Diagenetic phosphorus cycle

Parameterizations of the diagenetic P cycle explored in this study share many features with previously published model exercises (e.g., refs. ^8,10,36). Three solid P species—organic phosphorus (orgP), iron-bound phosphorus (P_Fe), and CFA—as well as dissolved inorganic phosphate (ƩPO₄³⁻) are included in the extended version of our diagenetic model. In contrast to previous studies, however, our model also includes a more intrinsic reaction rate law for CFA formation, which involves all the major components of CFA and parameterizes the effect of pH on P speciation and burial. To simulate pH, our model also includes proper descriptions of adsorption, the diagenetic Fe cycle, and authigenic carbonate precipitation and dissolution.

Decomposition of organic matter drives diagenetic reactions. The chemical formula of organic matter can be simplified as CN_rNP_rP, where _rN and _rP are the molar ratios of organic nitrogen and organic phosphorus relative to organic carbon. The major pathways for the decomposition of organic matter, including aerobic respiration, nitrate reduction, Mn reduction, Fe reduction, sulfate reduction, and methanogenesis are included in the model. As the sequence (and thus spatial distribution) of these pathways is dictated by their respective energy yields⁴⁰, a Monod scheme was used to describe the operation of these reactions^8,10,36.

For the mineralization of orgC in the extended model, we used a multi-G model⁴¹ developed from a reactive continuum-type model³². The advantage of this model is that it not only can represent the reactive continuum of organic matter, but also is suitable to apply to the bioturbated zone of the sediment pile⁴¹. We divided organic matter into 12 G in this study. Although each G has its own first-order rate constant, their fractions in total organic matter are determined by a gamma distribution⁴¹. The rate constant for each G_i is

while the fraction of each G_i is

where a is the average lifetime of more reactive orgC and v is the shape of orgC distribution³².

The C/P ratio of particulate organic matter typically increases with depth in the sediment pile. Following previous methods^36,42, we assume that this variation is generated by different C/P ratios in different organic components, with less reactive (more refractory) organic matter having higher C/P ratios. Thus, we further divided the 12 G fractions into two pools (α and β) with different C/P ratios. With this procedure, it is possible to reproduce empirical sedimentary profiles of organic phosphorus and dissolved phosphate (Supplementary Figure ²). The α pool includes the first 2 G fractions (G₁ and G₂), whereas the β pool includes the remaining 10 G fractions (G₃–G₁₂). The C/P ratios of the two pools are shown in Supplementary Table ⁵.

Five iron phases are included in the modeled flux to the sediment–seawater interface: (1) highly reactive iron hydroxides (Fe(OH)₃^α); (2) less reactive iron hydroxides (Fe(OH)₃^β); (3) unreactive iron hydroxides (Fe(OH)₃^γ); (4) magnetite (Fe₃O₄); and (5) biotite (Biot). Demarcation of iron hydroxides by reactivity is similar to the treatment employed by previous models^8,36. The rate law for magnetite dissolution is reasonably well established⁴³. Iron may also occur as other silicate-bound phases, but we use biotite as a representation of silicate iron (see ref. ⁴⁴). At FOAM, biotite dissolution appears to be closely linked to porewater pH. As for previous models⁸, iron-bound phosphorus is assumed to be associated with iron hydroxides, and the P/Fe molar ratio is described using a constant γ and a variable θ (Supplementary Tables ¹–⁵). Thus, the precipitation and dissolution of iron hydroxides are accompanied by, respectively, the scavenging and release of dissolved phosphate (Supplementary Table ²).

A major difference of this study from previous studies^5,8,10 is that we have parameterized the formation rate of CFA using its saturation state (see above), which is consistent with experimental results^15,16. A full description of this method can be found above, as well as in the ^{Supplementary Text} and Supplementary Table ³.

We have also included the iron phosphate mineral vivianite in the extended model. Although it has not been extensively documented in marine sediments, it is commonly found in restricted settings⁴⁵. Following ref. ⁴⁵, we have used the Michaelis–Menten kinetics for dissolved phosphate and iron in marine porewater to describe the formation of vivianite. Details of the formulation and parameters for vivianite can be found in Supplementary Tables ³ and ⁵.