The oceans have a much greater capacity to store heat than the atmosphere. This can be readily seen as follows. The heat capacity of a "slab" of ocean of depth h is YO = PrefCwh (i.e., density x specific heat x depth, with units of JK-1m-2). Let us compare this with the heat capacity of the atmosphere, which we may approximate by Ya = PscpH, where ps is the mean density of air at the surface and H is vertical scale height of the atmosphere (7-8 km). Inserting typical numbers—the ocean is one thousand times more dense than air and its specific heat is about 4 times that of air—and allowing for the fact that the ocean covers about 70% of the Earth's surface area, we find that y0/ya — 40 if h = 100 m, a typical ocean mixed layer depth, and y0/ya — 2000 if the whole 5 km depth of the ocean is taken in to account.
The thermal adjustment times of the two fluids are also consequently very different. Radiative calculations show that the timescale for thermal adjustment of the atmosphere alone is about a month. Thermal adjustment timescales in the ocean are very much longer. Observations suggest that sea surface temperatures are typically damped at a rate of X = 15 W m-2 K-1 according to the equation:
where T is the temperature anomaly of the slab of ocean (assumed well mixed) in contact with the atmosphere. Here, as in Chapter 11, Qnet is the net air-sea heat flux.
Setting Qnet = 0 for a moment, a solution to the above equation is T = Tinit exp ^ jA , where Tinit is an initial temperature anomaly that decays exponentially with an e-folding timescale of y0/X. Inserting typical numbers (see Table 9.3), we obtain a decay timescale of 300 d — 10 months if h is a typical mixed layer depth of 100 m. Setting h equal to the full depth of the ocean of 5 km, this timescale increases to about 40 y. In fact, as described in Section 11.2.2, the time scale for adjustment of the deep ocean is more like 1ky, because the slow circulation of the abyssal ocean limits the rate at which its heat can be brought to the surface. These long timescales buffer atmospheric temperature changes. Thus even if the ocean did not move and therefore did not transport heat and salt around the globe, the ocean would play a very significant role in climate, reducing the amplitude of seasonal extremes of temperature and buffering atmospheric climate changes.
The ocean also has a very much greater capacity to absorb and store energy than the adjacent continents. The continents warm faster and cool faster than the ocean during the seasonal cycle. In winter the continents are colder than the surrounding oceans at the same latitude, and in summer they are warmer (see Fig. 12.2). This can readily be understood as a consequence of the differing properties of water and land (soil and rock) in thermal contact with the atmosphere. Although the density of rock is three times that of water, only perhaps the upper 1m or so of land is in thermal contact with the atmosphere over the seasonal cycle, compared to, typically, 100 m of ocean (see Problem 1 at the end of this chapter, in which we study a simple model of the penetration of temperature fluctuations into the underlying soil). Moreover the specific heat of land is typically only one quarter that of water. The net result is that the heat that the ocean exchanges with the atmosphere over the seasonal cycle exceeds that exchanged between the land and the atmosphere by a factor of more than 100. Consequently we observe that the seasonal range in air temperature on land increases with distance from the ocean and can exceed 40°C over Siberia (cf. the surface air-temperature difference field, January minus July, plotted in Fig. 12.2). The amplitude of the seasonal cycle is very much larger over the continents than over the oceans, a clear indication of the ocean "buffer." This buffering is also evident in the very much weaker seasonal cycle in surface air temperature in the southern hemisphere, where there is much more ocean compared to the north. Note also the eastward displacement of air temperature differences over land in Fig. 12.2 (bottom), evidence of the role of zonal advection by winds.
Climatological analyses such as those presented in Chapter 5 define the normal state of the atmosphere; such figures represent the average, for a particular month or season, over many years. It is common experience, however, that any individual season will differ from the climatological picture to a greater or lesser extent. One winter, for example, may be colder or warmer, or wetter or drier, than average. Such variability—in both the atmosphere and the ocean—occurs on a wide range of timescales, from a few years to decades and longer. Understanding and (if possible) forecasting this variability is currently one of the primary goals of meteorology and oceanography. Given the large number of processes involved in controlling SST variability (see the discussion in Section 11.1.2), this is a very difficult task. The challenge is made even greater by the relatively short instrumental record (only 50-100 y) and the poor spatial coverage of ocean observations.
In middle to high latitudes, the direct forcing of the ocean by weather systems— cyclones and anticyclones—induce SST changes through their modulation of surface winds, air temperature, and humidity, and hence air-sea fluxes Q in Eqs. 11-6 and 11-7. These short-period atmospheric systems can yield long-lasting SST anomalies, because the large heat capacity of the ocean endows it with a long-term memory. Such SST anomalies do not have a regular seasonal cycle; rather they reflect the integration of "noise" (from weather systems) by the ocean. One can construct a simple model of the process as follows. In Eq. 12-1 we set Qnet = ReQmemt, where Qw is the amplitude of the stochastic component of the air-sea flux at frequency m associated with atmospheric eddies, and the real part of the expression has physical meaning.
Let us suppose that Qœ is a constant, so representing a "white-noise" process in which all frequencies have the same amplitude.2 The response of the SST anomalies that evolve, we assume, according to Eq. 12-1, is given by T = Re Twemt, where (see Problem 2 at end of chapter)
The T spectrum is plotted in Fig. 12.3a and has a very different character from that of the forcing. We see that mc = 1/yO defines a critical frequency that depends on the heat capacity of the ocean in contact with the atmosphere (set by h) and the strength of the air-sea coupling (set by 1). At frequencies m > mc the temperature response to white noise forcing decreases rapidly with frequency—the sloping straight line on the log-log plot. At frequencies m < mc the response levels out and becomes independent of m as evident from the grey curve in Fig. 12.3a. For the parameters chosen above, mc = 305-3, and so one might expect SST variations with timescales much shorter than 300 d to be damped out, leaving variability only at timescales longer than this. This simple model (first studied by Hassel-man, 1976), is the canonical example of how inertia introduced by slow elements of the climate system (in this case thermal inertia of the ocean's mixed layer) smooths out high frequencies to yield a slow response, a "reddening" of the spectrum of climate variability.
In comparison, Fig. 12.3b shows the observed temperature spectra of the atmosphere and of SST. Although the atmospheric spectrum is rather flat, the SST spectrum is much redder, somewhat consistent with the m-2 dependence predicted by Eq. 12-2 above. Simple models of the type described here, explored further in Problem 2 at the end of the chapter, can be used to rationalize such observations.
One aspect of observed air-sea interaction in midlatitudes represented in the above model is that atmospheric changes tend to precede oceanic changes, strongly supporting the hypothesis that midlati-tude year-to-year (and even decade-to-decade) variability primarily reflects the slow response of the ocean to forcing by atmospheric weather systems occurring on much shorter timescales. One might usefully call this kind of variability "passive"—it involves modulation by "slower" components of the climate system (in this case the ocean) of random variability of the "faster" component (the atmosphere).
In tropical latitudes, however, changes in SST and tropical air temperatures and winds are more in phase with one another, reflecting the sensitivity of the tropical atmosphere to (moist) convection triggered from below. This sensitivity of the atmosphere to tropical SST can lead to "active" variability—coupled interactions between the atmosphere and the ocean in which changes in one system mutually reinforce changes in the other, resulting in an amplification. In the next section we discuss how such active coupling in the tropical Pacific manifests itself in a phenomenon of major climatic importance known as El Nino.
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