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

4.6. ESTIMATION OF FRICTION PARAMETERS AND LAWS IN 1.5D SHALLOW-WATER GRAVI
Ocean Dynamics
DOI 10.1007/s10236-008-0151-8
Estimation of friction parameters and laws in 1.5D
shallow-water gravity currents on the f-plane,
by data assimilation
Achim Wirth · Jacques Verron
Received: 11 June 2008 / Accepted: 15 September 2008
© Springer-Verlag 2008
tel-00545911, version 1 - 13 Dec 2010
Abstract A 1.5-dimensional, 1.5-layer shallow water
model and an ensemble Kalman filter are used to evaluate
the feasibility of estimating friction parameters
and determining friction laws of oceanic gravity currents.
The two friction laws implemented are a linear
Rayleigh friction and a quadratic drag law. We demonstrate
that the assimilation procedure rapidly estimates
the total frictional force, whereas the distinction between
the two laws is evolving on a slower time scale.
We also demonstrate that parameter estimation can,
in this way, choose between different parametrisations
and help to discriminate between physical laws of nature
by estimating the coefficients presented in such
parametrisations.
Keywords Ocean dynamics · Gravity current ·
Friction laws · Parameter estimation ·
Data assimilation
1 Introduction
Buoyancy forces caused by density differences of fluids
are a major source of fluid motion in nature. When
these forces act adjacent to topography, gravity cur-
Responsible Editor: Tal Ezer
A. Wirth (B) · J. Verron
LEGI / MEOM, CNRS, BP 53,
38041 Grenoble Cedex 9, France
e-mail: achim.wirth@hmg.inpg.fr
J. Verron
e-mail: jacques.verron@hmg.inpg.fr
rents are created. The major part of the deep and
intermediate waters of the world ocean and marginal
seas have done at least part of their voyage to the
deep in the form of a gravity current. Oceanic gravity
currents play a role of paramount importance in the
formation of the water masses of the deep ocean and
are thus key to understanding the oceanic component
in the earth climate system. For the major part of
oceanic gravity currents, the earth’s rotation plays an
important role, as they evolve on a timescale much
larger than the rotation period of the planet earth. The
dominant force balance is, thus, between gravity and
the Coriolis force, that is geostrophic. Indeed, when the
turbulent fluxes of water masses and momentum are
neglected, such gravity currents flow along the inclined
ocean floor, changing neither depth nor composition.
Turbulent fluxes of tracers, that is mixing, entrainment
and/or detrainment, determine the change of the water
mass. Together with the turbulent fluxes of momentum
at the floor and interface of the gravity current, they
determine the change in position of the gravity current.
The answer to the question of the evolution of a gravity
current lies, thus, in the determination of the laws and
parameters of its turbulent fluxes.
The inter-comparison study of several ocean general
circulation models (OGCMs) (DYNAMO Group 1997;
Willebrand et al. 2001) clearly determined the high sensitivity
of the meridional heat transport (in the North
Atlantic) to the representation of the (Denmark Strait
and Faroe Bank Channel) overflows. The meridional
heat transport is very sensitive to small-scale details
and turbulence in the overflow regions not explicitly
resolved in OGCMs and the numerical representation
(the grid) of the overflow regions in the OGCMs. Dedicated
research on these sub-grid-scale processes is key