Bibliography - Alistair Adcroft

1. Adcroft, Alistair, July 2013: Representation of topography by porous barriers and objective interpolation of topographic data. Ocean Modelling, 67, doi:10.1016/j.ocemod.2013.03.002.
   [ Abstract ]

   We present a porous medium approach to representing topography, and a new algorithm for the objective interpolation of topography, for use in ocean circulation models of fixed resolution. The representation and algorithm makes use of two concepts; impermeable thin walls and porous barriers. Impermeable thin walls allow the representation of knife-edge sub-grid-scale barriers that block lateral flow between model grid cells. Porous barriers permit the sub-grid scale geometry to modulate lateral transport as a function of elevation. We find that the porous representation and the resulting interpolated topography retains key features, such as overflow sill depths, without compromising other dynamically relevant aspects, such as mean ocean depth for a cell. The accurate representation of the ocean depth is illustrated in a simple model of a tsunami that has a cross-basin travel time very much less dependent on horizontal resolution than when using conventional topographic interpolation and representation.

2. 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.

3. 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.

4. Nikurashin, M, Geoffrey K Vallis, and Alistair Adcroft, January 2013: Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nature Geoscience, 6(1), doi:10.1038/ngeo1657.
   [ Abstract ]

   Wind power inputs at the surface ocean are dissipated through smaller-scale processes in the ocean interior and turbulent boundary layer. Simulations suggest that seafloor topography enhances turbulent mixing and energy dissipation in the ocean interior.

5. 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.

6. Baughman, E, Anand Gnanadesikan, A DeGaetano, and Alistair Adcroft, November 2012: Investigation of the Surface and Circulation Impacts of Cloud Brightening Geoengineering. Journal of Climate, 25(21), doi:10.1175/JCLI-D-11-00282.1.
   [ Abstract ]

   Projected increases in greenhouse gases have prompted serious discussion on geoengineering the climate system to counteract global climate change. Cloud albedo enhancement has been proposed as a feasible geoengineering approach, but previous research suggests undesirable consequences of globally uniform cloud brightening. The present study uses GFDL�s CM2G global coupled model to simulate cloud albedo enhancement via increases in cloud condensation nuclei (CCN) to 1000 cm^−3 targeted at the marine stratus deck of the Pacific Ocean, where persistent low clouds suggest a regional approach to cloud brightening. We investigate the impact of this regional geoengineering on global circulation and climate in the presence of a 1% annual increase of CO_2. Surface temperatures returned to near Pre-Industrial levels over much of the globe with cloud modifications in place. In the first 40 years and over the 140 year mean, significant cooling over the Equatorial Pacific, continued Arctic warming, and large precipitation changes over the western Pacific, and a westward compression and intensification of the Walker Circulation were observed in response to cloud brightening. The cloud brightening caused a persistent La Nina condition associated with an increase in hurricane maximum potential intensity and genesis potential index, and decreased vertical wind shear between July and November in the tropical Atlantic, South China Sea, and to the east of Japan. Responses were similar with CCN = 500 cm^−3.

7. Delworth, Thomas L., Anthony Rosati, Whit G Anderson, Alistair Adcroft, Ventakramani Balaji, Rusty Benson, Keith W Dixon, Stephen M Griffies, Hyun-Chul Lee, Ronald C Pacanowski, Gabriel A Vecchi, Andrew T Wittenberg, Fanrong Zeng, and Rong Zhang, April 2012: Simulated climate and climate change in the GFDL CM2.5 high-resolution coupled climate model. Journal of Climate, 25(8), doi:10.1175/JCLI-D-11-00316.1.
   [ Abstract ]

   We present results for simulated climate and climate change from a newly developed high-resolution global climate model (GFDL CM2.5). The GFDL CM2.5 model has an atmospheric resolution of approximately 50 Km in the horizontal, with 32 vertical levels. The horizontal resolution in the ocean ranges from 28 Km in the tropics to 8 Km at high latitudes, with 50 vertical levels. This resolution allows the explicit simulation of some mesoscale eddies in the ocean, particularly at lower latitudes. We present analyses based on the output of a 280 year control simulation; we also present results based on a 140 year simulation in which atmospheric CO2 increases at 1% per year until doubling after 70 years. Results are compared to the GFDL CM2.1 climate model, which has somewhat similar physics but coarser resolution. The simulated climate in CM2.5 shows marked improvement over many regions, especially the tropics, including a reduction in the double ITCZ and an improved simulation of ENSO. Regional precipitation features are much improved. The Indian monsoon and Amazonian rainfall are also substantially more realistic in CM2.5. The response of CM2.5 to a doubling of atmospheric CO2 has many features in common with CM2.1, with some notable differences. For example, rainfall changes over the Mediterranean appear to be tightly linked to topography in CM2.5, in contrast to CM2.1 where the response is more spatially homogeneous. In addition, in CM2.5 the near-surface ocean warms substantially in the high latitudes of the Southern Ocean, in contrast to simulations using CM2.1.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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

13. Marshall, D, and Alistair Adcroft, April 2010: Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold’s first stability theorem. Ocean Modelling, 32(3-4), doi:10.1016/j.ocemod.2010.02.001.
    [ Abstract ]

    A family of eddy closures is studied that flux potential vorticity down-gradient and solve an explicit budget for the eddy energy, following the approach developed by Eden and Greatbatch (2008, Ocean Modelling). The aim of this manuscript is to demonstrate that when energy conservation is satisfied in this manner, the growth or decay of the parameterized eddy energy relates naturally to the instability or stability of the flow as described by Arnold’s first stability theorem. The resultant family of eddy closures therefore possesses some of the ingredients necessary to parameterize the gross effects of eddies in both forced-dissipative and freely-decaying turbulence. These ideas are illustrated through their application to idealized, barotropic wind-driven gyres in which the maximum eddy energy occurs within the viscous boundary layers and separated western boundary currents, and to freely-decaying turbulence in a closed barotropic basin in which inertial Fofonoff gyres emerge as the long-time solution. The result that these eddy closures preserve the relation between the growth or decay of eddy energy and the instability or stability of the flow provides further support for their use in ocean general circulation models.

14. Martin, T, and Alistair Adcroft, July 2010: Parameterizing the fresh-water flux from land ice to ocean with interactive icebergs in a coupled climate model. Ocean Modelling, 34(3-4), doi:10.1016/j.ocemod.2010.05.001.
    [ Abstract ]

    Icebergs are an important part of the fresh-water cycle and, until now, have not been explicitly represented in Intergovernmental Panel on Climate Change (IPCC) class coupled global circulation models (CGCMs) of the climate system. In this study we examine the impact of introducing interactive icebergs in a next-generation CGCM designed for 21st Century climate predictions. The frozen fresh-water discharge from land is used as calving to create icebergs in the coupled system which are then free to evolve and interact with the sea-ice and ocean components. Icebergs are fully prognostic, represented as point particles and evolve according to momentum and mass balance equations. About 100,000 individual particles are present at any time in the simulations but represent many more icebergs through a clustering approach. The various finite sizes of icebergs, which are prescribed by a statistical distribution at the calving points, lead to a finite life-time of icebergs ranging from weeks, for the smallest icebergs (60 m length), up to years for the largest (2.2 km length). The resulting melt water distribution seen by the ocean enhances deep-water formation, in particular on the continental shelves, relative to the model without icebergs.

15. 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.
    [ PDF ]
16. 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.

17. 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.

18. 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.

19. Griffies, Stephen M., and Alistair Adcroft, 2008: Formulating the equations of ocean models In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 281-318.
    [ Abstract PDF ]

    We formulate mathematical equations describing the thermo-hydrodynamics of the ocean and introduce certain numerical methods employed by models used for ocean simulations.

20. White, Laurent, and Alistair Adcroft, 2008: A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM). Journal of Computational Physics, 227(15), doi:10.1016/j.jcp.2008.04.026.
    [ Abstract ]

    A hierarchy of one-dimensional high-order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated. The schemes are also compared based on remapping experiments in closed domains. The piecewise quartic method (PQM) is presented, based on fifth-order accurate piecewise polynomials, and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models, which require the remapping to be conservative, monotonic and highly accurate. A limiter for this scheme is fully described that never decreases the polynomial degree, except at the location of extrema. We assess the use of high-order explicit and implicit (i.e., compact) estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method (PPM) and PQM. It is shown that all limited PQM schemes perform significantly better than limited PPM schemes and that PQM schemes are much more cost-effective.

21. 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.

22. Boccaletti, G, R Ferrari, Alistair Adcroft, D Ferreira, and J Marshall, 2005: The vertical structure of ocean heat transport. Geophysical Research Letters, 32, L10603, doi:10.1029/2005GL022474.
    [ Abstract ]

    One of the most important contributions the ocean makes to Earth's climate is through its poleward heat transport: about 1.5 PW or more than 30% of that accomplished by the ocean-atmosphere system (Trenberth and Caron, 2001). Recently, concern has arisen over whether global warming could affect this heat transport (Watson et al., 2001), for example, reducing high latitude convection and triggering a collapse of the deep overturning circulation (Rahmstorf, 1995). While the consequences of abrupt changes in oceanic circulation should be of concern, we argue that the attention devoted to deep circulations is disproportionate to their role in heat transport. For this purpose, we introduce a heat function which identifies the contribution to the heat transport by different components of the oceanic circulation. A new view of the ocean emerges in which a shallow surface intensified circulation dominates the poleward heat transport.

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