A method for the simultaneous use of tracers for oceanic circulation studies is developed. To permit the inclusion of tracers that are subject to biochemical transformation a simple model for photosynthesis, bacterial decomposition and chemical dissolution is formulated based on the use of Redfield ratios for the chemical compounds interaction. The finite difference analogue to the steady state tracer continuity equation, applied to the tracers chosen, leads to a set of simultaneous algebraic equations that in principle can be solved by matrix inversion methods. Two cases are considered: (1) The problem is indeterminate, which may be the case when too few tracers are available and/or some tracer equations are redundant. A solution is obtained by minimizing the transport vector; (2) The problem is incompatible, which may result from making use of many tracers. A solution is obtained by minimizing the errors in satisfying the tracer continuity equations. The method is applied to a 12-box model of the world oceans by considering the surface water, intermediate water, deep water and bottom water of the Arctic, Atlantic, Antarctic and Pacifichndian Oceans (with some simplification for the polar seas). Total dissolved inorganic carbon, alkalinity, phosphorus, oxygen and radiocarbon are used as tracers. A series of steady state solutions are presented and the uncertainties as dependant on box configuration and erroneous or nonrepresentative data are analysed. In the reference solution, circulation cells emerge where Antarctic surface water penetrates into intermediate levels of the two major oceans, from where it undergoes lifting and, at the surface, advection back towards the south. In the Atlantic, much of the penetrating water reaches as far north as to involve the Arctic deep water, which sinks and moves towards the deep Antarctic Ocean through the deep Atlantic. The total upwelling in the Antarctic Ocean is about 30 Sv. Turbulent exchange prevails between surface and intermediate waters in both major oceans with an average K, of about 1 cm 2 s -1 . Particular consideration is given to the transfer of carbon by computing the changes in total carbon and radiocarbon that are induced by fossil fuel combustion and nuclear bomb testing by using the steady state circulation and turbulent transfer deduced. It is concluded that better spatial resolution is required to determine the role of the ocean as a sink for injections of carbon and radiocarbon. DOI: 10.1111/j.1600-0889.1983.tb00025.x
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