Figure 1. Key features of the box model used in this study. (a): Schematic of the model design. Surface water and deep water boxes (blue) are each underlain by a reactive sediment layer (gray). Six time-dependent state variables are included: P = water column phosphorus concentration, O2 = water column oxygen concentration (deep water only), Corg = sediment organic carbon inventory, Porg = sediment organic phosphorus inventory, Fe-P = sediment iron-bound phosphorus inventory. Equations governing exchange fluxes and their relationship to state variables are given in the Supporting Information (Text S3, Fig. S4). (b): Principle of the sigmoid function used in the model. The attainable Fe-P inventory of the sediments is controlled by the dimensionless ratio between oxygen flux to sediments and sedimentation rate of organic matter (O2supply-demand ratio ).
3 Results and Discussion
3.1 Evidence for oscillations in past hypoxia and phosphorus regeneration
During HTMHI and MCAHI, multidecadal oscillations are observed in the LA-ICP-MS line scan profiles of Mo/Al and Br/P (Fig. 2, left). Spectral analysis of the full data series shows multiple peaks across the decadal to multidecadal bands. A clear peak is observed in the 60‒100 year band in both parameters (Fig. 2, center). This band is also characterized by high coherence and close-to-zero phase relation between Mo/Al and Br/P (Fig. 2, right), indicating in-phase oscillatory signals. Especially in the intervals of lower overall Mo/Al (e.g., 1.6‒1.2 ky BP; 5.4‒5.0 ky BP), the oscillation is clearly visible in the raw and bandpass-filtered data (Fig. 2, left and Supporting Information Figs. S2 and S3). This result implies that a close coupling existed between hypoxia and phosphorus regeneration on multidecadal timescales during past hypoxic events, and that both were highly variable on these timescales.