The marine phosphorus cycle significantly impacts global primary productivity and atmospheric oxygen (pO₂) levels over geologic timescales. Previous models of carbon-phosphorus-oxygen feedbacks have overlooked crucial parameters influencing the global phosphorus cycle. This study addresses this gap by developing new diagenetic models that fully parameterize marine phosphorus burial, incorporating key factors such as seawater calcium concentration, bottom-water oxygen, organic matter loading, and bioturbation. These diagenetic models are then coupled to a global carbon cycle model to explore the impact of varying calcium concentrations on global phosphorus cycling and atmospheric pO₂. Understanding this complex interplay is crucial for comprehending Earth's long-term climate and environmental changes. The research question revolves around how variations in seawater calcium concentration, a factor previously not fully considered, affects the marine phosphorus cycle and consequently, atmospheric oxygen levels. The study's purpose is to improve our understanding of the complex feedback mechanisms between the phosphorus cycle, the carbon cycle, and the Earth's oxygenation history, enhancing our ability to predict the planet's future response to environmental changes. The importance of this research stems from the profound impact of atmospheric oxygen and marine productivity on the evolution of life and global climate. A comprehensive model accounting for calcium's role is crucial to accurately reconstruct past environments and predict future changes.

Previous research has established the importance of the marine phosphorus cycle in regulating global primary productivity and atmospheric pO₂. However, existing models often simplify the complex diagenetic processes that govern phosphorus burial. Studies like those by Van Cappellen and Ingall (1996) highlighted the redox stabilization of the atmosphere and oceans through phosphorus-limited marine productivity, but lacked the detailed parameterization of phosphorus burial pathways. Other research focused on the role of iron-bound phosphorus in authigenic apatite formation (Slomp et al., 1996) and the influence of bioturbation on phosphorus burial (Boyle et al., 2014; Dale et al., 2016). These studies provided valuable insights into specific aspects of the phosphorus cycle, but a comprehensive model integrating various factors, including the influence of seawater calcium concentration, was still lacking. This study builds upon previous work by incorporating a more complete and accurate representation of phosphorus burial processes, including the kinetic control of CFA formation, the effect of seawater calcium concentrations on CFA precipitation, and their impact on global phosphorus burial and atmospheric oxygen levels.

The study employs a two-pronged modeling approach: First, a one-dimensional diagenetic model is developed to simulate the early diagenesis of phosphorus in marine sediments. This model incorporates six components: two solid phases (organic matter and carbonate fluorapatite – CFA) and four solutes ([Ca²⁺], [DIC], [DIP], and [F⁻]). The model includes reactions for the decomposition of organic matter and the formation of CFA, with the CFA formation rate parameterized as a function of its saturation state. This approach improves upon previous models that used simplified linear relationships. The basic model is then extended into a multicomponent model (SEDCHEM), incorporating the biogeochemical cycles of C, N, P, S, Fe, and Mn. This extended model incorporates multiple solid and solute species, accounting for processes such as aerobic respiration, nitrate reduction, Mn reduction, Fe reduction, sulfate reduction, methanogenesis, and the precipitation and dissolution of various minerals, including vivianite. The model also simulates pH variations during diagenesis using a total proton balance approach and includes a treatment of adsorption processes. The model parameters are carefully calibrated using data from various sources, including porewater and sediment profiles. Second, the output of the extended diagenetic model is coupled to a global carbon cycle mass balance model (modified from Van Cappellen and Ingall, 1996), enabling the exploration of the global effects of calcium concentration variations on carbon and phosphorus cycling and atmospheric pO₂. The coupled model uses look-up tables derived from diagenetic model results to parameterize phosphorus burial efficiency as a function of bottom-water oxygen, organic matter loading, marine calcium concentrations, and bioturbation. The coupled C-P-O model simulates the long-term evolution of atmospheric oxygen based on changing seawater calcium concentrations. Finally, the model predictions are compared with existing empirical data, including Cenozoic deep-sea sediment core data on phosphorus speciation and estimates of seawater calcium concentrations derived from various proxies like fluid inclusions, biogenic carbonates, and calcite veins in oceanic crust. This comparison serves to validate the model and assess its ability to reproduce observed trends.

The study's key findings highlight the significant and previously underappreciated role of seawater calcium concentration in regulating marine phosphorus burial and atmospheric oxygenation. The diagenetic models demonstrate a strong positive relationship between seawater calcium concentration and carbonate fluorapatite (CFA) formation. This is because higher calcium concentrations increase the saturation state of CFA, leading to greater CFA precipitation and thus phosphorus burial. The coupled carbon-phosphorus-oxygen model shows that increased seawater calcium concentrations lead to decreased seawater phosphorus concentrations due to enhanced CFA precipitation and reduced phosphorus recycling. More importantly, the increased CFA formation reduces the organic carbon-to-reactive phosphorus burial ratio. With a constant phosphorus flux to the ocean, this results in decreased atmospheric oxygen levels. The model predicts that a change in seawater calcium concentration from 10 mM to 20 mM could cause a greater than 50% reduction in atmospheric pO₂, from 21% to approximately 10%. Empirical analysis of Cenozoic deep-sea sediment core data shows a strong correlation between changes in CFA burial and variations in seawater calcium concentration over the past 80 million years, providing strong support for the model's predictions. The correlation between seawater calcium concentration and atmospheric pO₂ suggests that fluctuations in seawater calcium concentration throughout Earth's history may have significantly influenced atmospheric oxygen levels. For instance, the relatively low seawater calcium concentrations during the Carboniferous-Permian period may have contributed to the high atmospheric pO₂ during that time. Conversely, an increase in seawater calcium concentrations during the early Cambrian may coincide with an interval of ocean deoxygenation.

This study's findings significantly advance our understanding of the interplay between marine elemental cycles, tectonic processes, and atmospheric oxygenation. The results demonstrate that seawater calcium concentration, through its influence on carbonate fluorapatite formation, acts as a key external control on global phosphorus cycling and thus atmospheric pO₂. The model successfully reproduces the observed trends in deep-sea phosphorus speciation and seawater calcium concentration over the past 80 million years, strengthening confidence in the model's predictions and the proposed feedback mechanism. These findings offer a new perspective on the evolution of Earth's atmosphere and biosphere, emphasizing the importance of considering the major ion composition of seawater as a significant driver of long-term biogeochemical change. The strong link between tectonic cycles, which influence seawater composition, and atmospheric oxygen underscores the interconnectedness of Earth's systems. The results have implications for understanding past climate and environmental changes and for predicting future responses to ongoing environmental perturbations.

This research reveals a critical link between seawater calcium concentration, marine phosphorus burial, and atmospheric oxygenation, highlighting the significance of seawater major-ion composition in shaping Earth's long-term biogeochemical cycles. The developed diagenetic and coupled carbon-phosphorus-oxygen models demonstrate a strong positive correlation between seawater calcium concentration and CFA formation, influencing phosphorus burial efficiency and atmospheric pO₂. The model predictions are supported by empirical evidence from Cenozoic deep-sea sediments. Future research could focus on refining the models by incorporating additional factors, such as variations in organic matter quality and other diagenetic processes. Investigating the impacts of calcium concentration variations on other biogeochemical cycles would also be beneficial. The findings have significant implications for understanding past climate change, and future research into this feedback mechanism will enhance our ability to predict the impact of future environmental change.

While the models provide a significant advance in understanding the interactions between calcium, phosphorus, and oxygen, there are some limitations. The models rely on various simplifying assumptions, such as the use of average values for certain parameters and the simplified representation of complex biogeochemical processes. The accuracy of the model's predictions depends on the accuracy of the input parameters and the underlying assumptions. Further research is needed to refine the model's parameterizations and explore the impact of uncertainties in these parameters. The study focuses primarily on long-term changes and may not capture shorter-term variations in atmospheric oxygen and phosphorus cycling. Despite these limitations, the study provides significant insights into the role of calcium in regulating marine phosphorus burial and atmospheric oxygenation.