Introduction

The energy requirement for human activities is in increase, and hence it is necessary to increase the diversity of the energy acquisition types and efficiencies. Nuclear energy is one of the best sources of enormous energy supply with very little fuel and greenhouse gas emissions. The standards adopted by the International Atomic Energy Agency must be applied strictly for their operation; otherwise, accidents may cause to global disasters [1]. Nuclear power generation through nuclear power plants continues unabated manner, even though some accidents have occurred, among which are Three Mile Island (1979), Chernobyl (1986) and Fukushima (2011) nuclear accidents [2]. Experts of Fukushima Dai-Ichi Nuclear Power Plant Accident (FDNPPA) describe it as the largest nuclear accident after Chernobyl Nuclear Power Plant Accident, where the reactor had user error and caused a tremendous release of radioactivity to the environment [3,4,5,6,7,8,9,10,11,12,13]. Radionuclides can be transported thousands of miles away due to atmospheric events [14,15,16,17,18,19]. In the FDNPPA, the reactor cooling system was damaged by 9 magnitude earthquake and subsequent tsunami, and hence, the reactor melted partially [20]. After FDNPPA, radioactive fission products between the Fukushima Dai-Ichi Nuclear Power Plant (FDNPP) and neighbouring provinces have spread widely and led to serious soil pollution with regional as well as global radionuclides dispersions. Fission products from the accident spread not only in the entire northern hemisphere, but also in the southern hemisphere [21,22,23,24,25,26,27].

The most important biological effects of radionuclides from such accidents are due to the environment long half-lives of 137Cs (30.1 years) and 90Sr (29 years) isotopes. Their artificial radionuclides activities are important research topics in the air, soil and water [28,29,30,31,32,33,34,35,36,37]. The radionuclides concentrations determination is very important as for the living organisms’ health is concerned. One of the most significant steps is to evaluate the radionuclides concentrations in the region by means of a convenient model [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58]. Once the validity of such a model is established then it is possible to obtain appropriate information as for the transport amount of the activity concentrations in different radionuclides [59, 60]. In order to provide all these facilities, after the Chernobyl and Fukushima nuclear reactor accidents, various authors proposed different models and methods to analyse spatially the radioactive fallout clouds migration [2, 61,62,63,64,65,66,67,68,69,70,71].

Spatial [72, 73] and spatio-temporal models [74,75,76] have significant advantages in depicting the radionuclides effects on atmosphere [7] and surface transports [77,78,79]. It is possible to conclude that many researches have applied such spatial models from micro- [80,81,82] to macro-scales [82, 83]. The first examples of the spatial modeling is due to Halley [84], who showed the directions of monsoons and winds on equally divided maps, and concluded about the physical cause of these wind formation. Student [85], performed spatial modeling by dividing 1 mm2 into 400 equal parts to count the yeast cells. According to cell number in the unit area the probability distribution functions (PDFs has been obtained, which is regarded as the first spatial modeling study by many researchers. Spatial modeling is useful to determine the spatial distribution of geomagnetic fluctuations [86] in the determination of mineral metaformic rocks paragenesis [87], in seismic estimation studies [88], in the seismic body waves propagation determination [89], in hydrology [90], and in electromagnetic interactions studies [91], in the determination of 235U concentrations in marine sediments [92], in the climate changes clarification [93], and in the geophysical studies [74, 94,95,96,97,98].

The Point Cumulative Semivariogram (PCSV) technique is employed for spatial modelling and its calculations are based on mathematical principles. Its validity depends on the classical variance and covariance techniques for regular distribution in the spatial analyses that comply with the normal PDF. In practical works, the measurement locations are frequently irregularly spaced. Matheron [99] suggested a semi-variogram (SV) technique, which is a very useful metric that expresses the difference square between the regional variable (ReV) measurements depending on the distance. Later, Şen [100] proposed the Point Cumulative Semi-Variogram (PCSV) method, which has all the features of the classical SV, and at the same time, it further enhances the properties of classical SV. The PCSV method is used when the sampling points are scattered irregularly [97, 101,102,103].

In this study, after the occurrence of FDNPPA, PCSV [100] and TDM [104,105,106] methods are proposed to investigate transport characteristics, and the effects of 137Cs and 90Sr radionuclides radioactive fallout for Hazar Lake, Turkey. In this study the depth parameter is also considered. This latter method is preferred, because it has significant advantages for the transport and radioactive fallout characterization. The water depth is important to see the consequences of the global transport of the relevant radionuclides, and besides, it is important in the radionuclides concentrations amount [107]. For this reason, the lake depth is also included in the modelling process, so that a three-dimensional spatial analysis is suggested for the radioactive particles. Furthermore, re-assessments are made on spatial modeling and atmospheric radioactivity transport. Finally, the iso-radioactivity diagrams are drawn and interpreted for 137C and 90Sr radioactive fallout products.

Research area and experimental studies

The Hazar Lake and sampling selected stations in the research area are given in Fig. 1. The lake is one of the deepest (250 m) freshwater in the world [108, 109]. It extends in the northeast-southwest direction along the Eastern Anatolian Fault at an altitude of 1255 m and its width is 7 km with 25 km length [110, 111]. One of its interesting features is a tectonic feature directly above the Eastern Anatolian Fault Zone (EAFZ), which is a seismically active strike-slip left-hand fault zone in this part of the world [112]. The southern coastline of the lake is very flat and fault-controlled and limited by the rise of the Caspian Mountain (2350 m). The northern coastline is not associated with any faulting [110]. At places, where the active fault lines are known, higher environment natural radioactivity is identified than other regions [97].

Fig. 1
figure 1

a Hazar Lake and sampling stations. b 3D representation of the Hazar Lake sampling points. Each of the 8 stations created for sampling is divided into three groups as surface (s), middle (m) and deep (d) depths. b Shows the measurement of the distances from the reference station (number 1) to the other stations for PCSV modeling. After this measurement, the distances from station 2 to other stations are measured by passing to station 2, which is done for all groups (s, m, d) of all other stations (see “Point cumulative semivariogram modelling” section for theoretical explanations)

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Basin sediments mainly originate from two main drainage systems confluence with the lake at the south-western and north-eastern ends. The Kürkçayi River forms an important alluvial fan in the southwest drainage system, and it is the largest drainage system. The Northeast drainage system consists of several streams with small drainage areas. The main rock in the collection area consists mainly of magmatic, metamorphic and ophiolitic rocks of the Mesozoic and Palaeozoic periods. The mountainous area to the south of the lake consists of late Jurassic magmatic rocks and middle Eocene limestones [110, 111].

Water and bottom sediment sample stations constitute the material of this study and such a research has attracted the attention of many researchers in the past due to the morphological, geological and tectonic features as given in Fig. 1. A total of 24 water samples are taken from different depths (surface, medium and bottom) at each station in addition to 8 bottom sediment samples for determination the activity concentrations of 137Cs and 90Sr radionuclides.

Determination of 137Cs and 90Sr activity of water samples and bottom sediment samples

To pick up the water samples, a Nansen tube and a dipper are used to get the bottom sediment. Sterilized 1 L glass bottles are used for radioactivity analysis of water samples. Three samples are taken from the same bottle with the help of 100 mL beakers cleaned with pure water. After evaporating the water samples with the help of the heater (60 °C), the remains are taken by spatulas and placed in aluminium tables with a surface area of 11.34 cm2 and a depth of about 4–5 mm with pure water. After drying the sediment in the liquid phase in the trays, the activity concentration counts are performed with the gamma/beta sensor counting system (ST7 scintillation counter) to perform gamma/beta radioactivity analyses of the samples. A well-type gamma-spectrometric system with 2″ × 2″ NaI (TI) detector was used for the analysis of the radionuclides. The system has a 3.5 cm thick cylindrical lead shield that prevents external radiation. 60Co (1 μCi) and 226Ra (10 μCi) spot sources were used for energy calibration of the detector system.

To improve statistical confidence for each sample, the measurements are repeated 3 times and then the arithmetic mean is considered as representative. The following expression provides the activity concentrations are calculated for each sample.

$$A = \frac{C}{{\varepsilon \cdot P \cdot V_{s} }}\quad {\text{Bq}}/{\text{L}}$$
(1)

where C is the unit time count, ε is the detector efficiency, P is the probability for the characteristic gamma/beta rays, Vs is the volume of the sample, and A is gamma/beta activity in terms of Bq. The activity concentrations of 90Sr and 137Cs are evaluated using its 546 keV peak and 661.6 keV peak, respectively [113].

One of the aims is to carry out radioactivity analyses of the bottom sediment samples for possible change and transport of 137Cs and 90Sr in the bottom sediment. The extraction of the bottom sediment samples is done together with the water sampling procedure. After similar procedures in the water samples, the sediment samples are weighed by transferring to the tared planchets and thus a sediment amount is calculated for each sample. Sediment samples are collected using a stainless steel dipper. Sediment samples are put into polyethylene bags and stored at 4 °C and transported to the laboratory. The sediments are dried in an oven at 50° C for 48 h. All samples are counted by the gamma/beta sensor counting system for activity determination. The following expression is used for the activity concentrations of the samples [113].

$$A = \frac{C}{{\varepsilon \cdot P \cdot M_{s} }}\quad {\text{Bq}}/{\text{kg}}$$
(2)

where Vs in Eq. (1) is replaced Ms, which is the quantity of the sample.

The standard deviation of the measurements has changed between 5 and 10%. The internal quality control is checked using certified reference material, IAEA-384, within ± 1 standard deviation (SD) of the reference value. The accuracy and precision of radiochemical determination of 137Cs and 90Sr are approximately 5% [114].

Theoretical studies for radioactive fallout

Point cumulative semivariogram method

Variance and correlation techniques are frequently used in the literature to measure the degree of regional dependence in spatial variables. These methods cannot fully express regional dependence due to the non-normal PDFs or the irregularity of the sample locations [115].

The classic SV can makes reliable estimates for small distances when the distribution of sample points is regular within the region. As the distance increases, the number of data pairs decreases for the calculation of SV, which means less reliable estimation at larger distances [116]. The SV calculation process is similar to the time series analysis, and it helps to determine influence of distance, which specifies the area of dependence between uniformly distributed special points [117].

Şen [115], has proposed the Point Cumulative Semi-Variogram (PCSV) method, which is based on the relationship between the point and the area according to the absence of stationarity, and the irregular or random measurement sites distribution [118]. The PCSV method accounts for the regional effects of other sites within the study area, and the number of PCSVs is equal to the number of sites [119]. The PCSV can be defined as the sum of the half of the difference squared ranked according to distance values from smallest to the biggest distance. This method yields a non-decreasing experimental PCSV function for the site considered. The mathematical expression is given by Şen [100] as follows.

$$\gamma \left( {d_{i} } \right) = \frac{1}{2}\sum\limits_{i = 1}^{n - 1} {(Z_{c} - Z_{i} )^{2} }$$
(3)

where γ(di) is the PCSV value at distance, di, of the corresponding station; Zc is the regional variable value at the reference point, and Zi (i = 1, 2, …, n − 1) is the value of the regional variable at other sites. The implementation steps of the PCSV method can be summarized as follows:

  1. 1.

    The reference site is selected, let us say site c, the distances between this and the other sites (i = 1, 2, …, n − 1) are calculated. If there are n sites, n − 1 is the number of distances.

  2. 2.

    For each pair, there are half-square differences between two data values. In this way, each distance has its own half-square value as \(\frac{1}{2}(Z_{c} - Z_{i} )^{2}\), where Zc and Zi are the regional variable values in the corresponding region and in i-site, respectively.

  3. 3.

    The distances are sorted from smallest to the largest and the sums of consecutive half-square differences are calculated for each distance. This method gives a non-decreasing experimental PCSV function at the site according to Eq. (3).

  4. 4.

    For other sites, sample PCSVs are calculated in the similar way by repetition of the previous steps.

  5. 5.

    A theoretical PCSV curve is fitted to the experimental PCSV scatter diagram by means of MATLAB® software program.

Triple diagram method

Triple diagram method is based on the fact that three regional variables are shown on a single diagram using the Kriging methodologies [120,121,122,123]. The corresponding change can be seen in detail and useful way than the classical Cartesian coordinate system. The triple diagram method is used for iso-radionuclide map constructions from all the numerical results.

Results and discussion

There are many factors that affect the behaviour and propagation of radionuclides after a nuclear accident [124, 125]. Much of the radioactive particle propagation depends on environmental conditions and events [126]. Factors such as wind direction, precipitation, moisture, soil structure, vegetation cover, soil pH value affect the propagation of these nuclides [127]. The radioactive particles transported to far distances along the winds are stored on the earth surface [128] and then radiated into the ground by radioactive precipitation [129, 130], causing radioactive contamination [131]. Precipitation and flooding erode the land on which radionuclides are stored [128]. These dissolved radionuclides reach rivers [132] and ground waters [133]. Another factor that affects the radioactive substances is water transport, which has different characteristics such as solubility, transportability and precipitation of different radioactive grains. Due to the strong flow velocities of the surface waters, the clay minerals are easily transported with potassium, rubidium, cosmic ray and artificial radionuclides in suspended particles [134,135,136,137]. 137Cs is a radionuclide that radiates to the environment in the event of a nuclear accident, carried along long distances by meteorological events, and able to survive for a long-time in the ground [138]. After a nuclear accident, as well as the 137Cs that spread to the Earth’s atmosphere, the 90Sr goes down to the earth with sprinkles or rain like 137Cs [7, 20]. Along the tendency of radioactive isotopes to accumulate in soils, waters and rocks are closely related to the geological structure of the environment [139]. Many environmental factors such as precipitation regime, soil structure, vegetation cover and geology of each region are also effective in the process [140]. Depending on these differences, the radionuclides distributions rates vary. All the factors that are mentioned above affect the accumulation and distribution of 137Cs and 90Sr, and therefore, cause to the distribution of 137Cs and 90Sr depending on the distance between the sample stations.

Both experimental and theoretical works are carried out in Hazar Lake. The activity concentrations of radionuclides in analysed samples, water depths, locations and the gamma energies are used for calculations of these activity concentrations, which are given in Table 1.

Table 1 Sampling location coordinates and activity concentrations of water samples collected at Hazar Lake
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In this table, the letters a, b, and c represent the surface, medium and bottom depth distances of the corresponding sampling station, respectively.

In addition to the lake waters, concentrations of 137Cs and 90Sr are also determined in the bottom sediment samples (Table 2). Thus, it is understood that the radionuclide migration in water and bottom sediment changes in samples are more informative. The radionuclide measurements in Tables 1 and 2 have a standard deviation of ± 10%.

Table 2 Depths and activity values of bottom sediment stations
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Normal PDF is the most important and employed one in different research applications. As in classical statistic, the geostatistical analysis is also expected to conform to the normal PDF [141, 142]. The data may not be suitable for normal PDF, and therefore in this study, transformations are applied to fit the normal PDF. 90Sr in water and 137Cs and 90Sr activity concentrations in the bottom sediment abide with the normal PDF after logarithmic transformation. 137Cs activity concentrations in water accord with normal PDF without logarithmic transformation. Normal PDF tests, Q–Q plot method and Shapiro–Wilk normality test are performed to see if the data are normally distributed. The Shapiro–Wilk test is the most powerful in comparing the forces of normality tests [143]. Figure 2 shows the normal PDF graphs of the 137Cs and 90Sr activity concentrations in the water and the relation between the expected and observed values. Similarly, Fig. 3 indicates the normal PDF graphs of the 137Cs and 90Sr activity concentrations in the bottom sludge. In addition, Pearson’s r values are calculated to see the relationship between variables. Table 3 includes the results from the statistical analysis.

Fig. 2
figure 2

Frequency distribution and Q–Q plots of the 137Cs and 90Sr activity concentrations in the water

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Fig. 3
figure 3

Frequency distribution and Q–Q plots of the 137Cs and 90Sr activity concentrations in the bottom sediment

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Table 3 Descriptive statistics for samples
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Depths are taken into consideration as important factors in determining the radionuclide activity concentration. The activity concentrations variation according to bottom sediment samples and the surface, middle and bottom depths of water sampling points from different parts of the lake are plotted for respective radionuclides in Fig. 4a–d.

Fig. 4
figure 4

a Change of 137Cs activity for surface, middle and bottom water depths of the Hazar Lake, b change of 90Sr in water samples, c change of 137Cs in bottom sediment, d change of 90Sr in bottom sediment

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Figure 4a, b and Table 1 present the maximum activity concentrations for the surface, middle and bottom distances of the 137Cs and 90Sr isotopes in the water samples. These values are 0.964, 1.032, 0.946 Bq/L for 137Cs and 0.961, 1.275 and 0.885 Bq/L for 90Sr, respectively. Mean activity concentrations of 137Cs and 90Sr are calculated as 0.7325, 0.629, 0.651 Bq/L and 0.657, 0.619 and 0.663 Bq/L for the surface, middle and bottom depths, respectively.

The results for activity concentration in water and sediment in different parts of the world are given in Table 4 for comparison purpose with the values measured in this study, Fukushima Dai-Ichi nuclear power plant accident with no significant radioactivity Fukushima transfer to Turkey. Although this indicates that the result is negative, but this study shows the boundaries of the FDNPP effect, and this context provides an answer regarding the impact on Turkey. The accident offers an important result, because it serves the public interest.

Table 4 Comparison of radioactivity concentration in this study with values reported for other locations in the world
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Point cumulative semivariogram modelling

The distance-dependent changes in the regional variables in the study area (137Cs and 90Sr in this study) can be defined by the SV functions. The difference between the values of the regional variable at different sites is a function of the distance between these variables [156]. Since the PCSV method takes into account the effect of all the stations in any region, unlike the classical SV, the number of the PCSV graphs is equal to the number of stations. There are 24 different water-sampling sites, and therefore, 24 PCSV graphs (48 graphs in total) for 137Cs and 90Sr. Since there are eight positions for the bottom sediment samples, eight PCSV graphs (16 graphs in total) appear for each of the radionuclides. The least squares model fits theoretical curves to the scatter of PCSV values. The graphs show similar characteristics, and therefore, they are grouped as in Fig. 5. The stations with the same fit curves are given as the PCSV models in Fig. 5 and Table 5.

Fig. 5
figure 5

PCSV models plotted for 64 graphs in overall total. Since the PCSV method obtained one graph representing each station, the model curves that characterize the stations are drawn. The stations are then grouped as in Table 3 and the results are interpreted

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Table 5 Distribution of graphs drawn for 137Cs and 90Sr in water and bottom sediment samples of all stations according to PCSV models
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A sample graph for the theoretical PCSV and the representation of its parameters are given in Fig. 6a. Figure 6b shows the original program output, which is the graph of the 137Cs of 1c station in water. In this figure, the PCSV model curve remained almost constant after 13.11 km (range). The stationary point of PCSV is defined as “Sill” in the geostatistical literature. On the other hand, the 1c 90Sr PCSV graph also follows Model A (Table 5) with the range (1c, 90Sr) about 13 km.

Fig. 6
figure 6

a Theoretical PCSV graph and its parameters. b Experimental PCSV graph obtained for 137Cs water 1c station. This graphic is selected as an example and the original program is output

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The model-matching stations in Fig. 6b are grouped as Model A (Table 5), and the same processes are performed for each of the other 63 stations with records in Table 5 models in Fig. 5, where the theoretical PCSV graphs of the two radionuclides provide the following information.

If the distance between the sampling points increases, the variogram value also increases, and rises to an approximate constant value at a certain separation distance, which is referred to as the range. The appearance of the sill value in the PCSV graphs can be explained as the weak contribution from other remote stations. The PCSV graphs of 137Cs and 90Sr 1c stations have the sill value for 137Cs as 0.84, and for the 90Sr as 1.769. It is obvious that the sill values are different for two variables although the same range value exists in the same region. The large sill value for these two variables at the same distance indicates increase in the PCSV values, because the model curve approaches the PCSV axis. In this region 137Cs and 90Sr isotopes have the same range values, and the contribution of 137Cs from the other stations is greater than 90Sr. The distance up to the sill corresponds to the spatial dependence continues, which implies that the data are not related to one another along 13 km for the distribution of 137Cs and 90Sr around 1c station, and the distribution of 90Sr in area 3c is about 16 km. Samples that are close to each other with a lower distance than the range value is spatially interrelated. The greater the effective distance, the greater is the influence of the variable. Samples that are separated from each other by a greater distance than the range value are not spatially related. Inspection of the graphs indicates that the range value of each graph is different from each other, which is due to the difference in distance from each station to another. The origin of the graph indicates that the regional dependency is zero at h = 0 (where h is the length over the y-axis of the nugget effect).

The stations defined in the Model B group are represented in Table 5 and Fig. 5. Logarithmic change means that the contribution from other stations to the station concerned is not homogeneous. According to SV methodology, as distance increases, the relationship between points decreases. In this context, when Model B is examined one can see that the variogram value does not increase as much as the initial value, and the increase in long distances decreases. In other words, with increasing distance, there is a decreasing contribution. Ideally, the SV should cross its origin as the distance between samples approaches zero. However, many activity values show non-zero SV values as h approaches zero.

The nugget effect in Model B reflects the difference between close samples, but not exactly in the same position, and it is usually due to measurement error or the nature of the examined variable [157, 158]. The nugget effect varies in proportion to the increase in distance between the samples and the multiplicity of the data and finally it decreases with the compatibility of each other. If the nugget effect is large (small), the variance between the samples is high (low), and therefore, the variability is less.

Model C shows a change according to the Gaussian model and then goes on to a sudden increase. This model refers to phenomena that are similar in continuity or short distances [157, 159]. The variability is random after a different distance for each station on the x-axis, and the reason for this situation can be summarized for stations 1a and 1b match. After a certain distance from the surrounding stations (about 12 km), the contributions from other stations become more dominant, causing fluctuations in the concentration change. In addition, the presence of the nugget effect in the model indicates that these stations have their own characteristics. Indeed, there are only two stations that match Model B.

Model D shows a change according to Gaussian shape and has nugget effect. At stations 2a, 4c and 7b 137Cs complies with this model and have a very small nugget effect of 0.02, which indicates less variability in the isotope, because it is scattered more intensely than other stations.

Model E shows an exponential change, which starts from an intersection point on the horizontal (distance) axis. This implies that the 90Sr and 137Cs isotopes exhibit the similar distribution for the respective stations at smaller distances than this intersection distance, so that there is a regional dependency. When the PCSV curves of the stations for Model E in Table 5 are examined, it is observed that the 90Sr and the 137Cs are homogeneously distributed for distances smaller than 0.4–1.3 km.

Stations in Model F exhibit a parabolic behaviour at the origin implying variable contribution from the other stations to the relevant station. Model G exhibits a convex curve and reaches the sill value with the PCSV charts matching the relevant stations with this model, which shows that the curve remained stable after an average of 8 km. This implies that these stations had no effect on each other after 8 km. This distance is 9 km for 137Cs and approximately 7 km for 90Sr. After this effective distance, the radionuclides do not have a spatial association. The impact distance of the 137Cs relative to the 90Sr means that the effect of 137Cs continues at larger distances.

Model H is structurally similar to Model A but the only difference is in its nugget effect and similar interpretations can be made. Model I shows a logarithmic change unlike Model B, and it intersects the x-axis. Model J shows a logarithmic change and unlike Model B, but it does not have nugget effect, which indicates that the distributions of 90Sr concentrations at stations 2c, 3a and 8a are homogeneous at nearby distances and heterogeneous at rather far sites.

Modelling with triple diagram method

Iso-radioactivity maps are drawn in the sampling area by taking into account that 137Cs and 90Sr can be transported by flow in the water and bottom sediment media. These maps are the results of the triple diagram method, which shows the radionuclides transport characteristics at all depths in the lake. Figure 7 presents 137Cs distributions, which are obtained in 3-dimensions for transport characterization at all depths in lake waters.

Fig. 7
figure 7

Three-dimensional change of 137Cs in surface, middle and bottom waters of Hazar Lake

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It is possible to see visually the distribution of the whole 137Cs. Examination of the lake layers makes it partly possible to reach detailed interpretations in terms of depth. The triple diagram method is applied also for surface, medium, and deep depths for each radionuclide. The iso-radioactivity map for 137Cs in surface waters is given in Fig. 8, where there is a high activity intensity in the north–south direction in the middle part of the lake (0.964–0.896 Bq/L), and also the 137Cs mobility is high along this direction. As a consequence of the nuclear reactor accident, the 137Cs spread around the surrounding area, the radioactivity can be transported to distant places by meteorological phenomena and stay in the ground for a long time [160]. Almost 7–9% of the radionuclides in the soil containing 137Cs pass to the water. In addition, meteorological factors play an important role in the distribution and behaviour of 137Cs in different ecosystems [161, 162]. The bottom currents in the lake are quite strong and the lake has generally a wavy structure. These structural factors of the lake affect directly the transport of radionuclides.

Fig. 8
figure 8

Surface water 137Cs iso-radioactivity map

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In Fig. 990Sr exchanges are given in three-dimensional form in all lake depths. On the other hand, the surface waters 90Sr iso-radioactivity map is shown in Fig. 10 from which it is possible to see that the activity value has high 90Sr concentrations in the region surrounding the stations 3 and 4 (0.961–0.930 Bq/L). Furthermore, the activity intensity increases from the northern part to the coastal areas (0.860 Bq/L). According to other regions, the geology of the lake and the environment affect the distribution of the 90Sr more and this nucleus cloud spreads to the atmosphere through the rain waters and accumulates more in the soil and rocks. In these areas, the coastal sector has a clayey structure, which can directly contribute to the radionuclides absorption.

Fig. 9
figure 9

Three-dimensional change of 90Sr in surface, middle and bottom waters of Hazar Lake

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Fig. 10
figure 10

Surface waters 90Sr iso-radioactivity map

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Figure 11 is for the 137Cs iso-radioactivity distribution in the middle depth waters, where the radioactivity values reach the highest value of 1.032 Bq/L in the southwestern part of the lake and the activity ratios increase in the coastal areas with intense magmatic formations that are remarkable on the north-west coast of the lake.

Fig. 11
figure 11

Medium depth waters, 137Cs iso-radioactivity map

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Figure 12 indicates that in the case of medium depth waters for 90Sr the highest activity value (1.275 Bq/L) appears in the northern part of the lake. In the same way, it is observed that the activity towards shoreline increases in this region.

Fig. 12
figure 12

Medium depth waters, 90Sr iso-radioactivity map

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When the 137Cs iso-radioactivity map at the bottom depths (Fig. 13) is examined, it is found that the highest value (0.946 Bq/L) is reached in the south-west part of the lake as in the middle depth waters. In addition, activity density is high in the western part of the lake (0.872 Bq/L).

Fig. 13
figure 13

Bottom depth waters, 137Cs iso-radioactivity map

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In Fig. 14, at the bottom waters the highest activity of the 90Sr is in the northern part of the lake (0.885 Bq/L), similar to the middle depths. 90Sr is especially high around the eighth and second stations, which is about 40% of the coastal slope, which can be due to the large amount of soil, rock and similar deposits entering the lake. On the other hand, the eighth station is at the skirts of Hazar Baba Mountain, consists of metamorphic and volcanic rocks with completely natural radioactivity.

Fig. 14
figure 14

Bottom depth waters, 90Sr iso-radioactivity map

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Artificial radioactivity in the bottom sediment is found to have equivalent radioactivity values with very small differences. One can conclude that these radio-cores show a similar distribution in the sampling points. 2D and 3D graphics are drawn for the change in the bottom sediment of both radio-grains. The highest activity values are around Station 3. There is a continuous substance exchange between the lake and the surrounding coastal strip. Strong currents are observed in the bottom of the lake and on its surface, which entrain with various physical and chemical components. From the western coast of the lake, the Kürk River flows towards this station and 80,000 tons of clay-silt is pushed into the lake per year [108]. This factor is the most important effect when 137Cs and 90Sr values are high around this station (Figs. 15, 16).

Fig. 15
figure 15

137Cs a three-dimensional and b two-dimensional iso-radioactivity diagrams in the bottom sediment

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Fig. 16
figure 16

Bottom sediment, 90Sr a three-dimensional and b two-dimensional iso-radioactivity diagrams

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One can see in Figs. 15 and 16 the coexistence conditions are similar at the two radionuclides.

Conclusions

In this study, 137Cs and 90Sr activity concentrations are analysed in water and bottom sediment samples that are collected in Hazar Lake, Turkey. The collected data are modelled by Point Cumulative Semi-Variogram (PCSV) technique, which is an advanced geostatistical method. On the other hand, three-dimensional spatial analysis is also performed for map constructions, the comparison between the measurement results and the case of Fukushima accident is achieved for the purpose to determine whether radioactive material transfer risk reached to Turkey. Two important results are obtained as the measurements confirmed such that the water and bottom sediment samples contain some radionuclides from Fukushima, they are below the world averages, and hence, the results do not constitute a health problem for the public radiologically. This study provides a basis for identifying the possible impacts of nuclear power plants on the environment and possible future changes observations. On the modelling side, the Triple Diagram Method (TDM) provides the distribution of rather large variables easily by considering the innovative geostatistical method as, the Point Cumulative Semivariogram (PCSV). These two methods provide great convenience in interpreting large scale environmental systems in terms of related regional variables. The variation in the transport, propagation, and quantities of the variables can be easily interpreted and visually observed for the study regions.

Observed PCSVs for 137Cs in water samples are calculated according to five and for 90Sr to four different models. Concentrations of 137Cs and 90Sr from the same stations show very large distributional differences, and two artificial radionuclide have the mobility capacities that are weak in the bottom sediment samples with similar behaviours except for one of the PCSV graphs. It is possible to say that the contributions of the stations to each other and the environmental factors in the bottom sediment sampling sites are partly equal to the behaviour of these two radionuclides.

The PCSV and TDM methods gave important clues about the transport characteristics of the two radionuclides in the lake. These changes encourage one to monitor or characterize aforementioned methodologies for other radionuclides or harmful substances. The 137Cs concentrations are low in the waters in the north western part of the lake and the main reason is the presence of external water inlets in these parts for low concentration. PCSV clearly shows the transport characteristics of the radionuclide. The transport characteristics of 90Sr and 137Cs in the bottom sediment appear to be very similar. These two radionuclides are deposited in the northwest part of the lake, which is supported by TDM graphs. The behaviour of 137Cs and 90Sr in water has a negative correlation and hence, it is possible to conclude that the presence of two radionuclides in one medium at the same time has a negative effect as one increases and the other decreases. This inverse correlation is also supported by the case TDM graphs.

Finally, the lake has a tectonic structure and is in the middle of the elevations as a result of tectonic pit. The activity rates are relatively low compared to other parts of the world, leaving the burden of radioactive fallout on these mountain and hills.