Ocean and atmosphere feedbacks affecting AMOC hysteresis in a GCM

Abstract

Theories suggest that the Atlantic Meridional Overturning Circulation (AMOC) can exhibit a hysteresis where, for a given input of fresh water into the north Atlantic, there are two possible states: one with a strong overturning in the north Atlantic (on) and the other with a reverse Atlantic cell (off). A previous study showed hysteresis of the AMOC for the first time in a coupled general circulation model (Hawkins et al. in Geophys Res Lett. doi:10.1029/2011GL047208, 2011). In this study we show that the hysteresis found by Hawkins et al. (2011) is sensitive to the method with which the fresh water input is compensated. If this compensation is applied throughout the volume of the global ocean, rather than at the surface, the region of hysteresis is narrower and the off states are very different: when the compensation is applied at the surface, a strong Pacific overturning cell and a strong Atlantic reverse cell develops; when the compensation is applied throughout the volume there is little change in the Pacific and only a weak Atlantic reverse cell develops. We investigate the mechanisms behind the transitions between the on and off states in the two experiments, and find that the difference in hysteresis is due to the different off states. We find that the development of the Pacific overturning cell results in greater atmospheric moisture transport into the North Atlantic, and also is likely responsible for a stronger Atlantic reverse cell. These both act to stabilize the off state of the Atlantic overturning.

Appendix: Box model of AMOC recovery

When the hosing is reduced over the North Atlantic, in both SCOMP and VCOMP the salinity recovers from that in the AMOC off state, with saline (less fresh) anomalies appearing in upper 500 m of the region in which the hosing is applied. The salinity in VCOMP recovers faster. To illustrate why we consider a simple model where the upper North Atlantic is represented by a box with volume V ($\hbox {m}^3$) and salinity S (PSU). A circulation of strength Q ($\hbox {m}^3/\hbox {s}$), representing the reverse overturning cell, imports water of salinity $S_0>S$ (PSU). There is a surface fresh water flux F ($\hbox {m}^3/\hbox {s}$ of fresh water) from precipitation minus evaporation plus hosing. Hence the salinity budget of the box can be written

$$\begin{aligned} V \frac{dS}{dt} = Q(S_0 - S) - F S. \end{aligned}$$

In steady state

$$\begin{aligned} {\overline{Q}}(S_0 - {\overline{S}}) = {\overline{F}} ~{\overline{S}}. \end{aligned}$$

Now as the hosing input decreases, so does F, so we set $F={\overline{F}}-h$ where h represents the hosing decrease. The salinity in the box increases from that in the off state as $S = {\overline{S}} + \sigma$ and the circulation changes $Q={\overline{Q}}-q$ where we make the assumption that the circulation decreases as the salinity in the box (and hence density in the north Atlantic) increases (such as in Fig. 8b), so that $q=\beta \sigma$. Hence we have (assuming that the changes in salinity are small and hence neglecting $\sigma ^2$ and $\sigma h$ terms)

$$\begin{aligned} V \frac{d \sigma }{dt} = - ({\overline{Q}}+{\overline{F}}+\beta (S_0-{\overline{S}})) \sigma + h {\overline{S}} \end{aligned}$$

or

$$\begin{aligned} \frac{d \sigma }{dt} = - \frac{1}{\tau } \sigma + H \end{aligned}$$

where $\tau = V/({\overline{Q}}+{\overline{F}}+\beta (S_0-{\overline{S}}))$ and $H= h {\overline{S}}/V$. The timescale $\tau$ can be thought of as a residence time for salinity anomalies within the region.

The solution for this with $H=\lambda t$ (the hosing reducing linearly with time) using $\sigma =0$ at $t=0$ is

$$\begin{aligned} \sigma = \lambda \tau ^2 \left( e^{-t/\tau } - 1 + t/\tau \right) \end{aligned}$$

To compare this to our model experiments we need to calculate the timescale $\tau$ and hosing reduction $\lambda$ for both SCOMP and VCOMP. We assume that the changes in advection are dominated by the advection of salinity anomalies by the mean flow so that $\tau = V/({\overline{Q}}+{\overline{F}})$. This is true initially in experiments (Fig. 8f), however we note that allowing the reverse cell to decrease would reduce the timescale. We also ignore the contribution of advection by a gyre circulation which would increase the value of ${\overline{Q}}$ and hence also reduce the timescale. These assumptions are made to allow a comparison with the model and to illustrate the impact of the different off states on the salinification of the North Atlantic.

Using a box from 20 to 60$^\circ \mathrm{N}$ and up to 500 m deep we calculate the volume $V=3.5 \times 10^{15}$m$^3$ and the salinification by surface fluxes ${\overline{F}}$ to be $6.6 \times 10^5$ and $7.0 \times 10^5\,\hbox {m}^3{/}\hbox {s}$ for VCOMP and SCOMP respectively. We also estimate ${\overline{Q}}$ from the overturning cell strength at 20$^\circ \mathrm{N}$ to be $3.0 \times 10^6$ and $4.0 \times 10^6\,\hbox {m}^3{/}\hbox {s}$ respectively (Fig. 3). This gives a timescale $\tau$ of 31 years for VCOMP and 24 years for SCOMP. The hosing decreases by $500\,\hbox {m}^3{/}\hbox {s}$ every year, giving $\lambda =1.4 \times 10^{-19}\hbox {PSU{/}s}^{2}$ for both experiments

The predicted salinity change from this very simple model is shown in Fig. 13 along with the actual salinity increase. The predicted salinity increases are of a similar order of magnitude to that in the FAMOUS experiments and show the salinity in VCOMP increasing faster than that in SCOMP. This can be traced to the difference in circulation strength between the two experiments which changes the timescale of adjustment. Since SCOMP has a stronger reverse circulation than VCOMP, the residence timescale in the region is smaller and the salinity initially increases more slowly.