The development of deep-ocean anoxia in a comprehensive ocean phosphorus model

TL;DR

This paper analytically investigates a comprehensive ocean phosphorus model, revealing how deep ocean oxygen levels depend on key parameters and providing a mathematical framework to understand ocean biogeochemical dynamics.

Contribution

The paper demonstrates that the complex ocean phosphorus model can be solved analytically, identifying the conditions for oxic or anoxic deep ocean states and analyzing parameter dependencies.

Findings

Deep ocean phosphorus relaxes to equilibrium in 180,000 years.

Deep ocean is either oxic or anoxic depending on a critical parameter.

Methodology can simplify other large biogeochemical models.

Abstract

We analyse a model of the phosphorus cycle in the ocean given by Slomp and Van Cappellen (2007, https://doi.org/10.5194/bg-4-155-2007). This model contains four distinct oceanic basins and includes relevant parts of the water, carbon and oxygen cycles. We show that the model can essentially be solved analytically, and its behaviour completely understood without recourse to numerical methods. In particular, we show that, in the model, the carbon and phosphorus concentrations in the different ocean reservoirs are all slaved to the concentration of soluble reactive phosphorus in the deep ocean, which relaxes to an equilibrium on a time scale of 180,000 y, and we show that the deep ocean is either oxic or anoxic, depending on a critical parameter which we can determine explicitly. Finally, we examine how the value of this critical parameter depends on the physical parameters contained in the model. The presented methodology is based on tools from applied mathematics and can be used to reduce the complexity of other large, biogeochemical models.