Enhancing simplified models for the inversion of surface mesoscale dynamics from satellite data

In physical oceanography, observations are mainly acquired by space-borne
sensors that cannot measure the interior ocean state. As a result, most avail-
able data are limited to the sea surface, with gaps arising from satellite tra-
jectories and sensor coverage. To fill in these gaps, data inversion is usually
performed using reduced-order models. These models are based on assumptions
which simplify the flow dynamics. One such framework is the 1.5-layer quasi-
geostrophic model which resolves only the upper layer flow by considering that
the underlying layer remains at rest. However, it is actually a truncation of
the quasi-geostrophic (QG) framework which describes the dynamics of a three-
dimensional flow. Although motivated by the lack of sublayer data, reducing
the dynamics solely to its surface component remains a strong assumption.

We wish to mitigate the systematic error introduced by this truncation to
improve surface flow reconstruction. We also aim at keeping a sparse expression
for the correction as it allows the problem to remain well-constrained by the
observations. Using the QG equations, we introduce a truncation-correcting
term bridging the gap between the 1.5-layer model and its multilayer counter-
part. This correction is prescribed through the transport of the sublayer stream
function by the upper layer flow. Since the dynamics of the correction is re-
fined by the surface flow, it can be parameterized with a reasonable number of
parameters.

Using simulations of different complexity, we evaluate the performance of the
proposed method. As it identifies the correction term to a physical quantity, we
make use of the potential vorticity conservation in the sublayer to constrain our
parameterization. Correction is finally estimated using a variational method.
Results show a significant improvement over a state-of-the-art error modeling
strategy. The additional constraint helps reconstructing a much smoother field
for the surface flow. Our method also allows the correction term to compensate
for an incorrect deformation radius. This approach then mitigates the pas-
sive sublayer assumption while improving the reconstruction capabilities of the
model.