Flat-bottomed Ocean Research Articles

Bathymetry-Aware Mesoscale Eddy Parameterizations across Upwelling Slope Fronts: A Machine Learning–Augmented Approach

Abstract Mesoscale eddy buoyancy fluxes across continental slopes profoundly modulate the boundary current dynamics and shelf–ocean exchanges but have yet to be appropriately parameterized via the Gent–McWilliams (GM) scheme in predictive ocean models. In this work, we test the prognostic performance of multiple GM variants in noneddying simulations of upwelling slope fronts that are commonly found along the subtropical continental margins. The tested GM variants range from a set of constant eddy buoyancy diffusivities to recently developed energetically constrained, bathymetry-aware diffusivities, whose implementation is augmented by an artificial neural network (ANN) serving to predict the mesoscale eddy energy based on the topographic and mean flow quantities online. In addition, an ANN is employed to parameterize the cross-slope eddy momentum flux (EMF) that maintains a barotropic flow field analogous to that in an eddy-resolving model. Our tests reveal that noneddying simulations employing the bathymetry-aware forms of the Rhines scale–based scheme and GEOMETRIC scheme can most accurately reproduce the heat contents and along-slope baroclinic transports as those in the eddy-resolving simulations. Further analyses reveal certain degrees of physical consistency in the ANN-inferred eddy energy, which tends to grow (decay) as isopycnal slopes are steepened (flattened), and in the parameterized EMF, which exhibits the correct strength of shaping the flow baroclinicity if a bathymetry-aware GM variant is jointly used. These findings provide a recipe of GM variants for use in noneddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes. Significance Statement This study evaluates the predictive skill of parameterization schemes of water mass transports induced by ocean mesoscale eddies across continental slopes. Correctly parameterizing these transports in noneddying ocean models (e.g., ocean climate models) is crucial for predicting the ocean circulation and shelf–ocean exchanges. This work highlights the importance of bathymetric effects on eddy transports, as parameterization schemes that account for the influence of a sloping seafloor outperform those developed specifically for a flat-bottomed ocean. This work also highlights the efficacy of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes, for instance, by estimating the mesoscale eddy energy online to realize energy-dependent parameterization schemes in noneddying simulations.

A Gradient Based Subgrid‐Scale Parameterization for Ocean Mesoscale Eddies

AbstractMesoscale eddies play an important role in transport of heat and biogeochemical tracers in the global ocean circulation. Resolving these energetic eddies, however, is challenging in ocean general circulation models (OGCM) because it requires a horizontal grid spacing of ≲1/8° that is computationally expensive. As a result, we are required to parameterize mesoscale eddy effects on large‐scale ocean flows. In this work, we introduce a new subgrid‐scale (SGS) model that is developed based on a Taylor series expansion of resolved variables to parameterize subgrid mesoscale eddy transports and momentum fluxes in OGCM. We have performed an a priori study to evaluate the performance of our new gradient model using high‐resolution ocean simulations. Our results show that the gradient model well predicts the actual SGS thickness fluxes in the zonal and meridional directions in coarse‐resolution simulations with the grid spacing ≳1/4°. The unresolved kinetic energy at the ocean surface is also skillfully estimated. More importantly, unlike current mesoscale eddy parameterizations, which are mainly developed based on an assumption of flat bottom ocean, our new SGS model can capture the structure of unresolved standing meanders at the ocean surface. We have also developed a dynamic procedure for setting in non‐dimensional parameters in our new parameterization through a non‐ad hoc and tuning‐free method. Overall, this work suggests that implementing the gradient model in OGCM can improve the model accuracy with an affordable computational cost in eddy‐permitting and non‐eddying simulations.

The impact of the planetary β-effect on the vertical structure of a coherent vortex in the South China Sea

Vertical axes of mesoscale eddies with the coherent structure were observed to tilt southwestward significantly from the sea surface to bottom in the South China Sea. The dynamic mechanism for vertical tilting of eddies, however, is not well understood. In this study, the influence of the planetary β-effect on the vertical structure of a coherent eddy is investigated based on analytical considerations and numerical results produced by the MIT general circulation model (MITgcm). Both the analytical and numerical results demonstrate that, during the westward propagation of a mesoscale eddy, the momentum advection and divergence in the inner region of the eddy impact the propagation direction of the eddy on a β-plane. In the upper layer of the mesoscale eddy, the eddy propagation is mainly controlled by the β-effect and nonlinear effect (momentum advection). In the lower layer of an anticyclonic eddy, the eddy propagation direction is dominated by the advection and divergence, which leads to the westward shift of the eddy center in the upper layer. For a cyclonic eddy, by comparison, the vertical axis tilts to eastward from surface to bottom. The tilting distance is up to 30 km in a flat bottom ocean with the β value of 2.15 × 10−11 m−1 s−1. In addition, model results indicate that vertical stratification, eddy strength, and rough topography have significant influences on the vertical structure of a mesoscale eddy.

Eddy dynamics over continental slopes under retrograde winds: Insights from a model inter-comparison

Mesoscale eddies are ubiquitous in the ocean and play a key role in exchanges across continental slopes. In this study the properties of wind-driven baroclinic turbulence are investigated using eddy-resolving process simulations, focusing on the case of retrograde winds that arises around the margins of the subtropical gyres. In contrast to a flat-bottomed ocean, over steep slopes eddies develop from baroclinic instabilities are confined to the top few hundred meters. Deeper in the water column baroclinic instability and vertical momentum transfer are suppressed, so wind-input momentum is exported toward the open ocean by eddies before traversing down to the ocean bed. Close to the sloping topography, eddy energy sourced from the upper ocean is converted to potential energy, steepening isopycnals and driving bottom-trapped prograde flows. This process is associated with upgradient lateral buoyancy fluxes and downgradient isopycnal potential vorticity fluxes, and cannot be reproduced via linear stability calculations.These properties of wind-driven shelf/slope turbulence are contrasted against simulations with flat bathymetry. The key differences described above hinge on the flow close to the steep topographic slope, which may be sensitive to the model’s vertical coordinate system. The simulations are therefore replicated using models that employ geopotential coordinates, terrain-following coordinates, and isopycnal coordinates. Quantitative inter-model discrepancies in the momentum and energy budgets are much more pronounced in the presence of a steep bottom slope. However, the key findings of this study are consistent across the models, suggesting that they are robust and warrant incorporation into parameterizations of eddy transfer across continental slopes.

Effect of bottom slope in northeastern North Pacific on deep-water upwelling and overturning circulation

Hydrographic data show that the meridional deep current at 47°N is weak and southward in northeastern North Pacific; the strong northward current expected for an upwelling in a flat-bottom ocean is absent. This may imply that the eastward-rising bottom slope in the Northeast Pacific Basin contributes to the overturning circulation. After analysis of observational data, we examine the bottom-slope effect using models in which deep water enters the lower deep layer, upwells to the upper deep layer, and exits laterally. The analytical model is based on geostrophic hydrostatic balance, Sverdrup relation, and vertical advection–diffusion balance of density, and incorporates a small bottom slope and an eastward-increasing upwelling. Due to the sloping bottom, current in the lower deep layer intensifies bottomward, and the intensification is weaker for larger vertical eddy diffusivity (KV), weaker stratification, and smaller eastward increase in upwelling. Varying the value of KV changes the vertical structure and direction of the current; the current is more barotropic and flows further eastward as KV increases. The eastward current is reproduced with the numerical model that incorporates the realistic bottom-slope gradient and includes boundary currents. The interior current flows eastward primarily, runs up the bottom slope, and produces an upwelling. The eastward current has a realistic volume transport that is similar to the net inflow, unlike the large northward current for a flat bottom. The upwelling water in the upper deep layer flows southward and then westward in the southern region, although it may partly upwell further into the intermediate layer.

Exact Solutions of Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

Abstract The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer and no along-slope dependence of the variables; however, dependence in the cross-slope and vertical directions is retained. Density and the along-slope component of momentum are advected by the cross-slope velocity, with thermal wind balance maintained at all times. The time-dependent initial value problem is solved with constant initial stratification and no initial along-slope flow. Previously, this model has been used to study upwelling over flat-bottomed ocean, but the novel features in this work are the study of exact solutions for a family of sloping topographic profiles, for both upwelling and downwelling. The exact solutions are compared to numerical solutions from a primitive equation ocean model configured in a similar two-dimensional geometry. The exact solutions predict that deep undercurrents will develop only over steep topographic slopes and the cross-slope flow in the deep frictionless interior will be increasingly surface intensified as the topographic slope increases.

A Theory of Deep Stratification and Overturning Circulation in the Ocean

AbstractA simple theoretical model of the deep stratification and meridional overturning circulation in an idealized single-basin ocean with a circumpolar channel is presented. The theory includes the effects of wind, eddies, and diapycnal mixing; predicts the deep stratification in terms of the surface forcing and other problem parameters; makes no assumption of zero residual circulation; and consistently accounts for the interaction between the circumpolar channel and the rest of the ocean.The theory shows that dynamics of the overturning circulation can be characterized by two limiting regimes, corresponding to weak and strong diapycnal mixing. The transition between the two regimes is described by a nondimensional number characterizing the strength of the diffusion-driven compared to the wind-driven overturning circulation. In the limit of weak diapycnal mixing, deep stratification throughout the ocean is produced by the effects of wind and eddies in a circumpolar channel and maintained even in the limit of vanishing diapycnal diffusivity and in a flat-bottomed ocean. The overturning circulation across the deep stratification is driven by the diapycnal mixing in the basin away from the channel but is sensitive, through changes in stratification, to the wind and eddies in the channel. In the limit of strong diapycnal mixing, deep stratification is primarily set by eddies in the channel and diapycnal mixing in the basin away from the channel, with the wind over the circumpolar channel playing a secondary role. Analytical solutions for the deep stratification and overturning circulation in the limit of weak diapycnal mixing and numerical solutions that span the regimes of weak to strong diapycnal mixing are presented.The theory is tested with a coarse-resolution ocean general circulation model configured in an idealized geometry. A series of experiments performed to examine the sensitivity of the deep stratification and the overturning circulation to variations in wind stress and diapycnal mixing compare well with predictions from the theory.

Resonance and trapping of topographic transient ocean waves generated by a moving atmospheric disturbance

Proudman resonance amplifies the oceanic forced wave beneath moving atmospheric pressure disturbances. The amplification varies with water depth; consequently, the forced wave beneath a disturbance crossing topography radiates transient free waves. Transients are shown to magnify the effects of Proudman resonance for disturbances crossing the coast or shelf at particular angles. A Snell like reflection law gives rise to a type of resonance for relatively slow moving disturbances crossing a coast in an otherwise flat-bottomed ocean. This occurs for translation speeds less than the shallow water wave speed for disturbances approaching the coast at a critical angle given by the inverse sine of the Froude number of the disturbance. A disturbance crossing the shelf at particular angles can also excite seiche modes of the shelf via generation of a transient at the continental slope. Beyond a typically small angle of incidence, transients generated by a disturbance crossing the continental slope and coast will be trapped on the shelf by internal reflection. The refraction law for a fast-moving forced wave crossing an ocean ridge at greater than a small angle of incidence also results in trapped free-wave transients with tsunami-like periods propagating along the ridge. The subcritical resonance, excitation of shelf modes and trapping of the transients may have implications for storm surges and the generation of destructive meteotsunami.

Identification of the Mechanism of Interdecadal Variability in the North Atlantic Ocean

Abstract The aim of this paper is to identify the physical mechanism of interdecadal variability in simulations of the North Atlantic Ocean circulation with the Modular Ocean Model of the Geophysical Fluid Dynamics Laboratory. To that end, a hierarchy of increasingly complex model configurations is used. The variability in the simplest case, that of viscous, purely thermally driven flows in a flat-bottom ocean basin with a box-shaped geometry, is shown to be caused by an internal interdecadal mode. The westward propagation of temperature anomalies and the phase difference between the anomalous zonal and meridional overturning that characterize the interdecadal mode are used as “fingerprints” of the physical mechanism of the variability. In this way, the variability can be followed toward a less viscous regime in which the effects of continental geometry and bottom topography are also included. It is shown that, although quantitative aspects of the variability like period and spatial pattern are changing, the physical mechanism of the interdecadal variability in the more complex simulations can be attributed to the same processes as in the simplest model configuration.

Creation and coupling of Rossby waves over topography and the breakdown of WKB theory

The standard oceanic Rossby wave modes are separable solutions of the primitive equations linearized around a resting, flat-bottom ocean whose stratification depends upon depth only. These waves have a modal structure in the vertical and a propagating horizontal part that satisfies the shallow water equations with an equivalent depth He that is different for each mode. These waves propagate independently of each other over a flat-bottom, but become everywhere coupled over topography. This coupling can be primarily interpreted as defining new dynamical wave modes, i.e. generalized topographic Rossby waves, which can be constructed explicitly by means of WKB theory under the usual scale separation assumption. WKB solutions may locally breakdown, however, when the wavenumbers and frequency of the mode considered approximately satisfy locally the dispersion relation of another wave mode supported by the system. In such a region, called a mode conversion point, the WKB solution becomes degenerate and can no longer be expressed in terms of a single wave mode. There, linear resonance occurs and energy can be exchanged between two different rays. This paper presents an application of mode conversion theory for Rossby waves in a two-layer ocean propagating over a mid-ocean Gaussian ridge varying with longitude only. This theory is shown to predict satisfactorily the location of mode conversion points, and the amount of energy exchanged between rays. In such a framework, wave creation thus occurs at points where WKB breaks down.

Large-Scale Propagating Disturbances: Approximation by Vertical Normal Modes

Abstract Propagating features and waves occur everywhere in the ocean. This paper derives a concise description of how such small-amplitude, large-scale oceanic internal disturbances propagate dynamically against a slowly varying background mean flow and stratification, computed using oceanic data. For a flat-bottomed ocean, assumed here, the linear internal modes, computed using the local stratification, form a useful basis for expanding the oceanic shear modes of propagation. Remarkably, the shear modal structure is largely independent of orientation of the flow. The resulting advective velocities, which are termed pseudovelocities, comprise background flow decomposed onto normal modes, and westward planetary wave propagation velocities. The diagonal entries of the matrix of pseudovelocities prove to be reasonably accurate descriptors of the speed and direction of propagation of the shear modes, which thus respond as if simply advected by this diagonal-entry velocity field. The complicated three-dimensi...

Effects of Stratification and Bottom Topography on the Kuroshio Path Variation South of Japan. Part I: Dependence of the Path Selection on Velocity

Abstract Numerical experiments are executed using a two-layer inflow–outflow ocean model with simplified geometry to investigate the effects of stratification and bottom topography on the path variation of the Kuroshio south of Japan. In a flat-bottom ocean, the dependence of the Kuroshio path selection on its inflow velocity Vmax is basically the same as in a barotropic ocean, that is, the Kuroshio takes a straight path at low Vmax (regime I), a meandering path at high Vmax (regime II), and both paths at intermediate Vmax (regime III: multiple equilibrium state). However, the range of regime III shifts to higher Vmax by 0.10∼0.30 m s−1. Stratification causes and maintains the offshore shift of the current path south of Kyushu through the conservation of potential vorticity. As a result, a small meander stagnates southeast of Kyushu, not developing into a large meander even for higher Vmax since the vorticity supply from the coast is reduced. For the same reason, higher Vmax is needed to maintain a meande...

Topography and barotropic transport control by bottom friction

The problem of the stratified general circulation in the presence of topography is revisited. The novel effect examined here is that of localized, but large-scale, topographic anomalies on the wind-driven circulation, a problem whose relevance is found in the occurrence of many such features in the open ocean. Using the classical methods of homogenization theory, it is argued that the barotropic transport near topography can come under the direct control of bottom friction. This result differs substantively from either the well-known Sverdrup constraint (which applies to a flat-bottomed ocean, or to one with a resting deep layer) or its recent extensions that allow for planar bottom topographic profiles. Bottom friction emerges as a controlling parameter roughly in the event that the topography forms closed f/(H - h b ) contours, where H - hb is the total fluid depth, although the theoretical minimum requirements are somewhat looser than this. Our analytical predictions are supported by numerical experimentation with a multi-layer quasi-geostrophic model, and we examine some mean flow observations from the North and South Atlantic in light of the theory. In particular, the theory can rationalize the 100 Sv transport observed recently around the Zapiola Drift.

The influence of the mean state on interdecadal variability in flat-bottomed ocean models

It has been well-demonstrated that many flat-bottomed ocean models possess interdecadal oscillatory solutions. Recently, propagation of viscous (or coarsely resolved) Kelvin waves around the boundary has been implicated in the oscillations. In this paper, we examine how the mean state affects the character of the oscillation. We find that the stratification along the northern boundary has a large effect upon the oscillation. Mean states with an essentially unstratified north-east corner, lead to long period oscillations as the viscous boundary wave slowly crosses the northern boundary. Conversely, mean states with a stratified north-east corner, but unstratified north-west corner, lead to short-period, but larger-amplitude, oscillations since boundary wave propagation is arrested only in the north-west corner.We demonstate that the different character of oscillations under different zonal redistributions of a diagnosed flux are a consequence of the different mean states induced by the redistribution.

Steric and wind‐induced changes in TOPEX/POSEIDON large‐scale sea surface topography observations

Three years of TOPEX/POSEIDON altimeter data are analyzed with respect to large‐scale fluctuations in sea surface height observations and underlying physical processes. In midlatitudes the most conspicuous feature in the large‐scale changes in sea surface height are related to surface buoyancy fluxes, predominantly surface heat fluxes. The next prominent variability on subannual timescales is the adjustment of the ocean to varying winds stress fields in terms of planetary waves. The degree to which basin‐scale sea surface height variations relative to the steric component can be described as a time‐dependent Sverdrup balance is addressed for the Pacific Ocean. If a flat bottom ocean is assumed, a significant correlation of meridional mass transport variations inferred from TOPEX/POSEIDON and a simple Sverdrup model can be found in the Pacific Ocean north of 40°N, but it fails elsewhere. Numerical ocean general circulation models show a good agreement with the TOPEX/POSEIDON observations in all those components of ocean variability and allow further insight into the dynamics that govern observed sea surface height changes.

Eddy formation on a continental slope

We consider a uniform-density ocean in which the depth-independent horizontal velocity is driven by a two-gyre wind. Numerical solutions of the governing vorticity equation reveal that the solutions with a flat ocean bottom differ greatly from those in which a continental shelf and slope are present along the western boundary. In the ocean basin with a western continental shelf, steady inertial circulations readily lose stability to unsteady inertial circulations that spawn eddies. However, eddies do not form in the corresponding solutions for the flat-bottom ocean. Reducing the friction leads to flat-bottom solutions that shed eddies far offshore, but still differ significantly from the corresponding continental-slope solutions, where eddies pinch off near the western boundary.

Evidence of Time-dependent Sverdrup Circulation in the South Pacific from the Seasat Scatterometer and Altimeter

Abstract Seasat scatterometer and altimeter data are analyzed to investigate time-dependent Sverdrup dynamics in the Southern Ocean (40°S to 60°S) over seasonal time scales. Sverdrup dynamics are shown to be inadequate to describe the circulation in the South Atlantic and Indian oceans. The Sverdrup circulation in the South Pacific is reasonable north of 55°S. The changes in Sverdrup circulation from July to September 1978 indicate an eastward acceleration along 55°S and westward acceleration along 40°S, suggesting a southward shift in the subpolar eastward flow. Sea level in the South Pacific is estimated for July and September 1978 from scatterometer vector wind data based on Sverdrup dynamics assuming a flat-bottom ocean with barotropic flow. The changes in Sverdrup sea level are compared with the changes in sea level observed by the altimeter for the same time period. Both estimates indicate a rise in sea level along a zonal band centered at about 50°S. This sea level rise inferred from both the scatt...

Interannual Baroclinic Rossby Waves in the Midlatitude North Atlantic

Abstract Twenty-six year time sequences of upper thermocline temperature block-averaged in 5-degree latitude and longitude squares reveal strong, in-phase vertical coherence and low to moderate horizontal coherence over 550 km. Least-squares fitting theoretical cross spectra from a stochastic, first baroclinic mode Rossby wave model to cross spectra of the temperature–time sequences yields several best-fit wavenumber vectors that conform to the dispersion relation of first baroclinic mode Rossby waves in a flat bottom ocean with no mean current. The slope of the midocean ridge, which is as important as midlatitude beta, and the mean circulation were ignored. About 25%–55% of the cross-spectral energy can be attributed to the best-fit waves. A composite spectrum of the baroclinic potential energy of all the demonstrated Rossby waves is qualitatively similar to the spectrum of North Pacific first baroclinic mode Rossby waves, showing a peak around 6–7 years, but is 30 times larger in magnitude. The geograph...

Numerical study of the Subtropical Front and the Subtropical Countercurrent

Using a multi-level numerical model, it is shown that the Subtropical Front and the Subtropical Countercurrent can be reproduced realistically in a highly idealized model, as a consequence of the coupling effect of wind driven gyre circulation and differential heating. In the model, the North Pacific Ocean is idealized as a rectangular flat-bottomed model ocean, and is driven by wind stress, which features the Westerlies and the Trades, and by heat flux through the sea surface formulated after Haney (1971).

Effects of bottom topography and density stratification on variations of western boundary currents caused by periodic change in wind stress

Variations of the western boundary currents induced by a periodic change in wind stress are studied in a two-layer model with a continental slope along the western boundary. The variation of the total transport of the western boundary current over the continental slope shows a considerable phase lag with the wind stress and a decrease in amplitude compared with for the flat bottom ocean, though the interior barotropic response is to adjust almost instantaneously to the wind stress. The total transport variation of the western boundary current is well approximated by the upper layer transport variation. That is, almost complete separation of the upper- and lower-layer flows takes place over the slope, and only the upper layer flow contributes to the change in total transport of the western boundary current. Contributions of the interior barotropic and baroclinic responses to the upper layer transport variation depend on the forcing period. With decrease in the forcing period, the barotropic response becomes relatively important for determining the upper layer transport variation although the amplitude of the variation is smaller.