nearly in dynamic equilibrium. Figure 7 shows the schematic diagram of the model spin-up and the identical twin experiment. For the control run, an additional 6-year integration is performed with the wind stresses including random components, and its final output is used as the initial state (Fig. 8a). The 1-year experiment of the control run, calculated from this initial state, is regarded as the true ocean which gives the "observations". The mean interface depth (1-year average) of the control run is shown in Fig. 8b), which is subtracted from the absolute interface depth to make the time-varying part used as the altimetric observation (see below). The result of control run is also used to assess the success of the assimilation result quantitatively. For the assimilation run and the simulation run, a 1-year integration is added to the 22-year spin-up to make the initial state (Fig. 9a). Thus, the initial condition of these assimilation and simulation runs is different from that of the control run. The 1-year experiment of the simulation run is calculated under the same conditions as the assimilation run (initial condition and wind stress) except that the observation data are not assimilated. The simulation run is used as the reference to evaluate the success of the assimilation. It also gives the first guess of the mean interface depth field (Fig. 9b), idealizing the estimated mean SSH field from the climatological data. In Fig. 9c, the difference of the mean interface depth between the control run and the simulation run (the mean interface depth error of the simulation run) is shown. Large errors can be seen in the western boundary current and its extension regions. The mean eastward jet in the simulation run is weaker than that of the control run (Figs. 8b and 9b), and this is due to the large error in the extension region. The velocity data are based on particle trajectories (regarded as observed buoy trajectories) which are tracked in the control run using the Euler-Lagrangian technique (Awaji et al., 1991). We also derive the velocitv data from moored current meters. These are taken directly from the daily-averaged velocity field of the control run. The altimetric data are sampled every 17 days from the interface depth anomaly field along the assumed Geosat subtracks (Fig. 10) in the control run. Here, the anomaly field is the deviation from the 1-year mean interface depth shown in Fig. 8b.
4.2 Assimilation scheme
The optimal interpolation (OI) method used in many previous studies for the assimilation of altimetric data is extended here to assimilate the drifting buoy and altimetric data simultaneously (Daley, 1991; Ghil and Malanotte-Rizzoli, 1991).
The analysis value wa is obtained from the model calculated value wf and the observed value wo through Eq. (3):
where w is the column vector for all variables, w = (huv)T, and H is the observation matrix that transforms the forecast data to the values at the observed points. The observation of the interface depth, ho, is used for the estimated mean field plus the time-varying part derived from the altimeter (in this sense, the total SSH derived from the altimeter is assimilated into the model).
The matrix K is determined to minimize the error of the analysis field (Ghil and Malanotte Rizzoli, 1991).
where the Pf, Ro the error covariance matrices for the forecast and observed values, respectively, and are assumed as
where E is the error variance ratio of the model forecast and the observation, assumed to be 1 in is study and I is the unity matrix.
The model error covariance matrix is assumed to be a Gauss function for the interface depth and is obtained from the geostrophic relationship between the interface depth field and the velocity
