I had a number of interesting Twitter conversations today and thought I would write about one of them. It started with me retweeting something from Andy Revkin which showed the NOAA ocean heat content, down to a depth of 2000m, from 1960 to now. I include the figure below. It shows that the amount of energy in the oceans (to a depth of 2000m) has increased by about 3 x 1023J since about 1970.
Ocean heat content down to 2000m from 1960 to now (credit : NOAA)
Someone then responded to suggest that it should be temperature not energy so that a direct comparison can be made with atmospheric temperatures. I think this isn’t really correct as they are two different systems with different masses and different specific heat capacities. Anyway, if you do convert to temperature, you discover that the ocean temperature has increased by about 0.11oC since 1970. The rather predictable response to this calculation was, why do we care about such a small temperature increase?
Well, there are a number of reasons why we care. That the ocean heat content has continued to rise tells us that global warming (or global heating) continues, despite the slowdown in the rise in surface temperatures. Oceans are also part of our climate system. Adding energy to the oceans can change ocean circulation and can influence hurricanes and cyclones. Also, ENSO cycles can transport energy throughout the ocean, heating the ocean surface and releasing it into the atmosphere where it can increase atmospheric and land temperatures.
There is also another reason why we should care. Currently the oceans are absorbing a large fraction of the excess energy entering the climate system. If this fraction were to reduce, we will see the rise in surface temperatures accelerate. The response to this point was the claim that this would violate the 2nd law of thermodynamics since energy can’t go from a cooler body (oceans) to a warmer body (atmosphere). The claim being, I believe, that if the oceans are currently absorbing a majority of the excess energy, then this can’t change and hence we have nothing to be concerned about. Now, I think that applying the 2nd law of thermodynamics isn’t really correct here. We’re talking about radiation, not conduction.
I thought I would describe how I, as a physicists, think this works. Firstly, I’m not a climate scientist, so maybe I’ve got it wrong. Secondly, this is going to be quite simple and I will be ignoring a lot of the details. As usual, happy to be corrected if I’m wrong. If the planet was in equilibrium we’d be receiving as much energy from the Sun as we lose back into space. Currently, we appear to be undergoing a phase of global warming in which we receive more energy from the Sun than we’re losing back into space. About 70% of the planet’s surface is ocean which means that about 70% of the incoming energy hits the ocean, and 30% hits the land (ignoring the atmosphere for the moment). One might expect this to imply that 70% of the excess should go into the ocean, and 30% into the land.
However, the amount absorbed by the system will be determined by the difference between the incoming energy and the outgoing energy. The amount going out (or radiated) is essentially determined by the surface temperature. If the oceans and land had the same surface temperature, then we would expect the oceans to absorb about 70% of the excess energy. The sea surface temperature, however, tends to be lower (I believe – although I’ve become slightly concerned that this may be wrong, so may be a flaw in my argument) than the land temperature and hence, on average, the difference between the incoming and outgoing energy is likely to be greater for the oceans than for the land. Hence, the oceans absorb more than 70% of the excess. Currently, consequently, the oceans are absorbing more than 90% of the excess energy.
So, why am I saying this. Well as the oceans absorb more and more energy, the sea surface temperature will have to rise. The difference between the incoming and outgoing energy will have to drop, and the oceans will absorb a smaller fraction of the excess energy. This will then mean that a larger fraction will be available to heat the land and atmosphere and we will start to see the rise in surface temperatures accelerate. Unless global warming were to somehow stop (and it hasn’t) the surface temperatures will have to start rising faster again in the not too distant future.
Anyway, when I started to explain this in Twitter (which is tricky given the 140 character limit) I was asked what would happen if the sea surface temperature rose by 0.1oC. So, I thought I would have a go at working it out. The amount of energy radiated from the surface of the ocean per second is
0.7 x 4 π R2E σ T4,
where RE is the radius of the Earth, and T is the surface temperature of the oceans. The average sea surface temperature is about 290 K. If I solve for the energy radiated per second, I get 1.4314 x 1017 J s-1. Now, if I assume the sea surface temperatures increases instantaneously by 0.1oC to 290.1 K and redo the calculation, I get 1.4334 x 1017 J s-1. The difference is 1.98 x 1014 J s-1. If I multiply by the number of seconds in a year I get, 6 x 1021 J. In other words, if the sea surface temperature were to increase by 0.1oC, the oceans would radiate 6 x 1021 J more per year than they did at the lower temperature.
If you look at the figure included above, you’ll see that the ocean heat content is increasing at about 7.5 x 1021 J per year. So, if the sea surface temperature were to suddenly rise by 0.1oC (which it can’t), instead of the oceans absorbing more than 90% of the excess energy, they’d only be absorbing about 20%. Now, I know this isn’t actually possible and I’m not suggesting that anything like this will happen. All I’m trying to point out is that a relatively small change in the sea surface temperature could change the fraction of the excess energy going into the oceans and hence change the fraction that is available to heat the land and atmosphere.
Anyway, I don’t know if I’ve got this argument quite right. It has to be more complicated than I’ve described here. However, I think the basic calculation is about right. As the ocean heat content rises, it must increase the sea surface temperature. This will have to reduce the difference between the incoming and outgoing energy and will hence reduce the fraction of the excess energy being absorbed by the oceans. Consequently we will see an increase in the fraction available to heat the land and atmosphere. As usual, happy to be corrected by those who know more than I do.