Estimation of present and future levels of excess carbon-14 in the environment from the nuclear tests, (1)

The mathematical model with multi-compartments (reservoirs) and the computer program for the estimation of rates of change of the excess carbon-14 levels in environments caused by the successive nuclear tests to date are developed.A set of linear differential equations of the first order obtained from nonequilibrium conditions of carbon-14 are solved by Laplace transform. The procedure of the numerical calculations by the digital computer is presented. Input data for the computer are the amount of carbon-14 atoms in steady state in each reservoir, the exchange rate constants of carbon-14 between reserviors, and the explosion yields in megaton and dates of the nuclear tests. The calculated results are compared with the observed data. The reason of disagreements between calculated and observed concentrations of carbon-14 in several reservoirs is dicussed.The possible effect of a significant degree of direct exchange of carbon-14 between the troposphere and the deep sea reservoir in cyclic model is also examined by the computer-aided calculation. As a result of the comparison of the chain model with the cyclic one, it is found that by a slight modification of the chain model to the cyclic one, the calculated concentration of carbon-14 fits fairly well to the observed values.