start. Over the same time period, the mean sea level increases slightly, less than 2 m (heavy line in Fig. 5.141b), which is much smaller than the sea level decline of more than 16 m for the case of a warm start. As for the difference in the north-south sea surface height and the meridional overturning rate in the case of a cold start, both increase slowly and monotonically, as shown by the heavy lines in Figure 5.141c, d.
As discussed in Section 3.7, in the case of a cold start there is virtually no convective adjustment or new deepwater formation at the beginning of the simulation because the initial temperature is set to 0°C. The system gradually accumulates its energy, which can be used to maintain the circulation primarily from GPE generated through vertical mixing. Under surface heating, the upper ocean water at low latitudes is warmed up, and sea level there becomes higher than that at high latitudes; through vertical mixing, the GPE of the system increases.
Driven by the meridional pressure gradient at sea level, warm surface water flows to high latitudes where cooling induces convective overturning, causing GPE to be partially converted into kinetic energy which drives the overturning circulation. However, this is a much less dramatic process, as compared with the sudden onset of cooling in the case of a warm start.
By comparing these two spin-up processes, the role of the mechanical energy balance in setting up the thermal circulation in the ocean is clearly demonstrated. We see that surface thermal forcing itself cannot create much mechanical energy. Instead, cooling at high latitudes constitutes a major sink of GPE, although the GPE lost through cooling can be partially converted into kinetic energy of the mean state, maintaining a strong circulation. However, the abnormally strong circulation during the sudden cooling cannot be sustained, and the circulation eventually turns to a more gentle state that can be sustained by the energy supplied by vertical mixing.
Three-dimensional structure of the thermal circulation The difference in mean sea surface height between the southern and northern boundaries reflects the difference in temperature distribution in the upper ocean. Since the model is subject to a strong temperature relaxation condition on the upper surface, temperature in the surface layer is almost a linear function of latitude (Fig. 5.142a). The noticeable departure from the zonal distribution appears along the western boundary, which indicates a strong northward flow there.
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