PLUTONIUM DYNAMICS IN A DECIDUOUS FOREST ECOSYSTEM 517 



The model uses time-invariant transfer coefficients. Since this is an annual model seasonal 

 variations in transfers are not represented. The system was modeled interactively on a 

 computer with a differential-equation modeling program (Rust and Mankin, 1976). The 

 average steady-state value of all compartments and their variabilities was determined with 

 COMEX (Gardner, Mankin, and Shugart, 1976). COMEX is a computer program that 

 uses Monte Carlo methods for analyses of donor-controlled linear compartment models. 

 Its features are: (1) selection of transfer coefficients for each simulation from a 

 multivariate normal random-number generator (the distribution is determined by 

 specifying means and variances for all transfers); (2) solution of the system by matrix 

 calculus; and (3) output of results to SAS, a statistical analysis package (Barr et al., 

 1976), for analyses of state variables and relationships between state variables and model 

 transfers. From COMEX it is possible to evaluate the sensitivities of model compartments 

 to changes in transfer coefficients and provide estimates of variation in model predictions, 

 given variation in the model parameters. 



Results and Analyses 



First, the model was used to simulate plutonium dynamics in vegetative components of a 

 forest on the basis of the data set for the forest at Oak Ridge (basic model). Second, 

 simulations including the animal components of the forest were performed (expanded 

 model). Third, the variabihty in state variables under equilibrium conditions was 

 calculated for both cases, given variability in the model transfer coefficients. Last, a 

 correlation analysis was performed on the expanded model to identify important 

 plutonium transfers. 



The accumulation of plutonium in vegetative components of the forest (basic model) 

 was simulated, starting from an initial condition of 1.7 x 10^ pCi Pu/m^ (soil). The 

 results are shown in Fig. 2. The amount of plutonium in litter, ground vegetation, roots, 

 wood, and leaves reached steady state in approximately 120yr. After this time, less than 

 0.1% of the total soil plutonium had transferred to aboveground components. Tree roots 

 and litter were the principal biological reservoirs of plutonium in the forest. Expansion of 

 the model by couphng it to animal compartments resulted in only a sHght alteration in 

 model performance. At steady state the consumer and soil-fauna components contained 

 <0.01 and 21 pCi Pu/m^, respectively. The addition of soil fauna lowered the 

 steady-state amount of plutonium in litter from =^3000 to ^2500 pCi/m^. All other 

 components were negligibly affected. 



The selection of values of transfer-coefficient variability for the COMEX simulations 

 proved difficult. An accurate assignment of variation to each parameter would require 

 information on the form of the probabiHty density function of each transfer coefficient 

 (e.g., a frequency distribution of litter decay rates measured throughout the forest). 

 Presently, such statistical information is rarely available for a single parameter much less 

 an entire ecosystem. It is not uncommon for coefficients of variation (CV = standard 

 deviation/mean) to range from 0.5 to 3.0 for field measurements of biomass and 

 plutonium concentrations. Nevertheless, we have assigned CV values of 0.2 to transfer 

 coefficients on the assumption that variation is inversely related to sample size, and, with 

 a sufficient number of measurements from the forest, transfers could be quantified with 

 standard deviations much smaller than those normally encountered. We also assume that 

 in large samples these parameters will be normally distributed. Therefore the question 

 posed was, "Given that transfer coefficients can be measured with CV values equal to 



