Bibliography - Robert W Hallberg

1. Dunne, John P., Jasmin John, Elena Shevliakova, Ronald J Stouffer, John P Krasting, Sergey Malyshev, P C D Milly, Lori T Sentman, Alistair Adcroft, William F Cooke, Krista A Dunne, Stephen M Griffies, Robert W Hallberg, Matthew J Harrison, Hiram Levy II, Andrew T Wittenberg, Peter Phillipps, and Niki Zadeh, April 2013: GFDL's ESM2 global coupled climate-carbon Earth System Models Part II: Carbon system formulation and baseline simulation characteristics. Journal of Climate, 26(7), doi:10.1175/JCLI-D-12-00150.1.
   [ Abstract ]

   We describe carbon system formulation and simulation characteristics of two new global coupled carbon-climate Earth System Models, ESM2M and ESM2G. These models demonstrate good climate fidelity as described in Part I while incorporating explicit and consistent carbon dynamics. The two models differ almost exclusively in the physical ocean component; ESM2M uses Modular Ocean Model version 4.1 with vertical pressure layers while ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. On land, both ESMs include a revised land model to simulate competitive vegetation distributions and functioning, including carbon cycling among vegetation, soil and atmosphere. In the ocean, both models include new biogeochemical algorithms including phytoplankton functional group dynamics with flexible stoichiometry. Preindustrial simulations are spun up to give stable, realistic carbon cycle means and variability. Significant differences in simulation characteristics of these two models are described. Due to differences in oceanic ventilation rates (Part I) ESM2M has a stronger biological carbon pump but weaker northward implied atmospheric CO2 transport than ESM2G. The major advantages of ESM2G over ESM2M are: improved representation of surface chlorophyll in the Atlantic and Indian Oceans and thermocline nutrients and oxygen in the North Pacific. Improved tree mortality parameters in ESM2G produced more realistic carbon accumulation in vegetation pools. The major advantages of ESM2M over ESM2G are reduced nutrient and oxygen biases in the Southern and Tropical Oceans.

2. Hallberg, Robert W., Alistair Adcroft, John P Dunne, John P Krasting, and Ronald J Stouffer, May 2013: Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation. Journal of Climate, 26(9), doi:10.1175/JCLI-D-12-00506.1.
   [ Abstract ]

   Two comprehensive Earth System Models, identical apart from their oceanic components, are used to estimate the uncertainty in projections of 21st century sea level rise due to representational choices in ocean physical formulation. Most prominent among the formulation differences is that one (ESM2M) uses a traditional z-coordinate ocean model, while the other (ESM2G) uses an isopycnal-coordinate ocean. As evidence of model fidelity, differences in 20th century global-mean steric sea level rise are not statistically significant between either model and observed trends. However, differences between the two models’ 21st century projections are systematic and both statistically and climatically significant. By 2100, ESM2M exhibits 18% higher global steric sea level rise than ESM2G for all four radiative forcing scenarios (28 to 49 mm higher), despite having similar changes between the models in the near-surface ocean for several scenarios. These differences arise primarily from the vertical extent over which heat is taken up and the total heat uptake by the models (9% more in ESM2M than ESM2G). The fact that the spun-up control state of ESM2M is warmer than ESM2G also contributes, by giving thermal expansion coefficients that are about 7% larger in ESM2M than ESM2G. The differences between these models provide a direct estimate of the sensitivity of 21st century sea level rise to ocean model formulation, and, given the span of these models across the observed volume of the ventilated thermocline, may also approximate the sensitivities expected from uncertainties in the characterization of interior ocean physical processes.

3. Melet, Angelique, Robert W Hallberg, Sonya Legg, and K Polzin, March 2013: Sensitivity of the Ocean State to the Vertical Distribution of Internal-Tide Driven Mixing. Journal of Physical Oceanography, 43(3), doi:10.1175/JPO-D-12-055.1.
   [ Abstract ]

   The ocean interior stratification and meridional overturning circulation are largely sustained by diapycnal mixing. The breaking of internal tides is a major source of diapycnal mixing. Many recent climate models parameterize internal-tide breaking using the scheme of St Laurent et al. (2002). While this parameterization dynamically accounts for internal-tide generation, the vertical distribution of the resultant mixing is ad hoc, prescribing energy dissipation to decay exponentially above the ocean bottom with a fixed length scale. Recently, Polzin (2009) formulated a dynamically based parameterization, in which the vertical profile of dissipation decays algebraically with a varying decay scale, accounting for variable stratification using WKB stretching. We compare two simulations using the St Laurent and Polzin formulations in the CM2G ocean-ice-atmosphere coupled model, with the same formulation for internal-tide energy input. Focusing mainly on the Pacific Ocean, where the deep low-frequency variability is relatively small, we show that the ocean state shows modest but robust and significant sensitivity to the vertical profile of internal-tide driven mixing. Therefore, not only the energy input to the internal tides matters, but also where in the vertical it is dissipated.

4. Rugenstein, M, Michael Winton, Ronald J Stouffer, Stephen M Griffies, and Robert W Hallberg, January 2013: Northern high latitude heat budget decomposition and transient warming. Journal of Climate, 26(2), doi:10.1175/JCLI-D-11-00695.1.
   [ Abstract ]

   Climate models simulate a wide range of climate changes at high northern latitudes in response to increased CO2. They also have substantial disagreement on projected changes of the Atlantic meridional overturning circulation (AMOC). Here we use two pairs of closely related climate models - each containing members with large and small AMOC declines - to explore the influence of AMOC decline on the high latitude response to increased CO2. The models with larger AMOC decline have less high latitude warming and sea ice decline than their small AMOC decline counterpart. By examining differences in the perturbation heat budget of the 40�90�N region, it is shown that AMOC decline diminishes the warming by weakening poleward ocean heat transport and increasing the ocean heat uptake. The cooling impact of this AMOC forced surface heat flux perturbation difference is enhanced by shortwave feedback and diminished by longwave feedback and atmospheric heat transport differences. The magnitude of the AMOC decline within model pairs is positively related to the magnitudes of control climate AMOC and Labrador Sea convection. Because the 40degree 90degree N region accounts for up to 40% of the simulated global ocean heat uptake over one hundred years, the process described here influences the global heat uptake efficiency.

5. Straneo, F, P Heimbach, Olga V Sergienko, G Hamilton, G Catania, Stephen M Griffies, and Robert W Hallberg, et al., in press: Challenges to Understand the Dynamic Response of Greenland's Marine Terminating Glaciers to Oceanic and Atmospheric Forcing. Bulletin of the American Meteorological Society. doi:10.1175/BAMS-D-12-00100. 1/13.
   [ Abstract ]

   The recent retreat and speedup of outlet glaciers, as well as enhanced surface melting around the ice sheet margin, have increased Greenland's contribution to sea level rise to 0.6±0.1 mm/yr and its discharge of freshwater into the North Atlantic. The widespread, near-synchronous glacier retreat, and its coincidence with a period of oceanic and atmospheric warming, suggest a common climate driver. Evidence points to the marine margins of these glaciers as the region from which changes propagated inland. Yet the forcings and mechanisms behind these dynamic responses are poorly understood and either missing or crudely parameterized in climate and ice sheet models. Resulting projected sea level rise contributions from Greenland by 2100 remain highly uncertain. This paper summarizes current state of knowledge and highlights key physical aspects of Greenland's coupled ice-sheet/ocean/atmosphere system. Three research thrusts are identified to yield fundamental insights into ice sheet, ocean, sea ice and atmosphere interactions, their role in Earth's climate system, and probable trajectories of future changes: (1) focused process studies addressing critical glacier, ocean, atmosphere and coupled dynamics; (2) sustained observations at key sites; and (3) inclusion of relevant dynamics in Earth System Models. Understanding the dynamic response of Greenland's glaciers to climate forcing constitutes both a scientific and technological frontier given the challenges of obtaining the appropriate measurements from the glaciers' marine termini and the complexity of the dynamics involved, including the coupling of the ocean, atmosphere, glacier and sea ice systems. Interdisciplinary and international cooperation are crucial to making progress on this novel and complex problem. Capsule: An interdisciplinary and multi-faceted approach is needed to understand the forcings and mechanisms behind the recent retreat and acceleration of Greenland's glaciers and its implications for future sea level rise

6. Winton, Michael, Alistair Adcroft, Stephen M Griffies, Robert W Hallberg, Larry W Horowitz, and Ronald J Stouffer, January 2013: Influence of ocean and atmosphere components on simulated climate sensitivities. Journal of Climate, 26(1), doi:10.1175/JCLI-D-12-00121.1.
   [ Abstract ]

   We examine the influence of alternative ocean and atmosphere subcomponents on climate model simulation of transient sensitivities by comparing three GFDL climate models used for the CMIP5. The base model ESM2M is closely related to GFDL's CMIP3 climate model CM2.1, and makes use of a depth coordinate ocean component. The second model, ESM2G, is identical to ESM2M but makes use of an isopycnal coordinate ocean model. We compare the impact of this "ocean swap" with an "atmosphere swap" that produces the CM3 climate model by replacing the AM2 atmosphere with AM3 while retaining a depth coordinate ocean model. The atmosphere swap is found to have much larger influence on sensitivities of global surface temperature and Northern Hemisphere sea ice cover. The atmosphere swap also introduces a multi-decadal response timescale through its indirect influence on heat uptake. Despite significant differences in their interior ocean mean states, the ESM2M and ESM2G simulations of these metrics of climate change are very similar, except for an enhanced high latitude salinity response accompanied by temporarily advancing sea ice in ESM2G. In the ESM2G historical simulation this behavior results in the establishment of a strong halocline in the subpolar North Atlantic during the early 20th century and an associated cooling which are counter to observations in that region. The Atlantic meridional overturning declines comparably in all three models.

7. Dunne, John P., Jasmin John, Alistair Adcroft, Stephen M Griffies, Robert W Hallberg, Elena Shevliakova, Ronald J Stouffer, William F Cooke, Krista A Dunne, Matthew J Harrison, John P Krasting, Sergey Malyshev, P C D Milly, Peter Phillipps, Lori T Sentman, Bonita L Samuels, Michael J Spelman, Michael Winton, Andrew T Wittenberg, and Niki Zadeh, October 2012: GFDL's ESM2 global coupled climate-carbon Earth System Models Part I: Physical formulation and baseline simulation characteristics. Journal of Climate, 25(19), doi:10.1175/JCLI-D-11-00560.1.
   [ Abstract ]

   We describe the physical climate formulation and simulation characteristics of two new global coupled carbon-climate Earth System Models, ESM2M and ESM2G. These models demonstrate similar climate fidelity as the Geophysical Fluid Dynamics Laboratory’s previous CM2.1 climate model while incorporating explicit and consistent carbon dynamics. The two models differ exclusively in the physical ocean component; ESM2M uses Modular Ocean Model version 4.1 with vertical pressure layers while ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. Differences in the ocean mean state include the thermocline depth being relatively deep in ESM2M and relatively shallow in ESM2G compared to observations. The crucial role of ocean dynamics on climate variability is highlighted in the El Niño-Southern Oscillation being overly strong in ESM2M and overly weak ESM2G relative to observations. Thus, while ESM2G might better represent climate changes relating to: total heat content variability given its lack of long term drift, gyre circulation and ventilation in the North Pacific, tropical Atlantic and Indian Oceans, and depth structure in the overturning and abyssal flows, ESM2M might better represent climate changes relating to: surface circulation given its superior surface temperature, salinity and height patterns, tropical Pacific circulation and variability, and Southern Ocean dynamics. Our overall assessment is that neither model is fundamentally superior to the other, and that both models achieve sufficient fidelity to allow meaningful climate and earth system modeling applications. This affords us the ability to assess the role of ocean configuration on earth system interactions in the context of two state-of-the-art coupled carbon-climate models.

8. Goldberg, D N., C M Little, Olga V Sergienko, Anand Gnanadesikan, Robert W Hallberg, and M Oppenheimer, June 2012: Investigation of land ice-ocean interaction with a fully coupled ice-ocean model, Part 2: Sensitivity to external forcings. Journal of Geophysical Research, 117, F02038, doi:10.1029/2011JF002247.
   [ Abstract ]

   A coupled ice stream-ice shelf-ocean cavity model is used to assess the sensitivity of the coupled system to far-field ocean temperatures, varying from 0.0 to 1.80C, as well as sensitivity to the parameters controlling grounded ice flow. A response to warming is seen in grounding line retreat and grounded ice loss that cannot be inferred from the response of integrated melt rates alone. This is due to concentrated thinning at the ice shelf lateral margin, and to processes that contribute to this thinning. Parameters controlling the flow of grounded ice have a strong influence on the response to sub-ice shelf melting, but this influence is not seen until several years after an initial perturbation in temperatures. The simulated melt rates are on the order of that observed for Pine Island Glacier in the 1990s. However, retreat rates are much slower, possibly due to unrepresented bedrock features.

9. Goldberg, D N., C M Little, Olga V Sergienko, Anand Gnanadesikan, Robert W Hallberg, and M Oppenheimer, June 2012: Investigation of land ice-ocean interaction with a fully coupled ice-ocean model, Part 1: Model description and behavior. Journal of Geophysical Research, 117, F02037, doi:10.1029/2011JF002246.
   [ Abstract ]

   Antarctic ice shelves interact closely with the ocean cavities beneath them, with ice shelf geometry influencing ocean cavity circulation, and heat from the ocean driving changes in the ice shelves, as well as the grounded ice streams that feed them. We present a new coupled model of an ice stream-ice shelf-ocean system that is used to study this interaction. The model is capable of representing a moving grounding line and dynamically responding ocean circulation within the ice shelf cavity. Idealized experiments designed to investigate the response of the coupled system to instantaneous increases in ocean temperature show ice-ocean system responses on multiple timescales. Melt rates and ice shelf basal slopes near the grounding line adjust in 1-2 years, and downstream advection of the resulting ice shelf thinning takes place on decadal timescales. Retreat of the grounding line and adjustment of grounded ice takes place on a much longer timescale, and the system takes several centuries to reach a new steady state. During this slow retreat, and in the absence of either an upward-or downward-sloping bed or long-term trends in ocean heat content, the ice shelf and melt rates maintain a characteristic pattern relative to the grounding line.

10. Ilicak, M, Alistair Adcroft, Stephen M Griffies, and Robert W Hallberg, February 2012: Spurious dianeutral mixing and the role of momentum closure. Ocean Modelling, 45-46, doi:10.1016/j.ocemod.2011.10.003.
    [ Abstract ]

    This paper examines spurious dianeutral transport within a suite of ocean models (GOLD, MITgcm, MOM, and ROMS). We quantify such transport through a global diagnostic that computes the reference potential energy, whose evolution arises solely through transport between density classes. Previous studies have focused on the importance of accurate tracer advection schemes in reducing the spurious transport and closure. The present study highlights complementary issues associated with momentum transport. Spurious dianeutral transport is shown to be directly proportional to the lateral grid Reynolds number (ReΔ), with such transport significantly reduced when ReΔ<10. Simulations with the isopycnal model GOLD provide a benchmark for the smallest level of spurious dianeutral transport realizable in our model suite. For idealized simulations with a linear equation of state, GOLD exhibits identically zero spurious dianeutral mixing, and thus maintains a constant reference potential energy when all physical mixing processes are omitted. Amongst the non-isopycnal models tested in idealized simulations, ROMS generally produces smaller spurious dianeutral mixing than MITgcm or MOM, since ROMS makes use of a higher order upwind-biased scheme for momentum transport that enforces a small ReΔ. In contrast, MITgcm and MOM both employ unbiased (centered) discretizations of momentum transport, and therefore rely on lateral friction operators to control the grid Reynolds number. We find that a lateral shear-dependent Smagorinsky viscosity provides an effective means to locally reduce ReΔ, and thus to reduce spurious dianeutral transport in MITgcm and MOM. In addition to four idealized simulations, we quantify spurious dianeutral transport in realistic global ocean climate simulations using GOLD and MOM with a realistic equation of state for seawater, both with and without mesoscale eddies in the resolved flow field. The GOLD simulations have detectable levels of spurious cabbeling from along isopycnal advective truncation errors. Significantly larger spurious dianeutral transport arises in a non-eddying MOM simulation. In an eddying MOM simulation, spurious dianeutral transport is larger still but is reduced by increasing momentum friction.

11. Fox-Kemper, B, G Danabasoglu, R Ferrari, Stephen M Griffies, Robert W Hallberg, M M Holland, M E Maltrud, S L Peacock, and Bonita L Samuels, July 2011: Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations. Ocean Modelling, 39(1-2), doi:10.1016/j.ocemod.2010.09.002.
    [ Abstract ]

    A parameterization for the restratification by finite-amplitude, submesoscale, mixed layer eddies, formulated as an overturning streamfunction, has been recently proposed to approximate eddy fluxes of density and other tracers. Here, the technicalities of implementing the parameterization in the coarse-resolution ocean component of global climate models are made explicit, and the primary impacts on model solutions of implementing the parameterization are discussed. Three global ocean general circulation models including this parameterization are contrasted with control simulations lacking the parameterization. The MLE parameterization behaves as expected and fairly consistently in models differing in discretization, boundary layer mixing, resolution, and other parameterizations. The primary impact of the parameterization is a shoaling of the mixed layer, with the largest effect in polar winter regions. Secondary impacts include strengthening the Atlantic meridional overturning while reducing its variability, reducing CFC and tracer ventilation, modest changes to sea surface temperature and air-sea fluxes, and an apparent reduction of sea ice basal melting.

12. Ilicak, M, Sonya Legg, Alistair Adcroft, and Robert W Hallberg, April 2011: Dynamics of a dense gravity current flowing over a corrugation. Ocean Modelling, 38(1-2), doi:10.1016/j.ocemod.2011.02.004.
    [ Abstract ]

    In this study, we investigate the dynamics of a dense gravity currents over different sizes of ridges and canyons. We employ a high resolution idealized isopycnal model and perform a large number of experiments changing the aspect ratio of a ridge/canyon, the Coriolis parameter, the reduced gravity, the background slope and initial overflow thickness. The control run (smooth topography) is in an eddy-regime and the frequencies of the eddies coincide with those of the Filchner overflow Darelius et al., 2009. Our idealized corrugation experiments show that corrugations steer the plume downslope, and that ridges are more effective than canyons in transporting the overflow to the deep ocean. We find that a corrugation Burger number (Buc) can be used as a parameter to describe the flow over topography. Buc is a combination of a Froude number and the aspect ratio. The maximum downslope transport of a corrugation can be increased when the height of the corrugation increases (Buc increases) or when the width of the corrugation decreases (Buc increases). In addition, we propose a new parameterization of mixing as a function of Buc that can be used to account for unresolved shear in coarse resolution models. The new parameterization captures the increased local shear, thus increasing the turbulent kinetic energy and decreasing the gradient Richardson number. We find reasonable agreement in the overflow thickness and transport between the models with this parameterization and the high resolution models. We conclude that mixing effects of corrugations can be implemented as unresolved shear in an eddy diffusivity formulation and this parameterization can be used in coarse resolution models.

13. Adcroft, Alistair, Robert W Hallberg, John P Dunne, Bonita L Samuels, J Galt, C Barker, and D Payton, September 2010: Simulations of underwater plumes of dissolved oil in the Gulf of Mexico. Geophysical Research Letters, 37, L18605, doi:10.1029/2010GL044689.
    [ Abstract ]

    A simple model of the temperature-dependent biological decay of dissolved oil is embedded in an ocean climate circulation model and used to simulate underwater plumes of dissolved and suspended oil originating from a point source in the northern Gulf of Mexico. Plumes at different source depths are considered and the behavior at each depth is found to be determined by the combination of sheared current strength and vertical profile of decay rate. An upper bound on the supply rate of dissolved and suspended oil is estimated for the interior water column from contemporary analysis of the Deepwater Horizon blowout. For all plume scenarios, toxic levels of dissolved oil are found to remain confined to the northern Gulf of Mexico, and abate within a few weeks after the spill stops. An estimate of oxygen consumption due to microbial oxidation of oil suggests that the presence of oil alone will not lead to hypoxia, but a deep plume of oil and methane (which dissolves readily in water) does lead to localized regions of persistent hypoxia and anoxia in the vicinity of the source.

14. Gnanadesikan, Anand, K A Emanuel, Gabriel A Vecchi, Whit G Anderson, and Robert W Hallberg, September 2010: How ocean color can steer Pacific tropical cyclones. Geophysical Research Letters, 37, L18802, doi:10.1029/2010GL044514.
    [ Abstract ]

    Because ocean color alters the absorption of sunlight, it can produce changes in sea surface temperatures with further impacts on atmospheric circulation. These changes can project onto fields previously recognized to alter the distribution of tropical cyclones. If the North Pacific subtropical gyre contained no absorbing and scattering materials, the result would be to reduce subtropical cyclone activity in the subtropical Northwest Pacific by 2/3, while concentrating cyclone tracks along the equator. Predicting tropical cyclone activity using coupled models may thus require consideration of the details of how heat moves into the upper thermocline as well as biogeochemical cycling.

15. Griffies, Stephen M., Alistair Adcroft, Anand Gnanadesikan, Robert W Hallberg, Matthew J Harrison, Sonya Legg, C M Little, M Nikurashin, A Pirani, Bonita L Samuels, J Robert Toggweiler, and Geoffrey K Vallis, et al., September 2010: Problems and prospects in large-scale ocean circulation models In Ocean Obs '09, 21-25 September, Venice, Italy, ESA Special Publication, doi:10.5270/OceanObs09.cwp.38.
    [ Abstract ]

    We overview problems and prospects in ocean circulation models, with emphasis on certain developments aiming to enhance the physical integrity and flexibility of large-scale models used to study global climate. We also consider elements of observational measures rendering information to help evaluate simulations and to guide development priorities. http://www.oceanobs09.net/blog/?p=88

16. Griffies, Stephen M., 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.

17. Griffies, Stephen M., 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.
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18. 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.

19. Legg, Sonya, Tal Ezer, Stephen M Griffies, Robert W Hallberg, and L Jackson, et al., May 2009: Improving oceanic overflow representation in climate models: The gravity current entrainment climate process team. Bulletin of the American Meteorological Society, 90(5), doi:10.1175/2008BAMS2667.1.
    [ Abstract ]

    Oceanic overflows are bottom-trapped density currents originating in semienclosed basins, such as the Nordic seas, or on continental shelves, such as the Antarctic shelf. Overflows are the source of most of the abyssal waters, and therefore play an important role in the large-scale ocean circulation, forming a component of the sinking branch of the thermohaline circulation. As they descend the continental slope, overflows mix vigorously with the surrounding oceanic waters, changing their density and transport significantly. These mixing processes occur on spatial scales well below the resolution of ocean climate models, with the result that deep waters and deep western boundary currents are simulated poorly. The Gravity Current Entrainment Climate Process Team was established by the U.S. Climate Variability and Prediction (CLIVAR) Program to accelerate the development and implementation of improved representations of overflows within large-scale climate models, bringing together climate model developers with those conducting observational, numerical, and laboratory process studies of overflows. Here, the organization of the Climate Process Team is described, and a few of the successes and lessons learned during this collaboration are highlighted, with some emphasis on the well-observed Mediterranean overflow. The Climate Process Team has developed several different overflow parameterizations, which are examined in a hierarchy of ocean models, from comparatively well-resolved regional models to the largest-scale global climate models.

20. Muench, R D., A K Wåhlin, T M Özgökmen, Robert W Hallberg, and L Padman, December 2009: Impacts of bottom corrugations on a dense Antarctic outflow: NW Ross Sea. Geophysical Research Letters, 36, L23607, doi:10.1029/2009GL041347.
    [ Abstract ]

    Prominent seabed corrugations, axially oriented roughly down-slope, are present along the Antarctic continental slope. We use analytical and numerical model results to assess the potential impact of these corrugations on outflows of dense shelf water that contribute to Antarctic Bottom Water. Down-slope flow increases with increasing corrugation height and varies with along-slope wavelength. For parameters appropriate to the northwest Ross Sea, where heights and wavelengths are ∼10–20 m and ∼1.5 km, respectively, we estimate that the corrugations increase the down-slope transport of dense water, relative to the smooth bottom case, by ∼13%. Corrugations enhance entrainment and reduce along-slope speed of the dense outflow. Larger amplitude corrugations (∼100 m) observed in other regions may impact outflows elsewhere around the poorly mapped Antarctic continental margin. Our results emphasize the need to consider small-scale local topography when modeling dense outflows.

21. White, Laurent, Alistair Adcroft, and Robert W Hallberg, December 2009: High-order regridding–remapping schemes for continuous isopycnal and generalized coordinates in ocean models. Journal of Computational Physics, 228(23), doi:10.1016/j.jcp.2009.08.016.
    [ Abstract ]

    A hierarchy of high-order regridding–remapping schemes for use in generalized vertical coordinate ocean models is presented. The proposed regridding–remapping framework is successfully used in a series of idealized one-dimensional numerical experiments as well as two-dimensional internal wave and overflow test cases. The model is capable of replicating z-, sigma- and isopycnal-coordinate results, among others. Particular emphasis is placed on the design of a continuous isopycnal framework, which is a more general alternative to the layered isopycnal paradigm. Continuous isopycnal coordinates use target interface densities to define layers. In contrast to traditional layered isopycnal models, in which along-layer density gradients vanish, general coordinate approaches must deal with extra terms. For example, the calculation of pressure gradient force is more complicated and must be evaluated carefully. High-order reconstructions within boundary cells are crucial for obtaining sensible results and for reducing spurious diffusion near boundaries. Vertical advection is implicitly embedded in the remapping step and directly benefits from high-order schemes. Volume and all tracers are conserved to machine precision, which is a necessary ingredient for long-term ocean climate modeling. This hybrid vertical coordinate model provides the framework to easily capture the impact of different coordinate systems on dynamics.

22. 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.

23. 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.

24. 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.
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25. Harrison, Matthew J., and Robert W Hallberg, 2008: Pacific subtropical cell response to reduced equatorial dissipation. Journal of Physical Oceanography, 38(9), doi:10.1175/2008JPO3708.1.
    [ Abstract ]

    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.

26. 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.

27. 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.
28. 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), doi:10.1175/2008JPO3928.1.
    [ Abstract ]

    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.

29. Anderson, Whit G., Anand Gnanadesikan, Robert W Hallberg, John P 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.

30. Little, C M., Ventakramani Balaji, Thomas L Delworth, Robert W Hallberg, Hiram Levy II, Ronald J Stouffer, and Michael Winton, et al., 2007: Toward a new generation of ice sheet models. EOS, 88(52), 578-579.
    [ PDF ]
31. 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.

32. 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.

33. 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.

34. 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.

35. 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.

36. 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.

37. 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.

38. 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.

39. 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.

40. 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.

41. Hallberg, Robert W., 2001: Reply. Journal of Physical Oceanography, 31(7), 1926-1930.
    [ PDF ]
42. 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.

43. 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.

44. Griffies, Stephen M., 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.

45. Griffies, Stephen M., 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.

46. 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.

47. 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.

48. 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.

49. 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.

50. 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.

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