Sensitivity Analysis of a Dynamic Food Chain Model DYNACON Considering Korean Agricultural Conditions

Transcription

1 Sensitivity Analysis of a Dynamic Food Chain Model DYNACON Considering Korean Agricultural Conditions W. T. Hwang 1, G. C. Lee 1, K. S. Suh 1, E. H. Kim 1, Y. G. Choi 1, M. H. Han 1 and G.S. Cho 2 1 Korea Atomic Energy Research Institute, 150 Duckjindong, Yusonggu, Taejon, Korea 2 Korea Advanced Institute of Science and Technology, 3711 Kusongdong,, Yusonggu, Taejon, Korea ABSTRACT The sensitivity analysis of input parameters for a dynamic food chain model DYNACON was performed as a function of deposition time for the longlived radionuclides ( 137 Cs, 90 Sr) and the selected foodstuffs (cereals, milk). The influence of input parameters for short and longterm contaminations of the foodstuffs after a deposition was also investigated. The input parameters were sampled using a Latin hypercube sampling (LHS) technique, and their sensitivity indices were quantified as partial rank correlation coefficient (). s were strongly dependent on the contamination period of foodstuffs as well as the deposition time of radionuclides. In case of deposition during growing stage of agricultural plants, the input parameters associated with contamination by foliar absorption were relatively influential in longterm contamination as well as shortterm contamination. They were also influential in shortterm contamination in case of deposition during nongrowing stage. As the contamination period is longer, the influence of parameters associated with contamination by root uptake was increased. This phenomenon was more remarkable in case of the deposition during nongrowing stage than growing stage, and in case of 90 Sr deposition than 137 Cs deposition. In case of deposition during growing stage of pasture, the characteristic parameters of cattle such as feedmilk transfer factor and daily intake rate were relatively influential in the contamination of milk. INTRODUCTION To minimize the radiological consequences from radioactive materials released into the environment during a nuclear accident, the reliable dose assessment is essential. All environmental assessment models, which can describe the transport of radionuclides from a source through the calculation of dose to the public, only simulate approximate realworld phenomena due to physically complex systems. Additionally the parameter values in models are inherently uncertain from improper parameter estimation, and stochastic effects due to random measurement and sampling errors or natural variation. Understanding of these uncertainties is required to effectively interpret model prediction. The sensitivity analysis involves the determination of the change in the response of a model to change in individual model parameter. Thus, it is a procedure for improving the reliability of model predictions and saving a major effort in the collection of relevant data by identifying the main contributors of input parameters to model predictions. A dynamic food chain model DYNACON is a deterministic model for the assessment of radiological consequences in agricultural ecosystems following a nuclear accident (1). The model is based on a compartmental approach which predicts the radionuclide concentrations in the compartments representing various environmental media from radionuclide concentration on the ground. The transfer processes of radionuclides include foliar interception, weathering removal, growth dilution of agricultural plants, soil resuspension, percolation from surface soil to root zone soil, foliar absorption, leaching from root zone soil to deep soil, adsorption and desorption in soil, radioactive decay, root uptake, feedstuff ingestion and excretion of cattle, soil ingestion of cattle. Although the parameter values in the model are representative of Korean agricultural and environmental conditions, some values are taken from available foreign literatures due to the lack of sitespecific data. In this study, the sensitivity analysis of input parameters associated with the transfer processes of radionuclides in DYNACON is performed using a Latine hypercube sampling (LHS) technique based on a Monte Carlo approach. The sensitivity indices are quantified by partial rank correlation coefficient () based on ranktransformed values of sampled input parameters. The end point of the model is radionuclide concentrations in foodstuffs. MATERIAL AND METHODS It is necessary for the sensitivity analysis of input parameters to specify several items including the distribution of parameter values and the correlation coefficient between input parameters. A LHS is widely used as a sampling technique because it reflects good distributional characteristics of population with small size of a sample (2). The sensitivity indices calculated from ranktransformed values are more effective for representing a variety of relationships between parameter values (X) and model outputs (Y), and for minimizing the effects of extreme values than those calculated from actual values. Such a correlation coefficient is called the partial rank correlation coefficient (). The strength of a simple linear relationship in ranking r x 1

2 between variable X 1 and X 2 in usually measured with ρ, called Spearman's rho, is expressed as follows (3) : n + 1 n + 1 ( r )( ) x1i r x2i = 2 2 ρ 12 2 n+ 1 n+ 1 ( r x ) ( ) 1i r x2i (1) where n is the sampling number of each parameter. s can be obtained from correlation matrix (R) and inverse correlation matrix (R 1 ) as follows (3): X 1 X 2 Y ρ ρ ρ1 k ρ ρ ρ 2k R =... ρ k ρ... 1 k 2 ρ kk (2) b11 b12... b1k 1 = b21 b22... b2k R (3)... bk1 bk 2... bkk ij ( allothers) = bij biib jj (4) RESULTS AND DISCUSSION The sensitivity analysis of parameters for DYNACON was performed as a function of deposition time for the longlived radionuclides 137 Cs (T 1/2 =30 years) and 90 Sr (T 1/2 =29 years). In this study, though the consumption rate of rice is the highest in Korean, cereals were selected as a typical vegetation foodstuff because of limitation of experimental data for rice. Milk was selected as a typical animal foodstuff. Table 1 shows the distributional characteristics of parameter values selected in this study (4,5,6,7). The information on these input parameters was taken from available foreign literatures, if unavailable, it is based on engineering judgement of the authors. It was assumed that the input parameters associated with natural ecosystems such as sowing time, harvesting time, yield of agricultural plants and soil density are fixed. The correlation relationships between input parameters were not considered because the parameter values to be provided from the literatures are experimental results under a variety of conditions. s were calculated with 500 different parameter sets yielding a distribution of 500 model outputs using a LHS technique. For investigating the influence of input parameters for short and longterm contaminations, the integrated concentration (Bq d drykg 1 per Bq m 2 ) of cereals harvested during the first year (shortterm contamination) and the 50th year (longterm contamination) after a deposition was used as final model outputs. For milk, which is produced continuously, the integrated concentration (Bq d L 1 per Bq m 2 ) for a year (shortterm contamination) and 50 years (longterm contamination) was used as final model outputs. Fig. 1 shows the s of input parameters for the shortterm 137 Cs and 90 Sr contaminations of cereals. The influential input parameters ( 0) in 137 Cs deposition during growing stage of cereals (growth period : Jan. 1 ~ May 30, s represent the average of absolute s for deposition on Jan., March and May) were growth dilution rate (=2), foliar interception factor (6), resuspension factor (4) and foliar absorption rate (0). In 137 Cs deposition during nongrowing stage (s represent the average of absolute s for deposition on Jul., Sept. and Nov.), the influential input parameters were resuspension factor (0.96) and deposition velocity (0.91). The results of sensitivity analysis for 90 Sr deposition during growing stage were similar to those for 137 Cs deposition. While, in 90 Sr deposition during nongrowing stage, growth dilution rate (0.72) and concentration ratio (5) as well as resuspension factor (2) and deposition velocity (0.70) were influential. Fig. 2 shows the s of input parameters for the longterm 137 Cs and 90 Sr contaminations of cereals. In 137 Cs deposition during growing and nongrowing stages, the influence of input parameters for longterm contamination was similar to that for shortterm contamination. Additionally, in 90 Sr deposition during growing stage, the influential input parameters in longterm contamination were similar to those in shortterm contamination. 2

3 Table 1. Characteristics of input parameters used in sensitivity analysis(4,5,6,7). Symbol Description Units Range of value Cereals L. vegetables Milk Distribution type TF Transfer factor of 137 Cs from feed to milk d L 1 2.5E3 1.6E2 Transfer factor of 90 Sr from feed to milk d L 1 6.4E4 4.5E3 FI Feed intake rate of a daily cow drykg d IF Foliar interception factor m2 drykg DC Distribution coefficient of 137 Cs in soil ml g , , ,000 Distribution coefficient of 90 Sr in soil ml g , , ,000 DV Deposition velocity of resuspended radionuclide m s , , ,900 TR Foliar absorption rate for 137 Cs d 1 3.9E3 5.5E3 7.2E3 3.9E3 5.5E3 7.2E3 3.9E3 5.5E3 7.2E3 TA Foliar absorption rate for 90 Sr d 1 7.8E4 E3 1.4E3 7.8E4 E3 1.4E3 7.8E4 E3 1.4E3 TA RF Resuspension factor m 1 3.0E8 3.4E3 3.0E8 3.4E3 3.0E8 3.4E3 GD Halflife of radionuclide due to plant growth d SC Soil intake rate of a daily cow kg d UF CF Plant/soil concentration ratio for 137 Cs unitless E3 E1 1.9E E2 1.1 Plant/soil concentration ratio for 90 Sr unitless 2.2E2 6.6E1 7.4E E2 2.9 EH Halflife of radionuclide due to weathering d FX Adsorption rate of 137 Cs in soil d 1 1.9E4 1.9E2 DS PH FP BH Desorption rate of 137 Cs in soil Percolation rate from soil surface into root zone Fraction of radionuclide remaining after washing Biological halflife of 137 Cs for milk Biological halflife of 90 Sr for milk d 1 d 1 unitless d d 2.1E5 2.1E3 1.73E2 2.31E2 2.1E5 2.1E3 1.73E2 2.31E E5 2.1E3 1.73E2 2.31E UF (Note) The values in triangular distribution (TA) represent minimum, most probable and maximum values, respectively. ( : lognormal distribution, : normal distribution, TA : triangular distribution, UF : uniform distribution) 3

4 IF DC DV TR RF GD CF EH PH Inputparam eter NonGrowing (a) 137 Cs deposition IF DC DV TR RF GD CF EH PH Inputparam eter Non (b) 90 Sr deposition Figure 1. Partial Ranking Correlation Coefficient () of input parameters for shortterm contamination in cereals. But, in 90 Sr deposition of the nongrowing stage, concentration ratio (5), growth dilution rate (5) and distribution coefficient (0.76) were influential input parameters, unlike shortterm contamination. From these results, it is found that the contamination of cereals by foliar absorption is much stronger than that by root uptake. Even, in 137 Cs deposition during nongrowing stage, the input parameters associated with foliar absorption such as resuspension factor and deposition velocity are more influential than those associated with root uptake. Also, they are more influential except for longterm contamination resulting from 90 Sr deposition during nongrowing stage in which influential input parameters are primarily related with the contamination by root uptake. Fig. 3 shows the s of input parameters for the shortterm 137 Cs and 90 Sr contaminations of milk. The influential input parameters in 137 Cs deposition during growing stage of pasture (growth period : May 1 ~ Sep. 30, s represent the average of absolute s for deposition on May, Jul. and Sep.) were pasturemilk transfer rate (=7), daily intake rate (0.77), foliar interception factor (6), resuspension factor (0) and biological halflife (0). In 137 Cs deposition during nongrowing stage (s represent average of absolute s for deposition on Jan., March and Nov.), the influential input parameters were resuspension 5

5 factor (9) and deposition velocity (0).. IF DC DV TR RF GD CF EH PH Inputparam eter Non (a) 137 Cs deposition IF DC DV TR RF GD CF EH PH Inputparam eter Non (b) 90 Sr deposition Figure 2. Partial Ranking Correlation Coefficient () of input parameters for longterm contamination in cereals. TF FI IF DC DV TR RF GD SC CF EH FX DS PH BH Inputparameter Non 6

6 (a) 137 Cs deposition TF FI IF DC DV TR RF GD SC CF EH PH BH Inputparameter Non (b) 90 Sr deposition Figure 3. Partial Ranking Correlation Coefficient () of input parameters for shortterm contamination in milk. In 90 Sr deposition during growing stage, the influential input parameters were pasturemilk transfer rate (7), daily intake rate (0.76) and resuspension factor (1). In 90 Sr deposition during nongrowing stage, the influential input parameters were resuspension factor (0), pasturemilk transfer rate (0.72) and deposition velocity (5). Fig. 4 shows the s of input parameters for the longterm 137 Cs and 90 Sr contaminations of milk. In 137 Cs deposition during growing and nongrowing stages of pasture, the influence of input parameters for longterm contamination was similar to that for shortterm contamination. Also, in 90 Sr deposition during growing stage, the influence of parameters for longterm contamination was similar to that for shortterm contamination. But, in 90 Sr deposition of nongrowing stage, the influence of concentration ratio (0.72) and distribution coefficient (3) associated with contamination by root uptake was greater than influence of input parameters associated with contamination by foliar absorption such as resuspension factor and deposition velocity. TF FI IF DC DV TR RF GD SC CF EH FX DS PH BH Inputparameter Non (a) 137 Cs deposition 7

7 TF FI IF DC DV TR RF GD SC CF EH PH BH Inputparameter Non (b) 90 Sr deposition Figure 4. Partial Ranking Correlation Coefficient () of input parameters for longterm contamination in milk. In the contamination of milk, the characteristic input parameters of cattle such as pasturemilk transfer rate and daily intake rate are influential except for 137 Cs deposition during nongrowing stage. Among the input parameters associated with the contamination of pasture, the influence of parameters associated with contamination of leave surfaces is greater than those associated with contamination by root uptake except for longterm contamination by 90 Sr deposition during nongrowing stage. The influence of parameters with different deposition times and contamination periods is primarily caused by growth characteristics of agricultural plants, behavior characteristics of radionuclides in the environment, and breeding practices and metabolism of cattle. CONCLUSIONS The sensitivity analysis of input parameters for DYNACON was performed as a function of deposition time and contamination period for the longlived radionuclides and the selected foodstuffs. The sensitivity indices, s, were strongly dependent on radionuclide, foodstuff, deposition time and contamination period. In deposition during growing stage of agricultural plants, the parameters associated with contamination by foliar absorption were relatively influential in longterm contamination as well as shortterm contamination. They were also influential in shortterm contamination in case of deposition during nongrowing stage. As the contamination period is longer, the influence of parameters associated with contamination by root uptake was increased. This phenomenon was more remarkable in case of the deposition of nongrowing stage than growing stage, and in case of 90 Sr deposition than 137 Cs deposition. In case of deposition during growing stage of pasture, the input parameters associated with the characteristics of cattle such as feedmilk transfer factor and daily intake rate were relatively influential in contamination of milk. The results of this study may be serve as a useful information for improving the reliability of predictive results and saving a major effort in the collection of relevant data by identifying the main contributor of input parameters to model results. 8

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