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Export production\udreflects the amount of organic matter transferred from the ocean surface to\uddepth through biological processes. This export is in large part controlled\udby nutrient and light availability, which are conditioned by mixed layer\uddepth (MLD). In this study, building on Sverdrup's critical depth hypothesis,\udwe derive a mechanistic model of an upper bound on carbon export based on the\udmetabolic balance between photosynthesis and respiration as a function of MLD\udand temperature. We find that the upper bound is a positively skewed\udbell-shaped function of MLD. Specifically, the upper bound increases with\uddeepening mixed layers down to a critical depth, beyond which a long tail of\uddecreasing carbon export is associated with increasing heterotrophic activity\udand decreasing light availability. We also show that in cold regions the\udupper bound on carbon export decreases with increasing temperature when mixed\udlayers are deep, but increases with temperature when mixed layers are\udshallow. A meta-analysis shows that our model envelopes field estimates of\udcarbon export from the mixed layer. When compared to satellite export\udproduction estimates, our model indicates that export production in some\udregions of the Southern Ocean, particularly the subantarctic zone, is likely\udlimited by light for a significant portion of the growing season

A mechanistic model of an upper bound on oceanic carbon export as a function of mixed layer depth and temperature