compared with other terms. Comparatively speaking, AGPE density in the Atlantic Ocean is the highest, while in the Pacific Ocean it is the lowest.
The effect of nonlinearity of the equation of state of seawater is of vital importance in calculating AGPE; this can be further illustrated by processing the same climatolog-ical dataset, but with different equations of state. A linear equation of state is defined as p = p0 [1 - a(T - T0) + fi (S - S0) + yP], where p0 = 1,036.9 kg/m3, a = 0.1523 x 10-3/°C, fi = 0.7808 x 10-3, and y = 4.462 x 10-6/db. It is interesting to note that an equation of state with a linear dependence on pressure can substantially improve the calculation of the AGPE.
The calculation above is based on mass coordinates; thus the mass of each grid box is conserved during the adjustment. A traditional Boussinesq model does not conserve mass, so that the meaning of APE inferred from such a model is questionable. As an example, APE based on the Boussinesq approximations can be calculated and is noticeably smaller than that calculated from the truly compressible model (Table 3.4). (In such a calculation the volume of a water parcel remains unchanged after adjustment, even if its density is adjusted to the new pressure.) It is speculated that a smaller AGPE may affect the model's behavior during the transient state.
An interesting and potentially very important point is that AIE in the world's oceans is negative. For reversible adiabatic and isohaline processes, changes in internal energy obey de = -pdv. Since cold water is more compressible than warm water, during the exchange of water parcels the increase in internal energy associated with the cold water parcel is larger than the internal energy decline associated with the warm water parcel (Fig. 2.13). Thus,
AIE associated with the adjustment to the reference state is negative. In contrast, warm air is more compressible than cold air; therefore the corresponding AIE in the atmosphere is positive.
Although a special term (available GPE) has been given to the difference in GPE between the physical state and the reference state, such energy may not be completely released, owing to the existing geostrophic constraint in the ocean. Consider a two-dimensional, two-layer model ocean, with density p and p + Ap (Fig. 3.32). The slope of the interface is S, and the interface height is b = Sx + H/2 - SL/2. The total amount GPE in the physical state is
and the AGPE of the system is n = gAp L3S2 (3.150)
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