As there has been no sign of a Fermi explanation so far, I had a go for myself, largely with the help of this paper. Yes, I am aware that Lindzen is widely held to be a climate change denialist and therefore an evil monster, but I admire the way he writes clearly and convincingly and without belittling or talking down to his audience.The concentration of carbon dioxide has increased since the beginning of the industrial age from about 280 parts per million (ppm) to about 390 ppm. According to the simple 'textbook' model* of global warming, it is generally accepted that the warming from a doubling of carbon dioxide would only be about 1°C. That is, the amount of carbon dioxide currently in the atmosphere (about 390 ppm) would have to double to 780 ppm in order to cause a rise in global equilibrium temperature of 1°C. Simple arithmetic based on the rate of increase in CO2 (see the graph above) suggest that this would take almost 250 years to happen. Furthermore, because of the logarithmic effect - each doubling producing the same arithmetic increase - it would take 250+500 = 750 years to produce a 2°C rise. This is hardly catastrophic, and gives us some time to do something. I'll hang on to those incandescent bulbs for now.
But this is much less than current climate models suggest from the warming from a doubling of carbon dioxide. Why is that?
*To avoid any confusion, I mean the simple textbook model described here as ‘this model’, i.e. where it says “Thus this model predicts a global warming of ΔTs = 1.2 K for a doubling of carbon dioxide.”.
10 comments:
Sorry. Your problem is that you still don't really understand the basic science; as exemplified by this post. First off, you can (if you like) read Lindzen's work, but you should be aware (indeed you are aware) that he doesn't actually represent the mainstream of science. So if the task you set yourself was to learn how the sceptics view climate change, you might have succeeded; personally I don't find that a very interesting thing to do.
> "That is, the amount of carbon dioxide currently in the atmosphere (about 390 ppm) would have to double to 780 ppm in order to cause a rise in global equilibrium temperature of 1°C. "
No, this is wrong. Because of WV and other feedbacks, a doubling of CO2 leads to a temperature rise of 3 oC (unless you're talking about a theoretical world with no feedbacks. It isn't clear to me why you'd want to do that). Or at least, that is the std scientific position (you can quibble about the exact value of climate sensitivity if you like; James Annan has a variety of posts on it, for example http://julesandjames.blogspot.com/2011/01/better-late.html). Lindzen generally does his best to disguise this, and it looks like he has fooled you.
> Fermi explanation so far, I had a go for myself
Ah, I shouldn't have let you get away with that, either. You haven't explained anything. All you've done is said "CO2 levels of X cause warming of Y". That explains nothing.
If you want the very simple explanation of the GHE, then you've already found it:
http://en.wikipedia.org/wiki/Idealized_greenhouse_model
If you want a very simple explanation of how much warming you get from increasing CO2 by Y% then you can't have one: the full theory plus modelling of the earth system is too complex.
> I admire the way he writes clearly and convincingly and without belittling or talking down to his audience.
Good to see that your skepticism is fully engaged :-)
>> if the task you set yourself was to learn how the sceptics view climate change
My task was to find a clearly explained version of the problem. You are welcome to give a clear explanation, but you haven’t done so yet.
>>No, this is wrong. Because of WV and other feedbacks, a doubling of CO2 leads to a temperature rise of 3 oC (unless you're talking about a theoretical world with no feedbacks.
It should have been quite clear that I was talking about a theoretical world with no feedbacks. That is the ‘simple textbook model’. I have included a footnote to avoid any confusion.
>> James Annan has a variety of posts on it, for example http://julesandjames.blogspot.com/2011/01/better-late.html
Is this a lecture or a clear explanation with reasoning?
>>If you want the very simple explanation of the GHE, then you've already found it: http://en.wikipedia.org/wiki/Idealized_greenhouse_model
I’ve already pointed out it is a poor article. The bit which says “The radiative forcing for doubling carbon dioxide is 3.71 W m−2, in a simple parameterization” represents a jump in logic which is not explained. The article up to that point uses epsilon. It makes no connection between epsilon and the radiative forcing for CO2. Then there is another jump in logic is where it moves from “Thus this model predicts a global warming of ΔTs = 1.2 K for a doubling of carbon dioxide. “, which was the model I was talking about in the post, to “A typical prediction from a GCM is 3 K surface warming, primarily because the GCM allows for positive feedback, notably from increased water vapor. A simple surrogate for including this feedback process is to posit an additional increase of Δε=.02, for a total Δε=.04, to approximate the effect of the increase in water vapor that would be associated with an increase in temperature.”
It does explain that that there is some feedback going on, I concede, but it does not say anything about how the feedback works.
>>> I admire the way he writes clearly and convincingly and without belittling or talking down to his audience.
> Good to see that your skepticism is fully engaged :-)
I dislike people who talk down without explaining. That is the whole point of invoking Fermi, who believed that any complicated problem can be explained. In fact, talking down without giving clear explanations is one of the best ways of encouraging fringe and conspiracy beliefs. Generally, if someone refuses to explain something, I believe they are hiding something.
>> If you want a very simple explanation of how much warming you get from increasing CO2 by Y% then you can't have one: the full theory plus modelling of the earth system is too complex.
Right, we are gradually getting there.
Sorry, but you're still confused and failing to separate the "idealised" version from the "real world" version.
You say:
> According to the simple 'textbook' model... 1°C...
Fine, if you like. You're on the no-feedbacks case, as you've now made clear. Theoretically interesting, but irrelevant to the real world. But then you go on:
> That is, the amount of carbon dioxide currently in the atmosphere (about 390 ppm) would have to double to 780 ppm in order to cause a rise in global equilibrium temperature of 1°C... This is hardly catastrophic
So now you're talking about the real world, which is the feedbacks case. You can't muddle the two together and expect to make any sense.
>>So now you're talking about the real world, which is the feedbacks case. You can't muddle the two together and expect to make any sense.
It should surely be clear from the rhetorical question at the end that I do not consider the textbook model the end of the matter. You should be used to the style of this blog by now, which is to approach questions in small digestible chunks. The point so far was to establish that the textbook model does not predict any catastrophic rise in temperature (at least, not in the near term).
Do we have a 'Fermi explanation' for the logarithmic relationship between CO2 concentration and the associated radiative forcing? Wouldn't the naive physics view say that twice the CO2 causes twice the absorption and re-radiation of infra-red.
>>Do we have a 'Fermi explanation' for the logarithmic relationship between CO2 concentration and the associated radiative forcing?
We don't. I remember looking for this before and finding nothing. I have simply assumed it was correct, on the basis that the science is so bog-standard that it would be foolish to challenge it.
Having looked again I found a few obviously cranky sites that challenge even this assumption, but nothing like a Fermi explanation. Wikipedia is no help.
OK, the non feedback case is well understood but planetary radiative physics is not trivial, and misled a lot of very good physicists for quite a long time. I sense you want some technical detail
Here is a good article, but it does skim over some stuff
http://geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdf
If you are really interested a good textboox is here
http://www.amazon.co.uk/Principles-Planetary-Climate-Raymond-Pierrehumbert/dp/0521865565
For the 'simple version' is here, but beware
http://www.aip.org/history/climate/Radmath.htm
Thanks Pete - really good links and some solid information for once.
Incidentally the problem with very low CS (<1.5) is that it becomes impossible to explain interglacial cycles.
The magnitudes of the forcings (Milankovitch cycles + resulting changes in CO2 and albedo) are not enough to explain the difference in temperatures through interglacial cycles without some amplification from positive feedbacks
e.g.
http://www.atmos.washington.edu/2006Q2/211/articles_required/Lorius90_ice-core.pdf
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