Our first and most central assumptions are that because the flow has very large horizontal scale, smaller vertical scale, slow time variation relative to the earth's rotation rate, and is nearly inviscid and non-diffusive, it is in approximate geostrophic and hydrostatic balance. Geostrophy is the balance between Coriolis force and horizontal pressure gradient. Hydrostatic balance is that between vertical pressure gradient and gravity. Because the horizontal pressure distribution determines the flow, one way that we measure the ocean circulation is by attempting to map the pressure distribution. (The other is by measuring the flow directly.) However, the largest part of the horizontal pressure gradient arises from differences in sea surface height, which cannot be measured from a ship. From a ship it is possible to measure the distribution of sea water density, which depends on temperature, salinity and pressure, and from this to determine the horizontal pressure gradient at one level relative to another. In the absence of information about the absolute sea surface height or the absolute pressure along some geoidal surface within the ocean, velocities can be calculated only relative to those at another level. Because the surface currents are generally vigorous relative to those at depth, such a relative calculation is useful for the upper ocean; however, there are serious problems for the deeper ocean for which the currents are much slower.
Within the last decade or so there have been significant advances in the determination of large scale geostrophic circulation. So-called ``inverse methods'' use traditional hydrographic data (vertical temperature and salinity profiles), assume geostrophic balance, and find the reference velocity for each station pair, subject to constraints such as mass conservation or particular tracer balances. It is an application of generalized inverse methods whose formalism was developed to find the optimal solution in a least squares sense to underdetermined problems. The application to geostrophic circulation was developed by Wunsch [1978] and Roemmich [1981] in applications to the North Atlantic. Because mass conservation is a fundamental constraint, the hydrographic stations must form a closed box or boxes, or extend between continental boundaries. Applications to the North Pacific have been made by Roemmich and McCallister [1985], Bingham and Talley [1991], Wijffels [1993], and Nakano et al. [1994]; for the South Pacific, Wunsch et al. [1983]; and for the whole globe including the Pacific, Macdonald [1995]. Each of these includes transport results for individual currents or entire sections and may include additional constraints from direct current measurements. Bingham and Talley [1991] and Nakano et al. [1994] estimated Kuroshio transport using sections crossing the Kuroshio in two locations, one of which is Tsugaru Strait; the results have the advantage of not being based strictly on a level of no motion. Roemmich and McCallister [1985] and Wunsch et al. [1983], Wijffels [1993] and Macdonald [1995] produced estimates of meridional transports of heat and freshwater to be compared with those derived from surface fluxes. They show that there is net inflow to the Pacific from the south in the bottommost layer (Antarctic Bottom Water or Lower Circumpolar Water) and in the Antarctic Intermediate Layer, and net outflow to the south in the Pacific Deep Water layer lying between these inflows.
A more traditional approach to basin-wide circulation has been taken by Reid [1986, 1989, 1994] in studying the circulation of the South Pacific, South Atlantic and North Atlantic, respectively. The same principles, of geostrophy and mass conservation, are used without the inverse method formalism. The technique is to determine the reference velocity which satisfies these constraints and best matches a qualitative idea of the circulation, based on the tracer fields at all depths.
Geostrophic balance is expected to hold for most latitudes, and to break down at the equator where the local vertical component of the Coriolis force vanishes. Hayes [1982] and Eriksen [1982] showed by comparison of geostrophic estimates and direct velocity measurements in the equatorial undercurrent and in the deep equatorial Pacific, respectively, that geostrophy holds to within fractions of degrees from the equator. The principal difficulty in applying geostrophy at the equator is that internal waves create sufficiently large-scale and long-period features that cannot be removed by spatial averaging; these and other ageostrophic motions, which are important relative to geostrophic motions at the equator, cause isopycnals to be sloped at the equator, making geostrophic calculations from single hydrographic sections difficult. Hayes et al. [1983], Wyrtki and Kilonsky [1984], and Bryden and Brady [1985] averaged many sections crossing the equator in the Pacific to produce average density structures and hence comprehensive pictures of the mean general circulation in the upper tropical regime, based on an assumption of geostrophic balance.