, season of the year, local vegetation, soil type and its physicochemical properties as well as presence of certain bacteria and fungi species may affect elements circulation in ecosystems (Tamponnet et al. 2008). Unfortunately, it is usually not obvious which of the parameters play a key role in migration of element in the ecosystem considered.

A big number of factors affecting translocation of an element in woodland ecosystems significantly hampers modeling of this process. Transport of elements is influenced by a number of mutually independent or interrelated processes and depends on many parameters related to the current and former state of the environment. An insight in nature of these processes might be gained by analysis of the results received from statistical methods applied to the data obtained for different environmental components. It can be expected that proper statistical processing of the experimental data might reveal some of their specific features. These observations might be helpful in migration model designing creation.

In this, paper the results of ¹³⁷Cs and ^239,240Pu activities determination in forest soil horizons collected on the area of the Opole Anomaly were described. Because of supposed organic compounds importance in Cs and Pu ions retention, for each sample of horizon, the organic matter content OM was determined. The soil samples were collected in the sites located in the same forest complex. Vegetation at these sites was similar. All samples were collected within a few days in October. This approach enables reduction of variability in some parameters (e.g., soil humidity, or seasonal changes in vegetation) that might affect ¹³⁷Cs and ^239,240Pu migration in forest ecosystem.

Chemometric methods were used for examination of the results obtained.

2 Materials and Methods

2.1 Sampling Locations

Samples were collected in an area of the Opole Anomaly in October 2006. They were taken from Bory Stobrawskie forest, located in the north-east direction from Opole (PL). The sampling sites were located close to Zagwiździe (50°52′25″ N, 17°58′31″ E), Rzędów (50°44′46″ N, 18°08′38″ E), Staniszcze W. (50°38′55″ N, 18°20′56″ E), Olesno (50°52′31″ N, 18°24′54″ E), and Szumirad (50°50′20″ N, 18°14′36″ E). The soil samples were taken in the vicinity of at least 20-year-old trees, not less than 100 m from the roads. The ground surrounding the trees was in large part covered by fallen leaves and few forest bed plants were growing.

2.2 Sampling Methods

The consecutive soil layers were carefully taken starting from forest litter and finishing at approx. 30–35 cm depth to obtain sample of soil horizons. In our study, the samples of the horizons: Ol, Of, Oh, A, Ees, Bbr, and C were collected. Not all of the horizons appeared in each soil sample, usually a single profile, were composed of four to five horizons. The horizon sample was dried in 105°C until constant mass of the sample were recorded. Dry samples were manually cleaned to remove pieces of wood, cones, stones, and other intrusion bodies. This material was crumbled until no bodies on the 5-mm mesh sieve remained. The material obtained was kept in a tightly closed container.

2.3 ¹³⁷Cs and ^239,240Pu Activity Measurements

The measurement of ¹³⁷Cs activity in samples of woodland soil was carried out by means of a gamma spectrometer with a germanium detector HPGe (Canberra) of high resolution: 1.29 keV (FWHM) at 662 keV and 1.70 keV (FWHM) at 1332 keV. Relative efficiency was 21.7%. Energy and efficiency calibration of the gamma spectrometer was performed with the standard solutions MBSS 2 (Czech Metrological Institute, Praha), which covers an energy range from 59.54 keV to 1836.06 keV. Geometry of calibration source was a Marinelli beaker (volume of 447.7 ± 4.48 cm³), with a density of 0.985 ± 0.01 g/cm³, containing ²⁴¹Am, ¹⁰⁹Cd, ¹³⁹Ce, ⁵⁷Co, ⁶°Co, ¹³⁷Cs, ¹¹³Sn, ⁸⁵Sr, ⁸⁸Y, and ²⁰³Hg. Geometry of samples container was the 450 cm³ Marinelli beaker. The measuring process and analysis of spectra were computer controlled with use of the software GENIE 2000 (Canberra). The spectra were recorded for 24 h. Counting uncertainty did not exceed 4%.

Determination of plutonium in environmental samples requires separation of these isotopes in a pure form and fixing them on a steel plate, which enables alpha spectrometric measurements. This is realized by a radiochemical multi-stage procedure. In the first stage of this procedure, a dried and ashed (450–500°C) sample was leached with 6 M HCl. From the obtained solution, trace elements were co-precipitated with iron (III) hydroxide by 25% NH₄OH addition. The precipitate was dissolved in 6 M HCl and then separated from Fe by co-precipitation with calcium oxalate at pH = 3. Next, the precipitate was dried, burned in an oven, dissolved in 12 M HCl and then a second co-precipitation with iron (III) hydroxide was performed. In the next stage, the precipitate was dissolved in 8 M HNO₃, boiled on a sand bath with NaNO₂ until nitric oxides disappeared. This stage allows changing the oxidation state of plutonium to the Pu⁴⁺ form. The solution was introduced on an ion-exchange column filled with Dowex 1 × 8 (50–100 mesh). Before sample introduction, the column was washed with 8 M HNO₃ in order to exchange chloride ions on nitrate ions. After the sample was passed through the column, the next solutions were introduced as follows: 8 M HNO₃, 6 M HCl, and concentrated HCl in order to eliminate trace elements (Th, Am) which disturb Pu determination. In the final stage of anion exchange, Pu was eluted from the column using concentrated HCl with 0.1 M NH₄I, which changed the plutonium oxidation stage to +3. The obtained solution was evaporated to dryness with aqua regia to eliminate iodine and ammonium salts. Finally, Pu was electrodeposited onto stainless steel disks from 0.4 M ammonium oxalate with 0.3 M HCl and measured by alpha spectrometry (Komosa 1996).

Measurements were performed using the 7401 Canberra Alpha Spectrometer with a 1520 mixer/router and S-100 multichannel analyzer. The PIPS detector of 17 keV FWHM resolution was used. For quantitative analysis, the Canberra Genie-2000 software was used. Chemical yield was monitored by addition of a standard ²⁴²Pu solution to the sample. Measurements were performed usually during 600,000 s and radiochemical yield varied from 60 to 100%.

3 Computations

The area on which the samples were collected was not contaminated uniformly. It was obvious that location of the place from which the samples were taken affects its total ¹³⁷Cs or ^239,240Pu activity. To omit or, at least, to diminish the effect of unequal initial soil contamination, the relative activities a _r were calculated. The activities of isotope considered in consecutive horizons of the soil sample were added and then the activity of each horizon was divided by the sum calculated previously. It was expected that the relative activities would be more proper for assessment of mutual relationships between isotope concentrations in soil horizons than the activities on their own.

For statistical computations, the R language (R Development Core Team 2008) was utilized. R is a free software environment for statistical computing and graphics.

To gain information about possible structures in our data clustering methods were used. This method allows to assign objects to different groups, so that the data in each subset share some common traits. For our computation, the functions provided by the “cluster” library of R were used. Functions available in this library were described by Kaufman and Rousseeuw (2005). For each variable, the data were standardized by subtracting the variable's mean value and dividing by the variable's mean absolute deviation, and then all of the pairwise dissimilarities between observations in the data set were computed. Dissimilarities were Euclidean distances between points computed in space of standardized variables.

The overviews of cluster existence in data were shown on dendrograms—tree diagrams illustrating the arrangement of the clusters. Diagrams were constructed using “agnes” and “diana” functions from “cluster” library. Function “agnes” uses agglomerative nesting procedure, while “diana” realizes divisive hierarchical clustering.

Taking into account single point i belonging to cluster A, the a(i) parameter can be defined as average dissimilarity of i to all other points of A. For any other cluster B different from A, the average dissimilarity d(i,B) of i to all points of B can be calculated. The lowest value of d(i,B) can be found and it is denoted as b(i). The s(i) parameter is described by the following relationship:

$$ {s(i) = \frac{{b(i) - a(i)}}{{\max \left[ {a(i),b(i)} \right]}}} $$

(1)

For each i-th single point in cluster A it is s(i) = 0. The s(i) values are limited in the range from −1 to 1. If s(i) is close to 1, the i-th point assignment to cluster A is well justified. When s(i) is about 0, it is not clear at all whether i should be assigned to cluster A or to B. The negative, close to −1 values of s(i) suppose bad assignment of i-th point to cluster A. The s(i) values can be computed for all points in data set. For a given number of clusters k the mean value $\bar{s}$ can be computed. Interpretation of computations results was based on $\overline{s}$ parameter values. The silhouette coefficient SC is defined as the maximal value of all $\overline{s}$ computed for k = 2, 3 ... n − 1, where n is number of points. Subjective interpretation can be assigned to silhouette coefficient value. For SC lower than 0.26 no substantial structure in data can be supposed. Weak and probably artificial structures can be observed for SC in the range 0.26–0.50. A reasonable structure is supposed for SC between 0.51 and 0.70 and a strong structures for SC > 0.71 (Kaufman et al. 2005).

It was found that distributions of our data considerably differ from each other. This may cause problems in interpretation of significance test results. To avoid this problem, the data were separated into two groups and variables were transformed to make their distributions similar to the normal one. For this purpose the Box–Cox transformation was used. If the original random variable is x and the transformed one is x _t, the Box–Cox formula can be expressed by the following relationships (Eq. 2a–b):

$$ {x_t = {{\left( {x^m - 1} \right)} \mathord{\left/ {\vphantom {{\left( {x^m - 1} \right)} m}} \right. } m}}\;{\text{for}}\;{m} \ne 0 $$

(2a)

and

$$ {x_t = { \log }(x)}\;{\text{for}}\;{m} = 0 $$

(2b)

where m is the dimensionless exponent.

The exponents found for each column of data frame were utilized for x' computations.

Normality of variable distribution was verified using one sample Kolmogorov–Smirnov test.

For computations the transformed and standardized values of variables were taken. The data were standardized using the following formula:

$$ {x_{\text{st}} = \frac{{x - \bar{x}}}{\sigma }} $$

(3)

The existence of interrelations between variables was investigated. For this purpose, ordinary linear regression (OLS) and robust regression methods were chosen. Preliminary analysis of our results revealed possible problems due to data dispersion. In our computations, the robust regression methods were used, which are forms of weighted least squares regression. In robust regression, the linear equation y = xβ + ε is considered. To find estimators b of β, the following approach can be applied. Assuming a scaled probability distribution function ${f{{\left( {{e \mathord{\left/ {\vphantom {e s}} \right. } s}} \right)} \mathord{\left/ {\vphantom {{\left( {{e \mathord{\left/ {\vphantom {e s}} \right. } s}} \right)} s}} \right. } s}}$ of ε and setting ρ = –logf, the maximum likelihood estimator (MLE) minimizes

$$ {\sum\limits_{{i = 1}}^n \rho \left( {\frac{{y_i - x_i b}}{s}} \right) + n\;{ \log }s} $$

(4)

The MLE b of β solves

$$ {\sum\limits_{{i = 1}}^n {x_i } \psi \left( {\frac{{y_i - x_i b}}{s}} \right) = 0} $$

(5)

where Ψ is derivative of ρ with respect to b.

Equation 5 can be solved by iterated re-weighted least squares. For s value estimation, the median absolute deviation (MAD) was used. The Hampel, Huber, and Tukey (bisquare) M-estimators (MLE-like) were used in data processing. Each of these estimators is additionally described by its own parameters, but in our computations, we used the default values from function “rlm” (from “MASS” library in R language).

The M-estimation methods are robust to outliers in the response variable but are not resistant to outliers in the explanatory ones. The S-estimation was proposed to solve this problem, the method highly resistant to leverage points. But this method was also found to be inefficient. Advantages of M and S estimations were joined in MM-estimation.

Each estimator assigns a weight to residual e. For OLS, the weights w _OLS of each residual are the same (w _OLS = 1). Huber weights w _H are described by the following relationships (Eq. 6a–b):

$$ {w_{\text{H}} = 1}\;{\text{for}}\;\left| e \right| \le k $$

(6a)

and

$$ {w_{\text{H}} = \frac{k}{{\left| e \right|}}\;{\text{for}}\;\left| e \right|} > k $$

(6b)

In Huber weighting, observations with small residuals get a weight of 1. To the residuals bigger than k, decreasing with e weights are assigned.

The Tukey weights w _T are described by the relationships (Eq. 7a–b):

$$ {w_{\text{T}} = \left[ {1 - \left( {\frac{e}{k}} \right)^2 } \right]^2 }\;{\text{for}}\;\left| e \right| \le k $$

(7a)

and

$$ {w_{\text{T}} = 0}\;{\text{for}}\;\left| e \right| > k $$

(7b)

In biweighting, all observations with a non-zero and smaller than k residuals are down-weighted. Cases with e bigger than k are removed (Rousseeuw 1987; Venables and Ripley 2002; Fox 2002).

4 Results

In Table 1 statistical parameters of ¹³⁷Cs activities a _Cs, ^239,240Pu activities a _Pu and organic matter contents OM are listed. Activities a _Cs and a _Pu are expressed in kBq/kg and Bq/kg, respectively. OM is expressed in weight %. The following parameters of our data are shown: minimal value (min), lower quartile (q ₁), median (ME), upper quartile (q ₃), maximal value (max), mean value $\left( {\overline{x} } \right)$, standard deviation (SD), skewness (g ₁), kurtosis (g ₂), and relative variability coefficient (ratio of difference between maximal and minimal values to mean value, RVC).

Table 1 Parameters of ¹³⁷Cs activities a _Cs [kBq/kg], ^239,240Pu activities a _Pu [Bq/kg] and organic matter content OM [%]

The ^239,240Pu activities were approx. 1,000 lower than ¹³⁷Cs activities. For the isotopes investigated, the differences between mean and median as well as g ₁ and g ₂ values were similar, supposing similar and non-normal type of variables distribution. Values of the same parameters for OM also indicate non-normal variable distribution, but its type is dissimilar to the isotopes distributions. The relative variability coefficients of a _Cs and a _Pu were similar too and they were approx. 2.5 times bigger than RVC for OM.

In Fig. 1, the box plots showing ¹³⁷Cs relative activities distribution in soil horizons are drawn. In this plots lower base of the rectangle is a lower quartile, upper base is an upper quartile and a horizontal line dividing the rectangle is a median. Whiskers are formed by connecting the formed box with short horizontal lines drawn for quantile q = 0.95 (upper whisker) and quantile 0.05 (lower whisker).

Fig. 1

Boxplots of a _rCs in soil horizons and subhorizons

Figure 1 shows that the highest ¹³⁷Cs relative activities were found in the Oh and A horizons.

Figure 2 shows the box plots of ^239,240Pu distribution in soil horizons.

Fig. 2

Boxplots of a _rPu in soil horizons and subhorizons

The highest ^239,240Pu relative activities were found in the A horizon.

High activities of the investigated isotopes were observed in the lower organic horizons and in the upper inorganic. The plots in Figs. 1 and 2 indicate quite well maximal a _r in the soil region where organic horizon turns into inorganic one.

Figure 3 shows the organic matter distribution in soil horizons.

Fig. 3

Boxplots of organic matter content in soil horizons and subhorizons

As it could be expected, organic matter content continuously decreases downward the soil profile.

Investigation of clustering in data was performed for activities of radionuclides and organic matter content. Positions of points were determined by a _rCs, a _rPu, and OM variables, so that cluster formation was investigated in 3D space of parameters. Application of both agglomerative and divisive methods leads to similar structure of dendrogram. Figure 4 shows the dendrogram constructed using divisive algorithm. Additionally the horizon or subhorizon type was marked at each point.

Fig. 4

Dendrogram of structures appearing in data comprising a _rCs, a _rPu, and OM

A tendency to group formation based on subhorizon or horizon type can be observed. Most of the points representing organic subhorizons are located in structures on the left side of dendrogram whereas the inorganic ones are on the right side.

To examine whether clustering in data is apparent or true, the SC coefficient was determined. Figure 5 shows the $\overline{s}$ parameter dependence on number of clusters k.

Fig. 5

Mean s dependence on cluster number in data comprising a _rCs, a _rPu, and OM

The SC value of 0.639 was found for seven clusters. These results supposes existence of reasonable (but not strong) structure in the data. But for k = 4, 6 to 9 the $\overline{s}$ values are comprised in the range from 0.600 to 0.628. These values are only a bit smaller than SC. Taking this data into account, it is rather difficult to conclude that the certain number of clusters indicates well the structures existence in the data. It might be supposed that points with a _rCs, a _rPu, and OM coordinates tend to form some structures in respect to soil horizon or subhorizon type. But these structures are rather fuzzy and they may partly overlap with the nearest neighbors. For analysis of such kind of data, the fuzzy clustering methods might be utilized. These methods are used in many areas of environmental sciences. Among others, they are helpful in e.g., water, air, and soil pollution assessment (e.g., Lehn and Temme 1996; Chang et al. 2001; Argiriou et al. 2004; Grande et al. 2005; Ocampo-Duque et al. 2007) or assessment of toxic substances influence on the environment (e.g., Melcher and Matthies 1996; Friedrichs et al. 1996; Sârbu and Pop 2000; Salski 2007).

In Fig. 6, density of a _rCs distribution is shown. Position of individual points is marked with vertical dashes above the horizontal axis. In the upper part of the plot description of soil horizon or subhorizon, the type is shown for each point. No clear relationship between horizon type and point location on histogram can be observed. The distribution is positively skewed.

Fig. 6

Density of a _rCs distribution in soil horizons and subhorizons

In Fig. 7, density of a _rPu distribution is shown. Similar to a _rCs distribution, no clear relationship between horizon type and point location in the histogram can be observed. The distribution seems to be positively skewed, but density of points in the right side of the histogram is bigger and in the middle part of histogram is smaller than the ones for a _rCs distribution.

Fig. 7

Density of a _rPu distribution in soil horizons and subhorizons

The OM distribution shown in Fig. 8 is antimodal. The left side of the histogram is formed by points representing inorganic soil horizons while the right side contains points representing organic soil horizon. It can be concluded that OM distributions in inorganic and organic soil horizons are substantially different.

Fig. 8

Density of OM distribution in soil horizons and subhorizons

We would like to examine possible co-variabilities that may occur between variables. Linear relationship is the simplest one and its credibility can be assessed (considering some assumptions) by correlation coefficient r. Linear transformation of one variable into the second implies similar distribution of both variables. Though distributions of a _rCs and a _rPu are somewhat similar, both of them are essentially different from OM distribution. The shape of the histogram in Fig. 8 indicates necessity of OM data separation into two groups. The first group contains data from organic horizon and the second comprises data from inorganic horizon. Before further computations, the data were separated in two data frames containing a _rCs, a _rPu, and OM values for organic and inorganic horizons. To avoid problems in interpretation of significant test results, we have decided to transform the variables to make their distributions similar to the normal one. For this purpose, the Box–Cox transformation was used (Eq. 2a–b). In Table 2, the computed exponent m values and their standard errors, as well as mean values and standard deviations of transformed variables are shown.

Table 2 The values of m exponent and their standard errors SE_m, mean values and standard deviations SD_ar calculated for transformed a _rCs, a _rPu, and OM in organic and inorganic horizons

The values of transformed variables were standardized using Eq. 3. After standardization, the data concerning the relative activities and organic matter content in organic and inorganic horizons were joined together. Transformed and standardized ¹³⁷Cs relative activities from the O horizon were connected with those from inorganic horizons. The same operations were carried out for ^239,240Pu relative activities and for organic matter content. All operations performed did not change data arrangement in rows of data frame. In this way, the parameters investigated became continuous again through organic and inorganic soil horizons. The new a _rtCs, a _rtPu, and OM_t variables have mean values close to 0 and standard deviations close to 1. Normality of data distribution was examined with Shapiro–Wilk test. The lowest confidence level α _SW = 0.11 was computed for a _rtPu. The computations results show that normality of a _rtCs, a _rtPu, and OM_t distributions cannot be rejected regarding usually accepted critical α _SW = 0.05.

Existence of groups in the data may cause false evidence of relationship existence, e.g., results of computations using data in which two separated clusters of points can be recognized, might indicate false linear relationship between variables. But the results from CA showed rather poor grouping tendency in our data. It might be supposed that regression methods can be applied with a low risk of false interpretation of the computation results.

Linear correlation coefficients r between a _rtCs, a _rtPu, and OM_t and their confidence levels α _r were computed. Coefficient of correlation between a _rtCs and a _rtPu was 0.774 (α _r = 0.00), and this was the highest value among the computed ones. Correlations between a _rtCs, a _rtPu, and OM_t were negligible. For a _rtCs and OM_t the r value was 0.038 (α _r = 0.86). For a _rtPu and OM_t, the r value was 0.053 (α _r = 0.80).

Parameters of linear equation ${a_{\text{rtCs}} = b_0 + b_1 \times a_{\text{rtPu}} }$ describing relationship between ¹³⁷Cs and ^239,240Pu activities were computed using robust regression and OLS methods. In Table 3, values of the b ₀ and b ₁ parameters, their standard deviations SD, scaling factor s, estimation method, and M-estimator types are shown.

Table 3 Parameters of linear equation computed using robust regression methods

In Fig. 9, the plots of the relationship between a _rtCs and a _rtPu as well as lines representing fitted models are shown.

Fig. 9

Relationship between a _rtCs and a _rtPu

The lines presenting results from Huber and Tukey M-estimators nearly overlap with each other. For this reason, in Fig. 9, a single line is drawn to show results obtained from this methods. Utilization of the Hampel estimator and OLS method deliver the same b ₀ and b ₁ values, so, in Fig. 9, a single line represents both approaches.

Regardless of the estimation method or M-estimator type, the values of b ₀ and b ₁ parameters were similar. Comparison of b ₀ and SD_b0 values suppose that the intercept value is 0 in population. Linear relationship between variables can be simplified to ratio of transformed ¹³⁷Cs and ^239,240Pu relative activities.

Figure 10 show weights assigned to consecutive points from the plot in Fig. 9. For the Hampel estimator, all weights were 1, like in OLS. That is why the results computed in this regression models were the same for both methods.

Fig. 10

The weights w assigned to consecutive points from the plot in Fig. 9

Organic matter content influence on ¹³⁷Cs and ^239,240Pu accumulation was investigated. While very low values of correlation coefficient between OM and ¹³⁷Cs or ^239,240Pu were computed, one could suppose that it might be a result of outstanding OM observations. To verify this presumption, the robust regression methods were used to find linear relationships between OM_t and a _rtCs as well as OM_t and a _rtPu. But the computed slope values and their standard deviations did not allow to accept significancy of organic matter content influence on the investigated isotopes activity. The computed t statistics values for slopes did not exceed 0.32. The hypothesis that in population values of the slopes were 0 cannot be rejected. This result does not confirm conclusions of some authors mentioned in the “Introduction” section in this paper. However, absorption of Cs and Pu cations is determined not by organic matter generally but rather by some of its components. Concentration of certain compounds, originated from decaying of organic matter and affecting Cs and Pu cations retention, may depend on climate, plant species growing on the area, fungi, and microorganism activities and many others factors. Earlier investigation carried out on the area of the Opole Anomaly showed that ¹³⁷Cs activity only in the Ees horizon depends on organic matter content (Ziembik et al. 2009). It was also shown that common influence of two or more soil parameters is needed to affect significantly the ¹³⁷Cs activity in soil horizon. It is possible that Pu ions transport in soil also depends on more than only OM parameter. This conclusion can be a starting point for further investigations.

5 Conclusions

In our, samples the ¹³⁷Cs activity was about one thousand higher than ^239,240Pu activity. For both isotope activities, similar relative variability coefficients were computed. The RVC of organic matter content was approx. 2.5 times lower than the ones for ¹³⁷Cs and ^239,240Pu activities.

The CA method applied to points with a _Cs, a _Pu, and OM coordinates show a tendency to group formation based on subhorizon and horizon type. However, the clusters were not well separated, presumably partly overlapping with nearest neighbors. Poor tendency to cluster formation in the data allowed us to utilize regression methods in further computations.

The distributions of a _rCs, a _rPu, and OM were investigated. It was found that distributions of a _rCs and a _rPu were similar, whereas distribution of OM was substantially different. For further computations the data were divided into two groups. The first group comprised the data from O horizon and the second contains data from inorganic soil horizons. The data were transformed using the Box–Cox formula then standardized, and data from organic and inorganic horizons were joined together.

The co-variability of transformed variables was investigated using OLS and robust regression methods. No significant differences between results obtained from these methods were found. The linear dependence between a _rtCs and a _rtPu was affirmed. But due to variables transformation, this relationship was not essentially linear. No relationships between a _rtCs and OM_t as well as a _rtPu and OM_t were found.