Calculation of the oceanic angular momentum (OAM) - both its axial (AOAM) and equatorial (EOAM) components - requires detailed knowledge of the large-scale circulation and mass fields over the global ocean. Studies of OAM thus concern all aspects of the oceanic momentum and mass (i.e., salt and freshwater) budgets, including forcing fluxes at the atmospheric and solid Earth boundaries, which are crucial to a comprehensive approach to the study of Earth system dynamics and climate. The primary limitation in accurate computations of OAM and evaluation of its role in the planet's angular momentum budget is the poor data coverage, both in time and in space, of the vast global oceans. Without a good database to determine the variable circulation and mass fields, calculations of OAM in our investigation so far have relied on the output of global ocean numerical models. We summarize here results obtained using the eddy-resolving primitive equation model of Semtner and Chervin  and the simple barotropic model described by Ponte [1995b].
Our analysis of the Semtner and Chervin (SC)  model has focused on seasonal time scales. In a first study, Ponte and Rosen  used one year of output from the rigid-lid version of the model forced by climatological monthly mean winds to calculate AOAM. Seasonal variability in AOAM was dominated by the annual cycle, whose magnitude was of the right order to explain the residual in the solid Earth-atmosphere annual momentum budget. Seasonal amplitudes for planetary and relative AOAM components were comparable, but estimates of the former were only tentative, given the approximate nature of the sea level fields diagnosed from the rigid-lid model. Most of the mean signal in relative AOAM resulted from flows in the Antarctic Circumpolar Current region, but flows as far north as approximately 30S were needed to explain the seasonal cycle. Locally, the strongest variability in relative AOAM was found in the tropics at all depths, a manifestation of the zonal, recirculating character of the tropical circulation. The dynamical reasons for the enhanced signals in the tropics remains an interesting topic for study.
The torque balance was also briefly examined by Ponte and Rosen  (see also 3.1.3). The time rate of change of AOAM was very small compared to the applied wind torque. Calculation of bottom pressure torques via the geostrophic relation revealed a dominant balance between them and the surface wind torques in the model, implying a rapid transfer of angular momentum between the atmosphere and the solid Earth through the ocean. This torque balance was found to hold for latitudes totally blocked by continental boundaries as well as for latitudes that are only partially blocked (e.g. Drake Passage), suggesting the same angular momentum transfer mechanism for closed basin and Antarctic Circumpolar Current regions.
A new, free surface version of the SC model was run more recently using mean monthly ECMWF wind forcing for 1985-89. Salstein et al.  analyze AOAM quantities from output for the year 1989, again focusing on the seasonal time scale. A difference from the rigid-lid model was the much stronger seasonal cycle in the planetary AOAM term, associated with sea-level changes, which actually dominated the variability in AOAM. The latitudinal mass transfers involved seem to occur between tropics and extratropics, particularly in the southern hemisphere, and need to be examined further in the wider context of the ocean general circulation. In the context of the planet's angular momentum budget, the AOAM signal amounted to approximately 80% (10%) of the observed atmosphere-solid Earth residual at the annual (semiannual) period.
Salstein et al.  also examine EOAM signals and their role in excitation of polar motion. Currents and mass variability show similar importance in EOAM variability. The estimated EOAM signals exhibit substantial amplitudes when compared to relevant atmospheric and geodetic quantities, indicating the potential importance of oceanic contributions to the excitation of seasonal polar motion. The extent to which inclusion of the ocean improved the budget for the equatorial components was, however, still unclear, given the short period analyzed.
In addition to the work based on the SC model, to examine subseasonal OAM signals under both wind and atmospheric pressure forcing, Ponte [1995a] performed experiments with a constant-density, global ocean model driven with twice-daily surface wind stresses and atmospheric pressures from the NMC analysis for the period September 1992-93. Ponte found that variable currents and mass redistributions were both important in determining OAM in general. The importance of pressure forcing was dependent on whether the ocean responds to it as an inverted barometer. This was indeed the case in the model for periods longer than a few days, in agreement with altimeter-based analysis [Gaspar and Ponte, 1994; Ponte, 1995b]. Thus, at long periods, wind-driven variability was the primary cause for OAM signals. At periods shorter than ten days, larger deviations from the IB response occurred, and the effects of wind- and pressure-driven signals on OAM become comparable.
In the context of the planet's axial angular momentum budget, AOAM signals are generally negligible compared to that of the atmosphere except at periods shorter than ten days. At these scales, adding oceanic to atmospheric excitation series did not lead to better agreement with observed geodetic series, indicating low signal-to-noise ratios in the oceanic or perhaps all of the time series. With regard to EOAM and polar motion, the ocean is in general as important as the atmosphere at most time scales. Combined oceanic and atmospheric excitation series compared visibly better with geodetic series than did atmospheric series alone, particularly at high frequencies, establishing the ocean as a source of measurable signals in polar motion.
Comparisons with atmospheric and geodetic data lend some credibility to the OAM values calculated from the SC and constant-density models. In addition, at seasonal time scales, results from the two models agree qualitatively [Salstein et al., 1995]. Nevertheless, to improve the estimation of OAM, one needs to implement data assimilation schemes that make use of available data to constrain model output in an optimal way. Satellite observations of sea level, sea surface temperature, and other fields including subsurface in situ data will be crucial in this effort. With this in mind, work has been initiated in collaboration with I. Fukumori (JPL) to assimilate altimeter data into the constant-density model, using suboptimal Kalman filtering techniques described by Fukumori and Malanotte-Rizzoli . Besides testing the feasibility of the assimilation method, the goal is to check, in a synergistic way, the impact of altimeter data on calculation of OAM related quantities and on evaluation of the planet's angular momentum budget. Data assimilation, together with better satellite-derived data sets of atmospheric surface forcing fields (e.g., wind stress, precipitation), and model improvements, including better mass conservation schemes, should lead to improved estimates of OAM in the near future.