In the Cooling Case, the basin-mean temperature of the model declined quickly; the mean free surface of the model ocean went down from -1.7 m to -3.0 m. With such declines in the temperature and the free surface height, the meridional overturning rate went up greatly and reached a maximum value of more than 56 Sv; subsequently, it gradually declined (heavy lines in Fig. 3.44).
In the Warming Case, the basin-mean temperature of the model increased; the mean free surface of the model ocean went up from -1.7 m to -0.9 m. With such increases in temperature and free surface height, the meridional overturning rate went down greatly and reached a minimum value of slightly larger than 3 Sv; subsequently, it gradually recovered (thin lines in Fig. 3.44).
Changes in circulation are closely linked to changes in GPE in the system. In the Cooling Case, GPE of the model ocean went down greatly (Fig. 3.45). On the other hand, GPE in the Warming Case increased. The trend of GPE is opposite to that of AGPE: in the Cooling Case, AGPE increased quickly, and this indicated that more GPE was now available and could be released and converted into KE, thus giving rise to a strong circulation.
We emphasize that the strong circulation appearing in the Cooling Case is due to the release of GPE originally stored in the ocean. Although sudden cooling of the ocean can give rise to strong meridional circulation on decadal-centennial time scales, such a strong circulation cannot be maintained without a continuous supply of mechanical energy from external sources.
In fact, strong cooling does not create mechanical energy; instead, cooling can only convert GPE originally stored in the ocean into KE. As shown in Figure 3.46, for the Cooling Case (heavy line) there is a strong loss of GPE during the sudden onset of cooling (Fig. 3.46a), and this loss of GPE is primarily associated with convective adjustment (Fig. 3.46b). In this case, surface cooling appears as a weak sink of GPE, not a source (Fig. 3.46c).
Note that although a large amount of GPE is lost through convective adjustment, only a small amount of GPE can be converted into KE. Comparing Figure 3.46b and d, it is readily seen that the amount of GPE converted into KE is much smaller than the amount of GPE lost through convective adjustment.
During this period of rapid change, the source of GPE due to vertical mixing is much smaller than that of the steady state, because the model has not yet reached the quasi-equilibrium state (Fig. 3.46e).
Surface thermal forcing
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