MODEL FOR ESTIMATING Pu TRANSPORT AND DOSE 473 



evergreens, leaves and vestiges of fruits produced the previous growing seasons. In 

 addition to these seasonal and species variations, it is reasonable to suppose that the 

 roots, stems, leaves, fruits, and other organs of a given species grow at different times and 

 at different rates and that additional variations can be expected in response to 

 environmental factors, such as temperature, soil moisture, and availability of nutrients. 



To attempt a mathematical description of vegetation growth that includes all factors 

 mentioned above (and others not mentioned) would be a monumental undertaking. What 

 is needed at present is a simple expression of growth rate, as a continuous function, which 

 will provide a reasonable, but conservative, estimate of the potential overall concentration 

 of plutonium in plant materials that have been contaminated externally by airborne 

 deposits and/or internally by root uptake from soil. 



To obtain a rougli estimate of growth rate, we can define Xg as follows: 



_ ln[l+(Pn/Bo)] 

 ^g 365 ^^^ 



where Xg is the growth rate coefficient averaged over the year (day~^ ), ?„ is the net gain 

 in biomass during a growing season (g/m^ ), and Bq is the biomass at the beginning of the 

 growing season (g/m^ ). 



Odum (1971) has estimated that the average gross primary productivity (GPP) of 

 deserts and tundras is about 200 kcal m~^ yr""' . Since the fraction of GPP (0.2) used up 

 in respiration does not appear as new tissue, the dilution growth rate is proportional to 

 0.8 GPP = 160 kcal m"^ yr"^ At 4.5 kcal/g (dry weight) (Odum, 1971), this amounts to 

 a net gain of Pn = 36 g/m^ (approximately). The biomass of desert vegetation varies from 

 place to place. The mean biomass for Area 13 is Bq = 289 g/m^ (Wallace and Romney, 

 1972). Substituting these values of Pn and Bq in Eq. 9, Xg = 3 x 10""* day~^ . If we 

 assume that internally deposited plutonium is uniformly distributed above and below 

 ground, this would be the value to use in Eq. 8. If we assume that two-thirds of Pp is 

 above ground and one-third is below ground, the dilution growth rate for the external 

 (aboveground) component (Eq. 7) would be Xg = 2 x 10""* day~^ . 



Root Uptake and Plant/Soil Concentration Ratio. For plutonium to enter plants via 

 root uptake, it must first reach the roots. Plowing, of course, accomplishes this 

 "transport" quite rapidly by mixing the soil, but the downward movement of plutonium 

 in an undisturbed soil profile is such a slow process that much of the plutonium deposited 

 on the surface may stay near the surface for many years. To circumvent the variability 

 inherent in these and other soil processes affecting the behavior of plutonium in soils 

 (factors reviewed by Price, 1973a; Francis, 1973), we have made the simplifying and 

 conservative assumption that plutonium deposited on soil is diluted by only the top 5 cm 

 of soil and that root uptake is related to the resulting concentration in surface soil; i.e., 

 the probable concentration of plutonium in the root-zone soil is deliberately overesti- 

 mated. 



Most of the available data (Price, 1973a; Francis, 1973) on plutonium uptake by 

 plants has been derived from short-term greenhouse experiments. Typical values thus 

 derived for the plant/soil concentration ratio range t>om 10"'^ to 10~^. Uptake has 

 been shown to be enhanced by the reduction of pH or the addition of chelating agents. 

 There is some evidence that plutonium uptake by plants may increase with time 

 (Romney, Mork, and Larson, 1970) and that the mobihty of plutonium, i.e., its ability to 



