Etudes et évaluation de processus océaniques par des hiérarchies ...

120 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES
Ocean Dynamics
tel-00545911, version 1 - 13 Dec 2010
to improving the representation of the global ocean
climate variability.
For an introduction to the dynamics of oceanic gravity
currents, we refer the reader to Griffiths (1986).
A large number of experimental studies of gravity
currents on an inclined plane have contributed to our
understanding of their dynamics (see, e.g. Whitehead
et al. 1990; Sutherland et al. 2004). Most of these studies
focus on the large-scale instability and eddy formation
in such flows.
The understanding of the dynamics of gravity current
has profited largely from the study of simplified
stream-tube models. In stream-tube models, only average
(bulk) values of the dynamical variables are considered
at every cross section along the path of the gravity
current (see Smith 1975, 1977; Killworth 1977, 2001;
Price and Baringer 1994; Baringer and Price 1997).
Due to their linear nature, the integrated buoyancy
and Coriolis force can be calculated. The nonlinear
frictional forces and the turbulent fluxes, perturbing the
geostrophic equilibrium, have to be parametrised. The
evolution of the gravity current can then be studied as a
function of the parametrisations and parameter values
employed. Integrations of these semi-analytical streamtube
models along a path of varying topographic slope
were performed, and the parameter values are adjusted
in such a way that the pathway and water mass
characteristics compare favourably to observations. In
this way, stream-tube models have contributed substantially
to understanding the physics of oceanic gravity
currents. This adjustment procedure, however, does not
always lead to a deeper understanding of the physical
processes involved (see Emms 1998). The implementation
of stream-tube models or their physics in today’s
large-scale OGCMs is difficult. Although progress has
been made in better representing gravity currents in
large-scale OGCMs through bottom boundary layers
(see e.g. Killworth and Edwards 1999), their dynamics
is still a weak point of today’s numerical models of the
ocean circulation.
We focus here on the small-scale turbulent fluxes in
gravity currents. A variety of parametrisations of the
turbulent fluxes are proposed in the literature, but there
is no agreement on which parametrisation should be
favoured, not even to speak about the numerical values
of the parameters present in such parametrisation.
Pioneering work to systematically test various of such
parametrisations and determine parameter values has
recently been performed (see, e.g. Xu et al. 2006 for the
non-rotating case and Ezer 2005 and Legg et al. 2006 for
a case with rotation).
We expose here the first step of a pragmatic approach
to obtaining the laws and parameter values of
turbulent fluxes using data assimilation. More precisely,
it is not clear if the effect of bottom and interfacial friction
in a gravity current is more likely to follow a linear
Rayleigh friction law or a quadratic turbulent drag law
(Chésy law); and what are the values of the corresponding
friction coefficients? This is a question that has
been considered, e.g. for the ocean by Moonn and Tang
(1984) and for the case of the atmospheric boundary
layer over the ocean by Stevensen et al. (2002), without
using data assimilation. Both laws, the linear and
quadratic, are implemented in all major ocean models.
We therefore implement the two commonly used parametrisations
of the same physical process, bottom and
interfacial friction, in a numerical model that does not
explicitly resolve this process, and we estimate the parameters
in the parametrisations by assimilating data into
the model. The data assimilation experiment will then
not only tell us the optimal parameter values but also
allows for an evaluation of the parametrisations by providing
the error bars and/or the spread of the ensemble
(when an ensemble method is considered). Even more
striking, by allowing different parametrisation laws, the
data assimilation experiment will actually tell us which
law is the most appropriate in parametrising turbulent
fluxes. The data are provided by either observations
of oceanic gravity currents, laboratory experiments or
numerical data from a model that explicitly resolves the
process to be parametrised. However, in the present
work, we perform identical twin experiments, where
the “data” are provided by the same model as used
for the parameter estimation experiments, to study the
feasibility and the problems connected to estimating
parameters of parametrisations describing the same
physical process. For an introduction into parameter
estimation, we refer the reader to Evensen et al. (1998).
In the next section, we give a detailed description of
the physical problem and consider its mathematical formulation
and numerical implementation. In Section 3,
we discuss the assimilation method, that is, the ensemble
Kalman filter (EnKF), and its numerical implementation.
The twin experiments and results are presented
in Sections 4 and 5. Discussion, physical interpretation
of the results and perspectives are given in Section 6.
2 Idealised oceanic gravity current on the f-plane
2.1 The physical problem considered
In the experiments presented here, we use an idealised
geometry, considering an infinite gravity current on an
inclined plane with constant slope, and we do not allow
for variations in the long-stream direction. We thus