The 4D-VAR assimilation system used here is the same as in Masuda et al. [2003] covering the global ocean. The OGCM is version 3 of the GFDL Modular Ocean Model (MOM; Pacanowski and Griffies, 1999), which is equipped with several sophisticated parameterization schemes, for example, nonlocal K Profile Parameterization (Large et al., 1994) for mixed layer physics, Gent and McWilliams's scheme (Gent and McWiiliams, 1990) for isopycnal mixing, and quicker advection scheme (Leonald, 1979).
The horizontal resolution is 1in both latitude and longitude, with 36 vertical levels spaced from 10m near the sea surface to 400m at the bottom.
This model has good capability to reproduce ocean circulation processes and is expected to form a platform suitable for the use of the 4D-VAR adjoint model.

The assimilated elements in this study are the temperature and salinity from the World Ocean Database 1998 (for climatologies) and the World Ocean Database 2001, Reynolds SST values, and sea-surface dynamic-height anomaly data derived from TOPEX/Poseidon altimetry (Table. 1). All observational data were averaged onto 1 degree by 1 degree bins and then compiled as series of 10-day means for the surface data and monthly means for the subsurface data.

In our 4D-VAR approach, optimized 4-dimensional datasets are sought by minimizing a cost function.

The assimilation covers a 10-year time window starting from 1990. We chose the initial condition of model variables and air-sea fluxes (heat, fresh water, and momentum fluxes) as the control variables with the latter modified within the assimilation period as 10-day mean values (see Masuda et al. [2003] in more detail).

To generate a first guess field for data assimilation, this model is executed with no assimilation by using the National Centers for Environmental Prediction Department of Energy Atmospheric Model Intercomparison Project (NCEP-DOE-AMIP-II) for surface momentum flux, and the Comprehensive Ocean-Atmosphere Data Set produced at the University of Wisconsin-Milwaukee for other surface fluxes using a conventional flux correction method.

[References]
Gent, P. R. and J. C. McWilliams (1990): Isopycnal mixing in ocean circulation models, J. Phys. Oceanogr., 20, 150-155.

Large, W. G., J. C. McWilliams, S. C. Doney (1994): Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization, Rev. Geophys., 32, 363-403.

Leonard, B. P. (1979): A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering, 19, 59-98.

Masuda, S., T. Awaji, N. Sugiura, Y. Ishikawa, K. Baba, K. Horiuchi, N. Komori (2003): Improved estimates of the dynamical state of the North Pacific Ocean from a 4 dimensional variational data assimilation, Geophys. Res. Lett., 30, 16, 1868.

Pacanowski, R. C. and S. M. Griffies (1999): The MOM 3 Manual. Geophysical Fluid Dynamics Laboratory/NOAA, Princeton, USA, p.680.