Eddy Energy Budget Research Articles

Parameterizing Eddy Buoyancy Fluxes Across Prograde Shelf/Slope Fronts Using a Slope-Aware GEOMETRIC Closure

Abstract Accurate parameterizations of eddy fluxes across prograde, buoyant shelf and slope currents are crucial to faithful predictions of the heat transfer and water mass transformations in high-latitude ocean environments in ocean climate models. In this work we evaluate several parameterization schemes of eddy buoyancy fluxes in predicting the mean state of prograde current systems using a set of coarse-resolution noneddying simulations, the solutions of which are compared against those of fine-resolution eddy-resolving simulations with nearly identical model configurations. It is found that coarse-resolution simulations employing the energetically constrained GEOMETRIC parameterization can accurately reconstruct the prograde mean flow state, provided that the suppression of eddy buoyancy diffusivity over the continental slope is accounted for. The prognostic subgrid-scale eddy energy budget in the GEOMETRIC parameterization scheme effectively captures the varying trend of the domain-wide eddy energy level in response to environmental changes, even though the energy budget is not specifically designed for a sloping-bottomed ocean. Local errors of the predicted eddy energy are present but do not compromise the predictive skill of the GEOMETRIC parameterization for prograde current systems. This work lays a foundation for improving the representation of prograde current systems in coarse-resolution ocean climate models. Significance Statement The objective of this study is to evaluate different methods for predicting ocean volume transports caused by ocean mesoscale eddies across continental margins. This is important because these transports play a critical role in exchanges between coastal seas and open oceans, but cannot be resolved or well represented in ocean climate simulations. This study emphasizes the importance of accounting for the influence of sloping seafloors in controlling the eddy transport across the continental slope. This study also highlights the necessity of simultaneously predicting the eddy energy for better representation of the cross-slope eddy transport in ocean climate simulations.

Scale‐Awareness in an Eddy Energy Constrained Mesoscale Eddy Parameterization

AbstractThere is an increasing interest in mesoscale eddy parameterizations that are scale‐aware, normally interpreted to mean that a parameterization does not require parameter recalibration as the model resolution changes. Here we examine whether Gent–McWilliams (GM) based version of GEOMETRIC, a mesoscale eddy parameterization that is constrained by a parameterized eddy energy budget, is scale‐aware in its energetics. It is generally known that GM‐based schemes severely damp out explicit eddies, so the parameterized component would be expected to dominate across resolutions, and we might expect a negative answer to the question of energetic scale‐awareness. A consideration of why GM‐based schemes damp out explicit eddies leads a suggestion for what we term a splitting procedure: a definition of a “large‐scale” field is sought, and the eddy‐induced velocity from the GM‐scheme is computed from and acts only on the large‐scale field, allowing explicit and parameterized components to co‐exist. Within the context of an idealized re‐entrant channel model of the Southern Ocean, evidence is provided that the GM‐based version of GEOMETRIC is scale‐aware in the energetics as long as we employ a splitting procedure. The splitting procedure also leads to an improved representation of mean states without detrimental effects on the explicit eddy motions.

Constraining an eddy energy dissipation rate due to relative wind stress for use in energy budget-based eddy parameterisations

Abstract. A geostrophic eddy energy dissipation rate due to the interaction of the large-scale wind field and mesoscale ocean currents, or relative wind stress, is derived here for use in eddy energy budget-based eddy parameterisations. We begin this work by analytically deriving a relative wind stress damping term and a baroclinic geostrophic eddy energy equation. The time evolution of this analytical eddy energy in response to relative wind stress damping is compared directly with a baroclinic eddy in a general circulation model for both anticyclones and cyclones. The dissipation of eddy energy is comparable between each model and eddy type, although the numerical model diverges from the analytical model at around day 150, likely due to the presence of non-linear baroclinic processes. A constrained dissipation rate due to relative wind stress is then proposed using terms from the analytical eddy energy budget. This dissipation rate depends on the potential energy of the eddy thermocline displacement, which also depends on eddy length scale. Using an array of ocean datasets, and computing two forms for the eddy length scale, a range of values for the dissipation rate are presented. The analytical dissipation rate is found to vary from 0.25 to 4 times that of a constant dissipation rate employed in previous studies. The dissipation rates are generally enhanced in the Southern Ocean but smaller in the western boundaries. This proposed dissipation rate offers a tool to parameterise the damping of total eddy energy in coarse resolution global climate models and may have implications for a wide range of climate processes.

Seasonal Variation of Intra-Seasonal Eddy Kinetic Energy along the East Australian Current

By using satellite altimeter observations and the eddy-permitting Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2), the seasonal variation of eddy kinetic energy (EKE) along the East Australian Current (EAC) is investigated. Both observations and ECCO2 outputs indicate active intra-seasonal EKE along the EAC path. The ECCO2 result reveals that the intra-seasonal EKE is mainly concentrated in the upper 500 m layer, and shows a prominent seasonal cycle, strong in austral summer and weak in austral winter. Eddy energy budget diagnosis reveals that the evolution of EKE is controlled by barotropic instability of the mean EAC. The seasonal variation of baroclinic instability is opposite to the barotropic instability variation, but of a much smaller magnitude. Further analysis indicates that the seasonal cycle of mesoscale signals in this region is related to the transport variability of the EAC.

On the Genesis of the South China Sea Mesoscale Eddies

The climatology of the mesoscale eddies in the upper layer of the South China Sea (SCS) is investigated for an understanding of its genesis using the outputs from a 1/12.5° ocean reanalysis. Employed is a recently developed multiscale energetics formalism on the basis of a multiscale window transform (MWT) and the theory of canonical transfer. Three scale windows, namely, background flow, mesoscale eddy and synoptic eddy, are differentiated, and fields on different scales are reconstructed henceforth. Diagnosis of the mesoscale eddy energy budget reveals that barotropic and baroclinic instabilities, wind work, advection and pressure work are essential ingredients of the eddy energy sources and sinks in the SCS, but their contributions vary from region to region. In the southwestern part of the SCS, the regional mesoscale eddy energy is mainly generated by barotropic instability, while in the northeastern SCS, baroclinic instability and the wind working directly on the eddies are the two dominant eddy generation processes. The eddies southwest of Taiwan are damped by outward energy transport via advection, while the decay of those southeast of Vietnam is due to pressure work. The three-scale framework also reveals that the interaction between the mesoscale eddies and higher-frequency synoptic eddies mainly serves as a sink for the mesoscale eddy energy in the SCS, except for the northeastern SCS, where significant inverse cascade of kinetic energy is found.

Random Movement of Mesoscale Eddies in the Global Ocean

AbstractIn this study we track and analyze eddy movement in the global ocean using 20 years of altimeter data and show that, in addition to the well-known westward propagation and slight polarity-based meridional deflections, mesoscale eddies also move randomly in all directions at all latitudes as a result of eddy–eddy interaction. The speed of this random eddy movement decreases with latitude and equals the baroclinic Rossby wave speed at about 25° of latitude. The tracked eddies are on average isotropic at mid- and high latitudes, but become noticeably more elongated in the zonal direction at low latitudes. Our analyses suggest a critical latitude of approximately 25° that separates the global ocean into a low-latitude anisotropic wavelike regime and a high-latitude isotropic turbulence regime. One important consequence of random eddy movement is that it results in lateral diffusion of eddy energy. The associated eddy energy diffusivity, estimated using two different methods, is found to be a function of latitude. The zonal-mean eddy energy diffusivity varies from over 1500 m2 s−1 at low latitudes to around 500 m2 s−1 at high latitudes, but significantly larger values are found in the eddy energy hotspots at all latitudes, in excess of 5000 m2 s−1. Results from this study have important implications for recently developed energetically consistent mesoscale eddy parameterization schemes which require solving the eddy energy budget.

Annual versus semi-annual eddy kinetic energy variability in the Celebes Sea

Eddy kinetic energy (EKE) in the Celebes Sea (CS) is investigated using a global, eddy-resolving, ocean general circulation model (OGCM) output. The OGCM simulation shows that a strong EKE is confined in the upper 300-m layer. The period of EKE variability varies with depth. In the 0–100-m layer, EKE has a distinct annual cycle that is strong in winter (December–February) and weak in summer (June–August). However, in the 100–300-m layer, semi-annual variation is dominant, which shows stronger EKE in spring and fall and weaker EKE in summer and winter. An eddy energy budget analysis reveals that the barotropic eddy energy conversion rate has a vertical structure similar to that of EKE. Compared to the barotropic eddy energy conversion rate, the baroclinic eddy energy conversion rate is much smaller and does not match the EKE vertical pattern. The budget analysis indicates that the variation in EKE in the CS is governed by barotropic instability of the background circulation. Further analysis reveals that the variation in the regional background circulation with depth is due to a combination of the forcing of the local monsoon and the Mindanao Current (MC) in the western tropical Pacific.

On energy exchanges between eddies and the mean flow in quasigeostrophic turbulence

We study the term in the eddy energy budget of continuously stratified quasigeostrophic turbulence that is responsible for energy extraction by eddies from the background mean flow. This term is a quadratic form, and we derive Euler–Lagrange equations describing its eigenfunctions and eigenvalues, the former being orthogonal in the energy inner product and the latter being real. The eigenvalues correspond to the instantaneous energy growth rate of the associated eigenfunction. We find analytical solutions in the Eady problem. We formulate a spectral method for computing eigenfunctions and eigenvalues, and compute solutions in Phillips-type and Charney-type problems. In all problems, instantaneous growth is possible at all horizontal scales in both inviscid problems and in problems with linear Ekman friction. We conjecture that transient growth at small scales is matched by linear transfer to decaying modes with the same horizontal structure, and we provide simulations supporting the plausibility of this hypothesis. In Charney-type problems, where the linear problem has exponentially growing modes at small scales, we expect net energy extraction from the mean flow to be unavoidable, with an associated nonlinear transfer of energy to dissipation.

Implementation of a Geometrically Informed and Energetically Constrained Mesoscale Eddy Parameterization in an Ocean Circulation Model

AbstractThe global stratification and circulation, as well as their sensitivities to changes in forcing, depend crucially on the representation of the mesoscale eddy field in a numerical ocean circulation model. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies—termed Geometry and Energetics of Ocean Mesoscale Eddies and Their Rectified Impact on Climate (GEOMETRIC)—is proposed and implemented in three-dimensional channel and sector models. The GEOMETRIC framework closes eddy buoyancy fluxes according to the standard Gent–McWilliams scheme but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, provided through a prognostic eddy energy budget evolving with the mean state. It is found that coarse-resolution models employing GEOMETRIC display broad agreement in the sensitivity of the circumpolar transport, meridional overturning circulation, and depth-integrated eddy energy pattern to surface wind stress as compared with analogous reference calculations at eddy-permitting resolutions. Notably, eddy saturation—the insensitivity of the time-mean circumpolar transport to changes in wind forcing—is found in the coarse-resolution sector model. In contrast, differences in the sensitivity of the depth-integrated eddy energy are found in model calculations in the channel experiments that vary the eddy energy dissipation, attributed to the simple prognostic eddy energy equation employed. Further improvements to the GEOMETRIC framework require a shift in focus from how to close for eddy buoyancy fluxes to the representation of eddy energetics.

Emergent eddy saturation from an energy constrained eddy parameterisation

The large-scale features of the global ocean circulation and the sensitivity of these features with respect to forcing changes are critically dependent upon the influence of the mesoscale eddy field. One such feature, observed in numerical simulations whereby the mesoscale eddy field is at least partially resolved, is the phenomenon of eddy saturation, where the time-mean circumpolar transport of the Antarctic Circumpolar Current displays relative insensitivity to wind forcing changes. Coarse-resolution models employing the Gent–McWilliams parameterisation with a constant Gent–McWilliams eddy transfer coefficient seem unable to reproduce this phenomenon. In this article, an idealised model for a wind-forced, zonally symmetric flow in a channel is used to investigate the sensitivity of the circumpolar transport to changes in wind forcing under different eddy closures. It is shown that, when coupled to a simple parameterised eddy energy budget, the Gent–McWilliams eddy transfer coefficient of the form described in Marshall et al. (2012) [A framework for parameterizing eddy potential vorticity fluxes, J. Phys. Oceanogr., vol. 42, 539–557], which includes a linear eddy energy dependence, produces eddy saturation as an emergent property.

Eddy saturation and frictional control of the Antarctic Circumpolar Current

AbstractThe Antarctic Circumpolar Current is the strongest current in the ocean and has a pivotal impact on ocean stratification, heat content, and carbon content. The circumpolar volume transport is relatively insensitive to surface wind forcing in models that resolve turbulent ocean eddies, a process termed “eddy saturation.” Here a simple model is presented that explains the physics of eddy saturation with three ingredients: a momentum budget, a relation between the eddy form stress and eddy energy, and an eddy energy budget. The model explains both the insensitivity of circumpolar volume transport to surface wind stress and the increase of eddy energy with wind stress. The model further predicts that circumpolar transport increases with increased bottom friction, a counterintuitive result that is confirmed in eddy‐permitting calculations. These results suggest an unexpected and important impact of eddy energy dissipation, through bottom drag or lee wave generation, on ocean stratification, ocean heat content, and potentially atmospheric CO2.

Observed 3D Structure, Generation, and Dissipation of Oceanic Mesoscale Eddies in the South China Sea.

Oceanic mesoscale eddies with horizontal scales of 50–300 km are the most energetic form of flows in the ocean. They are the oceanic analogues of atmospheric storms and are effective transporters of heat, nutrients, dissolved carbon, and other biochemical materials in the ocean. Although oceanic eddies have been ubiquitously observed in the world oceans since 1960s, our understanding of their three-dimensional (3D) structure, generation, and dissipation remains fragmentary due to lack of systematic full water-depth measurements. To bridge this knowledge gap, we designed and conducted a multi-months field campaign, called the South China Sea Mesoscale Eddy Experiment (S-MEE), in the northern South China Sea in 2013/2014. The S-MEE for the first time captured full-depth 3D structures of an anticyclonic and cyclonic eddy pair, which are characterized by a distinct vertical tilt of their axes. By observing the eddy evolution at an upstream versus downstream location and conducting an eddy energy budget analysis, the authors further proposed that generation of submesoscale motions most likely constitutes the dominant dissipation mechanism for the observed eddies.

The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

AbstractLow-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

Mesoscale Eddy Energy Locality in an Idealized Ocean Model

Abstract This paper investigates the energy budget of mesoscale eddies in wind-driven two-layer quasigeostrophic simulations. Intuitively, eddy energy can be generated, dissipated, and fluxed from place to place; regions where the budget balances generation and dissipation are “local” and regions that export or import large amounts of eddy energy are “nonlocal.” Many mesoscale parameterizations assume that statistics of the unresolved eddies behave as local functions of the resolved large scales, and studies that relate doubly periodic simulations to ocean patches must assume that the ocean patches have local energetics. This study derives and diagnoses the eddy energy budget in simulations of wind-driven gyres. To more closely approximate the ideas of subgrid-scale parameterization, the authors define the mean and eddies using a spatial filter rather than the more common time average. The eddy energy budget is strongly nonlocal over nearly half the domain in the simulations. In particular, in the intergyre region the eddies lose energy through interactions with the mean, and this energy loss can only be compensated by nonlocal flux of energy from elsewhere in the domain. This study also runs doubly periodic simulations corresponding to ocean patches from basin simulations. The eddy energy level of ocean patches in the basin simulations matches the level in the periodic simulations only in regions with local eddy energy budgets.

Energy budget and actual evapotranspiration of an arid oasis ecosystem: Palmyra (Syria)

Continuous measurements of evapotranspiration (LE) using eddy covariance method and energy budget were performed over more than 1 year above the heterogeneous canopy of an arid oasis ecosystem in the central Syrian desert. Irrigation practice was traditional flooding with a 28-day turn of water delivery. The work focused on seasonal variations of energy budget over a 2-year period with emphasis on effects of rainfall, wind speed and radiative budget and irrigation practice on evapotranspiration. A time lag of 3 days was observed between irrigation and transpiration response from the vegetation and maximum evapotranspiration was only 5 mm/day. Even with water input from irrigation, winter rainfall seems to have an important impact on LE: comparisons of two situations in June 2002 and June 2003 showed an increase of 13% in values of LE/Rn − G. In many situations averaged hourly values of evapotranspiration increased with wind speed up to 3 m/s, then decreased suggesting strong evaporative control from the vegetation. Results from the energy balance closure showed significant differences in the slope of H + LE against Rn − G relationships between cold and hot month which was explained by specific radiative budget of desert areas.

Storm Track Dynamics

This paper reviews the current state of observational, theoretical, and modeling knowledge of the midlatitude storm tracks of the Northern Hemisphere cool season. Observed storm track structures and variations form the first part of the review. The climatological storm track structure is described, and the seasonal, interannual, and interdecadal storm track variations are discussed. In particular, the observation that the Pacific storm track exhibits a marked minimum during midwinter when the background baroclinicity is strongest, and a new finding that storm tracks exhibit notable variations in their intensity on decadal timescales, are highlighted as challenges that any comprehensive storm track theory or model has to be able to address. Physical processes important to storm track dynamics make up the second part of the review. The roles played by baroclinic processes, linear instability, downstream development, barotropic modulation, and diabatic heating are discussed. Understanding of these processes forms the core of our current theoretical knowledge of storm track dynamics, and provides a context within which both observational and modeling results can be interpreted. The eddy energy budget is presented to show that all of these processes are important in the maintenance of the storm tracks. The final part of the review deals with the ability to model storm tracks. The success as well as remaining problems in idealized storm track modeling, which is based on a linearized dynamical system, are discussed. Perhaps on a more pragmatic side, it is pointed out that while the current generation of atmospheric general circulation models faithfully reproduce the climatological storm track structure, and to a certain extent, the seasonal and ENSO-related interannual variations of storm tracks, in-depth comparisons between observed and modeled storm track variations are still lacking.

The Structure of Baroclinic Wave Packets

Abstract In this paper, the three-dimensional structure of baroclinic wave packets is studied using composites from ECMWF reanalysis data. Eddy variances and covariances associated with wave packets are examined in terms of the eddy energy budget and wave activity and fluxes, and the large-scale, phase-independent flow component associated with wave packets is studied using composites of the low zonal wavenumber component of the flow. The results suggest that the sources of upper-level eddy energy–wave activity associated with the wave packets are located over the central and upstream portion of the wave packet, and the downstream part of the wave packet is entirely maintained by radiation of energy–wave activity fluxes from the upstream end. The results are entirely consistent with previous studies of the energetics of individual wave evolution cases. The composites also show that the basic flow response to eddy transports associated with the wave packets consists mainly of a poleward shift of the jet ne...

GCM and Observational Diagnoses of the Seasonal and Interannual Variations of the Pacific Storm Track during the Cool Season

Abstract Previous work has found that the Pacific storm track intensity during the cool season is negatively correlated with the upper-tropospheric jet strength. In the seasonal march, such a variation manifests itself as the midwinter suppression of the storm track intensity, while in interannual variations the storm track intensity during midwinter is found to be weaker during years in which the Pacific jet is particularly strong. In this paper, GCM simulations and observational data have been analyzed to shed light on the physical mechanisms responsible for such variations. By examining the eddy energy budget and eddy structure, two different mechanisms have been found to contribute to the reduction in storm track activity associated with increases in jet intensity and baroclinicity in midwinter. For the seasonal variations, it was found that the major difference between fall and midwinter lies in the changing role of diabatic heating. During fall and spring, diabatic heating acts to generate eddy pote...

Eddy–Mean Flow Interaction in the Gulf Stream at 68°W. Part I: Eddy Energetics

From June 1988 to August 1990 twelve tall, high-performance, current meter moorings measured the Gulf Stream's velocity and temperature fields at nominal depths of 400 m, 700 m, 1000 m, and 3500 m along three lines centered at 68°W. The overall eddy variability during the 26-month experiment was dominated by six large amplitude trough formation events, with each event lasting approximately one month. To determine the source(s) of energy for this eddy variability, the eddy energy budget is evaluated. Traditionally, the baroclinic conversion of mean potential energy to eddy potential energy is defined as a downgradient heat flux. However, because a nondivergent heat flux can be downgradient even under conditions in which there is no barolinic conversion occurring, a better, more dynamically correct definition of a baroclinic conversion rate is a downgradient horizontally divergent heat flux. The horizontally divergent heat flux component is estimated to be approximately half the full horizontal heat flux vector. Nevertheless, the resulting “dynamical” baroclinic conversion rate is found to be positive and nearly an order of magnitude larger than the weakly positive barotropic conversion rate. Because the large troughs at 68°W are formed through a baroclinic conversion process, the Gulf Stream jet is judged to be baroclinically unstable at 68°W.

Evaporation from Lake Kinneret: 1. Eddy correlation system measurements and energy budget estimates

Evaporation rates over Lake Kinneret were directly and continuously measured by means of the eddy correlation system (ECS) for the relatively long periods of 20 and 44 days at the beginning and end of the summer (first and second periods), respectively. Results clearly show that wind speed and stability of thermal stratification over the water surface strongly affect evaporation from the lake. Consequently, large differences in measured daily evaporation rates were apparent during both periods. Evaporation rates, estimated by the energy budget method (EBM) were compared with the corresponding values measured directly by the ECS. Large differences were found between the estimated hourly evaporation rates and the measured ones, in both the values and the timing of maximal rates. In addition, the EBM calculated negative nocturnal evaporation rates, while the ECS measured positive values. Differences between estimated and measured evaporation rates monitored on a daily basis were also noted. The differences were larger for the first period, characterized by sharav events denoting climatic instability. High evaporation rates resulting from strong winds were not depicted by EBM estimates. The distributions of hourly evaporation rates over a 24 hour period or of the daily rates over an entire period as estimated by the EBM were very similar to those of net radiation, while corresponding distributions resulting from ECS measurements were very similar to those of wind speed. The daily average evaporation rate for the first period, calculated by the EBM, was smaller than the corresponding value resulting from ECS measurements. When applied on a hourly basis, the EBM gave a much more similar estimate. For the second period, there were no significant differences between the daily average based on the computed values (for both daily and hourly intervals) and the corresponding average based on the measured ones.