Assimilation of altimetry data in a high-resolution limited-area primitive equation model of the Southern Ocean

An eddy-permitting (44 km at 50°S) numerical model of the open ocean south of Australia is combined with satellite altimetry data in an assimilation study of Southern Ocean dynamics. The domain chosen is from 110 to 190° East and 30 to 70° South, encompassing both the Southeast Indian and Macquarie Ridge complexes. This region is thought to play an important role in the momentum balance of the Antarctic Circumpolar Current (ACC) and meridional heat and freshwater exchanges. The Hamburg Ocean Primitive Equation (HOPE) model (Wolff et al. 1997) is an implicit free-surface primitive-equation model discretised on an Arakawa E-grid. It is modified to operate in an open boundary configuration. For the barotropic mode, the open boundary condition is based on characteristic variables and extends the condition proposed by Flather (1976). The boundary condition preserves water volume while allowing the transmission of shallow-water gravity waves, an important feature with sequential data assimilation. Volume transports normal to the boundaries are required. Across the ACC, these are determined adaptively through a thermal wind calculation. On the northern boundary, prescribed transports model the Leeuwin Current and East Australia Current. For the baroclinic velocities, a modified Orlanski-type (Orlanski 1976) radiation condition is applied on the eastern boundary, while a zero-gradient condition is applied on the northern boundary. Because of the staggered grid in HOPE, the baroclinic velocities on the western boundary can be calculated prognostically as in the interior. For tracers a combination of relaxation towards climatology for inflow and upstream advection on outflow is applied along all the open boundaries. The model undergoes considerable drift in a forty-year spinup run. This results from a lack of sea-ice in the model, and inadequate surface forcing and deep-water formation. The reduced-order optimal interpolation System for Ocean Forecasting and Analysis (SOFA) of De Mey (1999) is integrated with HOPE to perform the assimilation. The order-reduction applies a transformation in the vertical between observed sea-level anomalies and the internal density structure, preserving both water-mass properties and potential vorticity on isopycnals (Cooper and Haines 1996). Such a model of water-column variability is consistent with that observed in repeat hydrographic sections of the WOCE SR3 line through the model domain. A dynamical analysis of the vertical projection scheme in an assimilation context shows that it excites primarily barotropic topographic Rossby waves. One year of data from the TOPEX/POSEIDON satellite mission is used in a series of trial assimilation runs. The assimilation system produces reasonable analyses of sea-level anomaly, and improved estimates of meridional eddy heatflux. A comparison with a WOCE hydrographic section succesfully captures a significant eddy feature, but at a reduced level. A trial is made of a modification to the vertical projection scheme that includes a degree of barotropic variability. This modification provides small but significant improvements to statistics of forecast performance and patterns of sea-level variability