A simple model of ocean circulation and biological processes

1 I A simple model of ocean circulation and biological processes 

A schematic representation of the two-layer ocean model including the equations for the surface and deep-ocean mass balance of dissolved constituent C (mol m ). j, particle flux (mol y ) Vo deep ocean volume (1.35 X IO m ) Vs. surface 

The only nutrient input to the ocean in this simple model is via rivers, with a flow rate of R (m y ) and the only output is burial in sediments, B (mol y ). The surface and deep reservoirs communicate by upward and downward advection or mixing, Vm (m y and by particle transport, J(moly ). The changes in concentration of component C with respect to time for the surface (S) and deep (D) reservoirs are  

In order to gain quantitative insight about fluxes the mixing rate, Vm, must be evaluated. This requires knowledge of the concentration distribution of a chemical tracer that has a loiown time history or a built-in radioactive clock. To achieve this we use the steady-state equation, and the mass balance of dissolved inorganic carbon (DIG) and the naturally occurring (i.e. not bomb-produced) radioactive isotope of carbon, with a half hfe of 5730 y. 

The flux of DIG firom the deep reservoir to the surface ocean is equal to the particle rain rate of carbon firom the surface reservoir minus the burial rate of organic carbon. The equation for DI G is exactly identical, with the exception that there is an additional loss term on the right side for radioactive decay  

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