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. 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. Within the last decade or so there have been significant advances in the determination of large scale geostrophic circulation.