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The ocean's nutrient cycles are important for the carbon balance of\udthe climate system and for shaping the ocean's distribution of dissolved\udelements. Dissolved iron (dFe) is a key limiting micronutrient, but\udiron scavenging is observationally poorly constrained, leading to large\uduncertainties in the external sources of iron and hence in the state of the\udmarine iron cycle.\ud \udHere we build a steady-state model of the ocean's coupled phosphorus,\udsilicon, and iron cycles embedded in a data-assimilated steady-state global\udocean circulation. The model includes the redissolution of scavenged iron,\udparameterization of subgrid topography, and small, large, and diatom\udphytoplankton functional classes. Phytoplankton concentrations are implicitly\udrepresented in the parameterization of biological nutrient utilization\udthrough an equilibrium logistic model. Our formulation thus has only three\udcoupled nutrient tracers, the three-dimensional distributions of which are found\udusing a Newton solver. The very efficient numerics allow us to use the model\udin inverse mode to objectively constrain many biogeochemical parameters by\udminimizing the mismatch between modeled and observed nutrient and\udphytoplankton concentrations. Iron source and sink parameters cannot jointly\udbe optimized because of local compensation between regeneration, recycling,\udand scavenging. We therefore consider a family of possible state estimates\udcorresponding to a wide range of external iron source strengths. All state\udestimates have a similar mismatch with the observed nutrient concentrations\udand very similar large-scale dFe distributions. However, the relative\udcontributions of aeolian, sedimentary, and hydrothermal iron to the total\uddFe concentration differ widely depending on the sources.\ud \udBoth the magnitude and pattern of the phosphorus and opal exports are well\udconstrained, with global values of 8. 1  ±  0. 3 Tmol P yr−1 (or,\udin carbon units, 10. 3  ±  0. 4 Pg C yr−1) and 171.   ±  3.  Tmol Si yr−1. We diagnose the phosphorus and opal exports\udsupported by aeolian, sedimentary, and hydrothermal iron. The geographic\udpatterns of the export supported by each iron type are well constrained\udacross the family of state estimates. Sedimentary-iron-supported export is\udimportant in shelf and large-scale upwelling regions, while hydrothermal iron\udcontributes to export mostly in the Southern Ocean. The fraction of the\udglobal export supported by a given iron type varies systematically with its\udfractional contribution to the total iron source. Aeolian iron is most\udefficient in supporting export in the sense that its fractional contribution\udto export exceeds its fractional contribution to the total source. Per\udsource-injected molecule, aeolian iron supports 3. 1  ±  0. 8 times more\udphosphorus export and 2. 0  ±  0. 5 times more opal export than the other\udiron types. Conversely, per injected molecule, sedimentary and hydrothermal\udiron support 2. 3  ±  0. 6 and 4.   ±  2.  times less phosphorus export, and\ud1. 9  ±  0. 5 and 2.   ±  1.  times less opal export than the other iron\udtypes

Inverse-model estimates of the ocean's coupled phosphorus, silicon, and iron cycles