Analysis of a relationship between the vertical distribution of inorganic carbon and biological productivity in the oceans

If the assumption of steady state is made then over large temporal and spatial scales, a balance between the downward flux and oxidation of organic detritus and upward mixing of inorganic carbon determines the vertical distribution carbon in the ocean. From a mathematical statement of this balance using an empirical formula for the downward organic flux determined by Suess (1980) I derive an expression for the vertical inorganic carbon profile containing one parameter C/sub p//k, the ratio of primary productivity measured by the 14C incubation method to the effective vertical eddy mixing coefficient. The best estimate for this ratio obtained by minimizing the variances between the available inorganic carbon concentration data and the derived curve is 1.5 x 10-3 mol C m-4. This ratio is consistent with average primary productivities in the range of 100-170 g C m-2 yr-1 if one uses recent k value estimates based on the radiocarbon and tritium measurements (Broecker et al., 1980; Stuiver and Quay, 1981) and is equivalent to 20-34 gCm-2 yr-1 of new production using the definition of Eppley and Peterson (1979)