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Journal of Environmental Quality 31:1930-1939 (2002)
© 2002 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America

TECHNICAL REPORTS
Landscape and Watershed Processes

Assessment of Spatial Variation of Cesium-137 in Small Catchments

Marcel van der Perk*,a, Ondrej Slávikb and Emil Fulajtárb

a Utrecht Centre for Environment and Landscape Dynamics (UCEL), Faculty of Geographical Sciences, Utrecht University, P.O. Box 80115, 2508 TC Utrecht, the Netherlands
b Soil Fertility Research Institute, Gagarinova 10, 82713 Bratislava, Slovakia

* Corresponding author (m.vanderperk{at}geog.uu.nl)

Received for publication May 21, 2001.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Surface contamination by bomb-derived and Chernobyl-derived 137Cs has been subject to changes due to physical decay and lateral transport of contaminated soil particles, which have resulted in an ongoing transfer of radionuclides from terrestrial ecosystems to surface water, river bed sediments, and flood plains. Knowledge of the different sources of spatial variation of 137Cs is particularly essential for estimating 137Cs transfer to fluvial systems and for successfully applying 137Cs as an environmental tracer in soil erosion studies. This study combined a straightforward sediment redistribution model and geostatistical interpolation of point samples of 137Cs activities in soil to distinguish the effects of sediment erosion and deposition from other sources of variation in 137Cs in the small Mochovce catchment in Slovakia. These other sources of variation could then be interpreted. Besides erosion and deposition processes, the initial pattern of 137Cs deposition, floodplain sedimentation, and short-range spatial variation were identified as the major sources of spatial variation of the 137Cs inventory.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
THE ACCIDENT at the Chernobyl nuclear power plant on 26 April 1986 has resulted in atmospheric deposition of long-lived radiocesium (137Cs; physical half-life 30.2 yr) over vast areas of Europe. The initial 137Cs deposition patterns were determined by dispersion and deposition processes governed by meteorological conditions during the first days after the accident. The territories of Ukraine, Belarus, and the European part of Russia were most affected. Nevertheless, areas further away from Chernobyl were also affected by relatively high levels of deposition due mostly to rainfall as the radioactive cloud passed over these areas (De Cort et al., 1998). Relationships between annual rainfall and initial deposition of previous bomb-derived 137Cs associated with the testing of nuclear weapons in the late 1950s and 1960s have been demonstrated by Basher and Mathews (1993), Owens and Walling (1996), and Bernard et al. (1998). At the local scale, deposition of bomb-derived 137Cs is often assumed to be uniform, resulting from the superposition of the patterns from individual rainstorms occurring in a period of several years (Ritchie and McHenry, 1990; Di Stefano et al., 1999). Conversely, variations in local rainfall during individual rainstorms are likely to become manifested in the Chernobyl-derived 137Cs deposition patterns (Walling et al., 1989). Furthermore, initial 137Cs deposition is locally affected by aerodynamic surface roughness controlled by local surface topography and land cover (Bachhuber et al., 1987; Owens and Walling, 1996). The presence of hills and transitions in the height and structure of vegetation cover causes airflow perturbations, which alter the rates of dry and wet atmospheric deposition.

In the years following the Chernobyl accident, surface contamination by 137Cs has been subject to changes not only due to physical decay, but also from lateral transport of contaminated water and soil particles. The mobility and fate of 137Cs in landscapes is largely determined by its geochemistry. Cesium is very soluble in water, but also is readily adsorbed by illitic clay minerals (Cremers et al., 1988). As a consequence, in mineral soils 137Cs becomes irreversibly fixed to clay minerals over time (Absalom et al., 1995). Accordingly, the transport of 137Cs from and redistribution within agricultural and natural catchments on the long term is mainly related to fine-sediment transport (Walling et al., 1989; Rowan, 1995), although the initial post-accidental 137Cs transport might largely have occurred in the dissolved form (Hilton et al., 1993; Slávik et al., 1997). The dependency between the age of deposition and the relative importance of dissolved and particulate 137Cs transport has been described by Smith et al. (1987). Both ways of transport have resulted in an ongoing transfer of 137Cs on hillslopes (Ritchie and McHenry, 1990; De Roo, 1991; Owens and Walling, 1996; Ferro et al., 1998; Golosov et al., 1999; Walling and He, 1999; Tyler and Heal, 2000) and from terrestrial ecosystems to surface water (Shukla, 1993; Monte, 1995; Sansone and Voitsekhovitch, 1996), bed sediments (Whicker et al., 1994), and floodplains (Walling and He, 1993; Van der Perk et al., 1999).

The combined effects of initial deposition and subsequent redistribution of Chernobyl-derived 137Cs have resulted in complex patterns of 137Cs within catchments. The short-distance variation of initial deposition has been identified as a complicating factor for the use of 137Cs as a tracer in soil erosion studies in areas affected by the Chernobyl accident (Di Stefano et al., 1999). Therefore, there is a need to further investigate the contribution of local variability of initial 137Cs deposition and redistribution to predict the spatial and temporal patterns of 137Cs in catchments. Such knowledge is particularly essential for estimating 137Cs transfer to fluvial systems and for successfully applying 137Cs as an environmental tracer in soil erosion studies (VandenBygaart et al., 1999).

This study aims to identify the different sources of 137Cs spatial variation in a small catchment in central Europe. For this purpose, a stepwise methodological approach of field research, followed by an iterative track of process modeling, geostatistical data analysis, and results interpretation, was pursued. This present contribution combines a straightforward sediment redistribution model and geostatistical interpolation of 137Cs activities at sample locations to distinguish the effects of sediment erosion and deposition from other sources of variation in 137Cs activities. Ultimately, the different spatial patterns were identified and interpreted.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Study Site
The study was undertaken in the small (3.67 km2) Mochovce catchment situated in a hilly part of the Danube Lowlands in western Slovakia (48°16' N, 18°26' E) (Fig. 1) . Because of rainfall events in April and May of 1986, Chernobyl-derived 137Cs was deposited in relatively large amounts in the Mochovce catchment and its surroundings. Based on pre–Chernobyl 137Cs activity concentrations in the cultivated topsoil layer measured by Slávik and Moravek (1982), the bomb-derived 137Cs deposition was estimated to be some 3.5 kBq m-2 in 1986. The average additional Chernobyl-derived deposition amounted to about 8.5 kBq m-2.



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  		Fig. 1. The Mochovce catchment with 137Cs sample locations (shown as open circles with black dots; the location of the sectioned core from the marshland is indicated by •). The contour interval is 10 m and forested areas are shaded in gray. The part of the catchment for which the digital elevation model (DEM) derivatives were calculated is indicated by a dashed line.

 
The main land use is termophilous oak (Quercus spp.) forest (2.1 km2) and arable land with a crop rotation dominated by wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), and rape (Brassica napus L.) (1.4 km2). The agricultural fields are 50 to 100 ha and are annually plowed to a depth of 24 to 30 cm perpendicular to the main channel. According to the nomenclature of the World Reference Base for Soil Resources (FAO/ISRIC/ISSS, 1998), Haplic Luvisols with a clayey loamy texture are the main soil type on the hillslopes under agricultural use. The soils on the steeper slopes in the southeastern part of the catchment have a more sandy loamy texture. In the valley bottom, Eutric Fluvisols are found, and in the forests areas, Calcic Regosols, Halplic Luvisols, and Eutroc Cambisols alternate. The forest soils have a large hydraulic conductivity due to numerous macropores, so overland flow does not occur (Den Besten and Wielinga, Utrecht University, personal communication, 2000).

An artificial, paved channel drains the upper part of the catchment. In the upper part of the catchment a nuclear waste facility (approximately 600 x 200 m) is present, which is artificially drained by the paved channel. In the central part of the catchment the natural spring zone feeds a small stream flowing through a marshland in the broad valley bottom before it reaches the catchment outlet. The marshland in the central part of the catchment is inundated occasionally during intensive rainfall events. The average base flow of the small stream amounts to about 0.002 m3 s-1 at the catchment outlet.

Digital Elevation Model
A geographic information system (GIS) database for the Mochovce catchment including, among others, a digital elevation model (DEM) and digital maps of land use, soil type, and soil texture at an original map scale of 1:10 000, was prepared in ArcView (Environmental Systems Research Institute, 1999) shape format or ArcInfo (Environmental Systems Research Institute, 1998) grid format. All maps were converted to PCRaster (Wesseling et al., 1996) format for further analysis.

The DEM was built by digitizing 2.5-m-interval contour lines from a 1:10 000 topographic map. Subsequently, from this contour map a triangular irregular network (TIN) was created and this TIN was converted to a regular grid with a cell size of 10 x 10 m. The following maps were derived from the DEM with PCRaster: slope, profile curvature, planar curvature, local drainage direction, upstream area, and slope length (see Burrough and McDonnell, 1998). Because neither surface runoff nor soil erosion occur in the forest area, the forested parts of the catchment were excluded in the calculation of the DEM derivatives. This implies that slope length and upstream area were calculated respectively from and until the forest edge.

To account for errors in the DEM and to overcome the limitations of the unidirectional flow algorithm for the local drainage direction calculation, the Monte Carlo method was adopted. To account for errors in the DEM for the calculation of the slope gradient a root mean square (RMS) error of 5 cm was added to the DEM with unconditional Gaussian simulation. An additional RMS error of 30 cm was added to calculate the local drainage direction map to simulate the effects of dispersion of water flow (see Van Deursen, 1995; Burrough and McDonnell, 1998). The derivatives mentioned above were calculated by taking the mean of the derivatives of 500 realizations of the DEM.

Soil Sampling and Laboratory Analysis
An extensive soil sampling was performed for 137Cs measurement in the Mochovce catchment. Because lateral 137Cs redistribution processes are practically not active in forest, the study focused mainly on the arable fields and marshlands in the catchment. In this area about 180 soil samples were collected from the topsoil up to a 35- to 55-cm depth during June and July 1999. Seventy-seven sampling points were located in a regular grid with a sampling interval of 100 x 200 m (Fig. 1) to obtain an unbiased estimation of the average 137Cs activity in the study area. To study local variation of 137Cs in soil a representative subcatchment in the northern part of the catchment (about 150 m wide and 300 m long) was selected. In this subcatchment, 80 sampling points were distributed over 12 transects perpendicular to the elevation contours at a mutual distance of about 30 m. Additional samples were collected in the valley bottom, especially the marshlands, and 16 samples were collected in a regular grid of 300 x 400 m in the forest area. During field sampling, soil texture, color, and soil erosion and deposition features were recorded. The sample locations were located by a topographic map at a scale of 1:10 000, compass, and distance measurement from reference points that had been georeferenced with GPS. The mean location error was estimated to be less than 10 m in the intensively sampled subcatchment and less than 15 m in the rest of the Mochovce catchment.

The soil was sampled with a 50-mm-diameter stainless steel corer to a depth of 35 to 50 cm. At each location, three subsamples of the soil were collected in a triangle at a mutual distance of 50 cm, which were bulked to one sample. To investigate the 137Cs depth profile in relation to floodplain sedimentation, one sample from the marshland in the central part of the study area was sectioned into 5-cm subsamples. To reduce sample size and transport costs, the sampling depth depended on the topographic position based on previous experience: on the ridges the sampling depth was 40 cm, at convex slopes where the soil was expected to be eroded the sampling depth was 35 cm, and at concave slopes and in the valley bottom where sediment accumulation was observed or expected the sampling depth was 50 cm. Control subsamples of the lowest 5 cm of the sampled profile proved that less than 2 to 7% of the 137Cs inventory of the sampled soil profile is present in this lowest layer, so that it can be assumed that the samples contained practically all 137Cs in the soil profile. The bulked samples were sealed in plastic bags for transportation to the laboratory. In the laboratory, the samples were dried at 105°C, weighed, homogenized, and sieved with a 2-mm sieve.

A subsample of 1 dm3 was put in a polyethylene container and sealed. The sealed samples were weighed and counted with a cylindrical semiconductor HPGe detector (Princeton Gamma-Tech, Princeton, NJ) and a SILENA-Livius (Milan, Italy) 4 x 4k multichannel analyzer for 6 to 18 h until the measurement error was less then about 10%. The resulting average measurement error amounted to 8.1 ± 1.3% (mean ± one standard deviation). The recorded {gamma} ray spectra were analyzed and evaluated with the SILGAMMA detector efficiency calibration procedure (SILGAMMA, 1984). The 137Cs activity concentrations (Bq kg-1) were corrected for variation in sample self-absorption (Slávik, 1990) and converted to area activities (Bq m-2) with the total weight of the sample fraction less than 2 mm and the total sampling area. Duplicate sampling shows that the relative error due to homogenization and analysis is less than 10%. The overall soil {gamma} spectrometry procedure has been validated by regular laboratory intercomparison exercises organized by the International Atomic Energy Agency.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soil Sampling
The area average value of observed 137Cs in the arable part of the catchment was estimated at 8756 Bq m-2 (standard deviation = 2496 Bq m-2; N = 77 grid samples). This corresponds with a total 137Cs area activity of 11.8 kBq m-2 in May 1986. Figure 2 shows a histogram of the sample data. The area average value of the observed 137Cs in the forest area was estimated at 10430 Bq m-2 (standard deviation = 3021 Bq m-2; N = 16 grid samples). This corresponds with a total 137Cs area activity of 14.1 kBq m-2 in May 1986, if 137Cs losses from the catchment due to erosion and wash-off are neglected.



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  		Fig. 2. Histogram of the 137Cs activity values for the sample grid (N = 77).

 
Figure 3 shows the depth profile of 137Cs in the sectioned core from the marshland in the central part of the Mochovce catchment. The 137Cs activity concentration increases slightly from about 20 Bq kg-1 in the top 5 cm of the soil profile to about 30 Bq kg-1 at 25 to 30 cm. Below 35 cm, the 137Cs activity concentration is considerably smaller, between 7 and 14 Bq kg-1.



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  		Fig. 3. Cesium-137 depth distribution of a sectioned core from the marshland in the central part of the Mochovce catchment (see Fig. 1 for location). The total 137Cs activity amounts to 16576 Bq m-2.

 

   SEDIMENT BUDGET MODEL
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Methods
To predict the areas of erosion and deposition, a simple sediment budget index was employed based on a rill erosion model described by Govers et al. (1993), which resembles the LS factor of the USLE model (Wischmeier and Smith, 1978). A relative measure for potential soil erosion was derived from the DEM with:

[1]
where Er = relative potential erosion rate per unit area, L = slope length (m), S = slope gradient, and n and m = exponents. The sediment transport capacity on a given location in the catchment was considered to be proportional to the potential for erosion (Govers et al., 1993):

[2]
where gt = transport capacity coefficient. The amount of eroded material per grid cell is transported downstream over the drainage network, as long as it does not exceed the transport capacity (see Van Deursen, 1995). The surplus is deposited. The accucapacitystate operator in PCRaster was used to obtain the amount of deposited material given the drainage network, the available eroded and transported material from the upstream area, and the transport capacity (PCRaster, 2001). The relative sediment budget index Dr is calculated by subtracting the eroded material from the deposited material. A positive value for Dr means deposition and a negative value for erosion. Sediment that reaches the channel was assumed to leave the catchment, so for this purpose the relative erosion rate in the artificial canal and in the brook channel was set to zero and the transport capacity set to a very large value.

The values of the exponents n and m and coefficient gt were a priori set to the values given by Govers et al. (1993)(1994). The parameter values were further calibrated with the observed spatial pattern of 137Cs in the intensively sampled subcatchment. This was done by visual comparison between the simulated transition between erosion and deposition and the transition and observed 137Cs values below and above the area average value of 137Cs in the arable part of the catchment (see above). Like the calculation of the other DEM derivatives, a Monte Carlo method was adopted to account for errors in the DEM and local drainage direction network. For this purpose, the same, previously mentioned root mean square errors were assumed and the Dr was calculated 500 times for different realizations of the DEM. The resulting mean value for Dr was saved for further analysis. In addition, the logtransformed sediment budget index was obtained by calculating log(Dr + 10). The offset of 10 was chosen to avoid negative values between the brackets.

Results
Table 1 lists the final parameter values of n, m, and gt. Although these parameter values were calibrated visually by trial and error, it was observed that the relative amount of eroded or deposited sediment is particularly sensitive to the respective values of n and m. The spatial pattern of sediment budget, that is, the location of the transition between erosion and deposition, is particularly sensitive to gt. Figure 4 shows the predicted pattern of the sediment budget index Dr.


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  		Table 1. Parameter values for the exponents n and m and the transport capacity coefficient (gt).

 


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  		Fig. 4. Predicted pattern of relative sediment budget index. Areas in which soil erosion occurs have a negative (-) sign and area in which deposition occurs have a positive (+) sign.

 

   RELATION BETWEEN CESIUM-137 ACTIVITY AND DIGITAL ELEVATION MODEL DERIVATIVES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Initially, the relation between 137Cs and the DEM derivatives was assumed to be constant for the whole catchment except for the samples from the forest, since soil erosion and deposition does practically not occur in the forest area (Den Besten and Wielinga, Utrecht University, personal communication, 2000). So, all samples except for the samples from the forest area were used in the subsequent analysis of relations between 137Cs and the DEM derivatives (N = 179).

Figure 5 shows a scatter diagram of the 137Cs values against the various DEM derivatives including Dr and DLr. This figure shows that 137Cs correlates positively with both Dr and DLr (Fig. 5b). Obviously, four samples are outliers in the sense that they do not adapt to the general trend between the 137Cs values and DLr. Further inspection of these samples shows that these are located in areas of either extreme erosion or deposition. One sample had a very sandy texture and an accompanying low 137Cs content compared with the other samples that had a sandy loam, loam, or clayey loam texture. Therefore, samples from areas with extreme erosion or deposition and all samples with a very sandy texture were removed from the data set in the subsequent analysis. The remaining number of samples amounted to 172.



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  		Fig. 5. (a) Scatter diagram for 137Cs activity values (Cs-137), sediment budget index (Dr), the logtransformed sediment budget index , slope, slope length (Sll), upstream area (Ups), profile curvature (Prc), and planar curvature (Plc); (b) 137Cs activity values against DLr without outliers; (c) 137Cs activity values against Prc without outliers.

 
To find a relationship between the observed 137Cs values and the DEM derivatives, we used a multiple linear regression with a step-wise variable selection (criteria: probability of F to enter <= 0.05; probability of F to remove >= 0.10). This yielded a regression model into which two variables, namely the logtransformed sediment budget index (Dr) and the profile curvature (PRC) (see Fig. 5b,c), are present:

[3]
where 137Cs = observed 137Cs (Bq m-2); DLr = logtransformed sediment budget index [= log(Dr + 10)]; PRC = profile curvature (m-1); and {epsilon} = residual error (Bq m-2).

The R2 amounts to 0.251, implying that the model explains 25% of the total variation in 137Cs in the Mochovce catchment. Correlation analysis (Table 2) shows that the correlation among DLr and PRC is not significant ({alpha} = 0.05) and the correlation coefficient is small (-0.102), so that the proportions of the variation explained by the respective DLr and PRC sum up to approximately the variation explained by the multiple linear regression model. The DLr variable explains about 22% of the total variation in 137Cs and PRC an additional 3%. The standardized ß regression coefficients amount to 0.464 for DLr and -0.148 for PRC, which indicates that the effect of DLr on the 137Cs activity is about three times larger than but reverse to the effect of PRC.


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  		Table 2. Correlation matrix for 137Cs, the logtransformed sediment budget index , and the profile curvature (PRC).

 
Figure 6 shows the 137Cs values predicted by Eq. [3]. At locations with high sediment deposition rates, enhanced 137Cs levels are found. The correlation between 137Cs and the sediment budget index can be explained by sediment transport processes induced by water flow over the drainage network, which were explicitly represented in the sediment budget model. An additional increase in 137Cs activity is found at concave slopes (negative profile curvature).



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  		Fig. 6. Cesium-137 activity in soil predicted with regression Eq. [3].

 
Linear regression of the subset of the 137Cs measurements at the regular grid (N = 75) to the same independent variables DLr and PRC yields an R2 of 0.145 and linear regression of the subset of the more intensively sampled subcatchment (N = 80) an R2 of 0.382. In this subcatchment, the 137Cs values are significantly ({alpha} = 0.05) greater in the transect along the forest edge than in the rest of the subcatchment (the respective mean 137Cs values amount to 10995 Bq m-2 and 8748 Bq m-2). Linear regression of the subset of the 137Cs measurements in the subcatchment without the 14 samples from this transect yields an R2 of 0.434.


   ANALYSIS OF RESIDUALS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
To further investigate the spatial patterns of 137Cs in the entire catchment that cannot be explained by using multiple linear regression with the simple soil erosion and deposition model described above, the residuals of regression Eq. [3] were explored. The experimental semivariogram (Fig. 7) of these residuals shows that they are spatially correlated. The fitted spherical model has a range of about 700 m, a sill of 8.0 x 106 (Bq m-2)2, and a nugget variance of 4.6 x 106 (Bq m-2)2. This implies that roughly 40% of the residual variation is spatially correlated.



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  		Fig. 7. Semivariogram of the residuals of the regression model (Eq. [3]).

 
Subsequently, the 137Cs activities were interpolated by means of universal point kriging (Cressie, 1993; Burrough and McDonnell, 1998) with Gstat (Pebesma and Wesseling, 1998). Similar to the regression procedure, DLr and PRC were used as external variables or so-called base functions in this universal kriging procedure. Because the application of universal kriging assumes spatially correlated residuals and the previous multilinear regression model independent residuals, the variogram estimator may be biased, in particular at large lags (Cressie, 1993). Repeating the calculation of the residuals with a generalized linear model resulted in a similar variogram model of the residuals, so we used the previous variogram model to interpolate the 137Cs values. Figure 8a presents the resulting interpolated 137Cs map and Fig. 8b the standard errors of the predictions. The magnitude of the prediction error mainly depends on the sampling configuration and the magnitude of the predicted 137Cs values. Accordingly, the prediction error is relatively small (about 2300 Bq m-2) in the subcatchment where a large number of samples were collected, about 2450 Bq m-2 in the areas sampled at an interval of 100 x 200 m, and relatively large (larger than 2700 Bq m-2) in the small valleys where increased 137Cs values are predicted.



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  		Fig. 8. Interpolation results. (a) Estimated 137Cs activity and (b) kriging standard deviation (Bq m-2). White spots indicate sampling locations.

 
The difference between the interpolated 137Cs (Fig. 8a) and the 137Cs predicted by the regression model (Fig. 6) reflects the spatial variation of 137Cs that was not predicted by the multiple linear regression model of soil erosion and deposition. In fact, this is the result of the interpolation of the residuals from the regression model (Fig. 9) .



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  		Fig. 9. Difference between 137Cs predicted by universal kriging (Fig. 8a) and by the regression model (Fig. 6). Positive values mean an underprediction by the regression model.

 
Figure 9 reveals four remarkable features of 137Cs deposition that are not explained by the regression model, namely a large-scale pattern with a northwest–southeast oriented belt of elevated 137Cs activity, a "hot spot" of 137Cs in the valley bottom in the center of the catchment, and increased 137Cs values on the floors of some side valleys and along the forest edge in the northern part of the Mochovce catchment. In the next section we attempt to interpret these spatial patterns.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
In the preceding sections we have explored the spatial variation of 137Cs in the Mochovce catchment. By adopting multiple linear regression with a sediment budget index calculated from DEM derivatives and the profile curvature we could explain about 25% of the total variation of 137Cs in the catchment. Approximately 22% of the total variation could be attributed to water erosion, as described by the logtransformed sediment budget index. The additional effect of about 3% by the profile curvature could be accredited to soil redistribution by tillage, which is proportional to profile curvature (Govers et al., 1994). Tillage operations cause the upper soil to be translocated from convex to concave parts of the slope. The intensity of soil redistribution by both water erosion and tillage operations depends strongly on soil attributes and land management, which have not been accounted for by the sediment budget model. Accordingly, the linear regression of the observed 137Cs values to the sediment budget index and profile curvature yielded a larger value for R2 for the more intensively sampled subcatchment, because soil attributes and land management in this subcatchment varied less compared with the entire catchment. Only the forest edge appeared to be a disturbing factor due to enhanced initial atmospheric deposition near the transition of surface roughness. Another reason for the larger value for R2 for the more intensively sampled subcatchment could be the smaller errors in the sampling locations in this area compared with the rest of the catchment, which resulted in a better match between the measured 137Cs values and calculated sediment budget index and profile curvature.

Obviously, the linear regression model between the sediment budget index and 137Cs is only a simplified representation of the actual processes, not only because the effects of soil attributes and land use are disregarded, but also because various feedback mechanisms influence the relation between soil redistribution and current 137Cs inventory. An example of such a feedback mechanism is the decline of the 137Cs activity concentration in the topsoil due to soil erosion, especially before the first tillage event after initial deposition of the 137Cs in 1986. The initial vertical 137Cs distribution over the soil profile is usually approximated by an exponential decrease with soil depth with most of the 137Cs in the top few centimeters (He and Walling, 1997). This would result in a reduction of the amount of 137Cs redistribution per successive erosion event. Although this effect is less pronounced if plowing causes the 137Cs to be more or less uniformly distributed over the plow layer, the 137Cs activity concentration of the topsoil changes over the years due to progressive lowering of the soil surface and the incorporation of soil containing no 137Cs from below the plow layer (see Walling and He, 1999). Also, the occurrence of different patterns of erosion and deposition caused by different rainfall events depending on, among others, the intensity of overland flow and the roughness of the soil surface, cause complex spatial patterns of the 137Cs activity concentrations in the topsoil. Nevertheless, the linear regression model seems to be adequate to describe the long-term effects of soil redistribution on the actual 137Cs distribution in the Mochovce catchment.

The spatial patterns of 137Cs predicted by the regression model (Fig. 6) and the interpolated pattern (Fig. 8) seem to be identical at first sight. This is caused by the fact that the differences between 137Cs estimated by universal kriging and predicted by the regression model (Fig. 9) generally amount to only 10 to 20% of the total 137Cs activity, and the spatial pattern of these differences partly coincides with the spatial pattern of the interpolated 137Cs values. This remaining spatial pattern reveals the effects of processes that the regression model does not account for. Figure 9 shows that the regression model underestimates the 137Cs activities in (i) the valley bottoms of the small side valleys, (ii) the "hot spot" in the main valley bottom, and (iii) the northwest–southeast oriented belt across the study area.

The underestimation of the 137Cs activities by the regression model in the small side valleys is probably due to overland flow during 137Cs deposition, in which the 137Cs was not able to come into contact with the soil particles and preferentially flowed to the lower landscape positions of the catchment (VandenBygaart et al., 1999). Sediment redistribution during rainfall events that occurred after initial 137Cs deposition and before the first plowing may also have resulted in a much greater proportion of 137Cs being deposited in the side valley floors than may be expected based on average soil erosion and deposition estimated by the sediment budget model. Furthermore, it may be due to an underestimation of the effects of soil redistribution due to tillage operations. Govers et al. (1994) claim that tillage erosion and deposition rates are at least of the same order of magnitude as average water erosion rates on hilly croplands in Europe. However, this study showed that the regression variable that can be related to tillage erosion and deposition (PRC) explains only 3% of the variation in 137Cs in the Mochovce catchment, and its effect on the 137Cs values was estimated to be about three times smaller than the variable that could be related to water erosion and deposition .

The "hot spot" in the valley bottom is located in the relatively flat marshy area just downstream of the natural spring of the stream draining the catchment. During high-intensity storm events, this area functions as a floodplain that is inundated from the river channel, which may lead to additional 137Cs inputs from the channel through deposition of contaminated sediments eroded from upstream parts of the hill slopes. The sectioned core providing a 137Cs depth profile from this marshland shows relatively large 137Cs activity concentrations over the top 35 cm of the soil profile (Fig. 3). Since the marshland has probably not been plowed, this 137Cs depth profile is probably the result of floodplain sedimentation with an average sedimentation rate of about 2.7 cm yr-1 since 1986. The process of dispersal of sediment-associated 137Cs from the river channel to floodplains was not incorporated in the simple sediment budget model, so it could not be identified quantitatively as a separate source of variation. Nevertheless, Fig. 9 demonstrates that floodplain sedimentation contributes to the variation in 137Cs activity in the central part of the study area.

In the central part of the study area, the large-scale pattern of the northwest–southeast oriented belt of increased 137Cs values is probably the result of variation in initial 137Cs deposition over the catchment during the first days following the Chernobyl accident. Apparently, this area received larger amounts of 137Cs, which has resulted in an increase of 137Cs values of 2000 to 2500 Bq m-2 compared with the surrounding area. Data from the Mochovce meteorological station located about 1.5 km north from the catchment show that a rainfall event occurred on 30 Apr. 1986, the day when the airborne radioactivity in Slovakia was maximal (3.9 Bq m-3) (Institute of Hygiene and Epidemiology, 1986). During this rainfall event that occurred between 1400 and 1530 h, the general wind direction was from the north-northwest (340°), that is, practically parallel to the observed pattern of increased 137Cs activities. This suggests that the pattern has probably been caused by local variability in the rain shower passing the catchment on this day.

The increased 137Cs activities in the valley floors, in the "hot spot" of 137Cs activity on the marshy floodplain, in the northwest–southeast oriented belt, and along the forest edge account for approximately 40% of the residual variation of the multiple linear regression model. This figure was based on the estimation of the nugget variance at distances approaching zero, which is very sensitive to the variogram model (e.g., spherical, exponential, or circular model), so it should only be considered as a rough estimation of the contribution of the mentioned sources of variation.

In general, 137Cs could be predicted with a precision of about 2450 Bq m-2 in areas sampled at an interval of 100 x 200 m and about 2300 Bq m-2 in the extensively sampled subcatchment. The proportion of this residual variation of the multiple linear regression model that is not spatially correlated represents the variation that results from (i) analysis errors, (ii) errors in the sediment budget model, and (iii) short-range variation in 137Cs. The mean relative analysis error of 137Cs was previously established to about 8%. Sampling errors and errors resulting from sample preprocessing are, although considered of minor importance, not incorporated in this figure. The errors in the sediment budget model include, beside some limitations of the model described above, errors in the derivation of the slope gradient and slope length from the digital elevation model. These DEM derivatives could be robustly estimated by the Monte Carlo method adopted, but may still be subject to considerable error at randomly chosen locations within the catchment, especially at the flat valley bottom (Burrough and McDonnell, 1998). It is plausible that most of the residual variation can be attributed to short-range spatial variation due to, for instance, accumulation of 137Cs in local depressions and furrows that are not represented by the DEM, or concentration of 137Cs adjacent to the crop stems (VandenBygaart et al., 1999). Probably, most of this short-range 137Cs redistribution has occurred during deposition of 137Cs in rainfall. Future research should investigate if the short-range variation is purely random or spatially structured at a finer-scale level (1–50 m).

The stepwise approach of sediment budget modeling, linear regression, and universal kriging adopted in this study has proved to be adequate to distinguish the effects of sediment erosion and deposition from other sources of variation in 137Cs activities. This approach might, however, be statistically suboptimal, particularly with respect to a bias in the estimation of the experimental variogram. In this study, we verified the variogram by repeating the variogram estimation with a generalized linear model. This yielded a similar variogram, which suggests that the bias had little effect on the estimated kriging errors. The universal-kriging predictions of the 137Cs activities may also be influenced little by the bias (see Cressie, 1993). In the ideal case, the model parameters of the sediment budget model, the regression parameters, and the experimental variogram would be estimated simultaneously to avoid the bias, but appropriate algorithms for this purpose are still lacking. The present approach could not distinguish the bomb-derived 137Cs fallout in the late 1950s and 1960s from the Chernobyl-derived 137Cs deposition that occurred mainly during one rainfall even in May 1986. The application and calibration of a dynamic, long-term 137Cs redistribution model based on the sediment budget index model adopted in this study could enable this distinction.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
This study demonstrates that combining a simple sediment budget model with universal kriging is a useful method to predict the spatial distribution of 137Cs in small catchments. The method yielded not only predictions of 137Cs values and the associated prediction errors for the Mochovce catchment, Slovakia, but also provided a better understanding of the contribution of various processes that caused the observed 137Cs patterns. It allowed us to separate the effects of sediment erosion and deposition from other sources in variation of 137Cs. Subsequently, these other sources of variation could be interpreted as being the result of the initial pattern of 137Cs deposition, floodplain sedimentation, and short-range spatial variation. For the entire study area, only about 25% of the variation in 137Cs activities could be attributed to soil erosion and deposition. The residual variation is probably largely due to overland flow during 137Cs deposition, which has caused local, short-range 137Cs redistribution as well as 137Cs accumulation in the valley bottoms. The sediment budget index model can serve as a valuable means to improve the prediction of soil erosion and deposition rates from 137Cs measurements, since the effects of soil redistribution on 137Cs in soil can be separated from effects of other sources of spatial variation. The approach could be further refined by investigating the short-range variation of 137Cs, estimating simultaneously the model parameters, and/or applying a dynamic 137Cs redistribution model to distinguish between bomb-derived and Chernobyl-derived 137Cs.


   ACKNOWLEDGMENTS
 
This study was performed as part of the EC-funded SPARTACUS project (Contract no. IC15-CT98-0215) and the IAEA Contract no. 302-D1-SLR-9045. The authors gratefully thank Jasper den Besten and Arnold Wielinga, Utrecht University, for collecting the soil samples. Marcel Hornak and the technicians from the Environmental Dosimetry Laboratory, VÚJE Trnava a.s., are thanked for their assistance during sampling and sampling analysis, and Dr. Marcel Suri, Dr. Jaroslav Hofierka, and Thomás Cebecauer, GeoModel Bratislava Ltd., are thanked for preparing the basic GIS database. Dr. Edzer Pebesma, Utrecht University, Dr. Ole Wendroth, ZALF, and three anonymous reviewers are acknowledged for their useful comments on the manuscript.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 SEDIMENT BUDGET MODEL
 RELATION BETWEEN CESIUM-137...
 ANALYSIS OF RESIDUALS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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