Although I don’t really feel like explicitly debunking what I see on some “skeptic” sites (Sou does enough for all of us 🙂 ) I do sometimes, to my eternal regret, read them. I recently came across a standard argument that the oceans are warming really slowly, so what’s the problem? The basic argument is that the 0-2000m Ocean Heat Content has increased by about J over the last 50 years. The oceans – to 2000m – have a total mass of around kg and a heat capacity of 4000 J kg-1 K-1, and hence this implies an increase in temperature of about 0.1oC, or about 0.02oC per decade. There you go. Nice and slow.
So, what’s the problem? Well, the oceans don’t warm uniformly. If you consider the figure below (from Balmaseda et al. 2013) you can see that about half of the energy goes into the upper 300m, one-quarter goes into the next 400m and another quarter goes into the region between 700m and 2000m. The surface, therefore, warms faster than the deep ocean.
One of the reasons I wanted to write this post is partly because I don’t think how energy is distributed in the ocean has been discussed very much and partly because if I write about it and stuff it up, someone will come along and correct me – so I might learn something. As I understand it, there is a well-mixed layer in the upper ocean in which turbulence and other processes act to rapidly mix the energy. In a sense, this well-mixed layer can be regarded as very quickly equilibrating with the rest of the climate system (atmosphere) and so the rate at which the temperature is rising in this well-mixed layer is a reasonable approximation for the rate at which the temperature is rising in the rest of the – non ocean – climate system. Essentially, one can approximate this well-mixed layer and the atmosphere as a single system.
Energy also diffuses down into the deeper ocean, but this tends to be quite a slow process. More correctly, the time it takes for the deep ocean to equilibrate with the rest of the climate system is very long (centuries). For example, if we were to suddenly increase atmospheric CO2 concentrations so as to produce a planetary energy imbalance, the atmosphere and well-mixed layer would initially warm very rapidly. As we approached equilibrium the rate of temperature increase would, however, slow and the system would retain a planetary energy imbalance that roughly matched the rate at which the energy was going into the deep ocean. As the deep ocean tended towards equilibrium with the rest of the climate system, the planetary energy imbalance would tend to zero. This, however, can take a very long time as the total amount of energy required to equilbrate the entire system is large.
At the beginning of the post, I indicated that some use the average rate of increase to argue that we’ll warm slowly because of the heat capacity of the oceans. This, however, is an underestimate since it assume that the temperature rises at the same rate throughout the ocean. This is clearly not correct and one can actually approximate the rate of increase of surface temperature by considering the well-mixed layer, rather than the whole ocean. For example, if we have a planetary energy imbalance of 0.5 Wm-2 then we’re increasing the total energy by about 1023J per decade. If, as per the figure above, about half goes into the well-mixed layer, and we assume this is the upper 300m (this is probably a bit too deep, as its probably more like 100-200m, but given that the energy would be proportionally less, probably good enough for this illustration), then the energy in the well-mixed layer increases at a rate of about J per decade. Given the heat content of this layer (300m of ocean with a heat capacity of 4000 J kg-1K-1) the temperature will rise at about 0.15oC per decade – not far off the rate at which the temperature is currently rising.
So, hopefully my explanation is correct, but the main thing I wanted to point out is that if one considers the average rate at which the temperature of the ocean is rising then you underestimate the rise in surface temperature by as much as a factor of 7-8. I should also add that all my numbers are simply estimates and I’m sure one could do this more accurately. The point, though, is that the large heat content of the oceans does not imply that we’ll warm slowly. It does imply that it will take a very long time for the entire system to equilibrate, but we’ll get close pretty quickly. As usual, if I have explained something poorly, or got something wrong, feel free to point that out.
[Edit : I updated some of the numbers as I’d slightly misread the Balmaseda et al. (2013) figure.]