Calculating the ocean's mean dynamic topography from a mean sea surface and a geoid

In principle the global mean geostrophic surface circulation of the ocean can be diagnosed by subtracting a geoid from a mean sea surface (MSS). However, because the resulting mean dynamic topography (MDT) is approximately two orders of magnitude smaller than either of the constituent surfaces, and because the geoid is most naturally expressed as a spectral model while the MSS is a gridded product, in practice complications arise. Two algorithms for combining MSS and satellite-derived geoid data to determine the ocean’s mean dynamic topography (MDT) are considered in this paper: a pointwise approach, whereby the gridded geoid height field is subtracted from the gridded MSS; and a spectral approach, whereby the spherical harmonic coefficients of the geoid are subtracted from an equivalent set of coefficients representing the MSS, from which the gridded MDT is then obtained. The essential difference is that with the latter approach the MSS is truncated, a form of filtering, just as with the geoid. This ensures that errors of omission resulting from the truncation of the geoid, which are small in comparison to the geoid but large in comparison to the MDT, are matched, and therefore negated, by similar errors of omission in the MSS. The MDTs produced by both methods require additional filtering. However, the spectral MDT requires less filtering to remove noise, and therefore it retains more oceanographic information than its pointwise equivalent. The spectral method also results in a more realistic MDT at coastlines. 1. Introduction An important challenge in oceanography is the accurate determination of the ocean’s time-mean dynamic topography (MDT). If this can be achieved with sufficient accuracy for combination with the timedependent component of the dynamic topography, obtainable from altimetric data, then the resulting sum (i.e., the absolute dynamic topography) will give an accurate picture of surface geostrophic currents and ocean transports.

The importance of wind and buoyancy forcing for the boundary density variations and the geostrophic component of the AMOC at 26°N

It is widely thought that changes in both the surface buoyancy fluxes and wind stress drive variability in the Atlantic meridional overturning circulation (AMOC), but that they drive variability on different time scales. For example, wind forcing dominates short-term variability through its effects on Ekman currents and coastal upwelling, whereas buoyancy forcing is important for longer time scales (multiannual and decadal). However, the role of the wind forcing on multiannual to decadal time scales is less clear. Here the authors present an analysis of simulations with the Nucleus for European Modelling of the Ocean (NEMO) ocean model with the aim of explaining the important drivers of the zonal density gradient at 26°N, which is directly related to the AMOC. In the experiments, only one of either the wind stress or the buoyancy forcing is allowed to vary in time, whereas the other remains at its seasonally varying climatology. On subannual time scales, variations in the density gradient, and in the AMOC minus Ekman, are driven largely by local wind-forced coastal upwelling at both the western and eastern boundaries. On decadal time scales, buoyancy forcing related to the North Atlantic Oscillation dominates variability in the AMOC. Interestingly, however, it is found that wind forcing also plays a role at longer time scales, primarily impacting the interannual variability through the excitation of Rossby waves in the central Atlantic, which propagate westward to interact with the western boundary, but also by modulating the decadal time-scale response to buoyancy forcing.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime

We compare laboratory observations of equilibrated baroclinic waves in the rotating two-layer annulus, with numerical simulations from a quasi-geostrophic model. The laboratory experiments lie well outside the quasi-geostrophic regime: the Rossby number reaches unity; the depth-to-width aspect ratio is large; and the fluid contains ageostrophic inertia–gravity waves. Despite being formally inapplicable, the quasi-geostrophic model captures the laboratory flows reasonably well. The model displays several systematic biases, which are consequences of its treatment of boundary layers and neglect of interfacial surface tension and which may be explained without invoking the dynamical effects of the moderate Rossby number, large aspect ratio or inertia–gravity waves. We conclude that quasi-geostrophic theory appears to continue to apply well outside its formal bounds.

Perturbed Rankine vortices in surface quasi-geostrophic dynamics

An analytical dispersion relation is derived for linear perturbations to a Rankine vortex governed by surface quasi-geostrophic dynamics. Such a Rankine vortex is a circular region of uniform anomalous surface temperature evolving under quasi-geostrophic dynamics with uniform interior potential vorticity. The dispersion relation is analysed in detail and compared to the more familiar dispersion relation for a perturbed Rankine vortex governed by the Euler equations. The results are successfully verified against numerical simulations of the full equations. The dispersion relation is relevant to problems including wave propagation on surface temperature fronts and the stability of vortices in quasi-geostrophic turbulence.

On the steadiness of separating meandering currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase.

Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase

Voltage-gated potassium currents within the dorsal vagal nucleus: inhibition by BDS toxin

Voltage-gated potassium (Kv) channels are essential components of neuronal excitability. The Kv3.4 channel protein is widely distributed throughout the central nervous system (CNS), where it can form heteromeric or homomeric Kv3 channels. Electrophysiological studies reported here highlight a functional role for this channel protein within neurons of the dorsal vagal nucleus (DVN). Current clamp experiments revealed that blood depressing substance (BDS) and intracellular dialysis of an anti-Kv3.4 antibody prolonged the action potential duration. In addition, a BDS sensitive, voltage-dependent, slowly inactivating outward current was observed in voltage clamp recordings from DVN neurons. Electrical stimulation of the solitary tract evoked EPSPs and IPSPs in DVN neurons and BDS increased the average amplitude and decreased the paired pulse ratio, consistent with a presynaptic site of action. This presynaptic modulation was action potential dependent as revealed by ongoing synaptic activity. Given the role of the Kv3 proteins in shaping neuronal excitability, these data highlight a role for homomeric Kv3.4 channels in spike timing and neurotransmitter release in low frequency firing neurons of the DVN.

Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.