## The lag in the seasons

The observant reader noted in figure 5.1 that not only is the seasonal cycle more muted in San Francisco, but also that the maximum temperatures occur later in the season, in September. This again is an effect of the large heat capacity of the system, as a simple argument shows. Suppose that a system is heated externally (e.g., by the sun) and is cooled by the effects of longwave radiation and that the cooling is proportional to the temperature itself. If the system has a very small heat capacity, then the heating and cooling must balance each other at all times. A consequence of this is that the cooling is greatest when the heating is greatest, and so the temperature itself is highest when the sun is highest in the sky. Indeed, we find that in continental climates the temperature is highest fairly soon after the summer solstice and coldest soon after the winter solstice: In Fig. 5.1, we see that New York is hottest in July and coldest in January.

If a system has a large heat capacity, it takes some time to warm up and cool down, and so the maximum temperatures occur some time after the maximum insolation and thus later in the summer. The same effect occurs on a daily basis: inland, the maximum daily temperature occurs shortly after noon, whereas at the seaside the maximum temperature is later in the afternoon. On a large scale, in the Northern Hemisphere midlatitudes, the maximum temperature occurs on average about 30 days after the maximum solar insolation, whereas in the more maritime Southern Hemisphere, the maximum occurs about 45 days after peak insolation (figure 5.2). At very high latitudes, where the Southern Hemisphere is covered by land (Antarctica) but the Northern Hemisphere by ocean (the Arctic ocean), the lag is longer in the Northern Hemisphere. A mathematical demonstration of this effect is given in appendix A of this chapter.

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