In order to reproduce realistically the climate state in seasonal to interannual time scale with a coupled atmosphere-ocean-land surface model, a 4D-VAR full-coupled data assmilation system has been constructed which enables us to incorporate both atmospheric and oceanic observational data into model. Applying the coupled data assimilation system, we performed an assimilation experiment to reproduce the years 1996-1998.
  Here we describe the procedure for making the coupled data assimilation product (see Fig1) which is the outcome of the “Kyousei” category #7 (K-7) of ”RR2002: Project for Sustainable Coexistence of Human, Nature, and the Earth”.

1 Coupled Model
The atmosphere.ocean coupled model employed here is the Coupled model for the Earth Simulator (CFES), which is composed of the Atmospheric GCM for the Earth Simulator (AFES) (Ohfuchi et al., 2004) and the Ocean.sea Ice GCM for the Earth Simulator (OIFES) (Komori et al., 2005). The AFES component is based on the atmospheric GCM by the Center for Climate System Research / National Institute for Environmental Studies (CCSR/NIES). The radiation code has been modified using MstrnX (Nakajima et al., 2000) and the simple diagnostic calculation of marine stratocumulus cloud cover has been implemented (Mochizuki et al., 2006). The OIFES component is developed from version 3 of the Modular Ocean Model (MOM3) produced by the Geophysical Fluid Dynamics Laboratory and the sea ice model of the International Arctic Research Center (Hibler III, 1980). The adjoint codes of the AFES and OIFES components are developed using Tangent linear and Adjoint Model Compiler (TAMC) (Giering and Kaminski, 1998) and Transformation of Algorithms in Fortran (TAF) (Giering and Kaminski, 2003). The resolution of the AFES component is horizontally the same as the commonly-used T42 spectral model and vertically 24 layers in σ coordinates and that of the OIFES component is 1 degree both in latitude and longitude and 45 layers in depth.

2 Tuning
In order to reduce the drift and to keep an appropriate balance on the coupled model, we tuned the several model parameters (oceanic isopycnal diffusivity, atmospheric relaxation time for relative humidity and so on) by the Green’s function method (Menemenlis et al., 2005). The method uses cost function just like 4D-VAR but solves directly the variational optimization problem with low degree of freedom by deriving the gradient from the perturbed model runs.

3 Spinup
In the spinup run, oceanic temperature and salnity observations, which actually are the continuous fields yielded as “Kyousei K-7”ocean data assimilation product, are incorporated into the model by IAU method(Bloom et al., 1996).

4 Firstguess Field
The firstguess field for each assimlation window is derived by the free model run released from IAU field at the beginning of each assimilation window. Assimilation windows are 9-month long (January to September 1997, July 1997 to March 1998, January to September 1998, ...), and have 3-month dupulications so that the continuities of adjacent windows are maintained and that we can pick up the middle of each window when the adjustment by the assimilation will work well.

5 Optimization
In 9-month scale, the basic state of coupled ocean-atomosphere field except weather mode is believed to be well regulated by the temperature memory of ocean sub-surface and by the adjustment of air-sea exchange flux. So adjustment factors ‘alpha’ are introduced into each bulk formula for latent heat, sensible heat, and momentum fluxes and these are chosen as control variables together with the oceanic initial conditions of the model variables. Each value of ‘alpha’ is optimized in each grid point for every 10-days (first, second 10-days and the rest of month) by the coupled assimilation.

where, is wind vector, specific heat of air, air temparature, surface temperature, specific humidity of air, saturated humidity.
  To reduce the degree of freedom for the control and to reflect the spatial structure properly, the spatial correlation of adjustment factors is introduced.

We introduce diffusion operator L, which has the diffusivity according to the decorrelation length, and standard diviation matrix S into the cost function (Bonekamp et al., 2001). Here means the logarithm of adjustment factors.

  The assimilated observational data for ocean in the experiment are monthly mean temperature and salinity field derived from the World Ocean Database 2001 (WOD2001), 10-daily averaged Reynolds SST field and the TOPEX/Poseidon 10-daily mean sea surface height anomaly. The continuous fields yielded as “Kyousei K-7”ocean data assimilation product are also used as quasi-observation to fill the gaps of very sparse observation. The atmospheric data are the PREP BUFR dataset taken from the National Centers for Environmental Prediction (NCEP) for air temperature, specific humidity and wind vector after some processing to obtain 10-daily mean and to perform appropriate quality checks. 10-daily mean 10m scalar wind from SSM/I observation are multipled by ECMWF wind direction data to obtain wind vector quasi-observation over the ocean.
  The optimization problem to minimize the cost is solved by the iteration with conjugate gradient method using the gradient calculated by the atmosphereocean coupled adjoint code.

6 Ensemble
Because weather mode in the shorter period than 10-days is not controlled in the optimization with the observational data, we performed coupled model integrations under 11 different atmospheric initial conditions using optimized ocean initial condition and adjustment factor. The ensemble of atmospheric initial conditions are taken, at 1-day intervals, from the first 5 days of the first month of the assimilation window and from the last 5 day of the month perior to the first month of the assimilation window. An ensemble member which seems to express the reality the best is selected for each window, and they are pieced together as a continuous data for three years .

References
S. C. Bloom, L. Takacs, A. M. da Silva, and D. Ledvina. Data assimilation using Incremental Analysis Updates. Mon. Wea. Rev., 124:12561271, 1996.

H. Bonekamp, G. van Oldenborgh, and G. Burgers. Variational assimilation of Tropical Atmosphere-Ocean and expendable bathythermograph data in the Hamburg Ocean Primitive Equation ocean general circulation model, adjusting the surface fluxes in the tropical ocean. J. Geophys. Res., 106:16693 16709, 2001.

R. Giering and T. Kaminski. Applying TAF to generate efficient derivative code of Fortran 77-95 programs. PAMM, 2(1):5457, 2003.

R. Giering and T. Kaminski. Recipes for Adjoint Code Construction. ACM Trans. On Math. Software, 24(4):437474, 1998.

W. D. Hibler III. Modeling a variable thickness sea ice cover. Mon. Wea. Rev, 108:19431973, 1980.

N. Komori, K. Takahashi, K. Komine, T. Motoi, X. Zhang, and G. Sagawa. Description of sea-ice component of Coupled Ocean-Sea-Ice Model for the Earth Simulator (OIFES). J. Earth Simulator, 4:3145, 2005.

D. Menemenlis, I. Fukumori, and T. Lee. Using Green’s functions to calibrate an ocean general circulation model. Mon. Wea. Rev., 133:12241240, 2005.

T. Mochizuki, T. Miyama, and T. Awaji. A simple diagnostic calculation of marine stratocumulus cloud cover for use in general circulation models. J. Geophys. Res., 2006. submitted.

T. Nakajima, M. Tsukamoto, Y. Tsushima, A. Numaguti, and T. Kimura. Modeling of the radiative process in an atmospheric general circulation model. Appl. Opt., 39:48694878, 2000.

W. Ohfuchi, H. Nakamura, M. K. Yoshioka, T. Enomoto, K. Takaya, X. Peng, S. Yamane, T. Nishimura, Y. Kurihara, and K. Ninomiya. 10-km mesh mesoscale resolving simulations of the global atmosphere on the Earth Simulator: Preliminary outcomes of AFES (AGCM for the Earth Simulator). J. Earth Simulator, 1:834, 2004.