For a water parcel with salinity S = 34.85 at the surface and T = 0°C, we have Y = 0.0355oC/1,000 db; if T = 20°C, Y = 0.1841°C/1,000 db; at the depth of 5,000 db and T = 0oC, Y = 0.118oC/1,000 db. As discussed in the previous section, Y increases with pressure, and this is primarily due to the increase of the thermal expansion coefficient with pressure. From the sea surface to 4 km depth, the typical adiabatic temperature range is approximately 0.6oC; however, the in situ temperature range is about 20oC. At depths below 4 km, the amplitude of the adiabatic temperature lapse rate and the vertical gradient of in situ temperature are comparable.

Why is Y so much different from the vertical gradient of the real temperature? This difference is primarily due to the fact that large-scale vertical motion is dynamically forbidden; thus, water masses in the deep ocean do not come through the local vertical movement. Instead, water masses are formed at high latitude and move down along isopycnal surfaces. Thus, the large vertical temperature gradient observed at low or mid latitudes is the result of lateral motions on a global scale.

2.4.8 Potential density

Seawater is almost incompressible; nevertheless, its density can change slightly due to pressure change. In fact, density in the ocean generally increases with depth; however, a major part of the vertical density gradient is due to the increase of pressure alone. In the study of dynamical oceanography, it is often desirable to identify density changes due to other physical factors, such as temperature and salinity. Thus, potential density was introduced and has been widely used.

Potential density is defined as the density of a seawater parcel if it is moved adiabatically and without changing its salinity from an initial pressure P to a reference pressure Pr. Its

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