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

128 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES
Ocean Dynamics
tel-00545911, version 1 - 13 Dec 2010
convergence followed by a slow convergence on the
manifold of slow convergence.
In the experiments discussed so far, we had a vanishing
observation error h obs = h true , that is, ˜σ = 0. This
is not consistent with the EnKF, as it requires ˜σ = σ .
It is, however, consistent with the fact that, in our
twin experiments, we do not have observation errors.
Furthermore, when performing parameter estimation
experiments with observational or laboratory data, ˜σ is
unknown. To determine the dependence of the experiment
on the observation error, we performed experiment
G10021, which is identical to G00021 except that
it includes an observational error η(x, t) with ˜σ = σ .
The results have no significant differences, demonstrating
again the robustness of the EnKF.
6 Discussion
The EnKF has once more proved to be a robust tool
for data assimilation. We established the possibility of
estimating the parameters in friction laws in gravity
currents by only observing its thickness. We showed
convergence to the true values in almost all examples,
even for values of the (Gaussian zero-mean) observation
error that are comparable to the thickness of the
gravity current. The speed of the convergence is very
much dependent on the parameters (ensemble size,
observation error and initial spread). In all cases, the
convergence can clearly be decomposed into two steps:
a fast convergence onto the manifold that corresponds
to the total friction followed by a slow convergence
on the manifold, corresponding to a discrimination between
the two friction laws.
It is also made clear that the implementation of the
EnKF is not straightforward but has to be guided by
physical, mathematical and numerical insight to adjust
and change the various parameters like the degrees of
freedom in the model, ensemble size (m), the observation
error, the initial spread of the ensemble and
the space-time resolution of the assimilation. All these
parameters are linked together in some non-linear
manner, and it is impossible to rigorously establish the
optimal values even when considering a rather simple
model, as it is done here. This makes data assimilation
an art founded in exact science.
The here-presented behaviour, as, for example, the
distinction between a fast and slow convergence, is
likely a general feature of parameter estimation when
several parametrisations are put in competition to
mimic the same physical process, and it is easy to
estimate the total action of the process but it needs
more specific information to distinguish between them.
The present work is the first step towards using data
assimilation to estimate the turbulent fluxes in gravity
currents. Moving beyond identical twin-experiments
and assimilating the data from a non-hydrostatic model
of the gravity current dynamics (HAROMOD, see
Wirth 2004 and Wirth and Barnier 2006, 2008) and
from laboratory experiments performed on the Coriolis
turn table at LEGI (Grenoble) is a subject of current
research which aims to evaluate types of parametrisations
and values of parameters to represent friction
in gravity currents. A better representation of gravity
currents in today’s numerical models of the dynamics
of the global ocean will improve their representation
of the abyssal water masses, the overturning circulation
and, thus, the global heat transport of the world ocean,
leading to better understanding of climate dynamics of
planet earth.
As already briefly mentioned in Section 5, by estimating
two or more parameters, one not only determines
the friction values but also the dependence of
the parameter on the Reynolds number. Indeed, we can
rewrite Eq. 5 as:
D = (τ + c D |u|)/h = ˜c D |u|)/h. (11)
where ˜c D = τ/|u| + c D decreases with the Reynolds
number, as it usually does over a solid surface (see
Schlichting and Gertsen 2000 pp. chap 1.3). Equation 11
can also be seen as the beginning of a Taylor series for
the friction coefficient as a function of the Reynolds
number. Including higher-order terms in the present
investigation would be against the empirical finding
that the drag coefficient decreases with the Reynolds
number. This is, however, not the case for the drag
coefficient at the ocean–atmosphere interface, which
is known to grow for large wind speeds due to the
increased roughness of the interface (waves) at large
wind speeds. The extension of the here-presented research
to such applications is straightforward. The herepresented
methodology is, thus, not restricted to the
dynamics of gravity currents. Key observations in the
ocean may help identify parametrisations of important
phenomena which are poorly parametrised so far
(overflows, friction, diapycnal mixing, mixing induced
by internal wave breaking, turbulent fluxes, etc.)
Using data from the non-hydrostatic numerical simulations
allows us to estimate not only the difficulties
expected when passing to real observations but demonstrates
that data assimilation is a systematic tool to
connect models of different complexity in a hierarchy.
Model hierarchies will play an increasing role in future
earth system research (see IPCC Fourth Assessment
Report 2007). Ongoing research aims at employing
the here-presented technique and tools to estimate