Reversed North Atlantic gyre dynamics in present and glacial climates

Abstract

The dynamics of the North Atlantic subpolar gyre (SPG) are assessed under present and glacial boundary conditions by investigating the SPG sensitivity to surface wind-stress changes in a coupled climate model. To this end, the gyre transport is decomposed in Ekman, thermohaline, and bottom transports. Surface wind-stress variations are found to play an important indirect role in SPG dynamics through their effect on water-mass densities. Our results suggest the existence of two dynamically distinct regimes of the SPG, depending on the absence or presence of deep water formation (DWF) in the Nordic Seas and a vigorous Greenland–Scotland ridge (GSR) overflow. In the first regime, the GSR overflow is weak and the SPG strength increases with wind-stress as a result of enhanced outcropping of isopycnals in the centre of the SPG. As soon as a vigorous GSR overflow is established, its associated positive density anomalies on the southern GSR slope reduce the SPG strength. This has implications for past glacial abrupt climate changes, insofar as these can be explained through latitudinal shifts in North Atlantic DWF sites and strengthening of the North Atlantic current. Regardless of the ultimate trigger, an abrupt shift of DWF into the Nordic Seas could result both in a drastic reduction of the SPG strength and a sudden reversal in its sensitivity to wind-stress variations. Our results could provide insight into changes in the horizontal ocean circulation during abrupt glacial climate changes, which have been largely neglected up to now in model studies.

Appendix

Ignoring frictional terms, the zonal and meridional time-independent momentum equations are:

$$ f u = - g \partial_y \eta + \partial_y \intop_z^0 b^\prime dz^\prime + \rho_0^{-1} \partial_z \tau_{zy} $$

(A1)

$$ - f v = - g \partial_x \eta + \partial_x \intop_z^0 b^\prime dz^\prime + \rho_0^{-1} \partial_z \tau_{zx}, $$

(A2)

with u and v being the zonal and meridional velocity components, f the Coriolis parameter, g local gravity, η the sea-surface elevation, ρ ₀ the average density, τ _zx and τ _zy the turbulent Reynolds stresses, and

$$ b = g \frac{\rho_0 - \rho}{\rho_0} $$

(A3)

the buoyancy.

Splitting the second term on the right hand side (r.h.s.) of Eqs. A1 and A2 we have:

$$ f u = - g \partial_y \eta + \partial_y \intop_{-H}^0 b dz - \partial_y \intop_{-H}^z b^\prime dz^\prime + \rho_0^{-1} \partial_z \tau_{zy} $$

(A4)

$$ - f v = - g \partial_x \eta + \partial_x \intop_{-H}^0 b dz - \partial_x \intop_{-H}^z b^\prime dz^\prime + \rho_0^{-1} \partial_z \tau_{zx}, $$

(A5)

where H is the ocean depth.

Here we can identify the Ekman, thermohaline and bottom velocity as defined by Fofonoff (1962) and Mellor et al. (1982):

$$ f [u_e,v_e] = \left[ \rho_0^{-1} \partial_z \tau_{zy} , - \rho_0^{-1} \partial_z \tau_{zx} \right] $$

(A6)

$$ f [u_t,v_t] = \left[ - \partial_y \intop_{-H}^z b^\prime dz^\prime, \partial_x \intop_{-H}^z b^\prime dz^\prime \right] $$

(A7)

$$ f [u_b,v_b] = \left[ - g \partial_y \eta + \partial_y \intop_{-H}^0 b dz, g \partial_x \eta - \partial_x \intop_{-H}^0 b dz \right]. $$

(A8)

We now define the vertically integrated zonal and meridional transports:

$$ M_x = \intop_{-H}^{0} u dz ;\quad M_y = \intop_{-H}^{0} v dz. $$

(A9)

Integrating vertically Eq. A4 we have:

$$ f M_x = - g \intop_{-H}^{0} \partial_y \eta dz + \intop_{-H}^{0} dz \partial_y \intop_{-H}^0 b dz - \intop_{-H}^{0} dz \partial_y \intop_{-H}^z b^\prime dz^\prime + \rho_0^{-1} \intop_{-H}^{0} \partial_z \tau_{zy} dz. $$

(A10)

The third term on the r.h.s. can be rewritten as follows using Leibnitz’s rule:

$$ \begin{aligned} \intop_{-H}^{0} dz \partial_y \intop_{-H}^{z} b^\prime dz^\prime & = \partial_y \intop_{-H}^{0} dz \intop_{-H}^{z} dz^\prime b^\prime - \intop_{-H}^{0} dz b \partial_y 0 + \intop_{-H}^{-H} dz b \partial_y (-H) \\ & = \partial_y \intop_{-H}^{0} dz \intop_{-H}^{z} dz^\prime b^\prime. \end{aligned} $$

(A11)

Thus:

$$ f M_x = - H g \partial_y \eta + H \partial_y \intop_{-H}^{0} b dz + \partial_y \intop_{-H}^{0} zb dz + \rho_0^{-1} \tau_{0y} $$

(A12)

$$ f M_y = H g \partial_x \eta - H \partial_x \intop_{-H}^{0} b dz - \partial_x \intop_{-H}^{0} zb dz - \rho_0^{-1} \tau_{0x}, $$

(A13)

whereτ _0x ,τ _0y are the zonal and meridional component of the surface wind-stress, respectively.

A further simplification can be made by applying again Leibnitz’s rule on the second and third term of the r.h.s.:

$$ H \partial_y \intop_{-H}^{0} b dz = H \intop_{-H}^{0} \partial_y b dz + H b_{-H} \partial_y H $$

(A14)

$$ \partial_y \intop_{-H}^{0} zb dz = \intop_{-H}^{0} z \partial_y b dz - H b_{-H} \partial_y H, $$

(A15)

where b _−H is the buoyancy at the bottom of the ocean. Substituting into Eqs. A12 and A13, the last term on the r.h.s. cancels out, yielding

$$ f M_x = - H g \partial_y \eta + H \intop_{-H}^{0} \partial_y b dz + \intop_{-H}^{0} z \partial_y b dz + \rho_0^{-1} \tau_{0y} $$

(A16)

$$ f M_y = H g \partial_x \eta - H \intop_{-H}^{0} \partial_x b dz - \intop_{-H}^{0} z \partial_x b dz - \rho_0^{-1} \tau_{0x}. $$

(A17)

The vertically integrated Ekman, thermohaline and bottom transports are thus:

$$ f [M_{xe}, M_{ye}] = \left[ \rho_0^{-1} \tau_{0y} , - \rho_0^{-1} \tau_{0x} \right] $$

(A18)

$$ f [M_{xt}, M_{yt}] = \left[ \intop_{-H}^{0} z \partial_y b dz , - \intop_{-H}^{0} z \partial_x b dz \right] $$

(A19)

$$ f [M_{xb}, M_{yb}] = \left[ - H g \partial_y \eta + H \intop_{-H}^{0} \partial_y b dz, H g \partial_x \eta - H \intop_{-H}^{0} \partial_x b dz \right], $$

(A20)

as discussed by Mellor et al. (1982). Equations A16 and A17, and their decomposition into Eqs. A18–A20 constitute our final equations.

Note that usually the surface elevation is unknown, which precludes calculating the transport directly from Eqs. A16 and A17. As explained by Mellor et al. (1982) this problem can be circumvented by rewriting these equations in terms of the potential energy at depth H ρ ₀ϕ and the bottom pressureρ ₀ P _b :

$$ \phi \equiv \intop_{-H}^{0} zb dz $$

(A21)

$$ P_b \equiv g \eta - \intop_{-H}^{0} b dz. $$

(A22)

These are related to the second and third terms on the r.h.s. of Eqs. A16 and A17 in the following manner:

$$ \partial_y \phi = \partial_y \intop_{-H}^{0} zb dz = \intop_{-H}^{0} z \partial_y b dz - H b_{-H} \partial_y H; $$

(A23)

$$ - H \partial_y P_b = - H g \eta + \partial_y \intop_{-H}^{0} b dz = - H g \eta + \intop_{-H}^{0} \partial_y b dz + H b_{-H} \partial_y H. $$

(A24)

Since the last term on the r.h.s. cancels out, Eqs. A16 and A17 can also be written as:

$$ M _x = \frac{1}{f} \left\{ -H \partial_y P_b + \partial_y \phi + \frac{\tau_{0y}}{\rho_0} \right\} $$

(A25)

$$ M _y = \frac{1}{f} \left\{ H \partial_x P_b - \partial_x \phi - \frac{\tau_{0x}}{\rho_0} \right\}. $$

(A26)

Cross-differentiating and adding up Eqs. A25 and A26 yields the equation for the advection of planetary potential vorticity, in which the bottom pressure term has been eliminated:

$$ \begin{aligned} {\mathbf M} \cdot \varvec{\nabla} \left( \frac{f}{H} \right) = & H^{-2} ( \partial_y H \partial_x \phi - \partial_x H \partial_y \phi ) \\ & + \partial_x \left( \frac{\tau_{0y}}{\rho_0 H} \right) - \partial_y \left( \frac{\tau_{0x}}{\rho_0 H} \right), \end{aligned} $$

(A27)

which allows estimating the flow by evaluating the r.h.s. of Eq. A27; the reader is referred to Mellor et al. (1982) and Mellor (1996) for a more detailed explanation of the exact procedure. In our case, however, because we are handling model output, all quantities are available and the transport can be computed directly from Eqs. A16 and A17.