This study examines the observability of a stratified ocean in a square flat basin on a midlatitude beta plane. Here, “observability” means the ability to establish, in a finite interval of time, the time-dependent ocean state given density observations over the same interval and with no regard for errors. The dynamics is linearized and hydrostatic, so that the motion can be decomposed into normal modes and the observability analysis is simplified. An observability Gramian (a symmetric matrix) is determined for the flows in an inviscid interior, in frictional boundary layers, and in a closed basin. Its properties are used to establish the condition for complete observability and to identify optimal data locations for each of these flows.
It is found that complete observability of an oceanic interior in time-dependent Sverdrup balance requires that the observations originate from the westernmost location at each considered latitude. The degree of observability increases westward due to westward propagation of long baroclinic Rossby waves: data collected in the west are more informative than data collected in the east. Likewise, the best locations for observing variability in the western (eastern) boundary layer are near (far from) the boundary. The observability of a closed basin is influenced by the westward propagation and the boundaries. Optimal data locations that are identified for different resolutions (0.01 to 1 yr) and lengths of data records (0.2 to 20 yr) show a variable influence of the planetary vorticity gradient. Data collected near the meridional boundaries appear always less informative, from the viewpoint of basin observability, than data collected away from these boundaries.