Figure 3. State variables in box model simulations of biogeochemical cycles during past hypoxic intervals in the Baltic Sea. (a‒b): sedimentary P inventories, (c‒d): oxygen concentration in deep water box, (e): sensitivity analysis showing mean values, at steady state, of state variables in response to changes in external P loading. (f): sensitivity analysis showing mean values, at steady state, of state variables in response to changes in vertical exchange between shallow and deep water boxes. Blue shaded areas in e‒f indicate simulations in which unstable oscillatory regime was observed.
Even in our simple model formulation, the frequency of the intrinsic oscillations is a complex function of the prescribed parameters. Frequency is influenced partly by the geometry of the Baltic Sea basins, which is a major factor controlling the residence time of P in both the shallow and deep layers in the model. Indeed, the periodicity of simulated oscillations during the HTMHI, when the sub-halocline hypoxic area of the Baltic was expanded due to glacio-isostatic effects (Jilbert et al., 2015) is slightly longer than that during the MCAHI (Fig. 3a‒d). However, the frequency of real-world oscillations may also be externally driven. Indeed, the inherent instability of the model can be triggered by variability in external driving forces as discussed below.
3.5 Influence of climatic drivers on oscillations
The observed oscillations in the sediment records indicate dominant periods of 60‒100 years, which is consistent with periods of the Atlantic Multidecadal Oscillation (AMO) that may have been present throughout the Holocene (Knudsen et al., 2011). The AMO in turn modulates the influence of the North Atlantic Oscillation (NAO) on the conditions in the Baltic Sea region (Börgel et al., 2020). Thus, it is reasonable to assume that the observed oscillations in Baltic Sea sediment records may to some extent have been driven by variable in climate forcing as well as the internal instability of biogeochemical cycles.
To explore the impact of climatic variability, we imposed a sinusoidal perturbation to the vertical exchange relative to the parameter settings for the model simulations of the MCAHI. Vertical exchange is chosen because it has a direct and influential impact on oxygen conditions and subsequent effects on the Fe-P inventory. In Fig. 4, oxygen power spectra are shown for a number of simulations with different amplitudes and periods of the vertical exchange perturbation. It is evident that for certain periods of climatic oscillations, the inherent model instability is triggered and the oxygen oscillations are strongly amplified compared to the unforced case (e.g., for amplitude = 3 m y-1 and T = 80 and 100 years). In such cases the period of oscillations is largely determined by the climate. This external influence could partly explain the generally shorter periods observed in the sediment records (60‒100 years) compared to the inherent oscillations of the model (130‒170 years).
3.6 Sensitivity to external phosphorus loading and vertical exchange
The presence of multidecadal oscillations in the model simulations is highly sensitive to external loading of P. Using a parameterization for the modern Baltic Sea, external loading of <8000 tonnes P/year yields solutions in which no oscillations are observed because the system remains in a quasi-permanent oxic state (Fig. 3e). As external loading increases, oscillations are observed within a range of approximately 8000‒12000 tonnes P/year. However at high external loading (>12000 tonnes P/year), oscillations disappear again because the system remains in a quasi-permanent hypoxic state.
The modern P loading to the Baltic Proper is approximately 25000 tonnes P/year, and loading during the late 20th century was significantly in excess of this value (Gustafsson et al., 2012). Such high loads are sufficient to suppress oscillatory behavior in the model, by sustaining high productivity and holding the system in a quasi-permanent hypoxic state. A simulation of the modern development of hypoxia since 1900 supports this observation (Supporting Information Figs. S6 and S7). Therefore, under constant future loading scenarios we would not expect to observe multidecadal oscillations in Baltic Sea hypoxia during the coming centuries.