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Yesterday, we computed the elasticity of Co2 concentrations with respect to economic output. Today, we’d like to report on what we know about the earth’s temperature elasticity with respect to CO2 concentrations. This of course is a far more “controversial” aspect of the climate change “debate.” The climate scientists have long said that the Earth’s temperature will rise by about 1 degrees Celsius for a doubling of CO2 over pre-industrial levels. You might therefore be saying to yourself, “that doesn’t sound like a catastrophe” … and it wouldn’t. Where the “catastrophe” comes in is based on the assumptions modelers are making about how much more warming the earth experiences because the earth itself is warming. In other words, to get “disaster” we need to model in “positive feedback” into the system.

Without getting into the sciency goodness of the many IPCC reports and the papers that do and do not make it into those reports, let it be known that there is absolutely no consensus about these feedback effects. In fact, based on what we have seen on the Earth to date, not only have they been smaller than advertised it is quite possible that the feedback is negative. But rather that wade into that “science” we could do something that real scientists used to do – go out and measure CO2 concentrations, and go out and measure temperature changes, and show people what has happened SO FAR.

Since the dendroclimatologists have put together long histories of the temperature and CO2 record, it is imaginable that someone could do this on a long pile of data. But I don’t have such data. What we DO know is that since 1880, CO2 concentrations have increased from 280ppm to 400ppm, or a 43% increase. What we also know is that the measured “average global temperature” has increased by 0.8 degrees Celsius over this same time. So we can also just take a look at the observations from this 130 record and estimate what the temperature elasticity with respect to CO2 seems to have been. Of course, it would be nice to take a longer snapshot, but we cannot given my tools here. Of course, if you look over shorter subsections of the data, you get to tell any story you want. For example, if we looked at the last 18 years or so, we’d conclude that the elasticity is zero. If we look from 1975-1995, we’d conclude that it is shockingly high. If we look from 1945 to 1975, we’d conclude, surprisingly perhaps, that temperatures fall in response to CO2, if we look earlier than that we get the conclusion that they are positively related … and as long as we don’t really know the right time frame over which to do this once we shrink the temperature record, recognize that this entire exercise is a bit dicey. You should note, too, that the estimated temperature elasticities would vary based on what part of the planet we are studying, so, for example, warming in the US has been lower than the planet at large, but I digress.

Soooo … what is the temperature elasticity? We need to estimate the percentage change in global temperatures from 1880 to today. We know that they have increased by 0.8 celsius, but over what starting point. In physics, the appropriate way to measure changes is by using the Kelvin scale, Now, the climate people always report global temperatures as “anomalies” – as differences in current temps as compared to some magical baseline number they believe to be “correct” – here is one illustration.  My sciency inclined readers may be perplexed that we report anomalies and not actual temperatures and assume that there is some attempt by the climate community at obfuscation here – we CAN measure the average temperature of the earth. But, the anomalies across the planet, or so I read on the sciency good websites, is that anomalies correlate well over vast distances of the planet whereas measured temperatures obviously are very different over short ranges. I actually don’t see how that makes any scientific difference, which leaves the sciency climate people open to the charge I suppose. What I find MOST interesting about the temperature record, wholly aside from the shenanigans scientists are playing by splicing thermometer records with satellite records, not calibrating historical records (which don’t come from any direct temperature measurements) with those techniques on today’s temperature record, the many adjustments made to the raw data, and so on, is that despite all of this, the huge noise that we recognize global temps are measured. While the measured global average temp is in the 15 degree celsius range, the “actual” temp may be anywhere between 15 and a half and 14 and a half – it should would be nice if all of the sciency good people out there reporting on climate would publish uncertainties every time they published temperature data. The current global average temp is about 15.7 celsius, and was therefore about 14.9 back when this whole thing started. In Kelvin, the temps have risen from 288.05K to 288.85K.

The temperature has increased by about 0.28%.

Computing the temperature elasticity with respect to CO2 we get 0.28% / 43% for an estimate of  0.0065. That seems rather insensitive in the grand scheme of things. This also seems rather preposterously low given what I have been reading. So please do tell me where I have gone off the rails here.

Now we can put yesterday’s data together with today’s data and we find that we can estimate the temperature elasticity with respect to GDP changes by multiplying each of our calculations – i.e. the temperature elasticity with respect to GDP is the product of the temperature elasticity with respect to CO2 and the CO2 elasticity with respect to GDP. From this we find that the temperature elasticity with respect to GDP is 0.02 x 0.0065 = 0.00013. Again, this appears to me preposterously small.

By this estimate, if global GDP were to double, which you could expect it to do over 20 years, then global temps would be expected to increase by 0.013%. If global temps today are 288.85K, then a doubling of GDP is expected to increase temps to 288.89K, an increase of 0.04 degrees celsius. That CAN’T be right.  Or can it?  Over the course of the century, if Earth’s GDP doubles every 20 years, that would still only be producing less than a degree of warming based on what the data have actually shown us.

Again, this is assuming that the impacts of CO2 on temps are linear which they are not, we know that the incremental temperature increase with incremental CO2 additions actually falls, and of course none of this says anything about the economics, that is for a future post. But again, I can’t believe my numbers are right – this is the first time i have sat down to compute them this way based on actual observations and not on what models and reports are telling me. Does anyone care to see where I screwed up? And more important, after we figure out the correct calculation, can anyone explain why this is not the way we present it? And can anyone explain the implications of this “finding?”

I need to revisit this a bit, it just can’t be right.

UPDATE: In the “science” I have found this paper which claims to measure a temperature elasticity. Incredibly, this thing made it into a peer-reviewed journal. As I look at it, albeit briefly, it appears that they are using emissions rates for calculating the elasticity, and NOT changes in the cumulative stock of CO2. Maybe there is some sciency good justification for this, but at a minimum you’d think in a peer reviewed paper they’d be asked to show the calculations both ways. FURTHERMORE, and I may be on drugs here, it looks like they used changes in the Centigrade scale to compute percentage changes in temperatures. Well, I understand that you need to choose some scale, but NO scientist will tell you that a 1 degree celsius increase in temps today from 15 to 16 celsius represents a 6.7% increase in temperature – that simply is antiscience. Now, is the Kelvin scale the right scale? I have no reason to think it is not as it is an absolute temperature scale. However, it appears the way they did their calculation was to avoid that issue entirely and computing changes in the changes, which means you can simply look at the changes in centigrade when emissions change, and compare those changes over time (this is OK because a one degree Kelvin change is equal to a one degree Centigrade change). Finally, I am having a pile of trouble seeing how this paper is even a paper. Aren’t we doing a simple calculation here? We don’t need reference to climate models or human attribution or anything like that. Just take the change in temps and compare that to the change in CO2. Again, am I missing something?

One Response to “Economic Climate Sensitivity, Part Two”

  1. Harry says:

    Great work, WC.

    Kelvin sounds reasonable, but then who am I to argue?

    If one were to be speaking Washingtonian Progressive, the scale would be expressed relative to the future budgeted federal baseline, so any measured temperature would be BELOW the expected increase, which means the next ice age starts in 2017 or four years later. This is ample reason to get the IPCC involved in preparations, maybe an international sweater drive along with, of course, ending carbon.

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