Bibliography - Robert W Hallberg

1. Griffies, Stephen, Robert W Hallberg, A Pirani, Bonita L Samuels, and Michael Winton, et al., January 2009: Coordinated ocean-ice reference experiments (COREs). Ocean Modelling, 26(1-2), doi:10.1016/j.ocemod.2008.08.007.
   [ Abstract ]

   Coordinated Ocean-ice Reference Experiments (COREs) are presented as a tool to explore the behaviour of global ocean-ice models under forcing from a common atmospheric dataset. We highlight issues arising when designing coupled global ocean and sea ice experiments, such as difficulties formulating a consistent forcing methodology and experimental protocol. Particular focus is given to the hydrological forcing, the details of which are key to realizing simulations with stable meridional overturning circulations. The atmospheric forcing from [Large, W., Yeager, S., 2004. Diurnal to decadal global forcing for ocean and sea-ice models: the data sets and flux climatologies. NCAR Technical Note: NCAR/TN-460+STR. CGD Division of the National Center for Atmospheric Research] was developed for coupled-ocean and sea ice models. We found it to be suitable for our purposes, even though its evaluation originally focussed more on the ocean than on the sea-ice. Simulations with this atmospheric forcing are presented from seven global ocean-ice models using the CORE-I design (repeating annual cycle of atmospheric forcing for 500 years). These simulations test the hypothesis that global ocean-ice models run under the same atmospheric state produce qualitatively similar simulations. The validity of this hypothesis is shown to depend on the chosen diagnostic. The CORE simulations provide feedback to the fidelity of the atmospheric forcing and model configuration, with identification of biases promoting avenues for forcing dataset and/or model development.

2. Griffies, Stephen, Alistair Adcroft, Ventakramani Balaji, Robert W Hallberg, Sonya Legg, T Martin, and A Pirani, et al., February 2009: Sampling Physical Ocean Field in WCRP CMIP5 Simulations: CLIVAR Working Group on Ocean Model Development (WGOMD) Committee on CMIP5 Ocean Model Output, International CLIVAR Project Office, CLIVAR Publication Series No. 137, 56pp.
   [ PDF ]
3. Hallberg, Robert W., and Alistair Adcroft, April 2009: Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-split time stepping. Ocean Modelling, 29(1), doi:10.1016/j.ocemod.2009.02.008.
   [ Abstract ]

   In ocean models that use a mode splitting algorithm for time-stepping the internal- and external-gravity modes, the external and internal solutions each can be used to provide an estimate of the free surface height evolution. In models with time-invariant vertical coordinate spacing, it is standard to force the internal solutions for the free surface height to agree with the external solution by specifying the appropriate vertically averaged velocities; because this is a linear problem, it is relatively straightforward. However, in Lagrangian vertical coordinate ocean models with potentially vanishing layers, nonlinear discretizations of the continuity equations must be used for each interior layer. This paper discusses the options for enforcing agreement between the internal and external estimates of the free surface height, along with the consequences of each choice, and suggests an optimal, essentially exact, approach.

4. Adcroft, Alistair, Robert W Hallberg, and Matthew J Harrison, 2008: A finite volume discretization of the pressure gradient force using analytic integration. Ocean Modelling, 22(3-4), doi:10.1016/j.ocemod.2008.02.001.
   [ Abstract ]

   Layered ocean models can exhibit spurious thermobaric instability if the compressibility of sea water is not treated accurately enough. We find that previous solutions to this problem are inadequate for simulations of a changing climate. We propose a new discretization of the pressure gradient acceleration using the finite volume method. In this method, the pressure gradient acceleration is exhibited as the difference of the integral “contact” pressure acting on the edges of a finite volume. This integral “contact” pressure can be calculated analytically by choosing a tractable equation of state. The result is a discretization that has zero truncation error for an isothermal and isohaline layer and does not exhibit the spurious thermobaric instability.

5. Fox-Kemper, B, R Ferrari, and Robert W Hallberg, 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. Journal of Physical Oceanography, 38(6), doi:10.1175/2007JPO3792.1.
   [ Abstract ]

   Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

6. Fox-Kemper, B, G Danabasoglu, R Ferrari, and Robert W Hallberg, 2008: Parameterizing submesoscale physics in global climate models. Clivar Exchanges, 13(1), 3-5.
   [ PDF ]
7. Harrison, Matthew J., and Robert W Hallberg, 2008: Pacific subtropical cell response to reduced equatorial dissipation. Journal of Physical Oceanography, 38(9), 1894-1912.
   [ Abstract PDF ]

   Equatorial turbulent diffusivities resulting from breaking gravity waves may be more than a factor of 10 less than those in the midlatitudes. A coupled general circulation model with a layered isopycnal coordinate ocean is used to assess Pacific climate sensitivity to a latitudinally varying background diapycnal diffusivity with extremely low values near the equator.

   The control experiments have a minimum upper-ocean diffusivity of 10⁻⁵ m² s⁻¹ and are initialized from present-day conditions. The average depth of the σ_θ = 26.4 interface (z_26.4) in the Pacific increases by 140 m after 500 yr of coupled model integration. This corresponds to a warming trend in the upper ocean. Low equatorial diffusivities reduce the z_26.4 bias by 30%. Isopycnal surfaces are elevated from the eastern boundary up to midlatitudes by cooling in the upper several hundred meters, partially compensated by freshening. Entrainment of intermediate water masses from below σ_θ = 26.4 decreases by 1.5 Sv (1 Sv 10⁶ m³ s⁻¹), mainly in the western tropical Pacific. The Pacific heat uptake (30°S–30°N) from the atmosphere reduces by 0.1 PW. This is associated with warmer entrainment temperatures in the eastern equatorial Pacific upwelling region. Equatorward heat transport from the Southern Ocean increases by 0.07 PW.

   Reducing the upper-ocean background diffusivity uniformly to 10⁻⁶ m² s⁻¹ cools the upper ocean from the tropics, but warms and freshens from the midlatitudes. Enhanced convergence into the Pacific of water lighter than σ_θ = 26.4 compensates the reduction in upwelling of intermediate waters in the tropics. Basin-averaged z_26.4 bias increases in the low background case.

   These results demonstrate basin-scale sensitivity to the observed suppression of equatorial background dissipation. This has clear implications for understanding oceanic heat uptake in the Pacific as well as other important aspects of the climate system. Diapycnal diffusivities due to truncation errors and other numerical artifacts in ocean models may need to be less than 10⁻⁶ m² s⁻¹ in order to accurately represent this effect in climate models.

8. Jackson, L, Robert W Hallberg, and Sonya Legg, May 2008: A Parameterization of shear-driven turbulence for ocean climate models. Journal of Physical Oceanography, 38(5), doi:10.1175/2007JPO3779.1.
   [ Abstract ]

   This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state. The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N²/|u_z|², where N is the buoyancy frequency and |u_z| is the vertical shear) and the buoyancy length scale over which the turbulence decays [L_b = Q^1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself. High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.

9. Legg, Sonya, L Jackson, and Robert W Hallberg, 2008: Eddy-resolving modeling of overflows In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 63-82.
10. Little, C M., Anand Gnanadesikan, and Robert W Hallberg, October 2008: Large-scale oceanographic constraints on the distribution of melting and freezing under ice shelves. Journal of Physical Oceanography, 38(10), 2242-2255.
    [ Abstract PDF ]

    Previous studies suggest that ice shelves experience asymmetric melting and freezing. Topography may constrain oceanic circulation (and thus basal melt–freeze patterns) through its influence on the potential vorticity (PV) field. However, melting and freezing induce a local circulation that may modify locations of heat transport to the ice shelf. This paper investigates the influence of buoyancy fluxes on locations of melting and freezing under different bathymetric conditions. An idealized set of numerical simulations (the “decoupled” simulations) employs spatially and temporally fixed diapycnal fluxes. These experiments, in combination with scaling considerations, indicate that while flow in the interior is governed by large-scale topographic gradients, recirculation plumes dominate near buoyancy fluxes. Thermodynamically decoupled models are then compared to those in which ice–ocean heat and freshwater fluxes are driven by the interior flow (the “coupled” simulations). Near the southern boundary, strong cyclonic flow forced by melt-induced upwelling drives inflow and melting to the east. Recirculation is less evident in the upper water column, as shoaling of meltwater-freshened layers dissipates the dynamic influence of buoyancy forcing, yet freezing remains intensified in the west. In coupled simulations, the flow throughout the cavity is relatively insensitive to bathymetry; stratification, the slope of the ice shelf, and strong, meridionally distributed buoyancy fluxes weaken its influence.

11. Anderson, Whit G., Anand Gnanadesikan, Robert W Hallberg, John Dunne, and Bonita L Samuels, June 2007: Impact of ocean color on the maintenance of the Pacific Cold Tongue. Geophysical Research Letters, 34, L11609, doi:10.1029/2007GL030100.
    [ Abstract ]

    The impact of the penetration length scale of shortwave radiation into the surface ocean is investigated with a fully coupled ocean, atmosphere, land and ice model. Oceanic shortwave radiation penetration is assumed to depend on the chlorophyll concentration. As chlorophyll concentrations increase the distribution of shortwave heating becomes shallower. This change in heat distribution impacts mixed-layer depth. This study shows that removing all chlorophyll from the ocean results in a system that tends strongly towards an El Niño state—suggesting that chlorophyll is implicated in maintenance of the Pacific cold tongue. The regions most responsible for this response are located off-equator and correspond to the oligotrophic gyres. Results from a suite of surface chlorophyll perturbation experiments suggest a potential positive feedback between chlorophyll concentration and a non-local coupled response in the fully coupled ocean-atmosphere system.

12. Balaji, Ventakramani, Thomas L Delworth, Robert W Hallberg, Hiram Levy II, Ronald J Stouffer, and Michael Winton, 2007: Toward a new generation of ice sheet models. EOS, 88(52), 578-579.
13. Adcroft, Alistair, and Robert W Hallberg, 2006: On methods for solving the oceanic equations of motion in generalized vertical coordinates. Ocean Modelling, 11(1-2), doi:10.1016/j.ocemod.2004.12.007.
    [ Abstract ]

    We note that there are essentially two methods of solving the hydrostatic primitive equations in general vertical coordinates: the quasi-Eulerian class of algorithms are typically used in quasi-stationary coordinates (e.g. height, pressure, or terrain following) coordinate systems; the quasi-Lagrangian class of algorithms are almost exclusively used in layered models and is the preferred paradigm in modern isopycnal models. These approaches are not easily juxtaposed. Thus, hybrid coordinate models that choose one method over the other may not necessarily obtain the particular qualities associated with the alternative method. We discuss the nature of the differences between the Lagrangian and Eulerian algorithms and suggest that each has its benefits. The arbitrary Lagrangian-Eulerian method (ALE) purports to address these differences but we find that it does not treat the vertical and horizontal dimensions symmetrically as is done in classical Eulerian models. This distinction is particularly evident with the non-hydrostatic equations, since there is explicitly no symmetry breaking in these equations. It appears that the Lagrangian algorithms can not be easily invoked in conjunction with the pressure method that is often used in non-hydrostatic models. We suggest that research is necessary to find a way to combine the two viewpoints if we are to develop models that are suitable for simulating the wide range of spatial and temporal scales that are important in the ocean.

14. Hallberg, Robert W., and Anand Gnanadesikan, 2006: The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the modeling eddies in the Southern Ocean (MESO) project. Journal of Physical Oceanography, 36(12), 2232-2252.
    [ Abstract PDF ]

    The Modeling Eddies in the Southern Ocean (MESO) project uses numerical sensitivity studies to examine the role played by Southern Ocean winds and eddies in determining the density structure of the global ocean and the magnitude and structure of the global overturning circulation. A hemispheric isopycnal-coordinate ocean model (which avoids numerical diapycnal diffusion) with realistic geometry is run with idealized forcing at a range of resolutions from coarse (2°) to eddy-permitting (1/6°). A comparison of coarse resolutions with fine resolutions indicates that explicit eddies affect both the structure of the overturning and the response of the overturning to wind stress changes. While the presence of resolved eddies does not greatly affect the prevailing qualitative picture of the ocean circulation, it alters the overturning cells involving the Southern Ocean transformation of dense deep waters and light waters of subtropical origin into intermediate waters. With resolved eddies, the surface-to-intermediate water cell extends farther southward by hundreds of kilometers and the deep-to-intermediate cell draws on comparatively lighter deep waters. The overturning response to changes in the winds is also sensitive to the presence of eddies. In noneddying simulations, changing the Ekman transport produces comparable changes in the overturning, much of it involving transformation of deep waters and resembling the mean circulation. In the eddy-permitting simulations, a significant fraction of the Ekman transport changes are compensated by eddy-induced transport drawing from lighter waters than does the mean overturning. This significant difference calls into question the ability of coarse-resolution ocean models to accurately capture the impact of changes in the Southern Ocean on the global ocean circulation.

15. Kunkel, C M., Robert W Hallberg, and M Oppenheimer, 2006: Coral reefs reduce tsunami impact in model simulations. Geophysical Research Letters, 33, L23612, doi:10.1029/2006GL027892.
    [ Abstract ]

    Significant buffering of the impact of tsunamis by coral reefs is suggested by limited observations and some anecdotal reports, particularly following the 2004 Indian Ocean tsunami. Here we simulate tsunami run-up on idealized topographies in one and two dimensions using a nonlinear shallow water model and show that a sufficiently wide barrier reef within a meter or two of the surface reduces run-up on land on the order of 50%. We studied topographies representative of volcanic islands (islands with no continental shelf) but our conclusions may pertain to other topographies. Effectiveness depends on the amplitude and wavelength of the incident tsunami, as well as the geometry and health of the reef and the offshore distance of the reef. Reducing the threat to reefs from anthropogenic nutrients, sedimentation, fishing practices, channel-building, and global warming would help to protect some islands against tsunamis.

16. Legg, Sonya, Robert W Hallberg, and J B Girton, 2006: Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and non-hydrostatic models. Ocean Modelling, 11(1-2), doi:10.1016/j.ocemod.2004.11.006.
    [ Abstract ]

    A series of idealised numerical simulations of dense water flowing down a broad uniform slope are presented, employing both a z-coordinate model (the MIT general circulation model) and an isopycnal coordinate model (the Hallberg Isopycnal Model). Calculations are carried out at several different horizontal and vertical resolutions, and for a range of physical parameters. A subset of calculations are carried out at very high resolution using the non-hydrostatic variant of the MITgcm. In all calculations dense water descends the slope while entraining and mixing with ambient fluid. The dependence of entrainment, mixing and down-slope descent on resolution and vertical coordinate are assessed. At very coarse resolutions the z-coordinate model generates excessive spurious mixing, and dense water has difficulty descending the slope. However, at intermediate resolutions the mixing in the z-coordinate model is less than found in the high-resolution non-hydrostatic simulations, and dense water descends further down the slope. Isopycnal calculations show less resolution dependence, although entrainment and mixing are both reduced slightly at coarser resolution. At intermediate resolutions the z-coordinate and isopycnal models produce similar levels of mixing and entrainment. These results provide a benchmark against which future developments in overflow entrainment parameterizations in both z-coordinate and isopycnal models may be compared.

17. Hallberg, Robert W., 2005: A thermobaric instability of Lagrangian vertical coordinate ocean models. Ocean Modelling, 8(3), doi:10.1016/j.ocemod.2004.01.001.
    [ Abstract ]

    Lagrangian- (and isopycnic-) vertical coordinate ocean models are subject to an exponentially growing numerical instability in weakly stratified regions when thermobaricity is not accurately compensated. Inaccurate compensation for compressibility in the pressure gradient terms leads to pressure gradient truncation errors (due to the vertical discretization) that can drive the Lagrangian coordinate surfaces to reinforce these errors. It is possible to avoid this instability while using the full non-linear equation of state for seawater by using an optimal alternate discretization of the pressure gradient terms and extracting a slowly spatially varying reference compressibility that approximates the compressibility of the ocean's mean state.

18. Arbic, B K., Stephen T Garner, Robert W Hallberg, and H L Simmons, 2004: The accuracy of surface elevations in forward global barotropic and baroclinic tide models. Deep-Sea Research, Part II, 51(25-26), 3069-3101.
    [ Abstract PDF ]

    This paper examines the accuracy of surface elevations in a forward global numerical model of 10 tidal constituents. Both one-layer and two-layer simulations are performed. As far as the authors are aware, the two-layer simulations and the simulations in a companion paper (Deep-Sea Research II, 51 (2004) 3043) represent the first published global numerical solutions for baroclinic tides. Self-consistent forward solutions for the global tide are achieved with a convergent iteration procedure for the self-attraction and loading term. Energies are too large, and elevation accuracies are poor, unless substantial abyssal drag is present. Reasonably accurate tidal elevations can be obtained with a spatially uniform bulk drag cd or horizontal viscosity KH, but only if these are inordinately large. More plausible schemes concentrate drag over rough topography. The topographic drag scheme used here is based on an exact analytical solution for arbitrary small-amplitude terrain, and supplemented by dimensional analysis to account for drag due to flow-splitting and low-level turbulence as well as that due to breaking of radiating waves. The scheme is augmented by a multiplicative factor tuned to minimize elevation discrepancies with respect to the TOPEX/POSEIDON (T/P)-constrained GOT99.2 model. The multiplicative factor may account for undersampled small spatial scales in bathymetric datasets. An optimally tuned multi-constituent one-layer simulation has an RMS elevation discrepancy of 9.54 cm with respect to GOT99.2, in waters deeper than 1000 m and over latitudes covered by T/P (66N to 66S). The surface elevation discrepancy decreases to 8.90 cm (92 percent of the height variance captured) in the optimally tuned two-layer solution. The improvement in accuracy is not due to the direct surface elevation signature of internal tides, which is of small amplitude, but to a shift in the barotropic tide induced by baroclinicity. Elevations are also more accurate in the two-layer model when pelagic tide gauges are used as the benchmark, and when the T/P-constrained TPXO6.2 model is used as a benchmark in deep waters south of 66S. For Antarctic diurnal tides, the improvement in forward model elevation accuracy with baroclinicity is substantial. The optimal multiplicative factor in the two-layer case is nearly the same as in the one-layer case, against initial expectations that the explicit resolution of low-mode conversion would allow less parameterized drag. In the optimally tuned two-layer M2 solution, local values of the ratio of temporally averaged squared upper layer speed to squared lower layer speed often exceed 10.

19. Simmons, H L., Robert W Hallberg, and B K Arbic, 2004: Internal wave generation in a global baroclinic tide model. Deep-Sea Research, Part II, 51(25-26), doi:10.1016/j.dsr2.2004.09.015.
    [ Abstract ]

    The energy flux out of barotropic tides and into internal waves ("conversion") is computed using a global domain multi-layer numerical model. The solution is highly baroclinic and reveals a global field of internal waves radiating way from generation sites of rough topography. A small number of sites where intense internal wave generation occurs accounts for most of the globally integrated work done on the barotropic tide and dominates sites such as the Mid-Atlantic ridge. The globally integrated conversion of the M2 barotropic tide is 891 Gigawatts and the globally integrated rate of working of the ocean by astronomical forcing is 2.94 Terawatts. Both of these estimates are close to accepted values derived from independent methods. Regional estimates of conversion are also similar to previous inferences, lending additional confidence that the solution has captured the essential physics of low-mode internal wave generation and that numerical prediction of conversion has skill in regions where no previous estimates are available.

20. Papadakis, M P., E P Chassignet, and Robert W Hallberg, 2003: Numerical simulations of the Mediterranean sea outflow: Impact of the entrainment parameterization in an isopycnic coordinate ocean model. Ocean Modelling, 5(4), 325-356.
    [ Abstract PDF ]

    Gravity current entrainment is essential in determining the properties of the interior ocean water masses that result from marginal sea overflows. Although the individual entraining billows will be unresolvable in large-scale ocean models for the foreseeable future, some large-scale simulations are now being carried out that do resolve the intermediate scale environment which may control the rate of entrainment. Hallberg [Mon. Wea. Rev. 128 (2000) 1402] has recently developed an implicit diapycnal mixing scheme for isopycnic coordinate ocean models that includes the Richardson number dependent entrainment parameterization of Turner [J. Fluid Mech. 173 (1986) 431], and which may be capable of representing the gravity current evolution in large-scale ocean models. The present work uses realistic regional simulations with the Miami Isopycnic Coordinate Ocean Model (MICOM) to evaluate ability of this scheme to simulate the entrainment that is observed to occur in the bottom boundary currents downstream of the Mediterranean outflow. These simulations are strikingly similar to the observations, indicating that this scheme does produce realistic mixing between the Mediterranean outflow and the North Atlantic Central Water. Sensitivity studies identify the critical Richardson number below which vigorous entrainment occurs as a particularly important parameter. Some of these experiments also show meddies detaching from the Mediterranean undercurrent at locations that appear to be highly influenced by topographic features.

21. Gnanadesikan, Anand, and Robert W Hallberg, 2002: Physical oceanography, thermal structure and general circulation In Encyclopedia of Physical Science and Technology, Vol. 12, New York, NY, Academic Press, 189-210.
    [ Abstract ]

    Physical oceanography is concerned with the study of the physical processes which control the spatiotemporal structure of such fields as density, temperature, and velocity within the ocean. A major thrust of this field is the development of an understanding of the general circulation, namely the circulation of the ocean on large scales (of order 100-10,000 km) and over long times (decades to millenia). The general circulation is what determines the large-scale chemical and thermal structure of the ocean and plays a major role in global climate and biogeochemistry. The large-scale circulation can be broken down into three cells, a surface cell where wind driving is important, a deep cell where mixing is important, and an intermediate cell where potentially both wind and mixing are important. This article discusses the physical framework necessary to understand these circulations and presents standard models which explain some key features of the large-scale structure.

22. Thompson, L, K A Kelly, D Darr, and Robert W Hallberg, 2002: Buoyancy and mixed layer effects on the sea surface height response in an isopycnal model of the North Pacific. Journal of Physical Oceanography, 32(12), 3657-3670.
    [ Abstract PDF ]

    An isopycnal model of the North Pacific is used to demonstrate that the seasonal cycle of heating and cooling and the resulting mixed layer depth entrainment and detrainment cycle play a role in the propgation of wind-driven Rossby waves. The model is forced by realistic winds and seasonal heat flux to examine the interaction of nearly annual wind-driven Rossby waves with the seasonal mixed layer cycle. Comparison among four model runs, one adiabatic (without diapycnal mixing or explicit mixed layer dynamics), one diabatic (with diapycnal mixing and explicit mixed layer dynamics), one with the seasonal cycle of heating only, and one with only variable winds suggests that mixed layer entrainment changes the structure of the response substantially, particularly at midlatitudes. Specifically, the mixed layer seasonal cycle works against Ekman pumping in the forcing of first-mode Rossby waves between 17° and 28°N. South of there the mixed layer seasonal cycle has little influence on the Rossby waves, while in the north, seasonal Rossby waves do not propagate. To examine the first baroclinic mode response in detail, a modal decomposition of the numerical model output is done. In addition, a comparison of the forcing by diapycnal pumping and Ekman pumping is done by a projection of Ekman pumping and diapycnal velocities on to the quasigeostrophic potential vorticity equation for each vertical mode. The first baroclinic mode's forcing is split between Ekman pumping and diapycnal velocity at midlatitudes, providing an explanation for the changes in the response when a seasonal mixed layer response is included. This is confirmed by doing a comparison of the modal decomposition in the four runs described above, and by calculation of the first baroclinic mode Rossby wave response using the one-dimensional Rossby wave equation.

23. Hallberg, Robert W., 2001: Reply. Journal of Physical Oceanography, 31(7), 1926-1930.
    [ PDF ]
24. Hallberg, Robert W., and Anand Gnanadesikan, 2001: An exploration of the role of transient eddies in determining the transport of a zonally reentrant current. Journal of Physical Oceanography, 31(11), 3312-3330.
    [ Abstract PDF ]

    The meridional Ekman transport in a zonally reentrant channel may be balanced by diabatic circulations, standing eddies associated with topography, or by Lagrangian mean eddy mass fluxes. A simple model is used to explore the interaction between these mechanisms. A key assumption of this study is that diabatic forcing in the poleward edge of the channel acts to create lighter fluid, as is the case with net freshwater fluxes into the Southern Ocean. For weak wind forcing or strong diabatic constraint, a simple scaling argument accurately predicts the level of baroclinic shear. However, given our understanding of the relative magnitudes of Ekman flux and deep upwelling, this is not the appropriate parameter range for the Antarctic Circumpolar Current. With stronger wind stresses, eddies are prominent, with baroclinic instability initially developing in the vicinity of large topography. Arguments have been advanced by a number of authors that baroclinic instability should limit the velocity shear, leading to a stiff upper limit on the transport of the current. However, in the simulations presented here baroclinic instability is largely confined to the region of topographic highs, and the approach to a current that is independent of the wind stress occurs gradually. Several recent parameterizations of transient eddy fluxes do not reproduce key features of the observed behavior.

25. Gnanadesikan, Anand, and Robert W Hallberg, 2000: On the relationship of the Circumpolar Current to Southern Hemisphere winds in coarse-resolution ocean models. Journal of Physical Oceanography, 30(8), 2013-2034.
    [ Abstract PDF ]

    The response of the Circumpolar Current to changing winds has been the subject of much debate. To date, most theories of the current have tried to predict the transport using various forms of momentum balance. This paper argues that it is also important to consider thermodynamic as well as dynamic balances. Within large-scale general circulation models, increasing eastward winds within the Southern Ocean drive a northward Ekman flux of light water, which in turn produces a deeper pycnocline and warmer deep water to the north of the Southern Ocean. This in turn results in much larger thermal wind shear across the Circumpolar Current, which, given relatively small near-bottom velocities, results in an increase in Antarctic Circumpolar Current (ACC) transport. The Ekman flux near the surface is closed by a deep return flow below the depths of the ridges. A simple model that illustrates this picture is presented in which the ACC depends most strongly on the winds at the northern and southern edges of the channel. The sensitivity of this result to the formulation of buoyancy forcing is illustrated using a second simple model. A number of global general circulation model runs are then presented with different wind stress patterns in the Southern Ocean. Within these runs, neither the mean wind stress in the latitudes of Drake Passage nor the wind stress curl at the northern edge of Drake Passage produces a prediction for the transport of the ACC. However, increasing the wind stress within the Southern Ocean does increase the ACC transport.

26. Griffies, Stephen, and Robert W Hallberg, 2000: Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Monthly Weather Review, 128(8), 2935-2946.
    [ Abstract PDF ]

    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.

27. Griffies, Stephen, Ronald C Pacanowski, and Robert W Hallberg, 2000: Spurious diapycnal mixing associated with advection in a z-coordinate ocean model. Monthly Weather Review, 128(3), 538-564.
    [ Abstract PDF ]

    This paper discusses spurious diapycnal mixing associated with the transport of density in a z-coordinate ocean model. A general method, based on the work of Winters and collaborators, is employed for empirically diagnosing an effective diapycnal diffusivity corresponding to any numerical transport process. This method is then used to quantify the spurious mixing engendered by various numerical representations of advection. Both coarse and fine resolution examples are provided that illustrate the importance of adequately resolving the admitted scales of motion in order to maintain a small amount of mixing consistent with that measured within the ocean's pycnocline. Such resolution depends on details of the advection scheme, momentum and tracer dissipation, and grid resolution. Vertical transport processes, such as convective adjustment, act as yet another means to increase the spurious mixing introduced by dispersive errors from numerical advective fluxes.

28. Hallberg, Robert W., 2000: Time integration of diapycnal diffusion and Richardson number-dependent mixing in isopycnal coordinate ocean models. Monthly Weather Review, 128(5), 1402-1419.
    [ Abstract PDF ]

    In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order t h2/ (where t is the time step, h is the isopycnal layer thickness, and is the diapycnal diffusivity), which cannot generally be satisfied since the layers could be arbitrarily thin. It is especially important that the diffusion time integration scheme have no such limit if the diapycnal diffusivity is determined by the local Richardson number. An iterative, implicit time integration scheme of diapycnal diffusion in isopycnal layers is suggested. This scheme is demonstrated to have qualitatively correct behavior in the limit of arbitrarily thin initial layer thickness, is highly accurate in the limit of well-resolved layers, and is not significantly more expensive than existing schemes. This approach is also shown to be compatible with an implicit Richardson number-dependent mixing parameterization, and to give a plausible simulation of an entraining gravity current with parameters like the Mediterranean Water overflow through the Straits of Gibraltar.

29. Winton, Michael, Robert W Hallberg, and Anand Gnanadesikan, 1998: Simulation of density-driven frictional downslope flow in z-coordinate ocean models. Journal of Physical Oceanography, 28(11), 2163-2174.
    [ Abstract PDF ]

    An important component of the ocean's thermohaline circulation is the sinking of dense water from continental shelves to abyssal depths. Such downslope flow is thought to be a consequence of bottom stress retarding the alongslope flow of density-driven plumes. In this paper the authors explore the potential for explicitly simulating the simple mechanism in z-coordinate models. A series of experiments are performed using a twin density-coordinate model simulation as a standard of comparison. The adiabatic nature of the experiments and the importance of bottom slope make it more likely that the density-coordinate model will faithfully reproduce the solution. The difficulty of maintaining the density signal as the plume descends the slope is found to be the main impediment to accurate simulation in the z-coordinate model. The results of process experiments suggest that the model solutions will converge when the z-coordinate model has sufficient vertical resolution to resolve the bottom viscous layer and horizontal grid spacing equal to its vertical grid spacing divided by the maximum slope. When this criterion is met it is shown that the z-coordinate model converges to an analytical solution for a simple two-dimensional flow.

30. Hallberg, Robert W., 1997: Localized coupling between surface and bottom-intensified flow over topography. Journal of Physical Oceanography, 27(6), 977-998.
    [ Abstract PDF ]

    Substantial bottom topography in a basin with planetary vorticity gradients strongly affects the vertical structure of the linear topographic and planetary Rossby waves that spin up the ocean circulation. There is no barotropic mode with large amplitude topography and stratification. It is shown that the lowest frequency two-layer quasigeostrophic waves that exist with stratification, planetary vorticity gradients, and large-amplitude bottom topography are more strongly concentrated in the vertical than Burger number 1 scaling would indicate (for most orientations of the wavevector) except where the bottom slope is nearly meridional. This concentration increases with decreasing frequency. Ray tracing in an ocean basin suggests that the two layers are linearly coupled in regions with parallel or antiparallel topographic and planetary vorticity gradients, but elsewhere small amplitude motion in the two layers is largely independent. Continuity within isopycnal layers implies that most of the circulation remains within isopycnal layers, even in the regions of linear coupling. The strength of surface(bottom)-intensified flow driven by coupling to bottom(surface)-intensified flow is approximately twice as strong as the surface(bottom) projection of the bottom(surface)-intensified flow. Primitive equation simulations concur with the quasigeostrophic results and indicate that the localized linear coupling between surface- and bottom-intensified flow pertains to a continuous stratification.

31. Hallberg, Robert W., 1997: Stable split time stepping schemes for large-scale ocean modeling. Journal of Computational Physics, 135, 54-65.
    [ Abstract PDF ]

    An explicit time integration of the primitive equations, which are often used for numerical ocean simulations, would be subject to a short time step limit imposed by the rapidly varying external gravity waves. One way to make this time step limit less onerous is to split the primitive equations into a simplified two-dimensional set of equations that describes the evolution of the external gravity waves and a much more slowly evolving three-dimensional remainder. The two-dimensional barotropic equations can be rapidly integrated over a large number of short time steps, while a much longer time step can be used with the much more complicated remainder. Unfortunately, it has recently been demonstrated that an inexact splitting into the fast and slow equations can lead to instability in the explicit integration of the slow equations. Here a more exact splitting of the equations is proposed. The proposed split time stepping scheme is demonstrated to be stable for linear inertia-gravity waves, subject to a time step limit based on the inertial frequency and internal gravity wave speeds.

32. Hallberg, Robert W., and P Rhines, 1996: Buoyancy-driven circulation in an ocean basin with isopycnals intersecting the sloping boundary. Journal of Physical Oceanography, 26(6), 913-940.
    [ Abstract PDF ]

    The dynamics that govern the spreading of a convectively formed water mass in an ocean with sloping boundaries are examined using an isopycnal model that permits the interface between the layers to intersect the sloping boundaries. The simulations presented here use a two-layer configuration to demonstrate some of the pronounced differences in a baroclinically forced flow between the response in a basin with a flat bottom and vertical walls and a more realistic basin bounded by a sloping bottom. Each layer has a directly forced signal that propagates away from the forcing along the potential vorticity (PV) contours of that layer. Paired, opposed boundary currents are generated by refracted topographic Rossby waves, rather than Kelvin waves. It is impossible to decompose the flow into globally independent baroclinic and barotropic modes; topography causes the barotropic (i.e., depth averaged) response to buoyancy forcing to be just as strong as the baroclinic response. Because layer PV contours diverge, boundary currents are pulled apart at different depths even in weakly forced, essentially linear, cases. Such barotropic modes, often described as "caused by the JEBAR effect," are actually dominated by strong free flow along PV contours. With both planetary vorticity gradients and topography, the two layers are linearly coupled. This coupling is evident in upper-layer circulations that follow upper-layer PV contours but originate in unforced regions of strong lower-layer flow. The interior ocean response is confined primarily to PV contours that are either directly forced or strongly coupled at some point to directly forced PV contours of the other layer. Even when the forcing is strong enough to generate a rich eddy field in the upper layer, the topographic PV gradients in the lower layer stabilize that layer and inhibit exchange of fluid across PV contours. The dynamic processes explored in this study are pertinent to both nonlinear flows (strongly forced) and linear flows (weakly forced and forerunners of strongly forced). Both small (f plane) and large (full spherical variation of the Coriolis parameter) basins are included. Transequatorial basins, in which the geostrophic contours are blocked, are not described here.

Direct link to page: http://www.gfdl.noaa.gov/bibliography/resultstest.php?author=1050