Thierry Huck

Baroclinic Instability: An Oceanic Wavemaker for Interdecadal Variability

Numerical simulations of coarse-resolution, idealized ocean basins under constant surface heat flux are analyzed to show that the interdecadal oscillations that emerge naturally in such configurations are driven by baroclinic instability of the mean state and damped by horizontal diffusion. When the surface heat fluxes are diagnosed from a spinup in which surface temperatures are strongly restored to apparent atmospheric temperatures, the most unstable regions diagnosed by large downgradient eddy heat fluxes are located in the basin northwest corner where the surface heat losses are largest. The long-wave limit of the baroclinic instability of idealized mean flows in a three-layer model with vertical shears as observed in the GCMs demonstrates that growth rates of order one cycle per year can be produced locally, large enough to amplify thermal anomalies in the face of lateral diffusion. The proposed instability mechanism that favors surface-intensified perturbations also explains the lack of oscillations if the restoring to a surface climatology is too strong. To assess whether this instability process of oceanic origin is robust enough to cause interdecadal variability of coupled ocean‐atmosphere models, a four-box ocean‐atmosphere model is constructed. Given the large heat capacity of the ocean as compared to the atmosphere, the dynamical system that governs the model evolution is reduced to only two degrees of freedom, the oceanic overturning thermohaline circulation and the interior north‐south temperature gradient. The authors show that, when the baroclinic instability growth rate exceeds the overall dissipation caused by turbulent eddy diffusion in the atmosphere and ocean and infrared back radiation, the dynamical system undergoes a Hopf bifurcation, and interdecadal oscillations emerge through a limit cycle.

Interdecadal Variability of the Thermohaline Circulation in Box-Ocean Models Forced by Fixed Surface Fluxes

Intrinsic modes of decadal variability are analyzed using box-geometry ocean models forced by constant surface fluxes. An extensive parameter sensitivity analysis of the oscillatory behavior is carried out with respect to the spherical/Cartesian geometry, the b effect, the Coriolis parameter, the parameterization of momentum dissipation and associated boundary conditions, the vertical and horizontal diffusivities, the convective adjustment algorithm, the horizontal and vertical model resolution, the forcing amplitude, and the basin width. The oscillations stand out as a robust geostrophic feature whose amplitude is mainly controlled by the horizontal diffusivity. Unsuccessful attempts to reproduce the variability in zonally averaged 2D models suggest that the 3D adjustment processes are necessary. However, the b effect is not necessary for decadal variability to occur, and therefore classical Rossby waves play no fundamental role in the mechanism. Various experiments with different geometry and forcing are conducted and do not support the necessity of viscous numerical boundary waves or any boundary in sustaining the oscillations. The models show two types of oscillatory behavior: 1) temperature anomalies propagating geostrophically westward in the eastward jet (northern part of the basin) and inducing an opposite anomaly in their wake and 2) stationary temperature anomalies in the northwest quarter that respond to the western boundary current transport changes and reinforce geostrophically this change until the opposite temperature anomaly built on the east finally reverses the meridional overturning anomaly. The analysis of the transition from steady to oscillatory states (using heat fluxes diagnosed at the equilibrium under restoring boundary conditions) and the comparison of the variability under various forcing fields suggest that the oscillations are triggered in the regions of strongest surface cooling. Finally, a simple box-model analogy is proposed that captures the crucial phase shift between meridional overturning and north‐south density gradient anomalies on these decadal timescales.

Contributions of Wind Forcing and Surface Heating to Interannual Sea Level Variations in the Atlantic Ocean

Interannual sea surface height variations in the Atlantic Ocean are examined from 10 years of highprecision altimeter data in light of simple mechanisms that describe the ocean response to atmospheric forcing: 1) local steric changes due to surface buoyancy forcing and a local response to wind stress via Ekman pumping and 2) baroclinic and barotropic oceanic adjustment via propagating Rossby waves and quasi-steady Sverdrup balance, respectively. The relevance of these simple mechanisms in explaining interannual sea level variability in the whole Atlantic Ocean is investigated. It is shown that, in various regions, a large part of the interannual sea level variability is related to local response to heat flux changes (more than 50% in the eastern North Atlantic). Except in a few places, a local response to wind stress forcing is less successful in explaining sea surface height observations. In this case, it is necessary to consider large-scale oceanic adjustments: the first baroclinic mode forced by wind stress explains about 70% of interannual sea level variations in the latitude band 18°–20°N. A quasi-steady barotropic Sverdrup response is observed between 40° and 50°N.

On the Robustness of the Interdecadal Modes of the Thermohaline Circulation

Ocean models in box geometry forced by constant surface fluxes of density have been found to spontaneously generate interdecadal oscillations of the thermohaline circulation. This paper analyzes the sensitivity of these oscillations to various physical effects, including the presence of mesoscale turbulence, various thermal surface boundary conditions, and the presence of wind forcing or bottom topography. The role of unstable long baroclinic waves is also reexamined in an attempt to understand the oscillation period. In idealized geometry, it is found that the low-frequency variability of the thermohaline circulation under quasi-constant surface fluxes is a robust feature of the large-scale circulation. It is not strongly affected by energetic mesoscale turbulence; the oscillation period is relatively invariant with respect to varying resolution and momentum and tracer horizontal mixing coefficients, although it loses some regularity as shorter and longer periods of variability emerge when the mesoscale activity increases in strength with smaller mixing coefficients. The oscillations are also retained as the ocean model is coupled to an interactive atmospheric energy balance model; the thermohaline modes are robust to a range of exchange coefficients that widens with the amplitude of the mean circulation. The presence of an additional wind-forced component generally weakens the oscillation, and depending on the relative strength of thermodynamic and dynamic forcings, the oscillation may be completely killed. A simple interpretation is given, highlighting the role of upward Ekman pumping in damping density anomalies. Finally, the interaction of these baroclinic modes with bottom topography depends strongly on the relative directions of the mean topographic features and the mean currents and baroclinic waves, but usually results in a damping influence.

Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations

What can we learn from performing a linear stability analysis of the large-scale ocean circulation? Can we predict from the basic state the occurrence of interdecadal oscillations, such as might be found in a forward integration of the full equations of motion? If so, do the structure and period of the linearly unstable modes resemble those found in a forward integration? We pursue here a preliminary study of these questions for a case in idealized geometry, in which the full nonlinear behavior can also be explored through forward integrations. Specifically, we perform a three-dimensional linear stability analysis of the thermally-driven circulation of the planetary geostrophic equations. We examine the resulting eigenvalues and eigenfunctions, comparing them with the structure of the interdecadal oscillations found in the fully nonlinear model in various parameter regimes. We obtain a steady state by running the time-dependent, nonlinear model to equilibrium using restoring boundary conditions on surface temperature. If the surface heat fluxes are then diagnosed, and these values applied as constant flux boundary conditions, the nonlinear model switches into a state of perpetual, finite amplitude, interdecadal oscillations. We construct a linearized version of the model by empirically evaluating the tangent linear matrix at the steady state, under both restoring and constant-flux boundary conditions. An eigen-analysis shows there are no unstable eigenmodes of the linearized model with restoring conditions. In contrast, under constant flux conditions, we find a single unstable eigenmode that shows a striking resemblance to the fully-developed oscillations in terms of three-dimensional structure, period and growth rate. The mode may be damped through either surface restoring boundary conditions or sufficiently large horizontal tracer diffusion. The success of this simple numerical method in idealized geometry suggests applications in the study of the stability of the ocean circulation in more realistic configurations, and the possibility of predicting potential oceanic modes, even weakly damped, that might be excited by stochastic atmospheric forcing or mesoscale ocean eddies.

The Different Nature of the Interdecadal Variability of the Thermohaline Circulation under Mixed and Flux Boundary Conditions

The differences between the interdecadal variability under mixed and constant flux boundary conditions are investigated using a coarse-resolution ocean model in an idealized flat-bottom single-hemisphere basin. Objective features are determined that allow one type of oscillation to be distinguished versus the other. First, by performing a linear stability analysis of the steady state obtained under restoring boundary conditions, it is shown that the interdecadal variability under constant flux and mixed boundary conditions arises, respectively, from the instability of a linear mode around the mean stratification and circulation and from departure from the initial state. Based on the budgets of density variance, it is shown next that the two types of oscillations have different energy sources: Under the constant-flux boundary condition (the thermal mode), the downgradient meridional eddy heat flux in the western boundary current regions sustains interdecadal variability, whereas under mixed boundary conditions (the salinity mode), a positive feedback between convective adjustment and restoring surface heat flux is at the heart of the existence of the decadal oscillation. Furthermore, the positive correlations between temperature and salinity anomalies in the forcing layer are shown to dominate the forcing of density variance. In addition, the vertical structure of perturbations reveals vertical phase lags at different depths in all tracer fields under constant flux, while under mixed boundary conditions only the temperature anomalies show a strong dipolar structure. The authors propose that these differences will allow one to identify which type of oscillation, if any, is at play in the more exhaustive climate models.

Optimal Surface Salinity Perturbations of the Meridional Overturning and Heat Transport in a Global Ocean General Circulation Model

Abstract Recent observations and modeling studies have stressed the influence of surface salinity perturbations on the North Atlantic circulation over the past few decades. As a step toward the estimation of the sensitivity of the thermohaline circulation to salinity anomalies, optimal initial surface salinity perturbations are computed and described for a realistic mean state of a global ocean general circulation model [Ocean Parallelise (OPA)]; optimality is defined successively with respect to the meridional overturning circulation intensity and the meridional heat transport maximum. Although the system is asymptotically stable, the nonnormality of the dynamics is able to produce a transient growth through an initial stimulation. Optimal perturbations are calculated subject to three constraints: the perturbation applies to surface salinity; the perturbation conserves the global salt content; and the perturbation is normalized, to remove the degeneracy in the linear maximization problem. Maximization us...

Optimal Surface Salinity Perturbations Influencing the Thermohaline Circulation

Optimal surface salinity perturbations influencing the meridional overturning circulation maximum are exhibited and interpreted on a stable steady state of a 2D latitude–depth ocean thermohaline circulation model. Despite the stability of the steady state, the nonnormality of the dynamics is able to create some transient growth and variability through stimulation by optimal perturbations. Two different measures are compared to obtain the optimum—one associated with the departure from steady state in terms of density, and the other with the overturning circulation intensity. It is found that such optimal analysis is measure dependent; hence, the latter measure is chosen for studying the following physical mechanisms. The response to the optimal initial sea surface salinity perturbation involves a transient growth mechanism leading to a maximum modification of the circulation intensity after 67 yr; the amplification is linked to the most weakly damped linear eigenmode, oscillating on a 150-yr period. Optimal constant surface salinity flux perturbations are also obtained, and confirm that a decrease in the freshwater flux amplitude enhances the circulation intensity. At last, looking for the optimal stochastic surface salinity flux perturbation, it is established that the variance of the circulation intensity is controlled by the weakly damped 150-yr oscillation. Two approaches are tested to consider extending such studies in more realistic 3D models. Explicit solutions (versus eigenvalue problems) are found for the overturning circulation measure (except for the stochastic optimal); a truncation method on a few leading eigenmodes usually provides the optimal perturbations for analyses on long time scales.

On the influence of the parameterization of lateral boundary layers on the thermohaline circulation in coarse-resolution ocean models

Because of the first order geostrophic balance in the ocean interior, the parameterization of lateral boundary layers has more influence than the parameterization of viscosity on the thermohaline overturning and the deep water properties in coarse-resolution ocean circulation models. Different formulations of momentum dissipation and associated boundary conditions are implemented within a planetary-geostrophic ocean circulation model for a Cartesian coordinate, flat-bottomed, β-plane, with restoring boundary conditions for the surface density and zero wind stress. Traditional Laplacian friction with a no-slip boundary condition produces an interior circulation in good agreement with geostrophy and the Sverdrup balance, but generates very large vertical (diapycnal) transports at lateral boundaries, especially upwelling in the western boundary current and downwelling in the northeast corner. The meridional and zonal overturning are thus enhanced, but drive to depth surface waters that are not as cold as the ones in the deep convection regions. Rayleigh friction with various frictional closures for the alongshore velocities within a no-normal-flow boundary condition framework efficiently reduces the diapycnal vertical transports along the boundaries, by allowing horizontal recirculation of geostrophic currents impinging into coasts. Hence, these parameterizations induce weaker overturnings, with colder deep water and a sharper thermocline resulting in higher poleward heat transports. We suggest that the upwelling along the boundaries is a consequence of the coarse-resolution dynamics and not only horizontal diffusion (termed the Veronis effect, horizontal diffusion produces large diapycnal fluxes once the isopycnals are tilted by coastal upwellings). Alternative parameterizations for the lateral boundary layers reduce this effect without the need for rotating the mixing tensor along isopycnals. This model comparison proves the need to clearly assess the extent of the diapycnal upwelling in the western boundary currents and to develop physically-based parameterizations of lateral boundary layers in order to improve coarse-resolution OGCMs.

Nonnormal multidecadal response of the thermohaline circulation induced by optimal surface salinity perturbations

Optimal perturbations of sea surface salinity are obtained for an idealized North Atlantic basin using a 3D planetary geostrophic model—optimality is defined with respect to the intensity of the meridional overturning circulation. Both optimal initial and stochastic perturbations are computed in two experiments corresponding to two different formulations of the surface boundary conditions: the first experiment uses mixed boundary conditions (i.e., restoring surface temperature and prescribed freshwater flux), whereas the second experiment uses flux boundary conditions for both temperature and salinity. The latter reveals greater responses to both initial and stochastic perturbations that are related to the existence of a weakly damped oscillatory eigenmode of the Jacobian matrix, the optimal perturbations being closely related to its biorthogonal. The optimal initial perturbation induces a transient modification of the circulation after 24 yr. The spectral response to the optimal stochastic perturbation reveals a strong peak at 35 yr, corresponding to the period of this oscillatory eigenmode. This study provides an upper bound of the meridional overturning response at multidecadal time scales to freshwater flux perturbation: for typical amplitudes of Great Salinity Anomalies, initial perturbations can alter the circulation by 12.25 Sv (1 Sv [ 10 6 m 3 s 21 ; i.e., 12.5% of the mean circulation) at most; stochastic perturbations with amplitudes typical of the interannual variability of the freshwater flux in midlatitudes induce a circulation variability with a standard deviation of 1 Sv (i.e., 5.5% of the mean circulation) at most.