Formulation and implementation of a “residual-mean” ocean circulation model (original) (raw)
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Geophysical & Astrophysical Fluid Dynamics, 2005
In the framework of the eddy dynamic model developed in two previous papers (Dubovikov, M.S., Dynamical model of mesoscale eddies, Geophys. Astophys. Fluid Dyn., 2003, 97, 311-358; Canuto, V.M. and Dubovikov, M.S., Modeling mesoscale eddies, Ocean Modelling, 2004, 8, 1-30 referred as I-II), we compute the contribution of unresolved mesoscale eddies to the large-scale dynamic equations of the ocean. In isopycnal coordinates, in addition to the bolus velocity discussed in I-II, the mesoscale contribution to the large scale momentum equation is derived. Its form is quite different from the traditional down-gradient parameterization. The model solutions in isopycnal coordinates are transformed to level coordinates to parameterize the eddy contributions to the corresponding large scale density and momentum equations. In the former, the contributions due to the eddy induced velocity and to the residual density flux across mean isopycnals (so called AE-term) are derived, both contributions being shown to be of the same order. As for the large scale momentum equation, as well as in isopycnal coordinates, the eddy contribution has a form which is quite different from the down-gradient expression.
Journal of Physical Oceanography, 2005
A global ocean circulation model is formulated in terms of the "residual mean" and used to study eddy-mean flow interaction. Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature. The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of information about the role of eddies in large-scale ocean circulation. In eddy-rich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 0.2 N m Ϫ2 , and carry momentum from the surface down to the bottom, where they are balanced by mountain form drag. From the optimized eddy stress, 3D maps of horizontal eddy diffusivity are inferred. The diffusivities have a well-defined large-scale structure whose prominent features are 1) large values of (up to 4000 m 2 s Ϫ1 ) in the western boundary currents and on the equatorial flank of the Antarctic Circumpolar Current and 2) a surface intensification of , suggestive of a dependence on the stratification N 2 . It is shown that implementation of an eddy parameterization scheme in which the eddy diffusivity has an N 2 dependence significantly improves the climatology of the ocean model state relative to that obtained using a spatially uniform diffusivity.
Specification of Eddy Transfer Coefficients in Coarse-Resolution Ocean Circulation Models*
Journal of Physical Oceanography, 1997
Parametric representations of oceanic geostrophic eddy transfer of heat and salt are studied ranging from horizontal diffusion to the more physically based approaches of Green and Stone (GS) and Gent and McWilliams (GM). The authors argue for a representation that combines the best aspects of GS and GM: transfer coefficients that vary in space and time in a manner that depends on the large-scale density fields (GS) and adoption of a transformed Eulerian mean formalism (GM). Recommendations are based upon a two-dimensional (zonally or azimuthally averaged) model with parameterized horizontal and vertical fluxes that is compared to three-dimensional numerical calculations in which the eddy transfer is resolved. Three different scenarios are considered:
Horizontal Residual Mean: Addressing the Limited Spatial Resolution of Ocean Models
Journal of Physical Oceanography, 2019
Horizontal fluxes of heat and other scalar quantities in the ocean are due to correlations between the horizontal velocity and tracer fields. However, the limited spatial resolution of ocean models means that these correlations are not fully resolved using the velocity and temperature evaluated on the model grid, due to the limited spatial resolution and the boxcar-averaged nature of the velocity and the scalar field. In this article, a method of estimating the horizontal flux due to unresolved spatial correlations is proposed, based on the depth-integrated horizontal transport from the seafloor to the density surface whose spatially averaged height is the height of the calculation. This depth-integrated horizontal transport takes into account the subgrid velocity and density variations to compensate the standard estimate of horizontal transport based on staircase-like velocity and density. It is not a parameterization of unresolved eddies, since it utilizes data available in ocean ...
Residual circulation in the ocean
… Processes and Their Parameterization: Proc.'Aha …, 2003
The Transformed Eulerian Mean formalism greatly simplifies the study of eddy mean flow interactions. However the standard formalism suffers of a number of limitations that make it not suitable for typical oceanic conditions. Here we show how to extend the formalism to represent properly boundary conditions and regions with steep isopycnal slopes. This formalism is then used to derive a parameterization for mesoscale motions in the ocean.
2019
The ability of a coarse-resolution ocean model to simulate the response to enhanced westerlies in the Southern Ocean is evaluated as a function of the eddy transfer coefficient (κ) commonly used to parameterize the bolus velocities induced by unresolved eddies (Gent and McWilliams, 1990). By implementing different eddy transfer coefficients, it is shown that a coefficient κ that is stratification-dependent and varies in space and time leads to an enhanced response of the eddy-induced meridional overturning circulation (MOC), which is close to the ratio obtained from a reference eddy-resolving simulation with the same model. The compensation caused by the intensified response of the eddy-induced MOC in experiments with either constantly uniform or spatially varying eddy transfer coefficients is consistently smaller. The enhanced eddy compensation from the experiment with stratification-dependent κ can be traced to changes in the vertical derivative of κ in time. Changes in κ also affect the response of the residual Southern Ocean MOC through its Eulerian component. In the stratification-dependent case, the increased meridional gradient of κ during 1998-2007 compared to 1960-1969 decreases the meridional gradient of the density slope, which in turn dampens the meridional gradient of sea surface height and therefore leads to a weaker response of the Eulerian circulation and of the residual circulation.
NeverWorld2: An idealized model hierarchy to investigate ocean mesoscale eddies across resolutions
We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with nonuniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.
Measures of the Fidelity of Eddying Ocean Models
Oceanography, 2006
Computational simulation is now an essential methodology of science, along with theory and observation. The ability of scientists to understand and predict planetary climate variability largely depends on the veracity of the climate simulations produced by numerical models of the interacting components of the Earth system. Oceanic and atmospheric models are numerical approximations to continuous forms of the equations governing fl uid fl ow and are "closed" by subgrid-scale parameterizations that represent physical processes on temporal and spatial scales that are not resolved by the chosen model grid. In the past two decades, the rate at which the world's fastest computers perform fl oating point operations (FLOPS) has increased by a factor of 10,000. This increase in computing capability has been exploited in several ways. Longer integrations for applications such as paleoclimate (Dijkstra and Ghil, 2005) and the inclusion into models of additional processes such as biogeochemical cycles and ecosystem dynamics (Moore et al., 2004), are two such examples. Another example, and the focus of the present study, is to increase the spatial resolution of models such that a greater fraction of the physical processes are explicitly resolved, and fewer are parameterized. Currently, such state-of-the-art decadal-timescale global ocean simulations are being conducted using models confi gured on grids with horizontal resolution of 5 to 10 km and 40 to 60 vertical levels or layers. Their duration, limited to several decades by the capability of presentgeneration computational platforms, is suffi cient to allow the fl ow to mostly adjust dynamically to its initial state ("spin-up" the circulation), but not to bring the model into thermodynamic equilibrium. The objective of the present study is to provide an indication of how realistically ocean models of this class are able to represent the mean and variability of the real upper-ocean general circulation in anticipation of the time when it will be possible to perform centennial climate integrations with them.
Sensitivity of an Ocean General Circulation Model to a Parameterization of Near-Surface Eddy Fluxes
Journal of Climate, 2008
A simplified version of the near-boundary eddy flux parameterization developed recently by Ferrari et al. has been implemented in the NCAR Community Climate System Model (CCSM3) ocean component for the surface boundary only. This scheme includes the effects of diabatic mesoscale fluxes within the surface layer. The experiments with the new parameterization show significant improvements compared to a control integration that tapers the effects of the eddies as the surface is approached. Such surface tapering is typical of present implementations of eddy transport in some current ocean models. The comparison is also promising versus available observations and results from an eddy-resolving model. These improvements include the elimination of strong, near-surface, eddy-induced circulations and a better heat transport profile in the upper ocean. The experiments with the new scheme also show reduced abyssal cooling and diminished trends in the potential temperature drifts. Furthermore, the need for any ad hoc, near-surface taper functions is eliminated. The impact of the new parameterization is mostly associated with the modified eddy-induced velocity treatment near the surface. The new parameterization acts in the depth range exposed to enhanced turbulent mixing at the ocean surface. This depth range includes the actively turbulent boundary layer and a transition layer underneath, composed of waters intermittently exposed to mixing. The mixed layer, that is, the regions of weak stratification at the ocean surface, is found to be a good proxy for the sum of the boundary layer depth and transition layer thickness.
Parameterization Improvements in an Eddy-Permitting Ocean Model for Climate
Journal of Climate, 2002
Different parameterizations for vertical mixing and the effects of ocean mesoscale eddies are tested in an eddy-permitting ocean model. It has a horizontal resolution averaging about 0.7Њ and was used as the ocean component of the parallel climate model. The old ocean parameterizations used in that coupled model were replaced by the newer parameterizations used in the climate system model. Both ocean-alone and fully coupled integrations were run for at least 100 years. The results clearly show that the drifts in the upper-ocean temperature profile using the old parameterizations are substantially reduced in both sets of integrations using the newer parameterizations. The sea-ice distribution in the fully coupled integration using the newer ocean parameterizations is also improved. However, the sea-ice distribution is sensitive to both sea-ice parameterizations and the atmospheric forcing, in addition to being dependent on the ocean simulation. The newer ocean parameterizations have been shown to improve considerably the solutions in non-eddy-resolving configurations, such as in the climate system model, where the horizontal resolution of the ocean component is about 2Њ. The work presented here is a clear demonstration that the improvements continue into the eddy-permitting regime, where the ocean component has an average horizontal resolution of less than 1Њ.