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TECHNICAL REPORTS

Landscape and Watershed Properties

Soil Redistribution Model for Undisturbed and Cultivated Sites Based on Chernobyl-Derived Cesium-137 Fallout

^a Univ. of Natural Resources and Applied Life Science (BOKU), Dep. für Wald- und Bodenwissenschaften, Institut für Bodenforschung, Peter Jordanstrasse 92, 1190 Vienna, Austria
^b Technical Univ. Vienna, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

^* Corresponding author (markus.hrachowitz{at}boku.ac.at)

Received for publication November 18, 2004.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
Measurements of ¹³⁷Cs fallout have been used in combination with a range of conversion models for the investigation of soil relocation mechanisms and sediment budgets in many countries for more than 20 yr. The objective of this paper is to develop a conversion model for quantifying soil redistribution, based on Chernobyl-derived ¹³⁷Cs. The model is applicable on uncultivated as well as on cultivated sites, taking into account temporal changes in the ¹³⁷Cs depth distribution pattern as well as tillage-induced ¹³⁷Cs dilution effects. The main idea of the new model is the combination of a modified exponential model describing uncultivated soil with a Chapman distribution based model describing cultivated soil. The compound model subsequently allows a dynamic description of the Chernobyl derived ¹³⁷Cs situation in the soil and its change, specifically migration and soil transport processes over the course of time. Using the suggested model at the sampling site in Pettenbach, in the Austrian province of Oberösterreich ¹³⁷Cs depth distributions were simulated with a correlation coefficient of 0.97 compared with the measured ¹³⁷Cs depth profile. The simulated rates of soil distribution at different positions at the sampling site were found to be between 27 and 60 Mg ha^–1 yr^–1. It was shown that the model can be used to describe the temporal changes of ¹³⁷Cs depth distributions in cultivated as well as uncultivated soils. Additionally, the model allows to quantify soil redistribution in good correspondence with already existing models.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
DUE TO ITS tracer properties the artificial radionuclide ¹³⁷Cs (t_0.5 = 30.2 yr) has been used to assess soil redistribution as well as sedimentation mechanisms for more than three decades (Tamura, 1964; McHenry and Ritchie, 1977). Up to 1986 ¹³⁷Cs originating from nuclear weapons tests was the basis of worldwide research. The permanent release of ¹³⁷Cs into the atmosphere as well as the climatic conditions resulted in regionally homogenous fallout in the northern as well as in the southern hemisphere (Shimada et al., 1996). After the catastrophic incident at the nuclear power Station in Chernobyl in 1986, high amounts of natural and artificial radionuclides were set free into the atmosphere. As it was a single, short-term event, the subsequent fallout was driven by local weather conditions rather than by global climatic conditions. The sharply defined contamination cloud first moved northwest before turning to a southwest direction. In combination with eventual precipitation events, the cloud caused different levels of fallout along its path (Bossew et al., 1995; DeCort et al., 1998; Lettner et al., 2000; Sutherland, 1994) and 99% of the Chernobyl fallout was distributed across Europe between 26 Apr. and 15 May 1986 (Golosov, 2003). In addition to the locally high variations of ¹³⁷Cs contamination, the amount of Chernobyl-derived ¹³⁷Cs in Central and Eastern Europe is about one to two magnitudes higher than the ¹³⁷Cs originating from nuclear weapons tests. In contrast with the spatial ¹³⁷Cs distributions, the depth distributions as well as the migration mechanisms in the soil are identical for both bomb-derived and Chernobyl-derived ¹³⁷Cs. In undisturbed grassland soils 70 to 90% of the ¹³⁷Cs is initially concentrated in the top 5 to 10 cm and they exhibit an exponential decrease with depth (Golosov et al., 1999; Martz and De Jong, 1991). Vertical migration mechanisms provoked by adsorption and desorption of ¹³⁷Cs to soil particles effect a slow but steady redistribution of ¹³⁷Cs into deeper soil layers dependent on the soil chemistry (Bossew et al., 1996; Schimmack and Bunzl, 1996; Strebl et al., 1996). As a result of radionuclide migration in undisturbed soils, exponential ¹³⁷Cs depth distributions start exhibiting subsurface peaks at depths between 2 and 5 cm, which are usually described by log-normal distributions (Konshin, 1992) or fitted curves (He and Walling 1997).

Radiometric methods for estimating soil redistribution are based on a comparison between total radiocaesium content at a point suspected of being subject to such a mechanism and the radiocaesium inventory at a reference point, which is not subject to soil redistribution. Many erosion evaluation models have been developed by numerous workers in the past years, ranging from empirical relationships (Ritchie and McHenry, 1975; Elliott et al., 1990) to the theoretically based proportional models (de Jong et al., 1983; Fredericks and Perrens, 1988) and mass-balance models for cultivated soils as well as diffusion and migration models for uncultivated soils, which both are state of the art (Kachanoski and DeJong, 1984; Kachanoski, 1993; Quine, 1995; He and Walling, 1997; Walling and He, 1999; Zhang et al., 2003). Comprehensive reviews of the existing methods and models were provided by Ritchie (1998), Walling and He (1999), as well as by Walling et al. (2002).

The wide range of existing models is based on nuclear weapons fallout. The low levels of this contamination imply the consideration of fresh annual ¹³⁷Cs influx. These models moreover can only be applied either to uncultivated or cultivated soils.

In this article we will introduce a new ¹³⁷Cs depth distribution and soil redistribution model, The model is designed for the use in Chernobyl-affected regions of Central and Eastern Europe only, which are currently predominantly contaminated by ¹³⁷Cs originating from Chernobyl (Bossew et al., 1995; Golosov, 2002), with contamination levels between one to two magnitudes higher than the bomb-derived fallout. The level of fresh, nuclear weapons test derived ¹³⁷Cs deposition is far below the uncertainties of sampling and analysis and is considered to be insignificant after 1986. The main feature of the model is its applicability to cultivated as well as uncultivated sites. The inclusion of exponential and time-dependent ¹³⁷Cs depth distributions enhances the concept of proportional models and might offer an easier-to-apply alternative to the very sophisticated though complex diffusion and migration models used for undisturbed soils. The results of the introduced model will then be compared and discussed with the results obtained by existing models.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
The Study Site
To demonstrate the applicability of the developed model, we selected a study site already used for erosion research: a maize field in the town of Pettenbach in the Central Austrian province of Oberösterreich (47°57'36'' to 47°57'49'' N lat; 14°01'56'' to 14°02'36'' E long; Fig. 1) . The town is located at the entrance of the Alm valley, the southwestern edge of the glaci–fluvial Traun–Enns plateau in the district of Kirchdorf. The plateau is dominated by quaternary sediments of the molasses zone between the rivers Traun and Enns. This sediment zone reaches from the Northern edge of the Alps in the South as far as to the Danube valley in the North. The area is part of the Traun drainage basin in the Northern Pre-Alpine Hillrange with an average annual precipitation of 1029 mm and a mean annual temperature of 9.4°C (Station Vorchdorf). The study field is located at an altitude between 520 and 540 m, with a length of approximately 550 m and an inclination of 6%, leveling out toward the toeslope. The predominant soil types at the site are Dystric Cambisols and Gleysols at the toeslope of the field, both with a loamy texture (20% clay, 50% silt, and 30% sand, d₅₀ = 0.022 mm). The soil has a remarkably low content of organic matter and therefore only a weakly developed A horizon of approximately 1 cm.

View larger version (95K): [in this window] [in a new window]   Fig. 1. Map of the sampling site in the Austrian province of Oberösterreich (BEV-Austrian National Survey).

Sampling and Analysis
An 80-mm core drill with a core height of 150 mm (Eijkelkamp Agrisearch Equipment, Giesbeek, the Netherlands) was used for sampling. Soil samples were taken in three zones at the site: (i) at the well inclined top of the slope, where soil erosion was expected, (ii) at the flat toe of the slope, where soil accumulation was expected, and (iii) on a flat meadow adjacent to the top of the slope, which served as undisturbed reference point for ¹³⁷Cs distributions. The position of the sampling points within the respective zones was chosen to allow sampling along a transect following the gradient of the field's slope.

At each of the three sampling points—the top of the slope, the toeslope, and the reference point—soil cores of 2 by 150 mm were taken, yielding a total sampling depth of 300 mm. The high spatial variability of Chernobyl-derived ¹³⁷Cs can distort the result. Hence, it was decided to produce composite samples at each sampling point to minimize statistical uncertainties (Sutherland, 1994; Golosov et al., 1999). Each composite sample consisted of three single samples positioned within a radius of 1 m from the actual sampling point. At each sampling point the three single sample cores were dissected into layers to produce a ¹³⁷Cs depth profile. The surface-near activity concentration is more important, for simulation purposes, than the activity concentration in deeper layers. Therefore, the layer-thickness was chosen to be 20 mm near the surface, increasing to 50 mm at the bottom of the profile (Table 1).

Improved Depth Distribution Models
It has been good practice to approximate ¹³⁷Cs depth distributions in the soil using exponential or lognormal distributions. The choice of which model to use was largely dependent on the time elapsed since contamination of the soil. Initially, exponential ¹³⁷Cs depth distributions were found. As a result of vertical migration processes, the shape of the distribution graph changed to lognormal. This change in the type of distribution with time prevented the development of a continuous description of the radiocaesium distribution in the soil because the two functions could not be interlinked. This would require setting up a two-dimensional relation of the form f (x, t), a function that could describe the spatial distribution of ¹³⁷Cs in the soil profile as well as the temporal behavior of ¹³⁷Cs in the soil, similar to the diffusion and migration model.

Additionally, due to their inability to describe temporal behavior, the above-mentioned distributions, except the diffusion and migration model, have never been included in conversion models to simultaneously describe both the migration behavior and loss of radiocaesium. This approach would create a more comprehensive picture of migration and redistribution processes in the soil.

Undisturbed Soil Profiles
To determine ¹³⁷Cs depth profiles, the soil sampling procedure was followed by the decay correction of all ¹³⁷Cs data to 1 May 1986 and the introduction of grain-size correction factors (He and Walling, 1996; Maringer and Jachs, 1996), which take into account the different affinity of ¹³⁷Cs to soil particles of different size. The model can then be fitted to the corrected measured values. The suggested model consists of two major terms. The first term is based on a simple exponential model (i.e., Eq. [1]), extended by an add-on based on a Chapman distribution (Eq. [2]). The add-on describes the development of the characteristic subsurface ¹³⁷Cs peak at a depth between 2 and 10 cm and typical for most uncultivated soils several years after contamination due to vertical migration. The second term simulates the incorporation of ¹³⁷Cs into the soil by tillage operation and the development of the uniform radiocaesium depth distribution typical for cultivated soils.

[1]

where A_U is the measured activity concentration at the surface (Bq kg^–1), ₁ is the shape parameter describing the development of the ¹³⁷Cs activity concentration with depth (cm^–1), and x is the depth (cm).

[2]

where a_U, b_U, c_U, and y_0U are the function parameters.

The fitting of the function parameters showed that they remain largely unchanged for undisturbed soils as the shape of ¹³⁷Cs depth distributions is very much alike in most undisturbed soils. The most suitable fitting parameters for the ¹³⁷Cs depth distributions at the examined sites were found to be

Though, it might be necessary to adjust c_U if the ¹³⁷Cs peak is located more than 2 to 3 cm below the soil surface.

The radiocaesium distributions themselves are hence simulated by A_U, describing the amount of ¹³⁷Cs at the soil surface, and by ₁, describing the decreasing ¹³⁷Cs activity concentration with depth. The multiplicative combination F(x) x G(x) of Eq. [1] and [2] then renders the modified exponential model (Fig. 2) .

View larger version (22K): [in this window] [in a new window]   Fig. 2. A comparison between the three different depth distribution simulation models.

The model, as currently described, can only represent the ¹³⁷Cs distribution at one time. Dynamic factors must be introduced to account for the temporal changes in the ¹³⁷Cs depth distribution. The inclusion of such temporal changes is crucial because a purely exponential concentration distribution can be found immediately after ¹³⁷Cs deposition, whereas the typical subsurface peak is usually well developed after 5 to 10 yr. The subsurface peak is characterized by the factor c_U. Thus, c_U is transformed into a function c_U(t), with 0 < c_U < 2. If c_U = 0, the Chapman term equals one, and the model exhibits a purely exponential behavior. Depending on the soil conditions, c_U will increase up to the value 2 within 10 to 15 yr, thereafter remaining constant at c_U (t 10–15 yr) = 2. A linear growth of c_U(t) simulates the process well. Additionally, the introduction of a dynamic ₁(t) allows for the description of vertical ¹³⁷Cs migration by flattening the distribution with time Eq. [1]. The development of ₁(t) is represented by

[3]

where ₁₍₀₎ is the constant ₁ at time of contamination t = 0 (cm^–1), t is the time elapsed since contamination until date of investigation (yr), and is the shape factor describing the decrease of ₁₍₀₎.

The ¹³⁷Cs activity concentration in the top soil layer A_U is also transformed into A_U(t). This function represents the temporal change by lowering the surface-near ¹³⁷Cs activity concentration. The exponential distribution at t = 0 has surface-near values higher than the final modified exponential distribution at t > 0.

[4]

where A_U(0) is the activity concentration at soil surface at t = 0 (Bq kg^–1), and is the shape factor describing the decrease of A_U(0).

The presented solution allows the description of an uncultivated and undisturbed soil profile. Note that all constants have been fitted to present-day conditions; this allows a retrospective description of what happened in the soil, but might require further adjustment in the future.

Considering Eq. [1], [2], [3], and [4], a composite model capable of describing ¹³⁷Cs depth distributions and their temporal behavior in uncultivated and undisturbed soil profiles can be set up (Fig. 3) . Combining and rearranging the presented equations yields a model represented by Eq. [5] as follows:

[5]

View larger version (17K): [in this window] [in a new window]   Fig. 3. Depth distribution variation described by the modified exponential model within 16 yr.

We, therefore, suggest describing the situation with a reversed Chapman distribution (Fig. 4) , which allows the simulation of a uniform distribution down to a certain depth, followed by a smooth transition to depths with lower ¹³⁷Cs activity concentrations, as follows:

[6]

where A_C(x,t) is the activity concentration at depth x and time t (Bq kg^–1), A_C0 is the auxiliary activity concentration at the surface at t = 0 (Bq kg^–1), ₃ is the shape parameter describing dilution process (yr^–1), and a_C, b_C, c_C, and y_0C are the function parameters fit to measured values.

View larger version (18K): [in this window] [in a new window]   Fig. 4. Chapman model based model describing the 137Cs depth distribution in cultivated soils.

The Chapman term was extended by an exponential term describing ¹³⁷Cs dilution over time in the soil profile. The exponential term characterizing the dilution process has a nearly linear appearance because it simulates a long-term process. The exponential term allows the consideration of tillage and the incorporation of contaminated soil layers into uncontaminated layers below the plow depth as soon as soil is eroded on the surface. An exponential function was chosen because the dilution effect gradually slows down. This is because the uniform ¹³⁷Cs level above the plow depth drops more in the time soon after contamination than later, when dilution processes have already reduced the activity concentration at the surface. Tillage-induced dilution is the major driving force behind the gradual change of ¹³⁷Cs depth distributions and its inclusion into the model is, therefore, crucial. The choice of the constant ₃ is based on long-term observations or on a comparison between the initial uniform ¹³⁷Cs depth distribution in the year after contamination and the present ¹³⁷Cs depth distribution.

Composite Model
Note that, on contamination, an exponential depth distribution was present in the soil in May 1986 after the Chernobyl disaster. This is because the soils are normally tilled at an earlier time in the year. Moreover, tillage does not thoroughly mix the soil if performed only once. Rather, it causes soil scraps to be rotated. Only the constant application of a plow over several years produces a uniform ¹³⁷Cs distribution in the soil profile. A transitional ¹³⁷Cs depth distribution is, therefore, assumed for a number of years, with emphasis on an exponential distribution soon after contamination, gradually developing into a uniformly distributed ¹³⁷Cs activity concentration.

The combination of the two introduced models allows a simulation of the changes of ¹³⁷Cs distributions in the soil (Fig. 5) . The idea behind the combination of the two independent models is that, at the time of contamination, the modified exponential is dominant. Over time, the weight changes toward the term describing the cultivated soil. The transition is simulated by introducing a weighting term. The more time passes, the more the emphasis in the model shifts toward the term describing the cultivated soil. Thus, at t = 0, the term simulating the undisturbed soil weights 100% and the term for the cultivated soil does not influence the result at all. At t >> 0, the weight of the term describing the undisturbed soil approaches 0, while the weight of the cultivated soil approaches 100%. A term based on an exponential function has been chosen for the simulation because the shift toward a uniform ¹³⁷Cs depth distribution is no doubt more significant in the first years after contamination than later. This assumption reflects the fact that the first post-contamination tillage flips soil scraps over, causing the high, surface-near activity to be incorporated into deeper soil layers with less activity. The more often the soil is plowed, the better the soil is mixed. This homogenizes the ¹³⁷Cs content in different depths, minimizing further changes.

View larger version (17K): [in this window] [in a new window]   Fig. 5. Model describing the transition between undisturbed and uniform 137Cs distribution.

[7]

where t is the observation time (yr), and ₂ is the shape parameter describing the influence of the weighting term (yr^–1).

The constant ₂, characterizing the weighting term, depends largely on the kind of cultivation, tillage practice, and soil conditions. It can generally be assumed to be in the range of 0.1 < ₂ (yr^–1) < 0.3.

From the moment of initial contamination until tilling, both the undisturbed and the cultivated site exhibit identical exponential ¹³⁷Cs depth distributions and total ¹³⁷Cs inventories. Tilling causes the development of a uniform depth distribution on the cultivated site, as explained in detail above, whereas the distribution on the undisturbed site remains exponential. For fitting the parameters A_C0 and ₃ to simulate the gradual development of the tillage induced uniform depth distribution, an auxiliary function—assuming a uniform depth distribution already at the time of contamination—has to be introduced.

In the composite model, the parameter A_C0 represents a virtual surface activity concentration on the cultivated field. If no sufficient long-term field data are available, the value has to be fitted to the radiocaesium contents measured on site to meet the requirements of the equation. The uniform auxiliary ¹³⁷Cs depth distribution function for t = 0 is set up for the cultivated field with A_C0 chosen so that the uniform auxiliary total ¹³⁷Cs inventory at t = 0 on the cultivated field is identical to the exponential one at the undisturbed site. The auxiliary function, therefore, shows the situation at t = 0, if the ¹³⁷Cs would have been distributed evenly with increasing depth at the time of contamination. Compared with the currently present uniform depth distribution, this allows determining a rate ¹³⁷Cs activity concentration dilution by fitting, expressed by A_C0 and ₃. Note that this procedure does not describe the actual processes in the soil, but merely substitutes unavailable field data. Nonetheless, the results show good coincidence with the real situation.

In the composite model (i.e., Eq. [7]) the transition from a purely exponential function to a Chapman function is clearly visible. After approximately 10 yr, depending on tillage practice and soil conditions, the model is substantially dominated by the Chapman term. Thus, an almost purely uniform ¹³⁷Cs depth distribution is present as far down as the plow depth. It is only influenced by soil transport and tillage, not by the original exponential depth distribution at t = 0, whose impact on the overall distribution slowly fades out. Another clear point is that, in a cultivated soil, the radionuclide–migration-induced subsurface ¹³⁷Cs activity peak typical for most uncultivated soils cannot develop properly due to annual disturbance by tillage.

Conversion Model
Once a valid model simulating the temporal behavior of ¹³⁷Cs in the soil profile is created, soil migration can be predicted without considering additional parameters. The radiocaesium distribution in the soil and its change over time provides sufficient information to quantify soil transport.

The idea is based on the comparison of the total ¹³⁷Cs inventory in a soil profile at a date t = t_i to the total inventory at a later date, usually in yearly increments, t = t_j. Such a procedure has been used for many years in the so-called proportional models. These models, however, do not take into account the characteristic of the respective radiocaesium profiles, dilution, or other factors. While the results do roughly estimate soil relocation, the models fail to describe the changes in the soil. In the suggested model, the proportional approach is still the centerpiece, but the processes in the soil are considered as well, as in mass balance or diffusion and migration models. The main assumption can be expressed as follows:

[8]

where A(x)_i is the activity concentration at depth x and time t_i (Bq kg^–1), A(x)_j is the activity concentration at depth x and time t_j (Bq kg^–1), x_s is the sampling depth (cm), and E is the erosion depth (cm).

Generally, radiocaesium can be represented by an activity concentration or, optionally, by an activity per area unit. This is possible because the two are interlinked by the dry density _d of the soil, which can be cancelled down in the equation when constant or using an average value. Practical considerations dictate using activity concentrations because ¹³⁷Cs is measured as activity concentration in the soil samples.

The assumption is that the difference of integrals between the lower boundary d = 0, which is represented by the soil surface, and the upper boundary d = x, which represents the sampling depth, between t = t_i and t = t_j equals the integral at t = t_i between the lower boundary d = 0, which again represents the soil surface, and the upper boundary d = E, which represents the depth of erosion within the chosen time increment, usually 1 yr (t_i t_j). This, in turn, assumes that ¹³⁷Cs loss is directly proportional to the amount of soil lost, that is, radiocaesium removal is solely associated with relocation of soil particles, not considering possible additional agents of ¹³⁷Cs remobilization.

The difference between the integrals, specifically the left side of Eq. [8], can be obtained by on-site measurements. First, one or ideally more sampling points have to be identified at the study site, and soil profiles have to be taken. A minimum sampling depth of 30 cm is recommended to account for the entire ¹³⁷Cs inventory, specifically the sampling depth should go as far down as the zone where no or only negligible amounts of ¹³⁷Cs are present to include at least 95% of the total radiocaesium. Second, an undisturbed reference point, not subject to soil redistribution, must be identified. In most cases, this point will be on flat grassland adjacent to the field sampling points. It can be assumed that the total ¹³⁷Cs inventory there corresponds to the inventory at the time of contamination and that the pattern of the radiocaesium depth distribution is only affected by downward migration processes. Note that the instant removal of a certain amount of deposited ¹³⁷Cs before incorporation in the soil is accounted for in the model, as all calculations are based on the ¹³⁷Cs inventory of the present day. As the migration can be simulated in the suggested model, sampling points in grassland or woodland are suitable as reference points. The next step is to create a function describing the reference point and the point located on the cultivated field. The initial ¹³⁷Cs depth distribution—considering migration effects—is assumed to be identical at the two points. The function subsequently allows the area below the integrals to be determined at t = t_i and t = t_i+j. Substituting Eq. [7] into Eq. [8] results in Eq. [9] as follows:

[9]

Since the left term is known, the integral can be solved and the equation can be rearranged to determine the erosion depth E. Note, however, that when rearranging and solving Eq. [9], E will appear on both sides of Eq. [9], implying the need for an iterative solution. The soil relocation can then be determined year by year, making the method a classic finite-difference method (for each following time step, the results for the previous time step have to be known). The respective annual erosion values do not show the exact actual rates in each year because the parameters in the equation are best-fit values. Often, no long-term time series of field data are available, making the best fit the only sensible estimation. Therefore, the mean erosion value within the analyzed time range should ultimately be used.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
The ¹³⁷Cs depth distributions at the sampling site met our assumptions and showed the expected patterns. The characteristic subsurface peak could be identified at the reference point (Fig. 2), and the distribution was almost uniform down to the plow depth at about 20 cm below ground level at the top as well as at the toe of the slope (Fig. 4). The ¹³⁷Cs activity concentrations and the total ¹³⁷Cs inventory recorded at the toeslope substantially exceeded the results from the steeper top of the slope (Table 1). Low dry density between 13 and 20 cm at the toeslope and density variability at the topslope are caused by a high level of bioactivity.

In general, the model is very sensitive to any change of parameters. This requires the model to be carefully fitted to the values measured on site. Moreover, the constants describing dilution and the influence of the two terms if no long-term data are available have to be carefully chosen.

The soil at all three points of the investigated site can be described with the suggested model and it shows similar results compared with simulations using an exponential and a lognormal model (Fig. 2, Table 2). In addition to simulating the ¹³⁷Cs distribution processes in the soil, the model, as presented above, is also capable of estimating soil relocation at the investigated site, independent from mass-balance considerations.

View this table: [in this window] [in a new window]   Table 2. Comparison of the results of different 137Cs depth distribution models.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
The presented model is capable of describing the behavior of Chernobyl-derived ¹³⁷Cs in undisturbed as well as in cultivated soils, combining the features of mass-balance and migration/diffusion models with the basic concept of proportional models, although no linear relation between ¹³⁷Cs loss and soil loss is used here.

The dynamic simulation of the radiocaesium depth distribution shows a high coincidence with observations in the soil. One factor is the modified exponential function for undisturbed soils. It simulates the depth distribution, including the development of the characteristic subsurface peak. At each time step it provides results of the same quality as the traditional log-normal simulation (Konshin, 1992). Note that for a qualitative and more exact description of ¹³⁷Cs migration processes in the soil, other models might be more suitable. The suggested model only roughly estimates the possible processes in the soil, without actually describing the physical migration mechanisms. It was merely designed to include an estimation of radionuclide migration into ¹³⁷Cs–soil erosion conversion models. For more physically sound descriptions, approaches like the compartment model (Strebl et al., 1996) are more favorable, because it divides the soil profile into compartments and associates different ¹³⁷Cs loss constants to each compartment.

The introduced model has been tested at sites in the Austria Danube catchment area. The different simulation approaches were analyzed using correlation coefficients and the sum of least squares as well as by comparing the simulated total ¹³⁷Cs content. The simulation of the reference site shows a higher correlation coefficient, a lower sum of least square, and a total ¹³⁷Cs inventory aberration of the same magnitude as the standard models. The description of tilled soil is based on a Chapman distribution, and shows very good agreement with field data. Results show correlation coefficients between the field data and the model from 0.93 to 0.97, and the aberration of total radiocaesium ranges from 1.64 to 2.20%. The model, therefore, seems to be a valid representation of reality.

The combination of the two basically independent models consequently allows the processes on a cultivated field to be described from the time of initial ¹³⁷Cs deposition to the present day. It is allowing flexibility and the simulation of different shapes of ¹³⁷Cs depth distributions depending only on a suitable choice of function parameters. Nevertheless, certain limitations remain. One is the abovementioned sensitivity to the chosen function parameters, calling for accurate sampling and analysis. Another point is that the dynamic parameters typically have to be estimated because insufficient long-term data are available. Note, therefore, that the simulation of ¹³⁷Cs migration processes is merely an assumption and no physically based description. Nonetheless, ¹³⁷Cs behavior can be estimated qualitatively.

The quantification of soil transport is the second application of the model. Clearly, the quality of the results depends largely on well-chosen function parameters. The calculated soil relocation at the test site in Austria is of the same magnitude as that provided by the traditional proportional model and the simplified mass balance model. One of the advantages of the suggested model is certainly the inclusion of the depth distribution pattern and its development over time. That allows a visualization of the ¹³⁷Cs-related, temporal processes in the soil. Moreover, the model allows the treatment of cultivated as well as uncultivated sites, which are not subject to tillage and therefore soil turbation. All other calibration models, which are currently state-of-the-art, have to use two different approaches when dealing with uncultivated and cultivated soils (DeJong et al., 1983; Elliott et al., 1990; Loughran and Campbell 1995; Walling and He, 1999). Another important point is that the model is site independent, that is, the recalibration that empirical models required for each new site is no longer necessary (Ritchie and McHenry, 1975; Elliott et al., 1990; Loughran and Campbell, 1995). The only remaining task for each site is to derive a best fit function describing radiocaesium behavior in the soil. The limitations of the model are its complexity and the high number of function parameters, which need fitting and cause a high sensitivity to poorly chosen parameters. The results of the model are, therefore, largely dependent on the method of fitting the function to the measured field data and on the availability of long-term field data, which improve the quality and the significance of the chosen parameters.

For the presented Chernobyl ¹³⁷Cs-based model the removal of a certain part of freshly deposited ¹³⁷Cs before its fixation in the soil as suggested by Walling and He (1999) has not been considered, as it is assumed that the current total ¹³⁷Cs inventory at the undisturbed reference site equals the initial ¹³⁷Cs distribution at the cultivated site, implying that ¹³⁷Cs, which has been removed before its incorporation in the soil, is already being accounted for.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 
The presented extended proportional model is an alternative to standard calibration models. It allows a dynamic description of the processes in the soil, combining problems of distribution patterns and their development, as well as the effects of soil relocation. Moreover, standard models can only be used either on undisturbed or cultivated soils. Yet, the presented model is applicable to both undisturbed and cultivated soils, making this the main feature of the new approach. This makes the radiocaesium method easier to apply for the user and finally allows a direct comparability of soil redistribution rates on uncultivated and cultivated sites. The model is basically designed to be purely descriptive, but it is also capable of short-term predictions. Long-term predictions should be interpreted with caution because the ¹³⁷Cs depth distribution might change in an unexpected way, such as in the case of terminating cultivation, or changing the crop or the plow used. In those cases the shape of the depth distribution could erratically change. Thus, the shape parameters of the model must be adjusted by refitting.

	ACKNOWLEDGMENTS

 
The work presented in this paper was part of an investigation of Austrian soils, within the European Union funded ÖPUL2000 project for erosion control. We greatly acknowledge the cooperation of the landowners, in permitting access to and soil sampling on their properties, and the assistance of J. Tykal, V. Gruber, and J. Kirchmeyer in field work.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

 

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