## THE SLoWiNG oF GLoBal WarmiNG

Perhaps the most important and least ambiguous effect of the ocean is that it acts to slow down global warming in a certain sense, although the effect is rather subtle. Furthermore, the ocean is not likely to significantly affect the final equilibrium temperature that the planet will reach if, let us say, co2 levels eventually double before leveling off. So just what does the ocean do? Let's try to explain it first just using words; appendix A to this chapter provides a mathematical treatment of the same issue.

In chapter 4 we noted that in the upper ocean there is a mixed layer, typically 50-100 m thick, in which the vertical distribution of temperature and salinity is almost uniform. This turbulent region is stirred by the winds and convection, and its heat capacity is about twenty times that of the atmosphere, which means that it responds rather slowly to such things as daily changes in the weather. However, compared to the deep ocean, it responds very quickly. Thus, for example, if the radiative forcing were to change because of global warming, the mixed layer might be expected to respond and come to a new equilibrium on the timescale of a few years. Now, the radiative forcing has been changing rather slowly over the past century or so, and the mixed layer has little difficulty keeping up. At most, the mixed layer is in equilibrium with the forcing levels in the atmosphere a decade ago, and likely just a few short years ago. The atmosphere, which has a much smaller heat capacity than the mixed layer, tends to respond to the mixed layer quickly. Thus, increased radiative forcing causes the ocean's mixed layer to warm quickly, and this warming in turn sets the atmospheric temperature.

However, the rest of the ocean takes longer—much longer—to equilibrate. To get a rough sense of how much longer this time might be, note that in round numbers the mixed layer is 50 m deep, the thermocline is 500 m deep, and the entire ocean, 5,000 m deep; roughly, the times scale accordingly. What effect might these differences have on global warming? Let us suppose that we add some greenhouse gases to the atmosphere and so increase the downward flux of radiation at the surface. Over a few years, the mixed layer warms up until it reaches an equilibrium—that is, a state in which it gives up as much heat as it is receiving—although the temperature of the deep ocean will hardly have risen at all over that period. However, the increased heat that the mixed layer is giving up is going, in part, to warm the ocean below, and it takes a long time, perhaps many centuries, for the deep ocean to fully equilibrate because it is so big. As the deep ocean warms, the mixed layer can give up less of its heat to the ocean below, and so can only balance the radiative forcing by further increasing its temperature, so that it gives its heat back to the atmosphere.

What is the consequence of this picture for global warming? We are slowly but steadily putting greenhouse gases into the atmosphere; the mixed layer responds to this input, and its temperature increases in concert. However, the deep ocean is far from equilibrium, which means that, even if we were to stop adding greenhouse gases to the atmosphere and the levels of greenhouse gases were to stabilize at some level, the temperature of the ocean's mixed layer, and so of the atmosphere, would continue to rise for a long period after that. Let us suppose that we continue putting CO2 into the atmosphere until its level has doubled from that in preindustrial times, and that this doubling occurs in the middle of the twenty-first century. We can expect the global averaged temperature to rise by between 1.3°C and 2.5°C, and probably around 1.8°C, from its preindustrial value by then.10 Suppose that at that time the political and technological stars align and we are able to prevent greenhouse gas levels in the atmosphere from increasing any further. The average surface temperature of Earth will nevertheless keep on increasing until the deep ocean has finally equilibrated, which will take an additional few hundred years or more.

There is considerable uncertainty as to what this final equilibrium temperature rise will be, but it may be much higher than the 1.8°C mentioned above; most estimates are between 2°C and 4.5°C, although higher values cannot be definitively excluded. If we were to eventually cease C02 emissions entirely, perhaps because fossil fuels run out, it would take centuries for the C02 to finally revert to levels near or a little above the preindustrial value (Archer 2010). During that period, temperatures would likely stay roughly constant for a few centuries before slowly falling back down to levels commensurate with the level of C02, as illustrated in figure 7.7. If C02 remains doubled for a century before emissions cease, the peak warming will probably be a little over 2°c, and if it triples the peak warming will be around 3°C, with uncertainties of about plus or minus 0.5°C. These peak levels will remain for centuries. Whichever way we slice it, global warming is a long-term problem.

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