Equations, Approximations and Methods in Ocean Modeling
Alistair Adcroft
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Abstract
Ocean Modeling, Remapping, and the ALE Method
John Dukowicz
Los Alamos National Laboratory, USA
Abstract
The different flavors of Finite Element and Finite Volume discretization for oceanic flows
Mohamed Iskandarani
RSMAS/MPO, University of Miami, USA
Overview - Inherent strengths and challenges of the various vertical coordinates used in ocean models
Robert Hallberg
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Spurious diapycnal mixing in ocean models from numerical advection
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Abstract
Issues arising from the nonlinear equation of state in isopycnal coordinate models
Robert Hallberg
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Are there remaining issues precluding the use of terrain-following coordinates in global climate models?
Gokhan Danabasoglu
National Center for Atmospheric Research, Boulder, USA
Issues regarding the use of hybrid coordinates
Rainer Bleck
NASA Goddard Institute for Space Studies, Columbia University, New York, USA
Abstract
-i.e., what modeling considerations give the best of the various coordinate options, and not the worst.
Discussion
What can be done to promote a unified treatment of physical parameterizations across various vertical coordinates? -or- Further discussion of other issues from this session at the discretion of the Organizer.
Voronoi Tessellations for Ocean Modelling: Methods, Modes and Conservations
Todd Ringler
Los Alamos National Laboratory, USA
Unstructured meshes and adaptivity for 3D multi-scale ocean modelling
Matthew Piggott
Imperial College, London, UK
Abstract
Finite element ocean modeling on unstructured 'prismatic' meshes
Laurent White
Université catholique de Louvain, Louvain-la-Neuve, Belgium
Abstract
Diabatic effects associated with mesoscale eddies
Richard Greatbatch
Department of Oceanography, Dalhousie University, Halifax, Canada
Abstract
A New Framework for Parameterizing Eddies in Ocean Climate Models
David Marshall (1) and Alistair Adcroft (2)
(1) Department of Physics, University of Oxford, UK, (2) Geophysical Fluid Dynamics Laboratory
Princeton, USA
Abstract
Parameterizing Mesoscale Eddies with Residual and Eulerian Schemes, and a Comparison with Eddy Permitting Models
Geoffrey K. Vallis
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Abstract
The energetics of internal solitary waves and the need for parameterizations of their effects
Kevin Lamb
Department of Applied Mathematics, University of Waterloo, Canada
The vertical mixing role of surface waves in ocean circulation models
Fangli Qiao
First Institute of Oceanography, State Oceanic Administration, China
Should we really resolve eddies in the ocean component of coupled climate models?
Rüdiger Gerdes
Alfred-Wegener-Institute Bremerhaven, Germany
Open boundary conditions
Eric Blayo
University of Grenoble, France
Abstract
Coastal/regional models are partly driven by their open boundaries, and the conditions which are applied at these artificial interfaces have a strong influence on the solution:
- Mathematical point of view
- Practical aspects: which conditions ? the role of external data
- Open issues
Two-way nesting
Laurent Debreu
Institut National de Recherche en Informatique et en Automatique, Saint Martin d'Heres, France
-Methods for ensuring transparent behaviour at boundaries, and conservation of mass and tracers: Technical and practical issues
Physical aspects (65mn talk + 25min discussion)
Internal physics
Jarle Berntsen (1), Alan M. Davies (2), and Jiuxing Xing (2)
(1) Universitetet i Bergen, Norway, (2) Proudman Oceanographic Laboratory, UK
Abstract
The ocean physics in coastal/regional models can be somewhat different from the physics at a larger scale:
- Which particular physics has to be represented in coastal/regional models?
- Small-scale processes and their parameterization
- Interactions with topography
- Hydrostatic versus non-hydrostatic
Wetting and Drying
Leo Oey
Princeton University, USA
Abstract
-The physical problem and its importance in coastal modelling; numerical methods and algorithms
Model validation
Lars Petter Roed
Norwegian Meteorological Institute, Oslo, Norway
-How shall we do it? Examples from recent exercises
Southern Ocean Simulations with and without Eddies
Robert Hallberg
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Lateral SGS Tracer Operators in Eddying Ocean Models: Who Needs Them?
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Abstract
WGOMD Coordinated Ocean Ice Reference Experiments
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Abstract
Surface Forcing of Ocean Models (Part 1, Part 2)
Claus Böning (1) and Rüdiger Gerdes (2)
(1) IFM-GEOMAR, Universitaet Kiel, Germany (2) Alfred-Wegener-Institute Bremerhaven, Germany
Quantitative model-data comparisons using altimeter data: Dependancy of the model skill on resolution
Thierry Penduff
Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France
Abstract
Resolving Mesoscale Eddy Spectrum: What is Needed?
Anne Marie Treguier
Laboratoire de Physique des Océans, IFREMER, Brest, France
Abstract
Using Ocean Data Assimilation to Estimate Transports and Processes
Detlef Stammer
Inst. fuer Meereskunde, Universitaet Hamburg, Germany
Impact of Ocean Initialization on Seasonal Forecast Skills
Magdalena Balmaseda
ECMWF, Reading, UK
Abstract
Data Assimilation with HYCOM
Eric Chassignet
COAPS, Florida State University, Miami, USA
Equations, Approximations and Methods in Ocean Modeling
Alistair Adcroft
Geophysical Fluid Dynamics Laboratory, Princeton, USA
We present an overview of the choices made in designing ocean climate models, specifically on the choice of equations, the assumptions there-in, and the choice of methods used to solve the equations. Historically, large-scale ocean models were incompressible (the flow is non-divergent) and Boussinesq (the modulation of density variations on horizontal acceleration is neglected, density variations are only active in the vertical momentum balance). The Boussinesq equations conserve volume and not mass, and form of energy conservation is unclear and controversial. In recent years, it has been realized that free-surface methods allow a return to the more fundamental, non-Boussinesq equations which properly account for steric effects (sea-level change due to ocean heat content), conserve mass and energy; consequently many models have now been adapted to solve the hydrostatic non-Boussinesq equations. Non-hydrostatic effects are deemed small at the resolution of current climate models.
Over the last decade, there has been much development in the algorithms and methods used in ocean models, particularly in incorporating methods from other branches of computational fluid dynamics. Although most ocean climate models are essential grid-point models, the principles of the finite volume method and high-resolution schemes have been embraced. One example is for tracer advection where adherence to properties of the physical system, such as conservation of extrema via non-linear flux limiting, prove to be more useful in yielding a meaningful solution than falsely oscillatory methods (e.g. unlimited linear schemes). It is our expectation that we will see more development in this area, applying such schemes to the model as a whole and not just to small parts (such as scalar advection).
Ocean Modeling, Remapping, and the ALE Method
John Dukowicz
Los Alamos National Laboratory, USA
Remapping and ALE are two related methodologies popular in various areas of computational mechanics but not yet in ocean modeling. Remapping is the conservative interpolation between two grids. A version of the technique may be put in flux form that leads to a useful transport algorithm called incremental remapping with several advantageous properties. ALE is a method of solving systems of conservation equations in two steps: a solution on an evolving Lagrangian grid, followed by a remapping to an arbitrarily specified second grid. Eulerian grid solutions may be viewed as ALE methods where the remapping back to the starting grid takes place after every time step. In general, ALE provides great flexibility and improved accuracy because the duration of the Lagrangian phase, and the specification of the remapping grid are quite arbitrary. Reducing the frequency of remapping is advantageous since remapping, as an interpolation, invariably introduces some loss of information. Moreover, ALE methods applied in ocean modeling are frequently column based and one-dimensional, and are therefore cheap and easy to implement.
Spurious diapycnal mixing in ocean models from numerical advection
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Numerical truncation errors associated with tracer advection in non-isopycnal coordinate ocean models (e.g., geopotential, pressure, sigma) can introduce a nontrivial level of spurious diapycnal diffusion, especially in the presence of a strong mesoscale eddy field. We present results from idealized eddying simulations using a z-coordinate model to suggest that the levels of spurious diapycnal mixing associated with a newer class of numerical advection operators is significantly less than the class of operators used in the previous decade. These results indicate that the problems with spurious diapycnal diffusion may be less egregious than originally characterized with the older numerical advection schemes.
Issues regarding the use of hybrid coordinates
Rainer Bleck
NASA Goddard Institute for Space Studies, Columbia University, New York, USA
Hybrid vertical coordinates of the ALE type (Arbitrary Lagrangian-Eulerian, Hirt et al. 1974) are being used successfully in ocean modeling to combine the advantages, and avoid the disadvantages, of Cartesian and isopycnic coordinates respectively. The "ideal" hybrid model is one that, by aligning coordinate surfaces with neutral surfaces to the greatest extent possible, suppresses numerically induced diapycnal mixing while at the same time providing sufficient vertical resolution in unstratified water columns to permit the use of diffusion-type (i.e., non-bulk) mixed layer closure schemes.
Today's purely isopycnic models do not terminate coordinate layers at their outcrop locations but extend them laterally as zero thickness layers. A simple ALE grid is created by assigning a finite thickness to such outcropped layers. This strategy yields a z-coordinate grid in high-latitude unstratified (or unstably stratified) ocean basins while retaining isopycnic grid representation elsewhere. The dynamic equations appropriate for an ALE grid are not radically different from those used in purely Cartesian or purely isopycnic models. The only algorithm not found in the latter is one that decides how the vertically integrated horizontal mass flux divergence at a particular grid point and at a particular time should be divided up among vertical motion of the grid point and vertical motion relative to the grid point. The main challenge is to make the isopycnic-to-z transition reversible in time. Some effort should also be invested into smoothing out the lateral transition between isopycnic and constant thickness portions of a layer.
To retain the main benefit of isoycnic modeling -- explicit suppression of diapycnal fluxes, easy implementation of GM fluxes -- in hybrid models, one should maximize the physical subspace covered by isopycnic layers. ALE schemes are far more effective in this regard than more traditional fixed-formula coordinate combinations (which often are called "hybrid" as well).
Naturally, maximizing the isopycnic subspace also maximizes numerical complexities inherited from purely isopycnic models, such as the evaluation of the horizontal pressure gradient force in a thermobaric medium. Present methods to infer the PGF from state variables carried along steeply inclined surfaces do not work well if based on in-situ density. Therefore, buoyancy and pressure effects in isopycnic models have traditionally been assessed on the basis of potential density (Spiegel and Veronis 1960). However, ambiguities in defining the latter in the presence of thermobaricity still create problems (mostly associated with the split of the PGF into 2 terms) not seen when computing the PGF on horizontal surfaces. Schemes based on virtual potential density (Sun et al. 1999) capture much of the effect of thermobaricity, but fields can be noisy due to "thermobaric" instability (Hallberg 2005).
The search for the optimal combination of isopycnic and Cartesian grid elements in global ocean and climate simulations is likely to continue for a long time. For example, the rendering of ENSO in a coupled model involving the hybrid model HYCOM has been found to benefit from the presence of isopycnic coordinate layers very close to the surface in the equatorial Pacific (Sun and Bleck 2006). Our approach therefore has been to (a) enlarge the isopycnic sub-domain by making the constant-thickness residuals of outcropped layers as thin as possible and (b) avoid adding layers that by virtue of their low "target" density default to constant thickness everywhere. Unfortunately, this strategy yields very uneven vertical grid spacing at high latitudes. In an effort to improve the rendering of deep convection in HYCOM, we have begun to increase the vertical spacing of grid points at high latitudes by assigning large minimum thickness values to the model's densest coordinate layers. If done judiciously, this will not obliterate near-surface isopycnal layers in the tropics (S.Sun, pers. comm.).
Unstructured meshes and adaptivity for 3D multi-scale ocean modelling
Matthew Piggott
Imperial College, London, UK
Over the past decade there has been significant growing interest in the use of unstructured mesh based methods in ocean modelling. These method include finite element and finite volume discretisation methods on meshes which may be unstructured in the horizontal only or in all three directions.
Moving from structured to unstructured meshes offers many potential benefits. In particular it allows for an excellent representation of complex coastlines and bathymetry, and the ability to use wildly different resolutions in different parts of the domain. For example enhanced resolution may be employed to better resolve important localised phenomena such as boundary layer separations and overflows, and also regions of particular socio-economic or scientific importance. Importantly, unstructured meshes allow for the efficient representation of any interaction between a range of coupled spatial scales. Due to their geometric flexibility this can be achieved with unstructured meshes without resorting to the unsatisfactory approach of mesh nesting due to the fact that smooth variations in mesh resolution are easily achieved.
Unstructured meshes are also the natural framework within which to formulate robust adaptive mesh capabilities. Extending the above multi-scale ability of the mesh, adaptive methods can be used to optimally resolve and track the formation and evolution of localised features in a priori unknown and/or evolving locations. This would be impossible with any fixed mesh, whether unstructured or not.
When utilising adaptive algorithms a model is able to automatically allocate computational resources in an optimal and dynamic manner, as dictated by evolving solution fields and estimates of model and discretisation errors. The aim is that this will lead to more efficient calculations, i.e. overall less mesh nodes would be required to yield a particular solution to a given accuracy; also for a given computational resource a hope is that it should allow problems to be solved which are more complex than is currently feasible.
In this presentation we describe some of our experiences with constructing a three-dimensional nonhydrostatic finite element ocean model using fully unstructured adaptive mesh techniques.
Of particular importance and focus here are mesh generation; mesh optimisation operations and mesh anisotropy; error measures; techniques for accurately describing model states close to hydrostatic and geostrophic balance on arbitrary irregular meshes; sharp interface representation; arbitrary mesh movement; and load-balanced parallelisation.
With any new modelling approach validation is crucial. Here a range of CFD benchmarks are presented where comparisons with laboratory and other well-validated numerical codes are possible. Applications and validation against idealised overflow problems, internal waves, flow past bathymetry, western boundary currents, basin and global scale tides, tsunami, wetting and drying in estuaries, and baroclinic circulation in the North Atlantic are also presented.
Finite element ocean modeling on unstructured 'prismatic' meshes
Laurent White
Université catholique de Louvain, Louvain-la-Neuve, Belgium
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Diabatic effects of mesoscale eddies
Richard Greatbatch
Department of Oceanography, Dalhousie University, Halifax, Canada
The theoretical development of Eden, Greatbatch and Olbers (2007) was briefly reviewed, showing how a physically meaningful separation of eddy fluxes into advective, diffusive and rotational parts can be achieved. It was emphasized that the rotational flux is chosen in such a way that the diffusive flux is a genuine diabatic flux associated, when the tracer being fluxed is buoyancy, with water mass conversion. A new approach to parameterising the advective flux based on a prognostic equation for eddy kinetic energy was presented and shown to perform well in non-eddy resolving models compared to corresponding eddy-resolving models of both the North Atlantic and the Southern Ocean (see Eden and Greatbatch, 2007). It was pointed out that the eddy-resolving experiments imply the existence of an additional advective thickness flux, associated with anisotropic mixing, e.g. due to the beta effect, that needs to be parameterized (see Eden, Greatbatch and Willebrand, 2007). Attention was then focused on the diffusive flux and the theory illustrated by considering the diffusive (lateral) eddy flux for heat in the surface mixed layer. The diffusive effect was illustrated by considering two eddying numerical models for the northwest Atlantic Ocean that differ only in that the interaction between the eddies and the surface heat flux is suppressed by construction in one of the experiments (Zhai and Greatbatch, 2006a). Comparing the sea surface temperature (SST) distribution in the two models clearly shows that in the fully interactive experiment, the eddies are effective in fluxing heat across the Gulf Stream and Labrador Current fronts. The estimated lateral diffusivity varies from near 102 north of the Gulf Stream to near 104 in SI units on the southern rim of the Gulf Stream and in the northwest corner region. Comparison was made with an estimate of the diffusivity computed using satellite data with generally favourable agreement. The satellite data shows that the dissipation time scale for SST anomalies in the North Atlantic ranges from near 30 days in the vicinity of the Gulf Stream to nearer 150 days in the quieter region of the Sargasso Sea (Zhai and Greatbatch, 2006b).
Finally a 1/12 th degree eddy resolving model of the North Atlantic Ocean was used to show that the dispersal of wind-induced near-inertial energy in the ocean is strongly influenced by the presence of a mesoscale eddy field and is drained to the deep ocean preferentially inside anticyclonic eddies. It was pointed that there is observational evidence of the trapping of near-inertial energy inside anticyclonic eddies in the ocean, and of mixing and dissipation near the critical depth where the vertical group velocity goes to zero. The model results argue that the process of local draining to depth and dissipation of near-inertial energy inside anticyclonic eddies is much more important than the traditional view by which near-inertial energy disperses downward and equatorward by the beta-dispersion effect (see Zhai, Greatbatch and Eden, 2007).
References
Eden, C., and R.J. Greatbatch, 2007, Towards a mesoscale eddy closure, Ocean Modelling, in press.
Eden, C., R.J. Greatbatch and D. Olbers, 2007, Interpreting eddy fluxes, J. Phys. Oceanogr., 37, 1282-1296.
Eden, C., R.J. Greatbatch and J. Willebrand, 2007, Diagnosing the eddy thickness flux from an eddy-resolving model, J. Phys. Oceanogr., 37, 727-742.
Zhai X. and R. J. Greatbatch, 2006a, Surface eddy diffusivity for heat in a model of the northwest Atlantic Ocean, Geophys. Res. Lett., 33, L24611, doi:10.1029/2006GL028712
Zhai X.and R. J. Greatbatch, 2006b, Inferring the eddy-induced diffusivity for heat in the surface mixed layer using satellite data, Geophys. Res. Lett., 33, L24607, doi:10.1029/2006GL027875.
Zhai X., R. J. Greatbatch and C. Eden, 2007, Spreading of near-inertial energy in a 1/12° model of the North Atlantic Ocean, Geophys. Res. Lett., 34, L10609, doi:10.1029/2007GL029895.
A New Framework for Parameterizing Eddies in Ocean Climate Models
David Marshall (1) and Alistair Adcroft (2)
(1) Department of Physics, University of Oxford, UK, (2) Geophysical Fluid Dynamics Laboratory
Princeton, USA
A new framework is developed for parameterizing eddies in ocean models. The proposed eddy closures flux potential vorticity (or layer thickness) down-gradient along density surfaces and satisfy an energy conservation relation by solving an explicit budget for the eddy energy. The latter is, in turn, related to the eddy transfer coefficient through a simple scaling relation. When energy conservation is satisfied in this manner, the growth or decay of the parameterised eddy energy can be related naturally to the instability or stability of the flow as described by Arnold's first stability theorem. The resultant family of eddy closures therefore possess some of the ingredients necessary to parameterize the gross effects of eddies in both forced-dissipative and freely-decaying turbulence. An important issue concerns parameterization of the dispersion and dissipation of the eddy energy, for which some simple schemes are suggested. These ideas are illustrated through applications to wind-driven circulation and freely decaying turbulence in idealised ocean basins. Preliminary results are also presented from an ocean general circulation model in which the Gent and McWilliams eddy closure is modified to include an explicit eddy energy budget. The resultant parameterized eddy energies are broadly in accord with observed distributions. We suggest that this general conservative approach may prove valuable for parameterizing geostrophic eddies in ocean climate models.
Parameterizing Mesoscale Eddies with Residual and Eularian Schemes, and a comparison with Eddy Permitting Models
Geoffrey K. Vallis
Geophysical Fluid Dynamics Laboratory, Princeton, USA
We explore and test certain parameterization schemes that aim to represent the effects of unresolved mesoscale eddies on the larger-scale flow. In particular, we examine a scheme based on the residual or transformed Eulerian mean formulation of the equations, in which the eddies are parameterized by a large vertical viscosity in the momentum equations, with no parameterization appearing in the tracer (e.g., temperature or salinity) evolution equations.
The residual scheme is compared both to a conventional parameterization that uses a skew diffusion (or equivalently advection by a skew velocity), and to eddy-permitting calculations. Although in principle equivalent to certain forms of skew flux schemes, the residual formulation is found to have certain advantages over the conventional scheme, in particular near the upper boundary where conventional schemes are sensitive to the choice of tapering, but the residual scheme less so. The residual scheme also enables the horizontal viscosity -- which is mainly applied to maintain model stability -- to be reduced. Finally, the residual scheme is somewhat easier to implement, especially in simulations with multiple tracers, and the tracer transport is easier to interpret. On the other hand, the residual scheme gives, at least formally, a transformed velocity, not the Eulerian velocity.
Open boundary conditions
Eric Blayo
University of Grenoble, France
Designing open boundary conditions (OBCs) is an important issue for regional modelling, since a local model is generally partly, if not mostly, driven by its boundaries. Most usual OBCs do not depend on the equations of the model in which they are used, which can lead to poor performances. It is shown that OBCs derived from the model equations can lead to improved results. At first order, this approach leads to the use of characteristic based OBCs. Such OBCs are available for barotropic dynamics, and are under development for baroclinic dytnamics. It is thus recommended in present applications to separate the treatment of barotropic and baroclinic dynamics, and to use characteristic based OBCs for the barotropic part and a relaxation method for the baroclinic part.
At higher order, this approach leads to the derivation of so called absorbing boundary conditions, which are presently under investigation in several groups worldwide.
Internal physics
Jarle Berntsen (1), Alan M. Davies (2), and Jiuxing Xing (2)
(1) Universitetet i Bergen, Norway, (2) Proudman Oceanographic Laboratory, UK
A discussion of the processes that may be represented in coastal and regional scale models such as meso-scale eddies is given. Many processes and phenomena such as internal waves, processes near internal fronts, and overflows may not be represented properly in regional scale models. Small scale topography will also be on a sub-grid scale. Interactions between stratified flow and topography is believed to play an important role in determining the vertical mixing and the large scale circulation. The mixing events will typically be on a sub-grid scale in most model studies, and must therefore still be parameterized. These processes that still may not be represented or at best poorly represented are discussed.
As we move towards model studies with finer horizontal grids, the hydrostatic assumption becomes questionable. Non-hydrostatic pressure effects are very important in for instance studies of internal wave propagation, breaking, and mixing and in overflow studies. A discussion of the grid sizes that are needed to resolve the non-hydrostatic effects is given, and also possible effects of under-resolving the non-hydrostatic are discussed.
Wetting and Drying
Leo Oey
Princeton University, USA
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Lateral SGS Tracer Operators in Eddying Ocean Models: Who Needs Them?
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Modellers using Z-coordinate codes generally include a subgrid scale (SGS) operator in addition to the advection operator when discretizing the tracer equation. These SGS operators generally arise from the class of physical parameterizations known as "neutral physics".With the construction of finer resolution simulations that include a nontrivial level of mesoscale eddies, the question arises whether to include neutral physics operators in these eddying simulations.
We argue in this talk that the present class of neutral physics operators, if employed in eddying simulations, serves to satisfy numerical, rather than physical, closure. Namely, the neutral physics operators provide a dissipation mechanism for small scale tracer variance without adding the huge levels of spurious diapycnal diffusion of a horizontally oriented diffusion operator. To put it more succinctly, the neutral physics operators are "sweeping" up numerical problems associated with numerical tracer advection.
A complement approach to eddying simulations is motivated by the practice in isopycnal models, where the lateral tracer transport problem is posed as pure advection, with no extra SGS operator. In the z-models, maintaining a trivial level of spurious mixing from numerical advection remains very difficult when presented with a vigorous eddying momentum field. Nonetheless, we argue that a new class of advection schemes moves the z-models into a regime where spurious mixing is far more modest than in the past, and possibly at a near negligible level. If this conjecture is valid, the z-models should drop the present class of SGS neutral operators when moving to the eddying regime, in which case they will be solving the same tracer equation as the isopycnal models.
WGOMD Coordinated Ocean Ice Reference Experiments
Stephen Griffies
Geophysical Fluid Dynamics Laboratory, Princeton, USA
Coordinated Ocean-ice Reference Experiments (COREs) are proposed as a tool to explore the behaviour of global ocean-ice models under forcing from a common atmospheric state. 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, with details key to realizing simulations with stable overturning circulations. As an outcome of this analysis, we introduce a grid resolution hypothesis, whereby models with sufficient resolution to capture certain subpolar Atlantic processes are less sensitive to hydrological cycle variations.
The atmospheric state from Large and Yeager (2004) was developed for coupled ocean and sea ice models. We found it to be suitable for our purposes, even though evaluation of this state originally focussed more on the ocean than the sea-ice. Simulations with this atmospheric state are presented from seven global ocean-ice models using the CORE-I design. These simulations test the hypothesis that global ocean-ice models run under the same atmospheric state produce qualitatively similar simulations. This hypothesis holds reasonably well (with notable exceptions) for upper ocean tropical behaviour, but is less valid when examining deeper properties, especially in the high latitudes.
Given the broad selection of models participating in this study, the simulations presented here can provide some feedback to the fidelity of the prescribed atmospheric state. That is, places where each model produces a similar behaviour that is biased relative to observations may signal a problem with the atmospheric state, thus suggesting areas requiring reexamination. Conversely, an outlier model may highlight problems in the model's fundamentals and/or configuration. Identifying problem areas promotes avenues for model development aimed at reducing the bias.
Quantitative model-data comparisons using altimeter data: Dependancy of the model skill on resolution
Thierry Penduff
Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France
The DRAKKAR consortium is building a hierarchy of ocean/sea-ice models (the DRAKKAR Group, 2007) based on the NEMO system (Madec et al, 2006) to simulate and study the dynamical processes involved in the oceanic variability and scale interactions over the last 50 years. Along with eddy-resolving 1/12°-1/15° regional and nested configurations, this hierarchy includes global models at 2° 1°, 1/2°, and 1/4° which share similar resolutions at the equator. These configurations differ by their subgrid-scale parameterizations and are forced daily through bulk formulae over the last five decades by the same reanalyzed and observed atmospheric fields ("DFS3", Brodeau et al, 2007). Quantitative methods (space-time collocation, filtering, statistical analyses, etc.) and tools are being developed to systematically quantify the skill of DRAKKAR simulations in terms of sea-level anomaly (SLA), temperature and salinity with respect to observed datasets (Penduff et al, 2007). The present abstract is focused on the impact of grid resolution and associated parameterizations on the model skills in terms of SLA variability in various frequency bands. The quasi-global AVISO altimetric sea-level anomaly database (1/3° weekly SLA, 1993-2004) is compared in various wavenumber-frequency bands with its collocated counterparts simulated by the 2°, 1/2° and 1/4° global models with identical forcing.
The two-step increase in resolution enhances simulated SLA standard deviations in all frequency bands over the global ocean in various ways. The 2° and 1/2° simulations only generate a fraction of the observed SLA variability: 20-50% in all frequency bands in northern mid-latitudes and southern mid/high-latitudes, and less than 10% at high frequency (i.e. periods shorter than 5 months) throughout the global ocean. The 1/4° resolution substantially enhances these levels both at high-frequency and at interannual periods, especially in the Gulf-Stream, Kuroshio, and in the Southern Ocean where SLA standard deviations reach 80% of their observed values. However, the 1/2° and 1/4° resolutions yield comparable variability levels in the tropics (+/-5-25° latitude bands) at all frequencies. In contrast, this beneficial impact of model resolution is absent from global maps of local correlation coefficients C (between collocated model and AVISO SLAs) drawn in various frequency bands. Increasing resolution even yields a decrease in C in the Southern Ocean. These results show the emergence at 1/4° of substantial intrinsic, non-linear variability, uncorrelated with the forcing and real ocean variability. However, along basin boundaries (0-100 km distance) in the 15-240 day period band, C values increase from 2° to 1/2° and remain the same at 1/4°, confirming that resolution finer than 1/4° is needed to further improve the annual-to-subannual boundary variability in climate simulations.
To better interpret the impact of resolution on the simulated spatiotemporal variability, the leading EOF of SLA observations (and corresponding principal component O(t)) was computed in the interannual frequency band in various basins. Simulated SLA timeseries were projected on this spatial mode, yielding for each simulation i the simulated counterparts Si(t) of O(t). In the North Atlantic, the first interannual EOF of observed SLA (Marshall et al (2001)'s "intergyre gyre") follows the NAO index variability by a few months. Our simulations reproduce this observed structure with a lag that monotically tends toward this observed value with increasing resolution. The ratios of Si(t) and O(t) variances, and their mutual correlations also increase continuously from 2° to 1/4° resolution, confirming the beneficial impact of increased resolution on interannual variability modes (timescales, phase, intensity). Such improvements are seen in the Tropical Pacific and Indian Oceans as well, and actually concern the leading four EOFs in these basins.
Beyond these examples, quantitative assessment methods and tools are being developed for and applied to all DRAKKAR simulations to monitor ongoing simulations, characterize the structure of model biases, assess the impact of numerical/physical choices and guide physical investigations.
References
Brodeau, L., B. Barnier, T. Penduff, A.M. Treguier, and S.K. Gulev, 2007: An ERA40-based atmospheric forcing for global ocean circulation models. Submitted to Ocean Modelling.
The DRAKKAR Group, 2007: Eddy-permitting ocean circulation hindcasts of past decades. CLIVAR Exchanges, 42 (vol 12 N°3), 8-10. (Unpublished manuscript).
Madec G., 2007: NEMO reference manual, ocean dynamics component : NEMO-OPA. Preliminary version. Note du Pôle de modélisation, Institut Pierre-Simon Laplace (IPSL), France, No 27 ISSN No 1288-1619.
Marshall, J., H. Johnson, and J. Goodman, 2001: A study of the interaction of the North Atlantic Oscillation with the ocean circulation. Journal of Climate, 14, 1399-1421.
Penduff, T., M. Juza, and B. Barnier, 2007: Assessing the realism of ocean simulations against hydrography and altimetry. CLIVAR Exchanges, 42 (vol 12 N°3), 11-12. (Unpublished manuscript).
Resolving Mesoscale Eddy Spectrum: What is Needed?
Anne Marie Treguier
Laboratoire de Physique des Océans, IFREMER, Brest, France
A few general ideas and avenues for further discussions are proposed in this talk. First, while eddy permitting models become more widely used, different modelling groups realize that even at medium or high resolution the details of numerical methods can make a big difference. This point has been underlined by S. Griffies (talk in this workshop) regarding the advection of tracers. Recent papers by the DRAKKAR modelling group demonstrate a large effect of the momentum advection scheme (Barnier et al, 2006). We show here a striking example from the Agulhas retroflexion region, with a very different pattern of ring formation and detachment when the numerics are changed in the global ORCA025 model (1/4° resolution at the equator). These new results however do not challenge the guideline proposed by Smith et al (2000), namely, that 1/10° or more is necessary for a first order representation of the Gulf Stream and the North Atlantic current. We lack similar statements about polar regions, where the dynamical length scale (Rossby radius of deformation) is even smaller. We note also that validating the high resolution models is more difficult because observations are sparse in space and time. Satellite altimetry, which is the best global measure of dynamical eddy variability, does not resolve globally the space scales smaller than 25km and time scales less than a few days.
One intriguing issue is the possibility that the so called "eddy-permitting" models, of resolution 1/4° or so, may be the worse models with respect to eddy paramerization. An exemple from a recent study by Chanut et al (2007) is shown: restratification after convection in the Labrador sea is roughly represented by a 1° model (through the parameterized lateral mixing). An eddy permitting 1/6° model with relatively small lateral viscosity and diffusion, and no GM parameterization, fails to represent the restratification and as a result convects too deep every winter. A 1/15° model explicitly represent the eddies responsible for the restratification, which leads to a much more realistic representation of the seasonal cycle of convection. At intermediate resolution (1/6° or 1/4°) it is difficult to decide which parameterization to use. Choosing the same GM and lateral mixing coefficients as in lower resolution models leads to broad and slow boundary currents, partially offsetting the improvements brought about by the refined grid. On the contrary, choosing small mixing parameterizations can also result in a degradation of the solution, as demonstrated in the Labrador Sea.
Very high resolution experiments (resolutions up to 500m, or 1/54° on the basin scale) suggest that the submesoscale dynamics significantly affects the model circulations, so that parameterization of submesoscale effects remains a problem even at 1/15° or 1/10°. A few results from experiments run on the Earth simulator as part of a Japan-French project (P. Klein, B.L. Hua, M. Levy, G. Madec) are shown, underlying the importance of submesoscale dynamics for the injection of tracer into the mixed layer or for vertical velocities. A high resolution model forced by synoptic winds produces very energetic near-inertial waves, with a spectral peak at frequency 2f (twice the inertial frequency) in the deep ocean. This unrealistic feature points toward a missing process, which may be the parameteric instability of near inertial waves.
Barnier, B., G. Madec, T. Penduff, J.M. Molines, A.M. Treguier, J. Le Sommer, A. Beckmann, A. Biastoch, C. Boening, J. Dengg, C. Derval, E. Durand, S. Gulev, E. Remy, C. Talandier, S. Theetten, M. Maltrud, J. McClean, B. De Cuevas 2006: Impact of partial steps and momentum advection schemes in a global ocean circulation model at eddy permitting resolution. Ocean Dynamics, p543-567, DOI: 10.1007/s10236-006-0082-1.
Chanut J., B. Barnier, W. Large, L. Debreu, T. Penduff and J.M. Molines, 2007: Mesoscale Eddies in the Labrador Sea and their Contribution to Convection and re-Stratification, J. Phys. Oceanogr., in press.
Smith, R. D., M. E. Maltrud, F. O. Bryan, and M. W. Hecht, 2000:Numerical simulation of the North Atlantic Ocean at 1/10°. J. Phys. Oceanogr., 30, 1532-1561Impact of ocean initial conditions on seasonal forecasts skill
Magdalena Alonso Balmaseda
ECMWF
It is widely accepted that skilful forecasts of ENSO at seasonal time scales rely on the knowledge of the ocean subsurface. However, there is open debate about the relative merits of the different ocean initialization strategies, usually in the context of initialization shock versus 'realistic' initial conditions. In this work we present the the impact of 3 different initialization strategies on the ECMWF System 3 seasonal forecasting system. It is shown that the benefits of ocean data assimilation for for seasonal forecasts outweight the drawbacks associated with larger initialization shock in the eastern Pacific. It is also shown that the wind product from atmospheric reanalysis produces better skill scores than the wind product from atmospheric only-runs. In addition, we present the impact of the different ocean observing systems on the seasonal forecast skill of SST.