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Ocean dynamics
Volume 56, Numbers 5-6, December 2006 , pp. 543-567(25)
http://dx.doi.org/10.1007/s10236-006-0082-1
© Springer 2006. Part of Springer Science+Business Media
Archimer
Archive Institutionnelle de l’Ifremer
http://www.ifremer.fr/docelec/
Impact of partial steps and momentum advection
schemes in a global ocean circulation model at eddy
permitting resolution.
Barnier BERNARD
1,
*, Gurvan MADEC
2
, Thierry PENDUFF
1
, Jean-Marc MOLINES
1
,
Anne-Marie TREGUIER
3
, Julien LE SOMMER
1
, Aike BECKMANN
4
, Arne BIASTOCH
5
,
Claus BÖNING
5
, Joachim DENGG
5
, Corine DERVAL
6
, Edmée DURAND
6
, Sergei
GULEV
7
, Elizabeth REMY
6
, ClaudeTALANDIER
2
, Sébastien THEETTEN
3
, Mathew
MALTRUD
8
, Julie MCCLEAN
9
, Beverly DE CUEVAS
10
1
Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France
2
Laboratoire d'Océanographie Dynamique et de Climatologie, Paris, France
3
Laboratoire de Physique des Océans, Ifremer Centre de Brest, Plouzané, France
4
Department of Physical Sciences, Division of Geophysics, University of Helsinki, Helsinki, Finland
5
IfM-GEOMAR, Leibniz-Institut für Meereswissenschaften an der Universität Kiel, Kiel, Germany
6
MERCATOR-Ocean, Toulouse, France
7
Shirshov Institut of Oceanography, Russian Academy of Science, Moscow, Russia
8
Fluid Dynamics Group, Los Alamos National Laboratory, Los Alamos, USA
9
Scripps Institution of Oceanography, UCSD, LA Jolla,USA
10
National Oceanography Centre, Southampton, UK
*: Corresponding author : Barnier BERNARD
- Email: bernard.barnier@hmg.inpg.fr
Abstract:
Series of sensitivity tests have been performed with a z-coordinate, global eddy permitting (1/4°)
ocean/sea-ice model (the ORCA-R025 model configuration developed for the DRAKKAR project), to
carefully evaluate theim pact of recent state of the art numerical schemes on model solutions. The
combination of an energy-enstrophy conserving scheme (EEN) for momentum advection with a partial
step (PS) representation of the bottom topography yields significant improvements in the mean
circulation. Well known biases in the representation of western boundary currents, such as in the
Atlantic the detachment of the Gulf Stream, the path of the North Atlantic Current, the location of the
Confluence and the strength of the Zapiola Eddy in the south Atlantic, are partly corrected.
Similar improvements are found in the Pacific, Indian and Southern Oceans, and characteristics of the
mean flow are generally much closer to observations. Comparisons with other state of the art models
show that the ORCA -R025 configuration generally performs better at similar resolution. In addition,
the model solution is often comparable to solutions obtained at 1/6° or 1/10° resolution in some
aspects concerning mean flow patterns and distribution of eddy kinetic energy. Although the reasons
for these improvements are not analysed in detail in this paper, evidence is shown that the
combination of EEN with PS reduces numerical noise near the bottom which is likely to affect current-
topography interactions in a systematic way. We conclude that significant corrections of the mean
biases presently seen in general circulation model solutions at eddy permitting resolution can still be
expected from the development of numerical methods which represent an alternative to increasing
resolution.
Keywords: Global ocean; Eddy-permitting ocean model; Momentum advection scheme; Partial step
topography; Eddy/topography interactions
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1. INTRODUCTION
In a special issue honouring the memory of Christian Le Provost, it is fitting for many of us who
collaborated with him, sometimes very closely and for almost twenty years, to place the work
presented here in relation to scientific issues he stood by. Christian Le Provost's first
involvement in the field of ocean circulation modelling was motivated by the World Ocean
Circulation Experiment (WOCE) in the mid 80's. His intuition was that among all processes
which have a crucial influence in shaping the mean circulation, two of particular importance
were overlooked: the mesoscale eddies and the constraint of the bottom topography. His early
work therefore concentrated on process studies searching for a better understanding and
modelling of the generation of eddies in the presence of topography (Verron and Le Provost –
1985, Verron, Le Provost and Holland, 1987) and the interaction of turbulent large scale flows
with topography (Barnier and Le Provost, 1993). He also emphasised the crucial importance of
numerics on the realism of model solutions (Blayo and Le Provost, 1993). Christian convinced
himself and his group that accurate modelling of the effect of bottom topography on ocean non-
linear flows is a key to achieve realistic simulations of the global ocean circulation. This belief
underlay the model intercomparison DYNAMO project (DYNAMO Group, 1997) which he
designed with Jürgen Willebrand (Willebrand et al., 1991).
Building and running ocean models able to simulate the world ocean circulation with
great realism require a great variety of scientific skills. Christian Le Provost was aware that
gathering all the necessary skills within a single research team as the one he was leading would
be difficult. Consequently, he always favoured community experiments, in the spirit of the
Community Model Experiment (CME) carried out under WOCE (Bryan and Holland, 1989,
Böning and Bryan, 1996). This concept of community projects, which Christian shared with
Jürgen Willebrand, Bill Holland and others, was at the core of the DYNAMO project. It has been
at the origin of the French CLIPPER project (Treguier et al., 1999), and is the basis of the
international DRAKKAR project which is briefly presented here. These are projects in which
Christian Le Provost actively participated.
The present paper is strongly inspired by the issues mentioned above. It presents recent
advances in modelling the general ocean circulation at eddy-permitting resolution achieved in the
framework of the European modelling project DRAKKAR. Indeed, eddy-permitting models are
still worth exploring and enhancing, despite the existing higher resolution models, since they will
be the target resolution of the next generation of climate models. Improvements presented here
mainly concern the representation of ocean flows in regions where the circulation is dominated
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by non-linearities and is strongly constrained by bottom topography. These results were obtained
by using a new numerical treatment of the non-linear advection term in momentum equations,
and a partial step representation of the bottom topography.
The paper is organised as follows. Section 2 describes the eddy permitting, global, 1/4°
model configuration implemented by the project, ORCA-R025. It also presents the mean
circulation produced by ORCA-R025 under a climatological atmospheric forcing. Section 3
evaluates the impact of new numerical choices regarding bottom topography and momentum, in
direct relation with Christian Le Provost early intuition, by comparison of ORCA-R025
simulations with observations and other state of the art model simulations at equivalent or higher
resolution. The last section is a conclusion which identifies key issues where problems remain
and ways of improvements.
2. GLOBAL 1/4° DRAKKAR CONFIGURATION ORCA-R025
2.1. DRAKKAR project
During the last decade, scientists participating in the DRAKKAR
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project fostered co-operative
activities within the European project DYNAMO (Dynamics of North Atlantic Models,
DYNAMO Group - 1997), and between their respective national projects, CLIPPER in France
(Treguier et al., 1999) and FLAME (Family of Linked Atlantic models) in Germany (Böning et
al., 2003). The challenge of developing realistic global ocean models suited for a wide range of
applications will be better met with an effective integration and co-ordination of activities and
complementary expertises of the groups. This yielded the DRAKKAR concept, a European
modelling project which provides the framework for joint and co-ordinated modelling studies
between research groups in France, Germany, Russia and Finland.
One primary concern of the project is related to the circulation and variability in the North
Atlantic Ocean as driven by the atmospheric forcing, by interactions between processes of
different scales, by exchanges between basins and regional circulation features (including the
Nordic Seas), and by the influence of the world ocean circulation (including the Arctic and
Southern Oceans and the Agulhas retroflection region). To achieve these scientific objectives,
DRAKKAR is carrying out co-ordinated realistic simulations of the ocean circulation at regional
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http://www.ifremer.fr/lpo/drakkar
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and global scales, with pertinent atmospheric forcing and resolutions high enough to insure
physical consistency over the range of scales which are dynamically important (i.e. from eddy to
global, from day to decade).
As first objective, the project has built a hierarchy of numerical model configurations,
from global to regional scale, each based on the NEMO
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modelling system which presently
includes the latest version of the primitive equation, free surface (Roullet and Madec, 2000),
ocean circulation code OPA9 (Madec et al., 1998) coupled to the multi-layered sea-ice code
LIM2 (Fichefet et al, 1997). This hierarchy of models includes the ORCA-R025 configuration,
an eddy-permitting, global ocean/sea-ice configuration with a resolution of 1/4° described below.
2.2. GLOBAL 1/4° DRAKKAR CONFIGURATION ORCA-R025
ORCA Grid common to all DRAKKAR configurations
In the OPA numerical code (Madec et al., 1998), the primitive equations are discretised on a C-
grid centered at tracer points. A family of tri-polar grids, ORCA grids, has been developed by
Madec (Personal communication) for global models (see Timmermann et al., 2005, for an
application of the ORCA grid at 2° resolution). The geographical south pole is conserved, and
from 80°S to 20°N, the grid is a regular Mercator-grid (isotropic, getting finer at high latitude as
the cosine of latitude). Following Murray's (1995) idea, the singularity of the North Pole is
treated by changing the coordinate system using two poles, one in Canada and the other in Asia.
Starting at 20°N, latitude circles of the Mercator-grid are progressively distorted into ellipses, the
great axes of which are oriented along a line joining the two poles of the northern hemisphere.
The grid is computed following the semi-analytical method of Madec and Imbard (1996). The
deformation of the grid is such that it remains quasi-isotropic, and is quasi-uniform in the Arctic.
Since the resolution of the grid is variable, the resolution of an ORCA grid is referred to the
latitude of the equator, where it is the coarsest. This family of grid is used for all DRAKKAR
configurations, including the regional ones (North Atlantic and Nordic Seas).
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NEMO: Nucleus for European Models of the Ocean
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Model grid, bathymetry and initial conditions
ORCA-R025 is a global configuration of NEMO implemented on an ORCA grid at 1/4°
resolution. Grid, masking and initial conditions are inherited from the global configuration of the
operational oceanography centre MERCATOR-Ocean
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(Remy et al., personal communication).
This configuration has 1442x1021 grid points and uses 46 vertical levels. Vertical grid spacing is
finer near the surface (6 m) and increases with depth to 250 m at the bottom. The maximum
depth in the model is 5844 m. The effective resolution which gets finer with increasing latitudes
is ∼27.75 km at the equator, ∼13.8 km at 60°S or 60°N. It gets to ∼7 km in the Weddell and Ross
Seas and ∼10 km in the Arctic.
The bathymetry is derived from the 2-minute resolution Etopo2 bathymetry file of NGDC
(National Geophysical Data Center), which is a combination of the satellite-based bathymetry
(Smith and Sandwell (1997) and IBCAO in the Arctic (Jakobsson et al., 2000). It has been
merged with the BEDMAP data (Lythe and Vaughan, 2001) beyond 72°S in the Antarctic. The
interpolation onto the model grid has been carried out by taking all the Etopo2 grid points falling
into an ORCA025 grid box, and taking the median of those points. This produces a smoothing of
the sub-grid scale topography. Penduff et al (2002) showed that topographic smoothing has a
strong influence on the model's circulation. We believe that topography should not vary too
much at the grid scale to avoid numerical noise. For this reason, we have applied an additional
smoothing (two passes of a uniform shapiro filter). Hand editing has been performed in a few
key areas. Initial conditions for temperature and salinity are derived from the Levitus (1998) data
set for the middle and low latitudes. For high latitudes we chose the PHC2.1 climatology (Steele
et al., 2001) and for the Mediterranean Sea the Medatlas climatology (Jourdan et al, 1998).
Numerical characteristics
A purpose of developing the NEMO code is to improve model physics and numerical algorithms.
Perhaps the most significant problem in eddy-permitting z-coordinate ocean models is the
misrepresentation of flow-topography interactions (Penduff et al., 2005). The previous version of
OPA (OPA 8.1, Madec et al., 1998) represented the topography as staircases whose steps have
the size of the model vertical levels: this is the "full step" (FS) topography, which approximates
the true ocean depth to the closest model level. By making the depth of the bottom cell variable
and adjustable to the real depth of the ocean, it is possible to better represent small topographic
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MERCATOR-Ocean: httm://www.mercator-ocean.fr
