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Stephen M. Griffies

Abstract

This paper formulates tracer stirring arising from the Gent–McWilliams (GM) eddy-induced transport in terms of a skew-diffusive flux. A skew-diffusive tracer flux is directed normal to the tracer gradient, which is in contrast to a diffusive tracer flux directed down the tracer gradient. Analysis of the GM skew flux provides an understanding of the physical mechanisms prescribed by GM stirring, which is complementary to the more familiar advective flux perspective. Additionally, it unifies the tracer mixing operators arising from Redi isoneutral diffusion and GM stirring. This perspective allows for a computationally efficient and simple manner in which to implement the GM closure in z-coordinate models. With this approach, no more computation is necessary than when using isoneutral diffusion alone. Additionally, the numerical realization of the skew flux is significantly smoother than the advective flux. The reason is that to compute the skew flux, no gradient of the diffusivity or isoneutral slope is taken, whereas such a gradient is needed for computing the advective flux. The skew-flux formulation also exposes a striking cancellation of terms that results when the GM diffusion coefficient is identical to the Redi isoneutral diffusion coefficient. For this case, the horizontal components to the tracer flux are aligned down the horizontal tracer gradient, and the resulting computational cost of Redi diffusion plus GM skew diffusion is roughly half that needed for Redi diffusion alone.

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Yalin Fan and Stephen M. Griffies

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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Tapio Schneider and Stephen M. Griffies

Abstract

A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction.

Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest.

In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data.

An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations.

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Stephen M. Griffies and Eli Tziperman

Abstract

The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (THC) is described and compared to the THC variability in the coupled ocean–atmosphere GCM of Delworth, Manabe, and Stouffer. The box model is placed in a linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of this state reveals one damped oscillatory THC mode in addition to purely damped modes. The variability of the model under a moderate amount of stochastic forcing, meant to emulate the random variability of the atmosphere affecting the coupled model's interdecadal THC variability, is studied. A linear interpretation, in which the damped oscillatory mode is of primary importance, is sufficient for understanding the mechanism accounting for the stochastically forced variability. Direct comparison of the variability in the box model and coupled GCM reveals common qualitative aspects. Such a comparison supports, although does not verify, the hypothesis that the coupled model's THC variability can be interpreted as the result of atmospheric weather exciting a linear damped oscillatory THC mode.

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Houssam Yassin and Stephen M. Griffies

Abstract

The discrete baroclinic modes of quasigeostrophic theory are incomplete, and the incompleteness manifests as a loss of information in the projection process. The incompleteness of the baroclinic modes is related to the presence of two previously unnoticed stationary step-wave solutions of the Rossby wave problem with flat boundaries. These step waves are the limit of surface quasigeostrophic waves as boundary buoyancy gradients vanish. A complete normal-mode basis for quasigeostrophic theory is obtained by considering the traditional Rossby wave problem with prescribed buoyancy gradients at the lower and upper boundaries. The presence of these boundary buoyancy gradients activates the previously inert boundary degrees of freedom. These Rossby waves have several novel properties such as the presence of multiple modes with no internal zeros, a finite number of modes with negative norms, and the fact that their vertical structures form a basis capable of representing any quasigeostrophic state with a differentiable series expansion. These properties are a consequence of the Pontryagin-space setting of the Rossby wave problem in the presence of boundary buoyancy gradients (as opposed to the usual Hilbert-space setting). We also examine the quasigeostrophic vertical velocity modes and derive a complete basis for such modes as well. A natural application of these modes is the development of a weakly nonlinear wave-interaction theory of geostrophic turbulence that takes topography into account.

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Houssam Yassin and Stephen M. Griffies

Abstract

Numerical and observational evidence indicates that, in regions where mixed-layer instability is active, the surface geostrophic velocity is largely induced by surface buoyancy anomalies. Yet, in these regions, the observed surface kinetic energy spectrum is steeper than predicted by uniformly stratified surface quasigeostrophic theory. By generalizing surface quasigeostrophic theory to account for variable stratification, we show that surface buoyancy anomalies can generate a variety of dynamical regimes depending on the stratification’s vertical structure. Buoyancy anomalies generate longer range velocity fields over decreasing stratification and shorter range velocity fields over increasing stratification. As a result, the surface kinetic energy spectrum is steeper over decreasing stratification than over increasing stratification. An exception occurs if the near surface stratification is much larger than the deep ocean stratification. In this case, we find an extremely local turbulent regime with surface buoyancy homogenization and a steep surface kinetic energy spectrum, similar to equivalent barotropic turbulence. By applying the variable stratification theory to the wintertime North Atlantic, and assuming that mixed-layer instability acts as a narrowband small-scale surface buoyancy forcing, we obtain a predicted surface kinetic energy spectrum between k −4/3 and k −7/3, which is consistent with the observed wintertime k −2 spectrum. We conclude by suggesting a method of measuring the buoyancy frequency’s vertical structure using satellite observations.

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A. J. George Nurser and Stephen M. Griffies

Abstract

We detail the physical means whereby boundary transfers of freshwater and salt induce diffusive fluxes of salinity. Our considerations focus on the kinematic balance between the diffusive fluxes of salt and freshwater, with this balance imposed by mass conservation for an element of seawater. The flux balance leads to a specific balanced form for the diffusive salt flux immediately below the ocean surface and, in the Boussinesq approximation, to a specific form for the salinity flux. This balanced form should be used in specifying the surface boundary condition for the salinity equation and the contribution of freshwater to the buoyancy budget.

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Stephen M. Griffies and Robert W. Hallberg

Abstract

This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scale-selective, state-dependent friction operator for use in eddy-permitting geophysical fluid models. This friction should prove most useful for large-scale ocean models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnal-coordinate ocean models.

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Jianjun Yin, Stephen M. Griffies, and Ronald J. Stouffer

Abstract

A set of state-of-the-science climate models are used to investigate global sea level rise (SLR) patterns induced by ocean dynamics in twenty-first-century climate projections. The identified robust features include bipolar and bihemisphere seesaws in the basin-wide SLR, dipole patterns in the North Atlantic and North Pacific, and a beltlike pattern in the Southern Ocean. The physical and dynamical mechanisms that cause these patterns are investigated in detail using version 2.1 of the Geophysical Fluid Dynamics Laboratory (GFDL) Coupled Model (CM2.1). Under the Intergovernmental Panel on Climate Change’s (IPCC) Special Report on Emissions Scenarios (SRES) A1B scenario, the steric sea level changes relative to the global mean (the local part) in different ocean basins are attributed to differential heating and salinity changes of various ocean layers and associated physical processes. As a result of these changes, water tends to move from the ocean interior to continental shelves. In the North Atlantic, sea level rises north of the Gulf Stream but falls to the south. The dipole pattern is induced by a weakening of the meridional overturning circulation. This weakening leads to a local steric SLR east of North America, which drives more waters toward the shelf, directly impacting northeastern North America. An opposite dipole occurs in the North Pacific. The dynamic SLR east of Japan is linked to a strong steric effect in the upper ocean and a poleward expansion of the subtropical gyre. In the Southern Ocean, the beltlike pattern is dominated by the baroclinic process during the twenty-first century, while the barotropic response of sea level to wind stress anomalies is significantly delayed.

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Stephen M. Griffies, Ronald C. Pacanowski, Martin Schmidt, and V. Balaji

Abstract

This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate ocean models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid models. Additionally, the effects of the undulating free surface height are directly incorporated into the baroclinic momentum and tracer equations. The novel issues related to local and global tracer conservation when allowing for the top cell to undulate are the focus of this work. The method presented here is quasi-conservative locally and globally of tracer when the baroclinic and tracer time steps are equal. Important issues relevant for using this method in regional as well as large-scale climate models are discussed and illustrated, and examples of scaling achieved on parallel computers provided.

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