5.1 Experiment 1. Simultaneous assimilation of the buoy and the altimetric data
It is useful to examine the characteristics of the altimetric data assimilation and efficiency of the simultaneous assimilation of both drifting buoy and altimetric data before the successive correction model of the mean SSH is carried out.
In the first case (Exp. 1-1), only the altimetric data are assimilated as the reference, and the characteristic of the altimetric data assimilation is examined. The simultaneous assimilation of the buoy and altimetric data is carried out as the second case (Exp. 1-2). In both cases, the 1-year average of the simulation run is used for the estimated mean interface depth (Fig. 9b) which has the RMS error of 64.1 m (corresponding to about 13cm in SSH). In Exp. 1-2, the velocity data derived from 32 drifting buoys with denser initial deployment in the energy western boundary current regions (Fig. 11) are used. and all data observed after the previous assimilation period are assimilated at the same time with the altimetric data, every 17 days, without considering the time lag.
The time series of the RMS errors for the interface depth are shown in Fig. 12. The most visible result of both cases is that the error level of the interface depth field does not change so much during the assimilation period. This is due to the fact that the error of the mean interface depth field contaminates the analysis field at each assimilation time. Thus, the time-varying part of the observed interface depth corrects only the time-varying part of the model output and cannot constrain the mean field of the model on synoptic scales. In practice, the RMS error for the time-varying part in Exp. 1-1 (not shown) is reduced to about 10m while the error for the absolute interface depth (mean plus time-varying part) is reduced to 50 m, indicating that the error of the mean interface depth is the major part in the absolute interface depth error. This result is consistent with that of Capotondi et al. (1995) who used the GEOSAT data combining the hydrographic mean field. They showed that the assimilation of altimetric data alone cannot constrain the mean field of the model. The error of the mean SSH field summarized in Table 2 does not change from the initial guess in Exp. 1-1, when only the altimetric data are assimilated.
The simultaneous assimilation of buoy and altimetric data (Exp. 1-2) can reduce the error of the interface depth field in contrast to Exp. 1-1. This shows that the drifting buoy data are effective in correcting the SSH field, which is also indicated in the previous subsection. The error of the velocitv is not reduced sufficiently. especially in the latter half of the experiment period (not shown). The velocity field is related not to the interface depth field but to its gradient, and the
