Lubos Motl vs the logarithm function

Eli Rabett has a post where he corrects Lubos Motl's blunders about the greenhouse effect, but he left a few crumbs for me. Motl writes (warning, link goes to Motl's blog, which has a design so ugly it makes most MySpace pages look pretty):

The Gentlemen at RealClimate.ORG have decided that my article about climate sensitivity and similar articles by others are too dangerous because they show that every new molecule of CO2 causes smaller greenhouse effect than the previous molecule: the absorption rate gradually approaches saturation. ...

So what do these eleven climate scientists think about the dependence of the strength of the greenhouse effect on the concentration? Well, they live in the state of scientific consensus which means, in this case, that none of them has any idea what the answer could be. So they invited an expert to clarify the situation. ...

Spencer Weart's main goal is to deny or somewhat diminish the importance of the following two observations:

  • the greenhouse effect gets weaker as the absorption of the appropriate spectral lines gets saturated
  • the overall greenhouse effect from several gases is smaller than a simple sum if their spectra overlap

But the fact that the response to CO2 increases is logarithmic has been mentioned many times at RealClimate for example:

Note that 2xCO2 is the preferred test since the impact of 10 ppmv depends on the base amount of CO2 (i.e. 280+10 ppmv has a different response that 380+10 ppmv due to the roughly logarithmic change of forcing with CO2 level). - gavin

The logarithmic response is even built in to the definition of climate sensitivity -- it's the warming you get from doubling CO2, not the warming from an increase of 10 ppmv.

And of course the other point that Motl claims RC is denying also been made many times there. For example, here

Motl continues.

The conventional quantity that usually measures the strength of the greenhouse effect is the climate sensitivity defined as the temperature increase from a doubling of CO2 from 0.028% of the volume of the atmosphere in the pre-industrial era to 0.056% of the volume expected before 2100. Currently we stand near 0.038% ...

In terms of numbers, we have already completed 40% of the task to double the CO2 concentration from 0.028% to 0.056% in the atmosphere. However, these 40% of the task have already realized about 2/3 of the warming effect attributable to the CO2 doubling.

In terms of numbers, 0.038/0.028 is a 36% increase. Because the response is logarithmic, we are more than 36% of the way to response from CO2 doubling. In terms of numbers it is log2(0.038/0.028)= 44%. This is not 2/3 as Motl would have it. Nor have we realized 44% of the warming, since it takes a long time for the oceans to warm up.

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I asked Lubos where the 2/3 figure came from: here's [his response](http://www.haloscan.com/comments/lumidek/6529479513990054138/?dt=118340…).

my source was Lindzen's figure that we're at 3/4 of it, and I reduced it to 2/3 to lower the degree of anger of participants. The number is indeed calculated from the W/m2 estimates of the forcings etc.

He refers to a [Lindzen paper](http://www.geocraft.com/WVFossils/Reference_Docs/Lindzen_2005_Climate_C…) which itself cites a [Hansen paper](http://pubs.giss.nasa.gov/abstracts/2004/Hansen_Sato.html) in support of the 3/4 figure (ref 3, end of page 3). Intriguing I know, but at this point I got distracted by work & failed to chase this up.

And of course roughly half of the (CO2) forcing has been masked by anthropogenic aerosols. Unless this (cooling) pollution increases proportionately to the LOG of CO2, it will become less important (relative to the warming effect) as time goes by.

The LOG effect helps a little bit, the sensitivity per molecule does decrease as the concentration goes up, but for a doubling of concentrations it only means we need two molecules at doubling, to do as much damage as one molecule pre-industrial.

Yes but if we have seen 44% of the consequences of a doubling of CO2 and a 0.7C temperature rise, in itself that implies a total rise of only 1.59C. Could you comment on that?
I know it is claimed that there is about 0.4C - 0.5C "stored up" in the oceans as well. But there is also a fairly good case that temperature rise until the early 1940's was mainly natural - there wasn't much anthrogenic CO2, and the correlation between solar activity and temperature is claimed to be good until around 1975-80 - implying that it may be that only the post 1975 rise is AGW.

Yeah, I called Motl out on this 44% vs. 66% thing in the comments section to his post on climate sensitivity. He responded with some mumbo-jumbo about how it really isn't logarithmic either. When I asked him for an elaboration on what the dependence is and how he gets 66%, he said he didn't have time to explain it there and that I could find it explained by Lindzen. It may be true that Lindzen explains where he comes up with this number somewhere; however, I have never seen it...I have just seen him state it without explanation like Motl.

Bill: Well, if you look, for example at the CRU temperature record, you will see that the 1975-2005 temperature rise is somewhere around 0.5 to 0.6C, so it isn't much less than the 0.7C value for the whole century. Then, as you note, you have to add roughly another 0.5C for being out of equilibrium. Then, as bigTom noted, there are the cooling effects of the aerosols (and, the warming effects of other GHGs). And, there may have been some small natural variation in temperature over that period. At the end of the day, you find that the warming over this period is not in disagreement with predicted climate sensitivity, but because of very large error bars it doesn't provide a very strong constraint on its value either. Better constraints are provided by other past events like the glacial--interglacial transitions.

By Joel Shore (not verified) on 14 Jul 2007 #permalink

Bill:

First of all no one - here - is claiming the correlation between solar activity and temperature was in fact good until 1975-1980. In order to pretend it was, the deniers have had to change the intervals on different parts of the same axis, EXCISE portions of their graphs, etc. The significance of them knocking off everything after 1975 is that the temperature went up very sharply then, so much so that we were definitely warmer than the "Medieval Warming Period." An "anthropogenic greenhouse gases causes all warming" model is a better fit for most periods than a "solar forcing causes it all" model. But a real one taking into account all of the factors involved is not only more logical, but a better fit. Solar output hasn't increased in about 50 years, has been declining for at least 11 years, and the cosmic rays produce clouds hypothesis has not shown any signs of factuality or relevance.

Second of all, since the start of the 19th century, coal-fired industrialization has spread all over the world. It's particulate/aerosol-heavy but also C02 heavy. The particulates come out of the air more easily than the carbon dioxide, so if you decrease particulate production, you're still left with the C02 accumulating from the 19th century on up till now. That carbon was sequestered as coal, we burned it, and only some of it went back into the oceans and the forests and the soils. Also, and fortunately, and perhaps only temporarily, greater C02 concentration means more getting absorbed by the oceans - until they get too hot to take any more in. That means more human-contributed C02 staying in the air from the 19th and early 20th centuries than you'd think, since the concentration of C02 in the air was lower then.

By Marion Delgado (not verified) on 14 Jul 2007 #permalink

In case there's any doubt, I explicitly looked a while back and the IPCC estimates include the logarithmic effect of added CO2.

"First of all no one - here - is claiming the correlation between solar activity and temperature was in fact good until 1975-1980. In order to pretend it was, the deniers have had to change the intervals on different parts of the same axis, EXCISE portions of their graphs, etc. The significance of them knocking off everything after 1975 is that the temperature went up very sharply then, so much so that we were definitely warmer than the "Medieval Warming Period."

Amen to that. The fit between the various "it's all solar" models, including the cosmic ray models, and historical records is largely imaginary. And, even if they did fit, they are irrelevant unless they can be shown to match the warming seen in the past 30 years or so. In the absence of such a fit, they in fact serve as evidence that what we are experiencing now is the result of a different process.

And, as I posted before, any model which relies on an alteration in incident energy from the Sun has the problem of predicting greater effect on daytime temperatures than at night, and on equatorial temperatures rather than polar; whereas the reality is the other way around, as would be predicted by a model based on enhanced atmospheric absorbtion of the earth's radiated IR.

And by happenstance, insufficiently buried probes left by Apollo astronauts didn't get drilled deep enough to detect temperatures of the underlying rock as intended; instead they gave surface temperature info, that when reassessed
http://www.astrobio.net/cgi-bin/h2ps.cgi?sid=2354&ext=.ps
turned out to have captured a record showing it wasn't the Sun changing, it was indeed the Earth:

"... a lunar nightâtime warming trend from midâ1972 to late 1975, which was consistent with a global dimming of Earth that occurred over the same period and was due to a general decrease of sunlight over land surfaces. (Widespread groundâbased radiation records from that period show that solar radiation reaching Earths surface during that period decreased significantly, for reasons that are not completely understood.)
"Huang's study demonstrated that signals from the energy budget of Earths climate system are detectable on the Moon ...."

By Hank Roberts (not verified) on 16 Jul 2007 #permalink

Z: Yes "Amen" and praise the lord. You AGW people sound more and more like a religion everyday why not just admit you are a church, and get tax exempt status, instead of pretending to be based in science which clearly you are not.

Dear Tom it is not considered good form to try and attribute to others your own disease, however such attempts are revealing.

"Amen" from the Hebrew root "AMN" (my transliteration, not official), meaning truth.

You seem to be laboring under the illusion that I am somehow being paid for believing in AGW, or espousing a belief in AGW. Actually the opposite is true; I donate money to organizations trying to ameliorate AGW. I also try to reduce my AGW impact, but since that kind of thing tends to save me money rather than cost me money, I won't mention it.

"...if you look, for example at the CRU temperature record, you will see that the 1975-2005 temperature rise is somewhere around 0.5 to 0.6C, so it isn't much less than the 0.7C value for the whole century. Then, as you note, you have to add roughly another 0.5C for being out of equilibrium. Then, as bigTom noted, there are the cooling effects of the aerosols (and, the warming effects of other GHGs). And, there may have been some small natural variation in temperature over that period. At the end of the day, you find that the warming over this period is not in disagreement with predicted climate sensitivity,..."

Joel, I think you may have cooled the planet an entire degree Celcius with all that arm waiving. You are now absolved of purchasing at least 10,000 metric tons of carbon credits from the Church of AGW. Keep up the good work Brother.