88 BACASTOW AND KEELING 



troposphere. In the preeeding paper, Ekdahl and Keeling show part of the 

 solution for a six-reservoir model involving both inaetive earbon and radiocar- 

 bon. This latter model obviously taxes one's patienee: to solve it completely 

 requires that 36 fifth-order determinants be worked out in addition to finding 

 the roots of two quintic equations. 



During the past decade, numerical approximation methods have been used 

 more and more frequently to solve problems involving perturbations in the 

 carbon cycle. In most cases the modelists prescribe annual steps in a perturbing 

 source and then, by digital computer, calculate successive redistributions within 

 the carbon pools. The short-term influence of industrial C0 2 in the atmosphere, 

 oceans, and biota has been considered in this way by Broecker, Li, and Peng, 8 

 and by Machta. By similar means Baxter and Walton 10 have predicted the 

 dilution of radiocarbon by industrial C0 2 . All these investigators retained linear 

 features of the earlier analytic models, even though more precise nonlinear 

 expressions could have been used. 



In one of the earliest but most interesting models of the carbon cycle, 

 Eriksson and Welander 1 considered nonlinear interactions between the atmo- 

 sphere, biota, and oceans. They numerically solved the complex governing 

 equations using a digital computer. No subsequent investigator has imitated their 

 technique. 



Our model portrays the natural reservoirs of the short-term carbon cycle in 

 the configuration shown in Fig. 1. The atmosphere, for some calculations, is 

 divided into an upper layer, the stratosphere, and a lower layer, the troposphere. 

 The land biota is split into two partially coextensive reservoirs. The long-lived 

 biota (with an average carbon transfer time of 60 years) models wood and 

 humus. The short-lived biota (average transfer time 2 x / 2 years) models annual 

 plants, leaves, and short-lived detritus. Both exchange carbon directly with the 

 atmosphere. The deep ocean, comprising the bulk of the ocean water, exchanges 

 carbon with the atmosphere only through a relatively thin surface layer. 



The physical justification for this model, especially the basis for dividing the 

 biota into two reservoirs, is discussed in greater detail by Keeling. 5 The use of 

 spatially averaged properties does not necessarily imply homogeneity or mixing 

 within the reservoirs. Insofar as possible, the symbols correspond to those used 

 by Bolin and Eriksson. 3 



INDUSTRIAL CARBON DIOXIDE 



Combustion of fossil fuels presently accounts for most of man's industrial 

 and domestic energy production. The rate of combustion has been rising since 

 the 18th century at about 4% per year except during the great economic 

 depression and two world wars of the present century. Even if nuclear fuels or 

 solar energy gradually displace fossil fuel as man's dominant source of energy, 

 demand for fossil fuel is likely to continue to rise as industrialization spreads to 



