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

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 steady-state 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 formulation thus has only three coupled nutrient tracers, the three-dimensional distributions of which are found 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 modeled and observed nutrient and phytoplankton concentrations. Iron source and sink parameters cannot jointly be optimized because of local compensation between regeneration, recycling, and scavenging. We therefore consider a family of possible state estimates corresponding to a wide range of external iron source strengths. All state estimates 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 the phosphorus and opal exports are well constrained, with global values of 8. 1  ±  0. 3 Tmol P yr⁻¹ (or, in carbon units, 10. 3  ±  0. 4 Pg C yr⁻¹) and 171.   ±  3.  Tmol Si yr⁻¹. We diagnose the phosphorus and opal exports 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 state estimates. 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 fraction of the global export supported by a given iron type varies systematically with its fractional contribution 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. Per source-injected molecule, aeolian iron supports 3. 1  ±  0. 8 times more phosphorus export and 2. 0  ±  0. 5 times more opal export than the other iron types. Conversely, per injected molecule, sedimentary and hydrothermal iron support 2. 3  ±  0. 6 and 4.   ±  2.  times less phosphorus export, and 1. 9  ±  0. 5 and 2.   ±  1.  times less opal export than the other iron types.