Transient Effects in the Distribution of Carbon-14 in Nature.

A prerequisite for accurate dating by means of carbon-14 is the existence of a steady state in the specific activity of the carbon in the atmosphere. The studies1 which have been made of carbon activity supported the view that there was a state of dynamic equilibrium in the carbon exchange between natural reservoirs. A disturbance in this state is known to arise from the discharge of the combustion products from fossil fuels into the atmosphere. The resulting dilution of the specific carbon activity of the atmosphere by the addition of this inert carbon dioxide (the Suess effect) has been discussed recently elsewhere.2 and will not be considered here. Of present interest is how a disturbance in the absolute amount of carbon-14 in a natural reservoir such as the atmosphere disappears through exchange with other reservoirs. There has been such a disturbance in the world equilibrium of carbon-14 by the explosion of nuclear bombs. The redistribution of the excess radiocarbon produced by nuclear explosions may be calculated as a function of time from the fundamental transient solutions which are presented here. These fundamental solutions are those obtained for an instantaneous increment of carbon-14 introduced into the stratosphere or the troposphere. The net result of all nuclear explosions to date may then be determined by summation of such solutions when the intensity and date of the explosions are given. This summation has been carried out by the authors and is presented elsewhere. The steady state conditions for ordinary carbon and radiocarbon determine exchange rate constants for radiocarbon. Arnold and Anderson4 have evaluated these constants from the steady state relations for a two and for a three reservoir model of the natural carbon reservoirs. Their "upper reservoir" includes the atmosphere, land-life, and humus; a second reservoir is the oceans. Their three reservoir model is formed by a separation of the oceans reservoir into two portions. The steady state behavior of a more elaborate model, consisting of five reservoirs, has been examined by Craig.5 The reservoirs in this model are: the atmosphere, the land biosphere, the land humus, the ocean mixed layer, and the deep oceans. The transient solution which is developed here uses Craig's reservoir model with a slight, extension. This extension consists in a division of the atmosphere into two reservoirs: the stratosphere and the troposphere. The justification for the development of this six reservoir model comes from the possibility that experimental observations of the carbon-14 transients which have been produced may give further information on the effective exchange rates between troposphere and stratosphere. Steady State Relations for the Six Reservoir Model. The reservoir model is shown schematically in Figure 1. The conditions for a steady state in the distribution of carbon-12 are expressed directly in terms of the rates of efflux Jik of carbon-12 from reservoir i to reservoir k. Steady state in the stratosphere gives, for example, -Jst+its=°. (1)