Bibliography - Alistair Adcroft

1. Griffies, Stephen, Alistair Adcroft, Ventakramani Balaji, Robert W Hallberg, Sonya Legg, T Martin, and A Pirani, et al., February 2009: Sampling Physical Ocean Field in WCRP CMIP5 Simulations: CLIVAR Working Group on Ocean Model Development (WGOMD) Committee on CMIP5 Ocean Model Output, International CLIVAR Project Office, CLIVAR Publication Series No. 137, 56pp.
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2. Griffies, Stephen, 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 2009: Problems and prospects in large-scale ocean circulation models In Ocean Obs '09, 21-25 September, Venice, Italy, ESA Special Publication, 1-23.
   [ Abstract PDF ]

   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

3. Hallberg, Robert W., and Alistair Adcroft, April 2009: Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-split time stepping. Ocean Modelling, 29(1), doi:10.1016/j.ocemod.2009.02.008.
   [ Abstract ]

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

4. 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.

5. 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.

6. Griffies, Stephen, 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.

7. 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.

8. 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.

9. 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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