Sensitivity of the Atlantic meridional overturning circulation to South Atlantic freshwater anomalies

Abstract

The sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) to changes in basin integrated net evaporation is highly dependent on the zonal salinity contrast at the southern border of the Atlantic. Biases in the freshwater budget strongly affect the stability of the AMOC in numerical models. The impact of these biases is investigated, by adding local anomaly patterns in the South Atlantic to the freshwater fluxes at the surface. These anomalies impact the freshwater and salt transport by the different components of the ocean circulation, in particular the basin-scale salt-advection feedback, completely changing the response of the AMOC to arbitrary perturbations. It is found that an appropriate dipole anomaly pattern at the southern border of the Atlantic Ocean can collapse the AMOC entirely even without a further hosing. The results suggest a new view on the stability of the AMOC, controlled by processes in the South Atlantic.

Appendix: Equivalent freshwater budget in the Atlantic Ocean

The volume budget of the Atlantic Ocean can be written as:

$$ \frac{\partial V}{\partial t}=\int\limits_{BS}v \hbox{d} x \hbox{d} z + \int\limits_{30S} v \hbox{d} x \hbox{d} z - EPR, $$

(4)

where v is the meridional velocity, BS and 30S indicate integration over a zonal transect in the Bering strait and at 30°S in the Atlantic Ocean respectively. EPR is the net evaporation over the basin and V is volume. The volume change in the basin is the balance between inflow from zonal boundaries and net evaporation.

Equivalent freshwater budget

Local salt conservation is expressed by:

$$ \frac{\partial S}{\partial t}+{\bf u}\cdot{\nabla} S=-\nabla {\mathcal{F}}_S, $$

(5)

where S is salinity, u is the horizontal velocity vector and $\mathcal{F}_S$ is the diffusive salt flux. Diffusive fluxes depend on model definition, so we do not write them explicitly here. Integrating Eq. 5 over the whole Atlantic basin, using Gauss theorem and assuming no salt flux at the surface and bottom and no diffusion across Bering strait, one obtains:

$$ \frac{\partial}{\partial t}\int\limits_{Atl}S \hbox{d} V-\int\limits_{30S}vS \hbox{d} x \hbox{d} z - \int\limits_{BS}vS \hbox{d} x \hbox{d} z=\int\limits_{30S} {\mathcal{F}}_S \hbox{d} x \hbox{d} z. $$

(6)

Using a reference salinity S ₀:

$$ S_0=\frac{\int_{30S}S {\hbox{d}}x {\hbox{d}} z}{\int_{30S} \hbox{d} x \hbox{d} z}, $$

(7)

an equivalent freshwater transport can be defined from Eq. 6:

$$ -\frac{1}{S_0}\frac{\partial}{\partial t}\int\limits_{Atl}S \hbox{d} V = -\frac{1}{S_0}\int\limits_{30S}vS \hbox{d} x \hbox{d} z -\frac{1}{S_0}\int\limits_{BS}vS \hbox{d} x \hbox{d} z -\frac{1}{S_0} \int\limits_{30S} {\mathcal{F}}_S \hbox{d} x \hbox{d} z, $$

written in short as:

$$ Q_t=M_{30S}-\frac{1}{S_0} \int\limits_{BS}vS \hbox{d} x \hbox{d}z + M_{d}+Res, $$

(8)

where Res is a residual.

Virtual freshwater transport at 30°S

The term M _30S in Eq. 8 is split in two parts:

$$ \begin{aligned} M_{30S}&=-\frac{1}{S_0}\int\limits_{30S}vS \hbox{d} x \hbox{d} z &= -\frac{1}{S_0}\int\limits_{30S}(\langle v \rangle + v')(\langle S \rangle + S') \hbox{d} x \hbox{d} z\\ &=-\frac{1}{S_0}\left(\int\limits_{30S}\langle v \rangle \langle S \rangle \hbox{d} x \hbox{d} z + \int\limits_{30S}v'S' \hbox{d} x \hbox{d} z\right), \end{aligned} $$

(9)

where, for a generic field f, the zonal operator is $\langle f\rangle=\int\limits_{60^{\circ}{\rm W}}^{20^{\circ}{\rm E}} f \hbox{d} x/\!\int \hbox{d} x$ and the azonal operator is $f'=f-\langle f \rangle$.

Using the two definitions:

$$ \begin{aligned} M_{ov} &=-\frac{1}{S_0}\int\limits_{30S}\tilde{v} (\langle S \rangle - S_0) \hbox{d} x \hbox{d} z \\ M_{az}&= -\frac{1}{S_0}\int\limits_{30S}v'S' \hbox{d} x \hbox{d} z, \end{aligned} $$

where for a generic field f the barotropic operator is $\overline{f}=\int f \hbox{d} z/\!\int \hbox{d} z$ and the baroclinic operator is $\tilde{f}=f-\overline{f}$, Eq. 9 becomes:

$$ M_{30S}=M_{ov} + M_{az}-\int\limits_{30S}v \hbox{d} x \hbox{d} z. $$

(10)

Using Eq. 10, the volume outflow of water at 30S can be represented by a virtual freshwater inflow.

Putting together Eqs. 4 and 10 into the virtual freshwater budget of Eq. 8 we obtain Eq. 3:

$$ EPR + Q_t + V_t = M_{ov} + M_{az} + M_d + M_{BS} +Res, $$

with V _t  = ∂V/∂t the volume drift in the basin, and defining $M_{BS}= \int_{BS}v \hbox{d} x \hbox{d} z-\frac{1}{S_0} \int_{BS}vS \hbox{d} x \hbox{d} z$. The inflow of freshwater in the basin must balance net evaporation and the drift in volume and salinity.

In the calculations, baroclinic velocity can be used instead of actual one, as long as Eq. 7 is used as the definition of S ₀. This stems from the definition of baroclinic velocity.

Freshwater budget in CLIO

The terms in Eq. 3 for the control state of the EMIC SPEEDO are reported in Table 2. Very similar numbers are obtained for the HCM. In the model, the freshwater anomalies are implemented as a virtual salt flux, which can easily be accounted for by a surface salt flux in Eq. 5. Here we include this term into EPR for simplicity.

Table 2 Values of the different terms in Eq. 3 as computed in the control run of the EMIC SPEEDO

The largest terms in the budget are EPR, M _ov and M _az by at least one order of magnitude. Moreover, the other terms are also less sensitive to the freshwater anomalies applied so that they are approximately constant, with the exception of Q _t . As discussed in Sect. 4 this depends on the details of the model used. As an example, in THCM, the term M _d plays instead a primary role, and behaves in a way similar to M _az in SPEEDO.