Forecast of gamma radiation dose rate based on mathematical models of ¹³⁷Cs migration in soil

The work is devoted to the study of the possibility of predicting the gamma dose rate from ¹³⁷Cs +¹³⁷mBa radionuclides that fell into the environment as a result of a large-scale radiation accident. Based on existing analytical models of cesium migration on the one hand and natural data on the vertical distribution of cesium in the soils of areas contaminated as a result of the Chernobyl accident on the other, a forecast of the dose rate of gamma radiation in the air over open areas was constructed. The experimental database contained 180 profiles from the Bryansk region of the Russian Federation and about 100 profiles, including global ones, from Bavaria (Germany). To approximate the radionuclide distribution in the soil, solutions of the convectivediffusion equation and the lognormal distribution were used. The best fit to the real distributions of the radionuclide in the soil was the χ² distribution, which is a solution of the convective-diffusion equation with an increasing diffusion coefficient, and the lognormal distribution. For both distributions, the dependences of the parameters (diffusion penetration rate and movement rate with soil moisture) on time were found. Assuming the universality of these dependences, a method for their reconstruction in time is proposed, for example, based on once selected profiles of global fallouts. The absorbed dose rate values in the air were calculated for up to 50 years after the fallout. The average difference between the experimental data, expressed as the ratio of the dose rate in the air at a height of 1 m above the soil from the profile of ¹³⁷Cs + ¹³⁴Cs radionuclides at time t to the dose rate in the air for radionuclides located on the soil surface from the calculated ones, was 9 % for the Bryansk region and 14 % for Bavaria. The calculated values of the absorbed dose rate in the air were verified using the results of its measurements in the Bryansk region in the period of 3–24 years after the fallout. They coincided with the measured values within 95 % of the measurement error interval throughout the entire measurement time period except for the 8th year after the accident, which confirms the adequacy of the radionuclide distributions in the soil used in the work.

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