Can rates of ocean primary production and biological carbon export be related through their probability distributions?

We describe the basis of a theory for interpreting measurements of two key biogeochemical fluxes—primary production by phytoplankton (p, μg C · L−1 · day−1) and biological carbon export from the surface ocean by sinking particles (f, mg C · m−2 · day−1)—in terms of their probability distributions. Given that p and f are mechanistically linked but variable and effectively measured on different scales, we hypothesize that a quantitative relationship emerges between collections of the two measurements. Motivated by the many subprocesses driving production and export, we take as a null model that large‐scale distributions of p and f are lognormal. We then show that compilations of p and f measurements are consistent with this hypothesis. The compilation of p measurements is extensive enough to subregion by biome, basin, depth, or season; these subsets are also well described by lognormals, whose log‐moments sort predictably. Informed by the lognormality of both p and f we infer a statistical scaling relationship between the two quantities and derive a linear relationship between the log‐moments of their distributions. We find agreement between two independent estimates of the slope and intercept of this line and show that the distribution of f measurements is consistent with predictions made from the moments of the p distribution. These results illustrate the utility of a distributional approach to biogeochemical fluxes. We close by describing potential uses and challenges for the further development of such an approach.