Geoscience Reference
In-Depth Information
14.2
ROMS 4D-Var
The ocean analysis system described here is based on the Regional Ocean Modeling
System (
Shchepetkin and McWilliams 2005
). ROMS is a hydrostatic, primitive
equations model that uses terrain following coordinates in the vertical and orthogo-
nal curvilinear coordinates in the horizontal to resolve the complex bathymetry and
land geometry that characterize many coastal regions. While ROMS is primarily
designed with coastal and regional applications in mind, it is also run routinely at
basin scales (e.g.
Haidvogel et al. 2008
). One of the great advantages of ROMS over
other ocean models is the high degree of flexibility that it affords the user in terms
of available numerical schemes, physical parameterizations, and open boundary
conditions. A detailed description of ROMS is beyond the scope of this chapter,
but more details about the model can be found at
http://www.myroms.org
.
14.2.1
Primal Versus Dual Formulation
The ROMS data assimilation system is based on an incremental 4-dimensional
variational approach (4D-Var). Two different approaches to 4D-Var are available as
part of ROMS: one based on the primal formulation, and the other based on the dual
formulation (
Courtier 1997
). The primal version of ROMS 4D-Var is very similar
to that used at several operational NWP centers, and follows closely that of
We ave r
et al.
(
2003
) for the ocean. The dual version of ROMS 4D-Var comes in two flavors:
one approach is based on the Physical-space Statistical Analysis System approach
(PSAS) of
Cohn et al.
(
1998
), while the other uses the indirect representer method
of
Egbert et al.
(
1994
). The details and differences between the three ROMS 4D-Var
algorithms are not important for what we describe here, and the interested reader
is referred to
Moore et al.
(
2011a
) for a complete description of each algorithm. In
later sections, however, it will be necessary to refer to some specific features of the
primal and dual formulations of ROMS 4D-Var, so we begin with a brief overview
of the fundamental ideas that underpin each system.
The ocean state vector for ROMS is composed of all ocean grid point values
of temperature (
), and the two components
of velocity (
u
,
v
). Following the standard notation of
Ide
(
1997
) and later extended
for the ocean by
Daget et al.
(
2009
) we will denote the ROMS state vector as
x
T
), salinity (
S
), sea surface height (
D
T
T
v
T
T
, where the vector elements of
x
denote column vectors of the
grid point values of the state variables. Using this notation, ROMS can then be
represented symbolically as:
S
T
T
u
T
;
;
;
;
x
.t
i
/
D
M.t
i
;t
i
1
/.
x
.t
i
1
/;
f
.t
i
/;
b
.t
i
//
(14.1)
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