67
Predicting, with an acceptable degree of realism, the evolution of climate on time scales of a
few decades can be achieved with a model incorporating only representations of the
atmosphere, ocean and sea-ice sub-systems. At Louvain-Ia-Neuve, we are developing such a
model of the climate system, and some results of the oceanic component will be presented
below.
The model. As pointed out by Niiler (1992), "the principal role of the oceans in maintaining
the present climate system of the Earth is the creation of large reservoirs of heat in tropical
latitudes and the transport of this thermal energy to the polar latitudes". Throughout the year,
the World Ocean transports about 1015 W - in thermal energy - from the low latitudes
toward the poles (e.g. Hastenrath, 1982), which is somewhat smaller than the meridional
atmospheric heat transport. Thus, by removing heat from the tropics and carrying it toward the
poles, the World Ocean significantly reduces the equator-poles contrasts. In addition, because
of their large heat capacity, the upper layers exhibit a large thermal inertia, moderating the
amplitude of the surface temperature seasonal cycle (e.g. Monin, 1975). Finally, the World
Ocean may act as a sink of carbon dioxide (e.g. Sarmiento, 1992).
The Louvain-Ia-Neuve Ocean General Circulation Model (OGCM) is rather similar to the
most classical OGCMs (e.g. Bryan, 1969). It is based on the usual set of assumptions, i.e, the
hydrostatic equilibrium and the Boussinesq approximation. The prognostic variables are the sea
surface elevation, the three components of the velocity, the potential temperature and the
salinity. The turbulence closure is achieved according to the simple formulae of Pacanowski
and Philander (1981). The space discretization uses the finite volume technique on an Arakawa
B-grid. The time stepping is of Euler-forward type, with a split-explicit mode splitting to
circumvent the severe numerical stability constraints associated with the propagation of external
inertia-gravity waves (Gadd, 1978; Killworth et ai., 1991; Deleersnijder and Campin, 1995).
More details about our OGCM may be found in Deleersnijder and Campin (1993,1995) and
in the Appendix. Hereafter, the curvilinear coordinate system underlying the horizontal
discretization is discussed.
Horizontal curvilinear coordinate system. In most OGCMs, the numerical grid is based
on the standard spherical coordinate system, which has singularities at both the North Pole and
the South Pole. As those singularities are approached, the latitudinal grid size tends to zero,
which may lead to numerical instabilities. Since the South Pole is located sufficiently far away
from the nearest oceanic region, the reduction of the latitudinal grid size has no harmful effect.
Thus, it is only in the Arctic Ocean that the grid or the numerical method has to be adapted to
circumvent this numerical instability problem.
Several methods to deal with the singularities of the spherical coordinates have been
examined (e.g. Williamson, 1979). Fourier-filtering along the longitudinal direction is used in
many OGCMs, in spite of the potential problems that may arise because not all the grid points
along a latitudinal circle are active.
Some years ago, the LODYC (Laboratoire d'Oceanographie Dynamique et de Climatologie,
Paris) model has been adapted to an orthogonal curvilinear grid obtained by shifting the
northern singularity into a land region, located in the neighbourhood of the North Pole (Marti et
ai., 1990; Marti et ai., 1992)
Another modification of the standard spherical coordinate system has been suggested
(Deleersnijder et ai., 1993; Eby and Holloway, 1994; Coward et ai., 1995), consisting in
Predicting, with an acceptable degree of realism, the evolution of climate on time scales of a
few decades can be achieved with a model incorporating only representations of the
atmosphere, ocean and sea-ice sub-systems. At Louvain-Ia-Neuve, we are developing such a
model of the climate system, and some results of the oceanic component will be presented
below.
The model. As pointed out by Niiler (1992), "the principal role of the oceans in maintaining
the present climate system of the Earth is the creation of large reservoirs of heat in tropical
latitudes and the transport of this thermal energy to the polar latitudes". Throughout the year,
the World Ocean transports about 1015 W - in thermal energy - from the low latitudes
toward the poles (e.g. Hastenrath, 1982), which is somewhat smaller than the meridional
atmospheric heat transport. Thus, by removing heat from the tropics and carrying it toward the
poles, the World Ocean significantly reduces the equator-poles contrasts. In addition, because
of their large heat capacity, the upper layers exhibit a large thermal inertia, moderating the
amplitude of the surface temperature seasonal cycle (e.g. Monin, 1975). Finally, the World
Ocean may act as a sink of carbon dioxide (e.g. Sarmiento, 1992).
The Louvain-Ia-Neuve Ocean General Circulation Model (OGCM) is rather similar to the
most classical OGCMs (e.g. Bryan, 1969). It is based on the usual set of assumptions, i.e, the
hydrostatic equilibrium and the Boussinesq approximation. The prognostic variables are the sea
surface elevation, the three components of the velocity, the potential temperature and the
salinity. The turbulence closure is achieved according to the simple formulae of Pacanowski
and Philander (1981). The space discretization uses the finite volume technique on an Arakawa
B-grid. The time stepping is of Euler-forward type, with a split-explicit mode splitting to
circumvent the severe numerical stability constraints associated with the propagation of external
inertia-gravity waves (Gadd, 1978; Killworth et ai., 1991; Deleersnijder and Campin, 1995).
More details about our OGCM may be found in Deleersnijder and Campin (1993,1995) and
in the Appendix. Hereafter, the curvilinear coordinate system underlying the horizontal
discretization is discussed.
Horizontal curvilinear coordinate system. In most OGCMs, the numerical grid is based
on the standard spherical coordinate system, which has singularities at both the North Pole and
the South Pole. As those singularities are approached, the latitudinal grid size tends to zero,
which may lead to numerical instabilities. Since the South Pole is located sufficiently far away
from the nearest oceanic region, the reduction of the latitudinal grid size has no harmful effect.
Thus, it is only in the Arctic Ocean that the grid or the numerical method has to be adapted to
circumvent this numerical instability problem.
Several methods to deal with the singularities of the spherical coordinates have been
examined (e.g. Williamson, 1979). Fourier-filtering along the longitudinal direction is used in
many OGCMs, in spite of the potential problems that may arise because not all the grid points
along a latitudinal circle are active.
Some years ago, the LODYC (Laboratoire d'Oceanographie Dynamique et de Climatologie,
Paris) model has been adapted to an orthogonal curvilinear grid obtained by shifting the
northern singularity into a land region, located in the neighbourhood of the North Pole (Marti et
ai., 1990; Marti et ai., 1992)
Another modification of the standard spherical coordinate system has been suggested
(Deleersnijder et ai., 1993; Eby and Holloway, 1994; Coward et ai., 1995), consisting in