316 TRANS URANIC ELEMENTS IN THE ENVIRONMENT 



Modeling Methods 



The model was formulated as a linear compartment model with donor-controlled flows 

 between compartments. The behavior of the state variables (Xj) was described by simple 

 differential equations of the form 



dXi 

 "dF 



= (inputs to Xj) - (losses from X[) 



TABLE 2 Values and Derivation of Annual Transfer Coefficients for Plutonium 

 Dynamics in a Contaminated Mixed Deciduous Forest* 



Transfer 



Derivation 



Value, yr" 



9.7 X 10-' 



0.95 

 1.7 X 10"* 



(1 10 g (ground vegetation produced) m ^ yr ' ] x (0.15 pCi 



Pu/g)/[1.7 X 10' pCiPu/m' (soil)] 

 95% lost to litter via plant mortality (105 g m"^ yr"' )/(110 



g/m^) 

 The initial value, ( 750 g (root production) m"^ yr"' ] x (4 pCi 



Pu/g)/[ 1.7 X 10'' pCi Pu/m^ (soil)] , was adjusted downward to 



make predictions of plutonium in roots at 30 yr match the cal- 

 culated inventory in Table 1 

 The initial value, [460 g (wood production) m~^ yr~' ] x (0.003 1.7 x 10~* 



pCi Pu/g)/[3000 g (roots)/m^ x 4 pCi Pu/g] , was adjusted up- 

 ward to make predictions of plutonium in wood at 30 yr match 



the inventory in Table 1 

 [400 g (leaf production) m"' yr"' ]/[ 10,500 g (standing 0.038 



wood)/m^ ] 

 92% of the forest canopy is returned in leaf fall to the litter 0.92 



each year (368 g m"^ yr"' )/(400 g/m') 

 Based on average values of branch-bole mortality in deciduous 0.0092 



forests (97 g m"' yr"' )/[ 10,500 g (wood)/m^ ] 

 Based on measurements of root mortaUty in deciduous forests 0.23 



(700 g m"' yr-' )/[3000 g (roots)/m' ] 

 Average decomposition rate for Fraximis and Plantanus litter 0.48 



(240 g m-^ yr"' )/[500 g (litter)/m' J 

 Parameter fitting; represents physical resuspension of soil to 8.5 x 10"' 



litter and not biological uptake 

 Small mammals are assumed to consume 33% of their biomass 0.03 



each day [3.5 g (consumed) m"^ yr"' ]/[110 g (ground 



vegetation)/m^ ] 

 Assumes most of the plutonium in small mammals is present in the 365 



gut and has a turnover time of 1 day ( 1 day/365 days)"' 

 Assumes 14% of the annual leaf fall is processed by soil fauna 0.10 



(50 g m-' yr-' )/[500 g (litter)/m' ] 

 Assumes a 30-day turnover time for soil fauna (30 days/ 12 



365 days)-' 

 Assumes ~1% of the amount ingested is soil [0.035 g (soil)/yr] x 1.4 x 10"'' 



(65 pCi Pu/g)/[1.7 X 10' pCi Pu/m' (soil)J 



•The diagrammatic model is shown in Fig. 1. Biomass data for deciduous forests were obtained 

 from Harris, (^Idstein, and Henderson, 1973; Harris et al., 1975; and SoUins, Reichle, and Olson, 

 1973. If plutonium concentrations are not shown, they cancel out of the calculation. 



Soil to ground 



vegetation 

 Ground vegetation 



to litter 

 Soil to roots 



Roots to wood 



Wood to leaves 



Leaves to litter 



Wood to litter 



Roots to soil 



Litter to soil 



Soil to litter 



Vegetation to 

 consumers 



Consumer to litter 



Litter to soil fauna 



Soil fauna to soil 



Soil to consumer 



