DYNAMIC MODELING OF RADIONUCLIDES FATE AND TRANSPORT IN THE TECHA RIVER AND ITS APPLICATION FOR DOSE RECONSTRUCTION D. Burmistrov †, V. Taranenko †, I. Linkov ‡ †

Urals Research Center for Radiation Medicine, Medgorodok, Chelyabinsk 454076, Russia Tel.: +7-3512-344384; Fax: +7-3512-344321; E-mail: [email protected], [email protected]; http://biophys.urcrm.chel.su ‡

Department of Physics, Harvard University, Cambridge, MA 02138, USA

ABSTRACT The Techa River was contaminated as a result of nuclear operations in the South Urals (Russia). Contaminated natural ecosystems have led to significant exposure to the Techa River residents. Released radionuclides accumulated in the river basin and therefore pose environmental and public health risks. Environmental modeling is required for filling inevitable gaps in the input data for dose reconstruction and radiation risk assessment. This paper presents a dynamic compartmental model for radionuclide transport in the Techa River specifically developed to address dose reconstruction. The model input parameters are highly uncertain due to environmental variability and gaps in data collection. In this paper we report the methodology for reduction of the parameter uncertainty using Bayesian updating. The developed model is being applied for the dose reconstructions and risk assessment as well as for the evaluation of the quality of the data on environmental contamination.

1. Model Description We have developed a model to describe the dynamics of radionuclide contamination in the upper part of the Techa River (about 10 km long, including two water reservoirs: the Koksharov and the Metlinsky ponds). This model was built to enable dose reconstruction for population exposed as a result

of radioactive contamination of the river in the 1950s [1,2]. The previous version of the model [2] described the following processes: 1. Transport of the liquid and solid radioactive waste by the water flow; 2. Sedimentation of solid particles released with radioactive wastes; 3. Exchange between dissolved radionuclides and those fixed on solid particles of the naturally suspended sediments; 4. Deposition of natural sediment particles; 5. Effective scoring of bottom sediments by the water flow (resuspension); 6. Decay of the released radionuclide as well as production and decay of their daughter products. We added to the present version of the model the process of water mixing by splitting the water compartments into two: the moving and the stable water compartments. We consider the water exchange between these two compartments as a simplified mixing process described by only one parameter: a mixing velocity. The addition this process provides a better description of the radionuclide accumulation in ponds discussed in [3]. The present version of the Techa River model contains eight uncertain parameters: 1. Settling velocity of the natural particles; 2. Settling velocity of the radioactive waste particles; 3. Mixing velocity for water in the ponds; 4. Resuspension rate (volume or fraction of bottom sediments scored by the water flow per day); 5. Specific β-activity in water of the Koksharov pond early in 1953; 6. The same value for the Metlinsky pond; 7. Specific β-activity of the bottom sediments in the Koksharov pond early in 1953; 8. The same value for the Metlinsky pond. In our previous studies [1,2] the uncertain model parameters were determined by fitting model predictions to the actual measurements for the total β-activity in water, and satisfactory model predictions were achieved. Nevertheless, this deterministic approach has limited application because it does not provide uncertainty estimates for the radionuclide concentrations in the compartments; and, therefore, can not be used to estimate the confidence intervals for radiation doses required in risk assessment. In this paper we treat the model uncertainty from probabilistic point of view. We start with the generic ranges for the values for the model parameters 1-8 derived from literature. As the first step we reduced the uncertainty in the model input parameters using measured distributions of the total water βactivity in 1953. Using this procedure, the updated probability distribution for the parameters 1 - 4 can be obtained with reduced uncertainties. These parameters can be used in the future for predictive modeling for the river contamination in 1949 – 1956 assuming that they do not change significantly. By 1953, the releases were small and the extensive environmental data collection was accomplished. Therefore we used this year for the Bayesian updating to avoid the influence of the source-term variations [3,5].

2. Reduction of Parameters Uncertainty Literature review and simplified model estimations were used to establish the prior distributions for the parameters 1 - 8 (Table 1). We assumed triangular shape for these distributions, that can be characterized by three parameters: minimal and maximal values and mode. In the Bayesian updating procedure, we compare model predictions and actual daily measurements for total β-activity in water. We found that deviations of measured values from their smoothed time-series for both ponds can be approximated well by a lognormal distribution with the logarithmic mean and standard deviation of 0 and 0.3 respectively. We assumed that the same distribution describes deviations of the actual measurements from the predictions obtained with our model. Figure 1 presents characteristic examples of the prior and posterior distributions for two parameters listed in Table 1: settling velocities for normal and released particles. The updated 95% confidence intervals and median values for all updated parameters are presented in Table 1. In many cases the updating was very successful, i.e. the updated parameter distributions were significantly narrower than the prior ones. Therefore, the Bayesian updating allowed estimation of site-specific distributions for the input model parameters based on uncertainty ranges obtained from literature and site-specific measurement data.

1.0

0.9

0.9

no i t cn uF n o it ub i rt si Devi t al u m uC

no i t cn uF n o it ub i rt si Devi t al u m uC

1.0

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

0

2

4

6

8

10

12

Settling velocity for natural particles, m/day

0

100

200

300

400

500

600

700

Settling velocity for release particles, m/day

Figure 1. Examples of prior (dotted line) and posterior (solid line) distributions for uncertain parameters of the Techa River model.

Table 1. Distributions for the most uncertain parameters of the Techa River model Prior Distributions Updated Distributions Parameter confidence interval Comments Min Max Mode Min Max Median 1) Settling velocity 0.3 13 0.8 1.4 3.4 2.3 Minimum and of natural maximum settling particles, m/day velocity for silt particles in stable clean water [4] 2) Settling velocity 30 700 80 150 440 284 Minimum and of release maximum settling particles, m/day velocity for finesand particles in stable clean water [4] 3) Mixing velocity, 10 1000 30 11 74 29 Model calculations m/day using the range of water transfer times estimated for the Metlinsky pond in [3] 4) Resuspension 0 0.0003 0.0001 1.4*10-5 3.5*10-5 2.4*10-5 Resuspension was rate, day-1 estimated to be less then 10% per year [5] 5) Initial water 0.012 2.07 0.15 0.47 1.3 0.79 Actual β-activity in the measurements at different points of Koksharov pond, the pond in 1953 µCi/l [3,5] 6) Initial water 0.012 2.07 0.15 0.18 1.2 0.55 There were no β-activity in the measurements in the Metlinsky pond Metlinsky pond, in 1953. Assumed µCi/l the same values as in the Koksharov pond. 7) Initial β-activity 11.7 23182 6000 4929 7963 6191 Actual measurements at of bottom different points of sediments in the the pond in 1953 Koksharov pond, [3,5] µCi/kg 8) Initial β-activity 4.4 69818 5300 3667 5834 4483 Actual measurements at of bottom different points of sediments in the the pond in 1953 Metlinsky pond, [3,5] µCi/kg

Figure 2 shows the results of the model predictions for the total β-activity in the ponds, calculated with the median values of parameters from Table 1. There is a satisfactory agreement between the model predictions and the actual measurements. Figure 2. Comparison of measured and calculated discharges of total β-activity from Koksharov and

100

80 y a/di C, yti vi t ca- βl at ot f o egr ah csi D

60 Koksharov pond 40

20

0

1500

Metlinski pond

1550

1600

1650

1700

Days after 01/01/1950 Metlinsky ponds for median values of updated parameters (Table 1). Measured values: circles (the Koksharov pond), squares (the Metlinsky pond). Calculated values: solid lines.

1750

Discussions Uncertainty and variability are inherent in the nature of radioecology. Therefore we need to use appropriate tools to deal with these issues.

One should weight current knowledge and associated

uncertainties to develop the optimal model for a specific ecosystem. Model oversimplification may ignore available data and knowledge on specific issues while excessive model complexity may lead to limited predictability and applicability of the model because the high uncertainty in model inputs results in even higher uncertainty in model outputs. The optimal model complexity also depends on the specific objectives of the researcher: if one is to describe a limited data set, a global comprehensive model may not be necessary. The uncertainty and variability inherent in radioecology requires probabilistic treatment of model inputs and outputs since no single value can describe the complexity of the processes involved in radionuclide fate and transport in the environment. The probabilistic treatment not only ensure a more realistic description of ecosystem parameters but also allows application of one of the most powerful tools developed to deal with such uncertainty. The Bayesian updating allows to reduce uncertainty in the model input using limited information about model outputs and, therefore, to improve model predictions. We have demonstrated how a wide range of variation of the generic values for input model parameters can be reduced based on the site-specific data collected for the Techa River. Bayesian updating procedure requires intensive computer calculations. The present study required several days of calculations on an Intel Pentium-166 based PC, while one model run for the given values of parameters takes less than one minute. Therefore, an efficient reduction of the uncertainty in complex environmental applications require to: 1) increase computational speed and efficiency, 2) improve model structure to decrease the number of uncertain model parameters, i.e. decrease model complexity, and 3) improve efficiency of Bayesian updating procedure itself. The main reason for the low efficiency of the Bayesian updating procedure consists in incomprehensive algorithm of random sampling: random sampling does not take into account all the information obtained in the previous calculations. In addition, methodology for incorporation of the available experimental data in the updating scheme should be further developed. Use of the all array of the available information is desired to obtain the maximal decrease in the model uncertainties. But excessive volume of experimental data could lead to a very complex model likelihood function and may result in considerable fluctuations in the posterior distributions. We are currently developing a sampling technique for Bayesian updating that should address these issues.

Acknowledgements This work was supported by a NATO Collaborative Research Grant (Environmental Security) and by the Russian-US Joint Coordinating Committee for Radiation Effects (Project 1.1, “Dose Reconstruction for the Ural Population”). The advice and suggestions of Marina Vorobiova are gratefully acknowledged.

References 1. Burmistrov D., Vorobiova M., Degteva M., Linkov I., Wilson R. (1997) “Radioactive Contamination of the Techa River: Environmental Records and Multimedia Modeling”, Conference Proceedings V.59, “Nuclear Data for Science and Technology”, SIF, Bologna, 1376-1380. 2. Burmistrov D. and Linkov I. (1998) “Radioactive Contamination of the Techa River.” in: Linkov I., Wilson R., eds. “Air Pollution in the Ural Mountains,” Kluewer, Amsterdam 1998. 3. Marey A. N., Ilyin D. I. et al (1953) “Impact of Mendeleyev’s plant wastes released into the Techa river and Tatysh Lake on the sanitary conditions and health of inhabitants of coastal villages” Moscow: Institute of Biophysics, Technical Report (In russian). 4. Van der Leeden F. (1990) “The water encyclopedia”, Lewis Publishers Inc. 5. Marey A. N. et al (1954) Impact of Mendeleyev’s plant wastes released into the Techa River and Tatysh Lake on the sanitary conditions and health of inhabitants of coastal villages” Moscow: Institute of Biophysics, Technical Report (In russian).

dynamic modeling of radionuclides fate and transport in ...

for filling i nevi table gaps in the input data for dose reconstructi on and radi ation risk ... 5. Specific β-activity in water of the Koksharov pond early in 1953;. 6.

127KB Sizes 0 Downloads 210 Views

Recommend Documents

Nonlinear dynamic modeling of surface defects in ...
Aug 6, 2008 - defective bearing rotor systems as the parameters of the system changes. ..... period of T ¼ 1/Ovc where Ovc ¼ ZOvc is the varying compliance frequency, so that: ~UрtЮ ¼ ~Uрt ю TЮ. (18) ... This information is needed to ...

Dynamic Bayesian Network Modeling of ...
building network of biological processes from gene expression data, that lever- ages several ... amino sequence matching, as provided by the Blast2GO software suite [5]. – Building a ... recovering the underlying network. Also, a large .... K2 and