Stable AMOC off state in an eddy-permitting coupled climate model

Abstract

Shifts between on and off states of the Atlantic Meridional Overturning Circulation (AMOC) have been associated with past abrupt climate change, supported by the bistability of the AMOC found in many older, coarser resolution, ocean and climate models. However, as coupled climate models evolved in complexity a stable AMOC off state no longer seemed supported. Here we show that a current-generation, eddy-permitting climate model has an AMOC off state that remains stable for the 450-year duration of the model integration. Ocean eddies modify the overall freshwater balance, allowing for stronger northward salt transport by the AMOC compared with previous, non eddy-permitting models. As a result, the salinification of the subtropical North Atlantic, due to a southward shift of the intertropical rain belt, is counteracted by the reduced salt transport of the collapsed AMOC. The reduced salinification of the subtropical North Atlantic allows for an anomalous northward freshwater transport into the subpolar North Atlantic dominated by the gyre component. Combining the anomalous northward freshwater transport with the freshening due to reduced evaporation in this region helps stabilise the AMOC off state.

Appendix: Freshwater budget calculation

The freshwater budget calculation used in this study is based on the method presented in Drijfhout et al. (2011) with modifications to include the effects of a northern and southern boundary, as well as specifics to the version of NEMO used (GO5, version 3.4 of NEMO) (Megann et al. 2013). Mean flow transports are based on 3 month means, while total transports (i.e. vS) are calculated online and are updated after each ocean model time step, which are later averaged over the years of interest removing the effects of the seasonal cycle on the budget. Following Drijfhout et al. (2011), the equation for the volume budget is as follows:

$$V_{t}=T_{S}-T_{N} -T_{Med}+PER-Res_{V},$$

(2)

where $V_t$ is the rate of change of the volume, $T_{(N/S)}$ are volume transports through the northern and southern boundaries, $T_{Med}$ is the volume transport through the Strait of Gibraltar, PER is the precipitation minus evaporation plus runoffs and $Res_V$ is the error generated by the choice of differencing scheme and temporal resolution of the data. The value of $Res_V$ is computed as a residual to close the budget. Since the model has a free surface $V_t$ is equivalent to the changes in the sea surface height using backwards differencing. The main differences between Eq. (2) and eqn. 4 in Drijfhout et al. (2011) are that we have left the choice of the northern and southern boundaries as arbitrary as opposed to choosing $34^\circ {\text{S}}$ and the Bering Strait and we have included a term, $T_{med}$ for the volume transports through the Strait of Gibraltar. In this configuration of NEMO the transports are computed without taking the changes in sea surface height into account. For the regions of interest used in this study the values of $\hbox {Res}_V$ are relatively small resulting in O($10^{-4}\hbox { Sv}$) for the North Atlantic subtropical gyre and O($10^{-5}\hbox { Sv}$) for the North Atlantic subpolar gyre, which in both cases is the smallest term in the budget with the remaining terms ranging from O($10^{-3}\hbox { Sv}$) to O(1 Sv). Choosing instantaneous values of sea surface height from the model restart files in the computation of $V_t$ leads to $Res_{V}$ having the same order as the precision in which the data is stored but, not all model restart files were available.

Similarly the salinity budget in terms of freshwater becomes the following:

$$M_{trend}-V_t=M_S-M_N-M_{Med}+M_{Mix}-Res_{V}+H,$$

(3)

where $M_{trend}$ is the rate of change of freshwater in the region of interest, $M_{(N/S)}$ are the northward/southward freshwater transports, $M_{med}$ is the freshwater transport through the Strait of Gibraltar, H represents the freshwater hosing and $M_{mix}$, computed as a residual, closes the budget capturing mixing and errors introduced by the temporal resolution of the data, as well as, the choice of reference salinity, $S_{o}$. The conversion between salinity based terms to the freshwater based terms in Eq. (3) is done through multiplying all the terms in the equation by ${-1}/S_{o}$. Note that we have dropped the negative sign before $M_{trend}$ in Eq. (3), contrary to Drijfhout et al. (2011) so that positive values indicate an increase in freshwater not salinity. In this case the hosing is included in the salinity budget and not the volume budget since it is computed as a redistribution of salinity in this model study. Combining Eqs. (2) and (3)gives the following expression for the fresh water budget:

$$\begin{aligned}M_{trend} &= (M_S+T_S )-(M_N+T_N)-(M_{Med}+T_{Med})\nonumber \\&\quad+M_{Mix}+PER+H.\end{aligned}$$

(4)

The ${\text{M}}_{(N/S)}$ terms can be divided into eddy and mean flow components since the ocean model output includes vS computed at every model time step. The eddy contribution to the freshwater transport is defined as follows:

$$\begin{aligned} M_{(eddy(N/S))}&= {} \frac{-1}{S_o}\int _{N/S}({\overline{vS}}-{\overline{v}}{\overline{S}})dA \nonumber \\&= {} M_{(N/S)}-M_{(mean(N/S))}, \end{aligned}$$

(5)

$$\Rightarrow {}M_{(N/S)}= M_{(mean(N/S))}+M_{(eddy(N/S))},$$

(6)

where the integral is taken over each zonal section of the Atlantic basin, ${\overline{vS}}$ is the total seasonal mean transport, ${\overline{v}}$ and ${\overline{S}}$ are the seasonal mean meridional velocity and salinity and $M_{(mean(S/N))}=-1/S_o\int _{N/S}{\overline{v}}{\overline{S}}dA$ represents the non-eddy transports, with the overbar denoting a mean computed over 3 months. A map of the eddy kinetic energy (Fig. 10) shows that the eddy field in HadGEM3 is very similar to other models of similar resolution (Delworth et al. 2012), perhaps even slightly closer to what is expected from observations. The eddy contribution is computed in a very similar way to Tréguier et al. (2012), in which it was also shown that the eddy contribution will be even stronger at higher model resolutions. Since the current model resolution is eddy-permitting it is not possible to completely resolve eddies at all latitudes, therefore caution must be taken in interpreting the role of the eddies in the high latitudes. Similar to what is done in Drijfhout et al. (2011), $M_{(mean(S/N))}$ can be divided into an overturning $M_{(ov(S/N))}$, azonal $M_{(az(S/N))}$ and the volume transport $T_{(S/N)}$ terms as follows:

$$M_{mean(N/S)}= M_{ov(N/S)} +M_{az(N/S)} -T_{(N/S)},$$

(7)

$$M_{ov(N/S)}= \frac{-1}{S_o}\int _{N/S}v^*\langle {}S\rangle {}dA,$$

(8)

$$M_{az(N/S)}= \frac{-1}{S_o}\int _{N/S}v^\prime {}S^\prime {}dA,$$

(9)

where $\langle {}f\rangle {}=\int {}fdx/\int {}x$ is the zonal mean, $f^\prime =f-\langle {}f\rangle$ is the difference from the zonal mean, ${\hat{f}}=\int {}fdA/\int {}dA$ is the zonal section mean or barotropic component and $f^*=\langle {}f\rangle {}-{\hat{f}}$ is the zonal mean baroclinic component for $f={\overline{v}}$ or $f={\overline{S}}$. Substituting Eqs. (6) and (7 8 9) into Eq. (4) gives the final form for the zonal freshwater budget equation:

$$M_{trend}={\varDelta }{}M_{ov}+{\varDelta }{}M_{az}+{\varDelta }{}M_{eddy}+{\varDelta }{}M_{Med}+M_{Mix}+PER+H,$$

(10)

where ${\varDelta }{}M_{ov}=M_{(ov(S))}-M_{(ov(N))}$, ${\varDelta }{}M_{az}=M_{(az(S))}-M_{az(N)}$, ${\varDelta }{}M_{eddy}=M_{(eddy(S))}-M_{(eddy(N))}$ and ${\varDelta }{}M_{Med}=-M_{Med}-T_{Med}$.

The are several possible valid choices of the reference salinity; the mean salinity over the entire volume of the region used in the budget calculation, the mean salinity over the section used as the northern (southern) boundary or the mean salinity from the Strait of Gibraltar. For this study it was chosen to use the mean salinity at the boundary between the North Atlantic subtropical and subpolar gyres for $S_o$, the reference salinity. Choosing one of the other salinities as a reference salinity creates a maximum difference of O(10–4 Sv), which is less than 10 % of the smallest value represented in our budget analysis. To further simplify the budget analysis only times when there is no hosing being applied are considered and the freshwater transport through the Strait of Gibraltar is combined with the mixing term, resulting in the following final equation for the budget analysis:

$$M_{trend}={\varDelta }{}M_{ov}+{\varDelta }{}M_{az}+{\varDelta }{}M_{eddy}+M_{mix}+PER.$$

(11)