Logutov, O.G., 2008. A multigrid methodology for assimilation of measurements into
regional tidal models. Ocean Dynamics, 58, 441-460, doi:10.1007/s10236-008-0163-4.
This paper presents a rigorous, yet practical,
method of multigrid data assimilation into regional
structured-grid tidal models. The new inverse tidal
nesting scheme, with nesting across multiple grids, is
designed to provide a fit of the tidal dynamics to data
in areas with highly complex bathymetry and coastline
geometry. In these areas, computational constraints
make it impractical to fully resolve local topographic
and coastal features around all of the observation sites
in a stand-alone computation. The proposed strategy
consists of increasing the model resolution in multiple
limited area domains around the observation locations
where a representativeness error is detected in order
to improve the representation of the measurements
with respect to the dynamics. Multiple high-resolution
nested domains are set up and data assimilation is
carried out using these embedded nested computations.
Every nested domain is coupled to the outer
domain through the open boundary conditions (OBCs).
Data inversion is carried out in a control space of the
outer domain model. A level of generality is retained
throughout the presentation with respect to the choice
of the control space; however, a specific example of
using the outer domain OBCs as the control space is
provided, with other sensible choices discussed. In the
forward scheme, the computations in the nested domains
do not affect the solution in the outer domain.
The subsequent inverse computations utilize the
observation-minus-model residuals of the forward computations
across these multiple nested domains in order
to obtain the optimal values of parameters in the
control space of the outer domain model. The inversion
is carried out by propagating the uncertainty from
the control space to model tidal fields at observation
locations in the outer and in the nested domains using
efficient low-rank error covariance representations.
Subsequently, an analysis increment in the control
space of the outer domain model is computed and the
multigrid system is steered optimally towards observations
while preserving a perfect dynamical balance.
The method is illustrated using a real-world application
in the context of the Philippines Strait Dynamics