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             Modelling the migration and accumulation of radiocesium
         (Cs-137) in soil: results, ecological half-lives, model prognosis
                           

Model for the vertical migration of 137Cs in the soil profile: Modelling and Measurements

The modeling of the 137Cs migration in the forest soil has been carried out with the equations of site “modelling”. For the calculation of the 137Cs activities with the system of differential equations a value of 0.016 a-1 has been applied for parameter λb. This value results from annual rates of 700 Bq/m-2 due to litter fall and 900 Bq/m due to water from the crowns of trees. The rates refer to an area with a deposition of 98 450 Bq/m2 (Fielitz 1994).

It can be estimated that at the zero-point of time (April 1986) 87% of the non-fixated radio-cesium is in the most upper soil layer. The value has been derived from the deposited activities of 51 798 Bq/m-2 (total) and 44 985 Bq/m-2 (caused by the Chernobyl accident). It is further assumed, that at the zero-point of time the portion of radionuclides, which cannot be attributed to the Chernobyl accident, is uniformly distributed in the deeper soil layers.

Additionally it is assumed, that the rates of migration, fixation and desorption in the humus layer (soil depth from 0 – 6 cm) are different from those of the soil layers in the Ah and Bv horizons. The rates λm, λf, und λd were determined by a least-squares fit, which uses the mean measured values (in %/cm/m2) of the 10 soil profiles from two years (2000 and 2004) for the 15 upper soil layers. The following values are computed:

λm(1,2,3) =  (0.59 ± 0.12) a-1 for soil depth 0 – 6 cm

λm(4-15) =  (0.50 ± 0.10) a-1 for soil depth > 6 cm

λf  =        (0.59 ± 0.18) a-1

λd  =        (0.68 ± 0.23) a-1

In figure 17 the measured values of the soil profiles are shown for 2004 as well as the modeled data. 

   Fig. 17: Mean 37Cs distribution in 10 soil profiles of area B1, in 2004 and 2004. Error bar = minimum and maximum values. The model data were calculated without (upper picture) and with (lower picture) consideration of fixation, desorption as well as litter fall and water from the crowns of trees.

Two different scenarios have been modeled: one scenario without fixation and without deposition of radio-cesium due to litter fall and water from the crowns of trees (upper picture) and another scenario with these parameters (lower picture).

It is clearly visible, that the agreement of measured and modeled data is much better when fixation and the annual 137Cs deposition onto the soil due to litter fall and water from the crowns of trees is taken into account. The mean deviation of the modeled data from the measured data is 0.77% with consideration of deposition, but 6.67% without. The good agreement of the modeled data with the measured vertical distribution of 137Cs in the soil profiles is a condition for a reliable long-term prognosis.

From the radioecological point of view it is particularly worth to know, in which time the 137Cs contamination of the environmental media decreases to half of its initial value. This time period is called ecological half-life (T1/2). The ecological half-life considers all factors, such as radioactive decay, changes of the contamination due to increase of the biomass of the plants, changes in the biological availability of the nuclides in the soil, as well as other factors, such as leaching, fixation etc. which cause a decrease of the contamination. The following ecological half-lives basing on the 10 soil profiles were determined with T1/2 = ln2 / λm (table 3).

 

Table 3: Ecological half-lives, calculated for forest soil profiles on the sample area B1

Parameter

with fixation    and desorption
(0 – 6) cm

with fixation    and desorption
> 6 cm

without fixation and desorption

migration λm (a-1)

0.59 ± 0.12

0.50 ± 0.10

0.7 ± 0.04

T1/2 (a)

1.17 ± 0.24

1.39 ± 0.28

2.57 ± 0.38

T1/2 (a/cm)

0.59 ± 0.12

0.69 ± 0.14

1.28 ± 0.19

 

The ecological half-life with a value of 1.2 years for the soil zone 0 – 6 cm, which corresponds approximately to the humus layer, is merely lower than the half-life for the deeper soil zone with a value of 1.4 years.

 

Model prognosis for the vertical distribution of 137Cs until 2020

The radioecological model was used to forecast the vertical distribution of 137Cs in the forest soil in the years 2010 and 2020 up to a depth of 50 cm (figure 18). The modeled values were calculated with fixation, desorption and with deposition of 137Cs due to litter fall and water from the crowns of trees. The same migration rate has been applied for the soil layers from 0 – 6 cm, another migration rate for the soil layers deeper than 6 cm. The migration of 137Cs to deeper soil layers will proceed slowly, but continuously. This will lead to noticeable changes in the vertical distribution of radio-cesium.

  

Fig. 18: Model prognosis of the 137Cs distribution in the forest soil of sample area B1,  2010 and 2020

While in 2004 the maximum of the activity is between 8 and 12 cm, in 2010 the maximum will be between 10 and 18 cm and in 2020 between 14 and 22 cm. The curve of the distribution will be further flattened around the maximum, so that the maximum values will extend to a larger soil range in 2020 than it is the case in 2004. Table 4 shows the distribution of the forecasted 137Cs activities, expressed in percentage values, for different soil ranges, each one comprising 10 cm.

Table 4: Model prognosis of the 137Cs activity distribution in forest soil 2004-2020

Soil layer

[cm]

Model prognosis 2004

137Cs [%/m2/cm]

Model prognosis 2010

137Cs [%/m2/cm]

Model prognosis 2020

137Cs [%/m2/cm]

0 - 10

38.9

23.1

9.8

10 - 20

48.1

53.1

41.6

20 - 30

9.1

18.0

35.4

30 - 40

3.2

4.3

10.2

40 - 50

0.8

1.4

3.0

According to this prognosis and assuming unchanged physical-chemical conditions, in 2020 the most upper 10 cm of the soil will contain only ¼ of the 137Cs activity compared with 2004. While the changes from 2004 to 2020 in the soil range from 10 – 20 cm will be relatively small, the activity in the deeper layer between 20 and 30 cm will increase by a factor greater than 3. However, since the roots of plants normally do not take up 137Cs in this deep soil range, this will lead to lower 137Cs contaminations of the plants growing on forest soils.

 

 

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