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1
Gent, Peter R. "The Gent–McWilliams parameterization: 20/20 hindsight." Ocean Modelling 39, no. 1-2 (January 2011): 2–9. http://dx.doi.org/10.1016/j.ocemod.2010.08.002.
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Grooms, Ian. "A Gaussian-product stochastic Gent–McWilliams parameterization." Ocean Modelling 106 (October 2016): 27–43. http://dx.doi.org/10.1016/j.ocemod.2016.09.005.
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Smith, Richard D., and Peter R. Gent. "Anisotropic Gent–McWilliams Parameterization for Ocean Models." Journal of Physical Oceanography 34, no. 11 (November 1, 2004): 2541–64. http://dx.doi.org/10.1175/jpo2613.1.
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Abstract An anisotropic generalization of the Gent–McWilliams (GM) parameterization is presented for eddy-induced tracer transport and diffusion in ocean models, and it is implemented in an ocean general circulation model using a functional formalism to derive the spatial discretization. This complements the anisotropic viscosity parameterization recently developed by Smith and McWilliams. The anisotropic GM operator is potentially useful in both coarse- and high-resolution ocean models, and in this study the focus is on its application in high-resolution eddying solutions, for which it provides an adiabatic alternative to the more commonly used biharmonic horizontal diffusion operators. It is shown that realistically high levels of eddy energy can be simulated using harmonic anisotropic diffusion and friction operators. Isotropic forms can also be used, but these tend either to overly damp the solution when a large diffusion coefficient is used or to introduce unacceptable levels of numerical noise when a small coefficient is used. A series of numerical simulations of the North Atlantic Ocean are conducted at 0.2° resolution using anisotropic viscosity, anisotropic GM, and biharmonic mixing operators to investigate the effects of the anisotropic forms and to isolate changes in the solutions specifically associated with anisotropic GM. A high-resolution 0.1° simulation is then conducted using both anisotropic forms, and the results are compared with a similar run using biharmonic mixing. Modest improvements are seen in the mean wind-driven circulation with the anisotropic forms, but the largest effects are due to the anisotropic GM parameterization, which eliminates the spurious diapycnal diffusion inherent in horizontal tracer diffusion. This leads to significant improvements in the model thermohaline circulation, including the meridional heat transport, meridional overturning circulation, and deep-water formation and convection in the Labrador Sea.
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Cessi, Paola. "An Energy-Constrained Parameterization of Eddy Buoyancy Flux." Journal of Physical Oceanography 38, no. 8 (August 1, 2008): 1807–19. http://dx.doi.org/10.1175/2007jpo3812.1.
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Abstract A parameterization for eddy buoyancy fluxes for use in coarse-grid models is developed and tested against eddy-resolving simulations. The development is based on the assumption that the eddies are adiabatic (except near the surface) and the observation that the flux of buoyancy is affected by barotropic, depth-independent eddies. Like the previous parameterizations of Gent and McWilliams (GM) and Visbeck et al. (VMHS), the horizontal flux of a tracer is proportional to the local large-scale horizontal gradient of the tracer through a transfer coefficient assumed to be given by the product of a typical eddy velocity scale and a typical mixing length. The proposed parameterization differs from GM and VMHS in the selection of the eddy velocity scale, which is based on the kinetic energy balance of baroclinic eddies. The three parameterizations are compared to eddy-resolving computations in a variety of forcing configurations and for several sets of parameters. The VMHS and the energy balance parameterizations perform best in the tests considered here.
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Ivchenko, V. O., S. Danilov, and J. Schröter. "Comparison of the Effect of Parameterized Eddy Fluxes of Thickness and Potential Vorticity." Journal of Physical Oceanography 44, no. 9 (September 1, 2014): 2470–84. http://dx.doi.org/10.1175/jpo-d-13-0267.1.
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Abstract Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent–McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.
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Marshall, David P., and Alberto C. Naveira Garabato. "A Conjecture on the Role of Bottom-Enhanced Diapycnal Mixing in the Parameterization of Geostrophic Eddies." Journal of Physical Oceanography 38, no. 7 (July 1, 2008): 1607–13. http://dx.doi.org/10.1175/2007jpo3619.1.
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Abstract The parameterization of geostrophic eddies represents a large sink of energy in most ocean models, yet the ultimate fate of this eddy energy in the ocean remains unclear. The authors conjecture that a significant fraction of the eddy energy may be transferred to internal lee waves and oscillations over rough bottom topography, leading to bottom-enhanced diapycnal mixing. A range of circumstantial evidence in support of this conjecture is presented and discussed. The authors further propose a modification to the Gent and McWilliams eddy parameterization to account for the bottom-enhanced diapycnal mixing.
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Jansen, Malte F. "A note on: “A Gaussian-product stochastic Gent–McWilliams parameterization”." Ocean Modelling 110 (February 2017): 49–51. http://dx.doi.org/10.1016/j.ocemod.2016.12.005.
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Grooms, Ian, and William Kleiber. "Diagnosing, modeling, and testing a multiplicative stochastic Gent-McWilliams parameterization." Ocean Modelling 133 (January 2019): 1–10. http://dx.doi.org/10.1016/j.ocemod.2018.10.009.
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Gent, Peter R., and Gokhan Danabasoglu. "Response to Increasing Southern Hemisphere Winds in CCSM4." Journal of Climate 24, no. 19 (October 2011): 4992–98. http://dx.doi.org/10.1175/jcli-d-10-05011.1.
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Results from two perturbation experiments using the Community Climate System Model version 4 where the Southern Hemisphere zonal wind stress is increased are described. It is shown that the ocean response is in accord with experiments using much-higher-resolution ocean models that do not use an eddy parameterization. The key to obtaining an appropriate response in the coarse-resolution climate model is to specify a variable coefficient in the Gent and McWilliams eddy parameterization, rather than a constant value. This result contrasts with several recent papers that have suggested that coarse-resolution climate models cannot obtain an appropriate response.
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Fan, Yalin, and Stephen M. Griffies. "Impacts of Parameterized Langmuir Turbulence and Nonbreaking Wave Mixing in Global Climate Simulations." Journal of Climate 27, no. 12 (June 5, 2014): 4752–75. http://dx.doi.org/10.1175/jcli-d-13-00583.1.
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Abstract The impacts of parameterized upper-ocean wave mixing on global climate simulations are assessed through modification to Large et al.’s K-profile ocean boundary layer parameterization (KPP) in a coupled atmosphere–ocean–wave global climate model. The authors consider three parameterizations and focus on impacts to high-latitude ocean mixed layer depths and related ocean diagnostics. The McWilliams and Sullivan parameterization (MS2000) adds a Langmuir turbulence enhancement to the nonlocal component of KPP. It is found that the Langmuir turbulence–induced mixing provided by this parameterization is too strong in winter, producing overly deep mixed layers, and of minimal impact in summer. The later Smyth et al. parameterization modifies MS2000 by adding a stratification effect to restrain the turbulence enhancement under weak stratification conditions (e.g., winter) and to magnify the enhancement under strong stratification conditions. The Smyth et al. scheme improves the simulated winter mixed layer depth in the simulations herein, with mixed layer deepening in the Labrador Sea and shoaling in the Weddell and Ross Seas. Enhanced vertical mixing through parameterized Langmuir turbulence, coupled with enhanced lateral transport associated with parameterized mesoscale and submesoscale eddies, is found to be a key element for improving mixed layer simulations. Secondary impacts include strengthening the Atlantic meridional overturning circulation and reducing the Antarctic Circumpolar Current. The Qiao et al. nonbreaking wave parameterization is the third scheme assessed here. It adds a wave orbital velocity to the Reynolds stress calculation and provides the strongest summer mixed layer deepening in the Southern Ocean among the three experiments, but with weak impacts during winter.
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Canuto, V. M., Y. Cheng, M. S. Dubovikov, A. M. Howard, and A. Leboissetier. "Parameterization of Mixed Layer and Deep-Ocean Mesoscales including Nonlinearity." Journal of Physical Oceanography 48, no. 3 (March 2018): 555–72. http://dx.doi.org/10.1175/jpo-d-16-0255.1.
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AbstractIn 2011, Chelton et al. carried out a comprehensive census of mesoscales using altimetry data and reached the following conclusions: “essentially all of the observed mesoscale features are nonlinear” and “mesoscales do not move with the mean velocity but with their own drift velocity,” which is “the most germane of all the nonlinear metrics.” Accounting for these results in a mesoscale parameterization presents conceptual and practical challenges since linear analysis is no longer usable and one needs a model of nonlinearity. A mesoscale parameterization is presented that has the following features: 1) it is based on the solutions of the nonlinear mesoscale dynamical equations, 2) it describes arbitrary tracers, 3) it includes adiabatic (A) and diabatic (D) regimes, 4) the eddy-induced velocity is the sum of a Gent and McWilliams (GM) term plus a new term representing the difference between drift and mean velocities, 5) the new term lowers the transfer of mean potential energy to mesoscales, 6) the isopycnal slopes are not as flat as in the GM case, 7) deep-ocean stratification is enhanced compared to previous parameterizations where being more weakly stratified allowed a large heat uptake that is not observed, 8) the strength of the Deacon cell is reduced. The numerical results are from a stand-alone ocean code with Coordinated Ocean-Ice Reference Experiment I (CORE-I) normal-year forcing.
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Viebahn, Jan, Daan Crommelin, and Henk Dijkstra. "Toward a Turbulence Closure Based on Energy Modes." Journal of Physical Oceanography 49, no. 4 (April 2019): 1075–97. http://dx.doi.org/10.1175/jpo-d-18-0117.1.
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AbstractA new approach to parameterizing subgrid-scale processes is proposed: The impact of the unresolved dynamics on the resolved dynamics (i.e., the eddy forcing) is represented by a series expansion in dynamical spatial modes that stem from the energy budget of the resolved dynamics. It is demonstrated that the convergence in these so-called energy modes is faster by orders of magnitude than the convergence in Fourier-type modes. Moreover, a novel way to test parameterizations in models is explored. The resolved dynamics and the corresponding instantaneous eddy forcing are defined via spatial filtering that accounts for the representation error of the equations of motion on the low-resolution model grid. In this way, closures can be tested within the high-resolution model, and the effects of different parameterizations related to different energy pathways can be isolated. In this study, the focus is on parameterizations of the baroclinic energy pathway. The corresponding standard closure in ocean models, the Gent–McWilliams (GM) parameterization, is also tested, and it is found that the GM field acts like a stabilizing direction in phase space. The GM field does not project well on the eddy forcing and hence fails to excite the model’s intrinsic low-frequency variability, but it is able to stabilize the model.
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Nakamura, Mototaka, and Yi Chao. "On the Eddy Isopycnal Thickness Diffusivity of the Gent–McWilliams Subgrid Mixing Parameterization." Journal of Climate 13, no. 2 (January 2000): 502–10. http://dx.doi.org/10.1175/1520-0442(2000)013<0502:oteitd>2.0.co;2.
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Bachman, Scott D. "The GM＋E closure: A framework for coupling backscatter with the Gent and McWilliams parameterization." Ocean Modelling 136 (April 2019): 85–106. http://dx.doi.org/10.1016/j.ocemod.2019.02.006.
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Manucharyan, Georgy E., Andrew F. Thompson, and Michael A. Spall. "Eddy Memory Mode of Multidecadal Variability in Residual-Mean Ocean Circulations with Application to the Beaufort Gyre." Journal of Physical Oceanography 47, no. 4 (April 2017): 855–66. http://dx.doi.org/10.1175/jpo-d-16-0194.1.
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AbstractMesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics are poorly understood. Climate models commonly use the Gent–McWilliams (GM) parameterization, taking the eddy streamfunction to be proportional to an isopycnal slope s and an eddy diffusivity K. This local-in-time parameterization leads to exponential equilibration of currents. Here, an idealized, eddy-resolving Beaufort Gyre model is used to demonstrate that carries a finite memory of past ocean states, violating a key GM assumption. As a consequence, an equilibrating gyre follows a spiral sink trajectory implying the existence of a damped mode of variability—the eddy memory (EM) mode. The EM mode manifests during the spinup as a 15% overshoot in isopycnal slope (2000 km3 freshwater content overshoot) and cannot be explained by the GM parameterization. An improved parameterization is developed, such that is proportional to an effective isopycnal slope , carrying a finite memory γ of past slopes. Introducing eddy memory explains the model results and brings to light an oscillation with a period ≈ 50 yr, where the eddy diffusion time scale TE ~ 10 yr and γ ≈ 6 yr are diagnosed from the eddy-resolving model. The EM mode increases the Ekman-driven gyre variance by γ/TE ≈ 50% ± 15%, a fraction that stays relatively constant despite both time scales decreasing with increased mean forcing. This study suggests that the EM mode is a general property of rotating turbulent flows and highlights the need for better observational constraints on transient eddy field characteristics.
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Xu, Yongfu, Shigeaki Aoki, and Koh Harada. "Sensitivity of the Simulated Distributions of Water Masses, CFCs, and Bomb 14C to Parameterizations of Mesoscale Tracer Transports in a Model of the North Pacific." Journal of Physical Oceanography 36, no. 3 (March 1, 2006): 273–85. http://dx.doi.org/10.1175/jpo2854.1.
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Abstract A basinwide ocean general circulation model of the North Pacific Ocean is used to study the sensitivity of the simulated distributions of water masses, chlorofluorocarbons (CFCs), and bomb carbon-14 isotope (14C) to parameterizations of mesoscale tracer transports. Five simulations are conducted, including a run with the traditional horizontal mixing scheme and four runs with the isopycnal transport parameterization of Gent and McWilliams (GM). The four GM runs use different values of isopycnal and skew diffusivities. Simulated results show that the GM mixing scheme can help to form North Pacific Intermediate Water (NPIW). Greater isopycnal diffusivity enhances formation of NPIW. Although greater skew diffusivity can also generate NPIW, it makes the subsurface too fresh. Results from simulations of CFC uptake show that greater isopycnal diffusivity generates the best results relative to observations in the western North Pacific. The model generally underestimates the inventories of CFCs in the western North Pacific. The results from simulations of bomb 14C reproduce some observed features. Greater isopycnal diffusivity generates a longitudinal gradient of the inventory of bomb 14C from west to east, whereas greater skew diffusivity makes it reversed. It is considered that the ratio of isopycnal diffusivity to skew diffusivity is important. An increase in isopycnal diffusivity increases storage of passive tracers in the subtropical gyre.
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Restrepo, Juan M. "Wave Breaking Dissipation in the Wave-Driven Ocean Circulation." Journal of Physical Oceanography 37, no. 7 (July 1, 2007): 1749–63. http://dx.doi.org/10.1175/jpo3099.1.
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Abstract If wave breaking modifies the Lagrangian fluid paths by inducing an uncertainty in the orbit itself and this uncertainty on wave motion time scales is observable as additive noise, it is shown that within the context of a wave–current interaction model for basin- and shelf-scale motions it persists on long time scales. The model of McWilliams et al. provides the general framework for the dynamics of wave–current interactions. In addition to the deterministic part, the vortex force, which couples the total flow vorticity to the residual flow due to the waves, will have a part that is associated with the dissipative mechanism. At the same time the wave field will experience dissipation, and tracer advection is affected by the appearance of a dissipative term in the Stokes drift velocity. Consistency leads to other dynamic consequences: the boundary conditions are modified to take into account the diffusive process and proper mass/momentum balances at the surface of the ocean. In addition to formulating how a wave–current interaction model is modified by the presence of short-time events that induce dissipation, this study proposes a stochastic parameterization of dissipation. Its relation to other alternative parameterizations is given. Two focal reasons make stochastic parameterizations attractive: one can draw from extensive practical modeling experience in other fields, and it ties in a very natural way to a wealth of observational data via statistics.
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Rühs, Siren, Victor Zhurbas, Inga M. Koszalka, Jonathan V. Durgadoo, and Arne Biastoch. "Eddy Diffusivity Estimates from Lagrangian Trajectories Simulated with Ocean Models and Surface Drifter Data—A Case Study for the Greater Agulhas System." Journal of Physical Oceanography 48, no. 1 (January 2018): 175–96. http://dx.doi.org/10.1175/jpo-d-17-0048.1.
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AbstractThe Lagrangian analysis of sets of particles advected with the flow fields of ocean models is used to study connectivity, that is, exchange pathways, time scales, and volume transports, between distinct oceanic regions. One important factor influencing the dispersion of fluid particles and, hence, connectivity is the Lagrangian eddy diffusivity, which quantifies the influence of turbulent processes on the rate of particle dispersal. Because of spatial and temporal discretization, turbulence is not fully resolved in modeled velocities, and the concept of eddy diffusivity is used to parameterize the impact of unresolved processes. However, the relations between observation- and model-based Lagrangian eddy diffusivity estimates, as well as eddy parameterizations, are not clear. This study presents an analysis of the spatially variable near-surface lateral eddy diffusivity estimates obtained from Lagrangian trajectories simulated with 5-day mean velocities from an eddy-resolving ocean model (INALT01) for the Agulhas system. INALT01 features diffusive regimes for dynamically different regions, some of which exhibit strong suppression of eddy mixing by mean flow, and it is consistent with the pattern and magnitude of drifter-based eddy diffusivity estimates. Using monthly mean velocities decreases the estimated diffusivities less than eddy kinetic energy, supporting the idea that large and persistent eddy features dominate eddy diffusivities. For a noneddying ocean model (ORCA05), Lagrangian eddy diffusivities are greatly reduced, particularly when the Gent and McWilliams parameterization of mesoscale eddies is employed.
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Scholz, Patrick, Dmitry Sidorenko, Ozgur Gurses, Sergey Danilov, Nikolay Koldunov, Qiang Wang, Dmitry Sein, Margarita Smolentseva, Natalja Rakowsky, and Thomas Jung. "Assessment of the Finite-volumE Sea ice-Ocean Model (FESOM2.0) – Part 1: Description of selected key model elements and comparison to its predecessor version." Geoscientific Model Development 12, no. 11 (November 25, 2019): 4875–99. http://dx.doi.org/10.5194/gmd-12-4875-2019.
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Abstract. The evaluation and model element description of the second version of the unstructured-mesh Finite-volumE Sea ice-Ocean Model (FESOM2.0) are presented. The new version of the model takes advantage of the finite-volume approach, whereas its predecessor version, FESOM1.4 was based on the finite-element approach. The model sensitivity to arbitrary Lagrangian–Eulerian (ALE) linear and nonlinear free-surface formulation, Gent–McWilliams eddy parameterization, isoneutral Redi diffusion and different vertical mixing schemes is documented. The hydrographic biases, large-scale circulation, numerical performance and scalability of FESOM2.0 are compared with its predecessor, FESOM1.4. FESOM2.0 shows biases with a magnitude comparable to FESOM1.4 and simulates a more realistic Atlantic meridional overturning circulation (AMOC). Compared to its predecessor, FESOM2.0 provides clearly defined fluxes and a 3 times higher throughput in terms of simulated years per day (SYPD). It is thus the first mature global unstructured-mesh ocean model with computational efficiency comparable to state-of-the-art structured-mesh ocean models. Other key elements of the model and new development will be described in follow-up papers.
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Mak, J., J. R. Maddison, D. P. Marshall, and D. R. Munday. "Implementation of a Geometrically Informed and Energetically Constrained Mesoscale Eddy Parameterization in an Ocean Circulation Model." Journal of Physical Oceanography 48, no. 10 (October 2018): 2363–82. http://dx.doi.org/10.1175/jpo-d-18-0017.1.
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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.
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Poulsen, Mads B., Markus Jochum, James R. Maddison, David P. Marshall, and Roman Nuterman. "A Geometric Interpretation of Southern Ocean Eddy Form Stress." Journal of Physical Oceanography 49, no. 10 (October 2019): 2553–70. http://dx.doi.org/10.1175/jpo-d-18-0220.1.
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AbstractAn interpretation of eddy form stress via the geometry described by the Eliassen–Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape, and orientation with respect to the mean flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent–McWilliams eddy transfer coefficient that depends on eddy energy and a nondimensional geometric parameter α, bounded in magnitude by unity. The parameter α expresses the efficiency by which eddies exchange energy with baroclinic mean flow via along-gradient eddy buoyancy flux—a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. The eddy efficiency is subject to pronounced vertical structure and is maximum at ~3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.
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Colas, François, Xavier Capet, James C. McWilliams, and Zhijin Li. "Mesoscale Eddy Buoyancy Flux and Eddy-Induced Circulation in Eastern Boundary Currents." Journal of Physical Oceanography 43, no. 6 (June 1, 2013): 1073–95. http://dx.doi.org/10.1175/jpo-d-11-0241.1.
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Abstract A dynamical interpretation is made of the mesoscale eddy buoyancy fluxes in the Eastern Boundary Currents off California and Peru–Chile, based on regional equilibrium simulations. The eddy fluxes are primarily shoreward and upward across a swath several hundred kilometers wide in the upper ocean; as such they serve to balance mean offshore air–sea heating and coastal upwelling. In the stratified interior the eddy fluxes are consistent with the adiabatic hypothesis associated with a mean eddy-induced velocity advecting mean buoyancy and tracers. Furthermore, with a suitable gauge choice, the horizontal fluxes are almost entirely aligned with the mean horizontal buoyancy gradient, consistent with the advective parameterization scheme of Gent and McWilliams. The associated diffusivity κ is surface intensified, matching the vertical stratification profile. The fluxes span the across-shore band of high eddy energy, but their alongshore structure is unresolved because of sampling limitations. In the surface layer the eddy flux is significantly diabatic with a shallow eddy-induced circulation cell and downgradient lateral diapycnal flux. The dominant eddy generation process is baroclinic instability, but there are significant regional differences between the upwelling systems in the flux and κ that are not consistent with simple instability theory.
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Saenz, Juan A., Qingshan Chen, and Todd Ringler. "Prognostic Residual Mean Flow in an Ocean General Circulation Model and its Relation to Prognostic Eulerian Mean Flow." Journal of Physical Oceanography 45, no. 9 (September 2015): 2247–60. http://dx.doi.org/10.1175/jpo-d-15-0024.1.
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AbstractRecent work has shown that taking the thickness-weighted average (TWA) of the Boussinesq equations in buoyancy coordinates results in exact equations governing the prognostic residual mean flow where eddy–mean flow interactions appear in the horizontal momentum equations as the divergence of the Eliassen–Palm flux tensor (EPFT). It has been proposed that, given the mathematical tractability of the TWA equations, the physical interpretation of the EPFT, and its relation to potential vorticity fluxes, the TWA is an appropriate framework for modeling ocean circulation with parameterized eddies. The authors test the feasibility of this proposition and investigate the connections between the TWA framework and the conventional framework used in models, where Eulerian mean flow prognostic variables are solved for. Using the TWA framework as a starting point, this study explores the well-known connections between vertical transfer of horizontal momentum by eddy form drag and eddy overturning by the bolus velocity, used by Greatbatch and Lamb and Gent and McWilliams to parameterize eddies. After implementing the TWA framework in an ocean general circulation model, the analysis is verified by comparing the flows in an idealized Southern Ocean configuration simulated using the TWA and conventional frameworks with the same mesoscale eddy parameterization.
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Lucas, M. A., J. J. Hirschi, J. D. Stark, and J. Marotzke. "The Response of an Idealized Ocean Basin to Variable Buoyancy Forcing." Journal of Physical Oceanography 35, no. 5 (May 1, 2005): 601–15. http://dx.doi.org/10.1175/jpo2710.1.
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Abstract The response of an idealized ocean basin to variable buoyancy forcing is examined. A general circulation model that employs a Gent–McWilliams mixing parameterization is forced by a zonally constant restoring surface temperature profile, which varies with latitude and time over a period P. In each experiment, 17 different values of P are studied, ranging from 6 months to 32 000 yr. The model's meridional overturning circulation (MOC) exhibits a very strong response on all time scales greater than 15 yr, up to and including the longest forcing time scales examined. The peak-to-peak values of the MOC oscillations reach up to 125% of the steady-state maximum MOC and exhibit resonance-like behavior, with a maximum at centennial to millennial forcing periods (depending on the vertical diffusivity). This resonance-like behavior stems from the existence of two adjustment time scales, one of which is set by the vertical diffusion and the other of which is set by the basin width. Furthermore, the linearity of the response as well as its lag with the forcing varies with the forcing period. The considerable deviation from the quasi-equilibrium response at all time scales above 15 yr is surprising and suggests a potentially important role of the ocean circulation for climate, even at Milankovich time scales.
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Lüschow, Veit, Jin-Song von Storch, and Jochem Marotzke. "Diagnosing the Influence of Mesoscale Eddy Fluxes on the Deep Western Boundary Current in the 1/10° STORM/NCEP Simulation." Journal of Physical Oceanography 49, no. 3 (March 2019): 751–64. http://dx.doi.org/10.1175/jpo-d-18-0103.1.
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AbstractUsing a 0.1° ocean model, this paper establishes a consistent picture of the interaction of mesoscale eddy density fluxes with the geostrophic deep western boundary current (DWBC) in the Atlantic between 26°N and 20°S. Above the DWBC core (the level of maximum southward flow, ~2000-m depth), the eddies flatten isopycnals and hence decrease the potential energy of the mean flow, which agrees with their interpretation and parameterization in the Gent–McWilliams framework. Below the core, even though the eddy fluxes have a weaker magnitude, they systematically steepen isopycnals and thus feed potential energy to the mean flow, which contradicts common expectations. These two vertically separated eddy regimes are found through an analysis of the eddy density flux divergence in stream-following coordinates. In addition, pathways of potential energy in terms of the Lorenz energy cycle reveal this regime shift. The twofold eddy effect on density is balanced by an overturning in the plane normal to the DWBC. Its direction is clockwise (with upwelling close to the shore and downwelling further offshore) north of the equator. In agreement with the sign change in the Coriolis parameter, the overturning changes direction to anticlockwise south of the equator. Within the domain covered in this study, except in a narrow band around the equator, this scenario is robust along the DWBC.
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Couvelard, Xavier, Florian Lemarié, Guillaume Samson, Jean-Luc Redelsperger, Fabrice Ardhuin, Rachid Benshila, and Gurvan Madec. "Development of a two-way-coupled ocean–wave model: assessment on a global NEMO(v3.6)–WW3(v6.02) coupled configuration." Geoscientific Model Development 13, no. 7 (July 10, 2020): 3067–90. http://dx.doi.org/10.5194/gmd-13-3067-2020.
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Abstract. This paper describes the implementation of a coupling between a three-dimensional ocean general circulation model (NEMO) and a wave model (WW3) to represent the interactions of upper-oceanic flow dynamics with surface waves. The focus is on the impact of such coupling on upper-ocean properties (temperature and currents) and mixed layer depth (MLD) at global eddying scales. A generic coupling interface has been developed, and the NEMO governing equations and boundary conditions have been adapted to include wave-induced terms following the approach of McWilliams et al. (2004) and Ardhuin et al. (2008). In particular, the contributions of Stokes–Coriolis, vortex, and surface pressure forces have been implemented on top of the necessary modifications of the tracer–continuity equation and turbulent closure scheme (a one-equation turbulent kinetic energy – TKE – closure here). To assess the new developments, we perform a set of sensitivity experiments with a global oceanic configuration at 1/4∘ resolution coupled with a wave model configured at 1/2∘ resolution. Numerical simulations show a global increase in wind stress due to the interaction with waves (via the Charnock coefficient), particularly at high latitudes, resulting in increased surface currents. The modifications brought to the TKE closure scheme and the inclusion of a parameterization for Langmuir turbulence lead to a significant increase in the mixing, thus helping to deepen the MLD. This deepening is mainly located in the Southern Hemisphere and results in reduced sea surface currents and temperatures.
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Canuto, V. M., and Y. Cheng. "ACC Subduction by Mesoscales." Journal of Physical Oceanography 49, no. 12 (December 2019): 3263–72. http://dx.doi.org/10.1175/jpo-d-19-0043.1.
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AbstractThe mesoscale contribution to subduction in the Southern Ocean was studied by Sallée and Rintoul in 2011 (SR11) using the following mesoscale model. The adiabatic (A) regime was modeled with the Gent–McWilliams streamfunction, the diabatic (D) regime was modeled with tapering functions, the D–A interface was taken to be at the mixed layer depth, and the mesoscale diffusivity either was a constant or was given by a 2D model. Since the resulting subductions were an order of magnitude smaller than the data of ±200 m yr−1 as reported by Mazloff et al. in 2010, SR11 showed that if, instead of the above model-dependent mesoscale diffusivities, they employed the ones reported in 2008 by Sallée et al. from surface drifter observations, the subductions compared significantly better to the data. On those grounds, SR11 suggested a 10-fold increase of the diffusivity. In this work, we suggest that, since the mesoscale diffusivity is but one component of a much large mesoscale parameterization, one should first assess the latter’s overall performance followed by an assessment of the predicted Antarctic Circumpolar Current (ACC) subduction. We employ the mesoscale model formulated by Canuto et al. in 2018 and 2019 that includes recent theoretical and observational advances and that was assessed against a variety of data, including the output of 17 other OGCMs. The ACC diffusivities compare well to drifter data from Sallée et al., and the ACC subduction rates are in agreement with the data.
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Müller, S. A., F. Joos, N. R. Edwards, and T. F. Stocker. "Water Mass Distribution and Ventilation Time Scales in a Cost-Efficient, Three-Dimensional Ocean Model." Journal of Climate 19, no. 21 (November 1, 2006): 5479–99. http://dx.doi.org/10.1175/jcli3911.1.
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Abstract A cost-efficient, seasonally forced three-dimensional frictional geostrophic balance ocean model (Bern3D) has been developed that features isopycnal diffusion and Gent–McWilliams transport parameterization, 32 depth layers, and an implicit numerical scheme for the vertical diffusion. It has been tuned toward observed chlorofluorocarbon (CFC-11) inventories and deep ocean radiocarbon signatures to reproduce the ventilation time scales of the thermocline and the deep ocean. Model results are consistent with the observed large-scale distributions of temperature, salinity, natural and bomb-produced radiocarbon, CFC-11, anthropogenic carbon, 39Ar/Ar, and estimates of the meridional heat transport. Root-mean-square errors for the temperature and salinity fields are 1 K and 0.2 psu, comparable to results from the Ocean Carbon-Cycle Model Intercomparison Project. Global inventories of CFC-11 and anthropogenic carbon agree closely with observation-based estimates. Model weaknesses include a too-weak formation and propagation of Antarctic Intermediate Water and of North Atlantic Deep Water. The model has been applied to quantify the recent carbon balance, surface-to-deep transport mechanisms, and the importance of vertical resolution for deep equatorial upwelling. Advection is a dominant surface-to-deep transport mechanism, whereas explicit diapycnal mixing is of little importance for passive tracers and contributes less than 3% to the modeled CFC-11 inventory in the Indo-Pacific. Decreasing the vertical resolution from 32 to 8 layers causes deep equatorial upwelling to increase by more than a factor of 4. Modeled ocean uptake of anthropogenic carbon is 19.7 GtonC over the decade from 1993 to 2003, comparable to an estimate from atmospheric oxygen data of 22.4 ± 6.1 GtonC.
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Deacu, Daniel, and Paul G. Myers. "Effect of a Variable Eddy Transfer Coefficient in an Eddy-Permitting Model of the Subpolar North Atlantic Ocean." Journal of Physical Oceanography 35, no. 3 (March 1, 2005): 289–307. http://dx.doi.org/10.1175/jpo-2674.1.
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Abstract The effect of using a variable eddy transfer coefficient for the Gent–McWilliams (GM) parameterization in a (1/3)°-resolution ocean model of the subpolar North Atlantic Ocean is investigated. Results from four experiments with different implementations of this coefficient are compared among themselves as well as with two control experiments. A series of improvements have been obtained in all of the experiments that use a low level of explicit horizontal tracer diffusion. These include a better representation of the overflow waters originating from the Nordic seas, leading to a more realistic deep western boundary current and to increased eddy activity in the deep ocean in the eastern North Atlantic. In the same experiments, the GM velocities “help” the Labrador Sea Water to spread from the deep convection region to the currents that surround it without incurring significant spurious diapycnal mixing. Thus, two classical pathways for the spreading of this water are established. Moreover, the simulated Labrador Current and the near-surface circulation in the eastern North Atlantic are in better agreement with flow patterns inferred from observations. The increased release of available potential energy obtained in the experiments with variable eddy transfer coefficients is responsible for the simulation of a flow that varies less in time. An overly strong countercurrent still occurs in the Labrador Sea in these experiments, and it has a negative impact on the pathway of the North Atlantic Current in the “Northwest Corner” and on the hydrography of the Labrador Sea. Nonetheless and overall, the use of the variable eddy transfer coefficient has led to better representations of the general circulation and hydrography in the subpolar North Atlantic.
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Sallée, Jean-Baptiste, Kevin Speer, Steve Rintoul, and S. Wijffels. "Southern Ocean Thermocline Ventilation." Journal of Physical Oceanography 40, no. 3 (March 1, 2010): 509–29. http://dx.doi.org/10.1175/2009jpo4291.1.
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Abstract An approximate mass (volume) budget in the surface layer of the Southern Ocean is used to investigate the intensity and regional variability of the ventilation process, discussed here in terms of subduction and upwelling. Ventilation resulting from Ekman pumping is estimated from satellite winds, the geostrophic mean component is assessed from a climatology strengthened with Argo data, and the eddy-induced advection is included via the parameterization of Gent and McWilliams, together with eddy mixing estimates. All three components contribute significantly to ventilation. Finally, the seasonal cycle of the upper ocean is resolved using Argo data. The circumpolar-averaged circulation shows an upwelling in the Antarctic Intermediate Water (AAIW) density classes, which is carried north into a zone of dense Subantarctic Mode Water (SAMW) subduction. Although no consistent net production is found in the light SAMW density classes, a large subduction of Subtropical Mode Water (STMW) is observed. The STMW area is fed by convergence of a southward and a northward residual meridional circulation. The eddy-induced contribution is important for the water mass transport in the vicinity of the Antartic Circumpolar Current. It balances the horizontal northward Ekman transport as well as the vertical Ekman pumping. While the circumpolar-averaged upper cell structure is consistent with the average surface fluxes, it hides strong longitudinal regional variations and does not represent any local regime. Subduction shows strong regional variability with bathymetrically constrained hotspots of large subduction. These hotspots are consistent with the interior potential vorticity structure and circulation in the thermocline. Pools of SAMW and AAIW of different densities are found along the circumpolar belt in association with the regional pattern of subduction and interior circulation.
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Eden, Carsten, Richard J. Greatbatch, and Jürgen Willebrand. "A Diagnosis of Thickness Fluxes in an Eddy-Resolving Model." Journal of Physical Oceanography 37, no. 3 (March 1, 2007): 727–42. http://dx.doi.org/10.1175/jpo2987.1.
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Abstract Output from an eddy-resolving model of the North Atlantic Ocean is used to estimate values for the thickness diffusivity κ appropriate to the Gent and McWilliams parameterization. The effect of different choices of rotational eddy fluxes on the estimated κ is discussed. Using the raw fluxes (no rotational flux removed), large negative values (exceeding −5000 m2 s−1) of κ are diagnosed locally, particularly in the Gulf Stream region and in the equatorial Atlantic. Removing a rotational flux based either on the suggestion of Marshall and Shutts or the more general theory of Medvedev and Greatbatch leads to a reduction of the negative values, but they are still present. The regions where κ < 0 correspond to regions where eddies are acting to increase, rather than decrease (as in baroclinic instability) the mean available potential energy. In the subtropical gyre, κ ranges between 500 and 2000 m2 s−1, rapidly decreasing to zero below the thermocline in all cases. Rotational fluxes and κ are also estimated using an optimization technique. In this case, |κ| can be reduced or increased by construction, but the regions where κ < 0 are still present and the optimized rotational fluxes also remain similar to a priori values given by the theoretical considerations. A previously neglected component (ν) of the bolus velocity is associated with the horizontal flux of buoyancy along, rather than across, the mean buoyancy contours. The ν component of the bolus velocity is interpreted as a streamfunction for eddy-induced advection, rather than diffusion, of mean isopycnal layer thickness, showing up when the lateral eddy fluxes cannot be described by isotropic diffusion only. All estimates show a similar large-scale pattern for ν, implying westward advection of isopycnal thickness over much of the subtropical gyre. Comparing ν with a mean streamfunction shows that it is about 10% of the mean in midlatitudes and even larger than the mean in the Tropics.
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Juricke, Stephan, Tim N. Palmer, and Laure Zanna. "Stochastic Subgrid-Scale Ocean Mixing: Impacts on Low-Frequency Variability." Journal of Climate 30, no. 13 (July 2017): 4997–5019. http://dx.doi.org/10.1175/jcli-d-16-0539.1.
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In global ocean models, the representation of small-scale, high-frequency processes considerably influences the large-scale oceanic circulation and its low-frequency variability. This study investigates the impact of stochastic perturbation schemes based on three different subgrid-scale parameterizations in multidecadal ocean-only simulations with the ocean model NEMO at 1° resolution. The three parameterizations are an enhanced vertical diffusion scheme for unstable stratification, the Gent–McWilliams (GM) scheme, and a turbulent kinetic energy mixing scheme, all commonly used in state-of-the-art ocean models. The focus here is on changes in interannual variability caused by the comparatively high-frequency stochastic perturbations with subseasonal decorrelation time scales. These perturbations lead to significant improvements in the representation of low-frequency variability in the ocean, with the stochastic GM scheme showing the strongest impact. Interannual variability of the Southern Ocean eddy and Eulerian streamfunctions is increased by an order of magnitude and by 20%, respectively. Interannual sea surface height variability is increased by about 20%–25% as well, especially in the Southern Ocean and in the Kuroshio region, consistent with a strong underestimation of interannual variability in the model when compared to reanalysis and altimetry observations. These results suggest that enhancing subgrid-scale variability in ocean models can improve model variability and potentially its response to forcing on much longer time scales, while also providing an estimate of model uncertainty.
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Ardhuin, Fabrice, and Alastair D. Jenkins. "On the Interaction of Surface Waves and Upper Ocean Turbulence." Journal of Physical Oceanography 36, no. 3 (March 1, 2006): 551–57. http://dx.doi.org/10.1175/jpo2862.1.
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Abstract The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.
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Deremble, Bruno, Takaya Uchida, William K. Dewar, and Roger M. Samelson. "Eddy‐Mean Flow Interaction With a Multiple Scale Quasi Geostrophic Model." Journal of Advances in Modeling Earth Systems 15, no. 10 (October 2023). http://dx.doi.org/10.1029/2022ms003572.
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AbstractParameterization of mesoscale eddies in coarse resolution ocean models is necessary to include the effect of eddies on the large‐scale oceanic circulation. We propose to use a multiple‐scale Quasi‐Geostrophic (MSQG) model to capture the eddy dynamics that develop in response to a prescribed large‐scale flow. The MSQG model consists in extending the traditional quasi geostrophic (QG) dynamics to include the effects of a variable Coriolis parameter and variable background stratification. Solutions to this MSQG equation are computed numerically and compared to a full primitive equation model. The large‐scale flow field permits baroclinically unstable QG waves to grow. These instabilities saturate due to non‐linearities and a filtering method is applied to remove large‐scale structures that develop due to the upscale cascade. The resulting eddy field represents a dynamically consistent response to the prescribed background flow, and can be used to rectify the large‐scale dynamics. Comparisons between Gent‐McWilliams eddy parameterization and the present solutions show large regions of agreement, while also indicating areas where the eddies feed back onto the large scale in a manner that the Gent‐McWilliams parameterization cannot capture. Also of interest is the time variability of the eddy feedback which can be used to build stochastic eddy parameterizations.
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Dettling, Nicolas, Martin Losch, Friederike Pollmann, and Torsten Kanzow. "Towards parameterizing eddy-mediated transport of Warm Deep Water across the Weddell Sea continental slope." Journal of Physical Oceanography, June 3, 2024. http://dx.doi.org/10.1175/jpo-d-23-0215.1.
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Abstract The transport of Warm Deep Water (WDW) onto the Weddell Sea continental shelf is associated with a heat flux and strongly contributes to the melting of Antarctic ice shelves. The small radius of deformation at high latitudes makes it difficult to accurately represent the eddy-driven component of onshore WDW transport in coarse-resolution ocean models so that a parameterization becomes necessary. The Gent and McWilliams/Redi (GM/Redi) scheme was designed to parameterize mesoscale eddies in the open ocean. Here, it is assessed to what extent the GM/Redi scheme can generate a realistic transport of WDW across the Weddell Sea continental slope. To this end, the eddy parameterization is applied to a coarse-resolution idealized model of the Weddell Sea continental shelf and slope, and its performance is evaluated against a high-resolution reference simulation. With the GM/Redi parameterization applied, the coarse model simulates a shoreward WDW transport with a heat transport that matches the high-resolution reference and both the hydrographic mean fields and the mean slopes of the isopycnals are improved. A successful application of the GM/Redi parameterization is only possible by reducing the GM diffusivity over the continental slope by an order of magnitude compared to the open ocean value to account for the eddy-suppressing effect of the topographic slope. When the influence of topography on the GM diffusivity is neglected, the coarse model with the parameterization either under or overestimates the shoreward heat flux. These results motivate the incorporation of slope-aware eddy parameterizations into regional and global ocean models.
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Loose, Nora, Gustavo M. Marques, Alistair Adcroft, Scott Bachman, Stephen M. Griffies, Ian Grooms, Robert W. Hallberg, and Malte F. Jansen. "Comparing Two Parameterizations for the Restratification Effect of Mesoscale Eddies in an Isopycnal Ocean Model." Journal of Advances in Modeling Earth Systems 15, no. 12 (December 2023). http://dx.doi.org/10.1029/2022ms003518.
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AbstractThere are two distinct parameterizations for the restratification effect of mesoscale eddies: the Greatbatch and Lamb (1990, GL90, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485_1990_020_1634_opvmom_2_0_co_2.xml?tab_body=abstract-display) parameterization, which mixes horizontal momentum in the vertical, and the Gent and McWilliams (1990, GM90, https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485_1990_020_0150_imiocm_2_0_co_2.xml) parameterization, which flattens isopycnals adiabatically. Even though these two parameterizations are effectively equivalent under the assumption of quasi‐geostrophy, GL90 has been used much less than GM90, and exclusively in z‐coordinate models. In this paper, we compare the GL90 and GM90 parameterizations in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. From a theoretical perspective, GL90 is more attractive than GM90 for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness‐weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The striking resemblance between the GL90 and GM90 simulations persists from non‐eddying through eddy‐permitting resolution. We conclude that GL90 is a promising alternative to GM90 for isopycnal coordinate models, where it is more consistent with theory, computationally more efficient, easier to implement, and numerically more stable. Assessing the applicability of GL90 in realistic global ocean simulations with hybrid coordinate schemes should be a priority for future work.
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Mak, J., J. R. Maddison, D. P. Marshall, X. Ruan, Y. Wang, and L. Yeow. "Scale‐Awareness in an Eddy Energy Constrained Mesoscale Eddy Parameterization." Journal of Advances in Modeling Earth Systems 15, no. 12 (December 2023). http://dx.doi.org/10.1029/2023ms003886.
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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.
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Yankovsky, Elizabeth, Scott Bachman, K. Shafer Smith, and Laure Zanna. "Vertical Structure and Energetic Constraints for a Backscatter Parameterization of Ocean Mesoscale Eddies." Journal of Advances in Modeling Earth Systems 16, no. 7 (July 2024). http://dx.doi.org/10.1029/2023ms004093.
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AbstractMesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy‐permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime.
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Robertson, Robin, and Changming Dong. "An evaluation of the performance of vertical mixing parameterizations for tidal mixing in the Regional Ocean Modeling System (ROMS)." Geoscience Letters 6, no. 1 (November 29, 2019). http://dx.doi.org/10.1186/s40562-019-0146-y.
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AbstractVertical mixing is important in the ocean for maintaining its stratification, redistributing temperature and salinity, distributing nutrients and pollutants, and the energy cascade. It plays a key role in ocean energy transport, climate change, and marine ecosystems. Getting the mixing right in ocean circulation and climate models is critical in reproducing ocean and climate physics. Ocean models, like the Regional Ocean Modeling System (Rutgers ROMS 3.4), provide several options for determining vertical mixing through the vertical mixing parameterization schemes. To evaluate which of these methods best reproduces realistic vertical mixing by internal tides, simulations of baroclinic tides generated by a seamount were performed using seven different vertical mixing parameterizations: Mellor-Yamada 2.5 (MY), Large-McWilliams-Doney’s Kpp (LMD), Nakanishi-Niino’s modification of Mellor-Yamada (NN), and four versions of Generic Length Scale (GLS). The GLS versions in ROMS 3.4 severely overmixed the water column within a day and were not considered realistic. We suspect that a coding error has been introduced for it. We focused on the performance of the MY, LMD, and NN vertical mixing parameterizations. LMD was found to overmix the water column. The performance of MY and NN were nearly equivalent and both well reproduced the observed velocity and diffusivity fields. NN performed slightly better by having a lower rms for M2 and K1, less benthic mixing, more mid-water column mixing, less overmixing, and fewer extremely high diffusivities (> 1 m2 s−1).
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Kenigson, Jessica S., Renske Gelderloos, and Georgy E. Manucharyan. "Vertical Structure of the Beaufort Gyre Halocline and the Crucial Role of the Depth-Dependent Eddy Diffusivity." Journal of Physical Oceanography, December 29, 2020. http://dx.doi.org/10.1175/jpo-d-20-0077.1.
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AbstractTheories of the Beaufort Gyre (BG) dynamics commonly represent the halocline as a single layer with a thickness depending on the Eulerian-mean and eddy-induced overturning. However, observations suggest that the isopycnal slope increases with depth, and a theory to explain this profile remains outstanding. Here we develop a multi-layer model of the BG, including the Eulerian-mean velocity, mesoscale eddy activity, diapycnal mixing, and lateral boundary fluxes, and use it to investigate the dynamics within the Pacific Winter Water (PWW) layer. Using theoretical considerations, observational data, and idealized simulations, we demonstrate that the eddy overturning is critical in explaining the observed vertical structure. In the absence of the eddy overturning, the Ekman pumping and the relatively weak vertical mixing would displace isopycnals in a nearly parallel fashion, contrary to observations. This study finds that the observed increase of the isopycnal slope with depth in the climatological state of the gyre is consistent with a Gent-McWilliams eddy diffusivity coefficient that decreases by at least 10-40% over the PWW layer. We further show that the depth-dependent eddy diffusivity profile can explain the relative magnitude of the correlated isopycnal depth and layer thickness fluctuations on interannual timescales. Our inference that the eddy overturning generates the isopycnal layer thickness gradients is consistent with the parameterization of eddies via a Gent-McWilliams scheme but not potential vorticity diffusion. This study implies that using a depth-independent eddy diffusivity, as is commonly done in low-resolution ocean models, may contribute to misrepresentation of the interior BG dynamics.
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Xie, Chenyue, Huaiyu Wei, and Yan Wang. "Bathymetry-aware mesoscale eddy parameterizations across upwelling slope fronts: A machine learning-augmented approach." Journal of Physical Oceanography, September 8, 2023. http://dx.doi.org/10.1175/jpo-d-23-0017.1.
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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 non-eddying 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 non-eddying simulations employing the bathymetry-aware forms of the Rhines scale-based scheme and GEOMETRIC scheme (Wang and Stewart, 2020; https://doi.org/10.1016/j.ocemod.2020.101579) 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 non-eddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes.
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Legay, Alexandre, Bruno Deremble, Thierry Penduff, Pierre Brasseur, and Jean‐Marc Molines. "A Framework for Assessing Ocean Mixed Layer Depth Evolution." Journal of Advances in Modeling Earth Systems 16, no. 10 (October 2024). http://dx.doi.org/10.1029/2023ms004198.
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AbstractThe ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes (“restratification,” “stable,” “deepening,” and “strong deepening”) are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration.