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
tel-00545911, version 1 - 13 Dec 2010
gence in parameter space followed by a slow convergence
within the manifold of slow convergence is not
a peculiarity of the here-presented investigations but
a general feature when estimating non-independent
parameters.
In all the estimation experiments considered so far,
we only considered gravity currents which were initially
in a geostrophic equilibrium, a condition we like to
relax in the sequel. We remind the reader that the control
run replaces the observations of an actual gravity
current, and by allowing it to differ from geostrophy,
we evaluate the parameter estimation when applied to
gravity currents not in a geostrophic equilibrium. The
data assimilation experiment is, however, unchanged
and based on the assumption that the current is in
geostrophic equilibrium, which means that it is ignoring
not only the friction parameters but also the initial
velocity distribution. This creates an inconsistency especially
in the early evolution before the gravity current
adjusts to geostrophy. We found that the difficulty
arises not so much from inertial oscillations of the notadjusted
gravity current (the control run), but from the
fact that the kinetic energy in the non-adjusted runs is
smaller. The assimilation reacts by imposing high values
of the drag coefficient (c D ) to drain energy from the
assimilation runs. The drag coefficient, rather than the
linear friction constant, increases as the fastest downslope
motion of the only partially adjusted gravity current
is at locations with the largest slope, where the
geostrophic velocities are also highest. The increase
in the drag coefficient is so large that all members
of the ensemble actually leave the parameter square
shown in Fig. 6 for experiment G1021, but they come
back later in the assimilation experiment. Once the
energy levels are comparable and the control run is
geostrophically adjusted, we observe a fast convergence
onto the manifold of slow convergence. The guess for
c D , however, is too high (and τ correspondingly small)
in all realisations so that the true value is not a likely
candidate of the ensemble and subsequent assimilation
has a very slow convergence, on the manifold of slow
convergence, to the true value. It is no surprise that
opting for a larger value of the observation error, as
done in G02221, gives better results due to the lower
confidence of the model in the observations; the initial
increase is slowed down and the subsequent convergence
to the true value is helped by the fact that the
spread of the ensemble is larger and the true value
is a likely candidate of the ensemble (Fig. 6). Again,
we see a fast convergence onto the manifold of slow
Fig. 6 Distribution of the ensemble in τ/τ 0 (horizontal direction)
and c D /c D0 (vertical direction) space, both normalised by the
values of the control run, for the three experiments: G01021 (left
row), G02021 (middle row) and G02221 (right row), for different
times: After 7 days (upper line) and after seven iterations of the
7-day dynamics (lower line). The values of τ and c D are normalised
by the true value used in the control run. The initial
distribution is the same as Fig. 5. After 7 days, all members of
the ensemble in G01021 are outside the area shown