A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 360

boundary conditions from a global or regional model assimilating with 3DVAR.
Both the adjoint and linear perturbation (also called the forward representer) model
codes were derived for the most part with the help of the Parametric Fortran
compiler (PFC), Erwig et al. 2007 .
Some general circulation models of the complexity of NCOM have seen
similar efforts undertaken in the past decade: a 4D-Var assimilation system was
developed for the Ocean Parallelise (OPA) model ( Weaver et al. 2003 ), for the MIT
general circulation model (MITgcm, Marotzke et al. 1999 )alsousedintheECCO
consortium assimilation experiments ( Stammer et al. 2002 ), and a similar system
was built for the regional ocean model system (ROMS), Moore et al. 2004 . Unlike
the other models using fixed z-levels (OPA and MITgcm) or s-coordinates (ROMS)
NCOM uses a combination of both sigma layers, z-levels and a generalized vertical
coordinate.
It is a common practice to test a recently developed assimilation system with
climatological data or identical twin experiments in which the observations are
simulated by the numerical model. There is hardly a case of failure in twin
experiments, yet a successful assimilation with twin experiments never guarantees
success with real data. On the other hand, climatological data are overly smooth in
both space and time (due mostly to linear interpolation) and lack the variability
associated with real observations. To avoid these simplified cases, the newly
developed NCOM 4D-Var system is tested with real and synthetic observations
generated by the modular ocean data assimilation system (MODAS) Fox et al. 2002 ,
as well as with real observations collected from satellites and a fleet of gliders during
the second autonomous ocean sampling network (AOSN II) in the Monterey Bay.
There are no specific applications of 4D-Var in the Monterey Bay, let alone
its weak constraint formulation. Strong constraint variational assimilation ( Broquet
et al. 2009 ) has been applied to the California current system (CCS), including an
application to estimate surface forcing correction ( Broquet et al. 2011 ), using the
inverse Regional Ocean Modeling System (IROMS, Di Lorenzo et al. 2007 ) with
horizontal resolutions of 10 and 30 km. The CCS is a large area that includes the
Monterey Bay, although these applications did not specifically target the Monterey
Bay, given their rather coarse resolutions. Most of the assimilation experiments that
have been carried for the Monterey Bay were based on sequential methods such as
3DVAR and ensemble-based Kalman filters: Chao et al. ( 2009 ), Haley et al. ( 2009 ),
and Shulman et al. ( 2009 ). This study presents an application of the weak constraint
4D-Var in the Monterey Bay in a proof-of-concept context, using synthetic and real
observations. The first objective is to demonstrate the system's ability to reduce large
discrepancies between the model and the observations, when the latter are assigned
very low errors. Therefore, this paper is more focused on the technical development
of the weak constraint 4D-Var system.
A brief description of the numerical model is presented in the next sec-
tion, followed by the 4D-Var system derivation and implementation in Sect. 15.3 .
Section 15.4 deals with the experiments setup and results, and concluding remarks
follow in Sect. 15.5 .