664 TRANS URANIC ELEMENTS IN THE ENVIRONMENT 



The ratio Vj/Qj is the residence time of plutonium in the lake with respect to outflow 

 (Trj). If the rate of loss by sedimentation is proportional to the concentration in the 

 water column, then the term Sj/Vi can be replaced by Ci/Tk;, where Tr; is the residence 

 time of plutonium in the water column with respect to losses via sedimentation. In this 

 case Eq. 2. can be written as 





d^i _ Ai0i — 1 '<i-i -1-1 I " " I p (-.^ 



The mean residence time Tr; of plutonium in each lake is given by 



111 



^ZJ- (4) 



TRi Trj T'rj 



For Lake Superior and Lake Michigan, there is no inflow from the other lakes, i.e., 

 Ii ~ I2 ~ (Fig. 1); for Lake Huron, however, I3 = Q2C2 + QiCi . The above systen. of 

 equations (Eq. 3) is equivalent to the concentration— time model described by Lerman 

 (1972) to describe the behavior of ^°Sr in the Great Lakes. For plutonium, losses by 

 radioactive decay are, of course, negligible. Since the values of Ai0i, Vj. and Qj are known 

 (Table 3) and a can be assumed as a first approximation to be zero, the only 

 undetermined parameter in the model is T'r. 



TABLE 3 Physical and Hydrological Data 

 for the Great Lakes 



The results of evaluating Eq. 3 are shown in Fig. 3. The monthly values of 0j used 

 were taken from Lerman (1972). For deposition from 1973 to 1977, values measured at 

 Argonne National Laboratory were used for each lake (Golchert. Duffy, and Sedlet, 

 1978). Values of T'r were chosen to reproduce the earliest available measured 

 concentration in each lake. This approach was taken to evaluate subsequent changes in 

 the value of T'r. In all lakes but Lake Erie, the mean residence time is around 2 to 3 yr. 

 Under such conditions short-term (monthly) fluctuations in deposition are averaged out 

 in the water column, and the calculated time— dependence of plutonium levels shows a 

 smooth variation over the past 25 yr or so. Since plutonium in waters of the Great Lakes 

 has been measured at the "tail-end" of the concentration— time record, reconstruction of 

 previous levels in the water column is an exercise in extrapolation. However, the choice of 

 residence times, T'r, summarized in Table 2, gives a very reasonable prediction of recent 

 levels in all the lakes as well. In other words, values of T'r, which by definition correctly 



