On variational data assimilation methods for 1D and 2D fluvial hydraulics

We study variational data assimilation methods (optimal control of
PDEs) as applied to river flows (shallow water 1D and 2D). In river
hydraulics, available observations are generally very few
measurements of elevation (quasi-continuous in time), while velocity
or discharge measurements are often not available. This lack of
observations are even more true during flood events.

In a first step, we show that standard variationnal data
assimilation methods (standard eulerian observations are available)
can be applied successfully to river hydraulics (real data, Pearl
river, China): the inflow elevation and/or discharge are retreived
when using water measurements at three gauge stations.

Then, we study the assimilation of lagrangian data. Since in practice
the eulerian observations can be not sufficient to take full
advantage of data assimilation for some identification purposes, we
use extra lagrangian data extracted from remote sensing observations
(video images). The trajectory of particles advected by the flow can
bring some information on the surface velocity using transport
equations. Numerical twin experiments demonstrate that this method
makes it possible to improve the identification of model parameters
(local topography and/or inflow discharge).

Finally, we elaborate a joint data assimilation – coupling method
based on the optimal control process. The basic idea is to superpose
locally a 2D flow model ("a local zoom")

over the 1D global flow model (river network). The coupling is done
weakly since it is based on the optimal control of a 2D-1D relaxed
model.
Then, we take advantage of the optimal control based procedure to
define the joint data assimilation – coupling algorithm.
We show the efficiency of the method by considering a toy flooding
event.
Keywords. Variationnal data assimilation, river hydraulics, parameter
identification, lagrangian data, 1D and 2D shallow-water models,
joint data assimilation – coupling procedure.