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.