Abstract. The ocean's nutrient cycles are important for the carbon balance of the climate system and for shaping the ocean's distribution of dissolved elements. Dissolved iron (dFe) is a key limiting micronutrient, but iron scavenging is observationally poorly constrained leading to large uncertainties in the external sources of iron and hence in the state of the marine iron cycle. Here we build a model of the ocean's coupled phosphorus, silicon, and iron cycles embedded in a data-assimilated steady-state global ocean circulation. The model includes the redissolution of scavenged iron, parameterization of subgrid topography, and small, large, and diatom phytoplankton functional classes. Phytoplankton concentrations are implicitly represented in the parameterization of biological nutrient utilization through an equilibrium logistic model. Our coupled nutrient model thus carries only three nutrient tracers whose three-dimensional steady-state distributions can be found efficiently using a Newton solver. The very efficient numerics allow us to use the model in inverse mode to objectively constrain many biogeochemical parameters by minimizing the mismatch between modelled and observed nutrient and phytoplankton concentrations. We consider a family of possible solutions corresponding to a wide range of external iron source strengths. Iron source and sink parameters cannot jointly be optimized because of local compensation between regeneration, recycling, and scavenging. All optimized solutions have a similar mismatch with the observed nutrient concentrations and very similar large-scale dFe distributions. However, the relative contributions of aeolian, sedimentary, and hydrothermal iron to the total dFe concentration differ widely depending on the sources. Both the magnitude and pattern of carbon and opal export are well constrained with global values of (10.3 ± 0.4) Pg C yr−1 and (171. ± 3.) Tmol Si yr−1. We diagnose the carbon and opal export supported by aeolian, sedimentary, and hydrothermal iron. The geographic patterns of the export supported by each iron type are well constrained across the family of solutions. Sedimentary-iron supported export is important in shelf and large-scale upwelling regions, while hydrothermal iron contributes to export mostly in the Southern Ocean. The globally integrated export supported by a given iron type varies systematically with the fractional contribution of its source to the total iron source. Aeolian iron is most efficient in supporting export in the sense that its fractional contribution to export exceeds its fractional contribution to the total source by as much as ~ 30 % for carbon and ~ 20 % for opal export. Conversely, sedimentary and hydrothermal iron are less efficient with a fractional export that is less than their fractional sources. For the same fractional contribution to the total source, hydrothermal iron is less efficient than sedimentary iron for supporting carbon export but about equally efficient for supporting opal export.
Thermodynamic Analysis of Ocean Circulation
