## Graphs from the Zombie Wars

#### Posted on 6 January 2011 by keithpickering

Cross-posted at The Numerate Historian

There are a few of us who actually enjoy arguing with “climate zombies” (a term coined by Joe Romm at ClimateProgress, and one too often apt) in comments and political forums online. If you hang around long enough, you’re bound to hear some of the silliest crackpottery one can imagine. For a long time Skeptical Science has been an important resource for me, so I’m happy to have a chance to give back.

Recently, I pointed out to an adversary that CO2 and temperature were highly correlated, and to support my assertion I posted the following graph, which I did in Excel. For these graphs, the temperature data is from HADCRUTv3; and the CO2 data is from two sources: Mauna Loa (1959-2009) and the Law Dome ice core (pre-1959; using the 20-year smoothed values).

The blue CO2 line overlays the red Temperature line very nicely, and shows the relationship quite well. But there’s a big problem here: there is no vertical scale. And in fact, there can’t be a single vertical scale on a graph like this, because the two lines are valued very differently: temperature anomaly, in degrees Celsius, ranges between –.8 and +.6, while CO2, in parts per million, ranges between 280 and 390. In order to get the two lines to overlay in Excel, I had to alter the scale of the temperature line quite significantly, by multiplying each datapoint by a constant and adding a second constant. Ideally, I would like to put two vertical scales in place so that each line could be scaled separately. But Excel won’t allow that. Of course, adding and multiplying by constants makes no difference at all to the correlation; but my opponent was unimpressed and immediately accused me of data manipulation. How do you counter an argument like that when your opponent is nearly innumerate?

One thing you could do is draw two vertical scales on the graph, to make things perfectly explicit. Excel won’t do that, but there is other software out there that does. I happen to be familiar with GMT, an open-source mapping tool that also has extensive graphing capabilities. So let’s re-create the above graph in GMT but with two vertical scales, one for each dataset. Here is the result:

Well that’s better, but some zombies just won’t die. My opponent decided to attack the whole idea of correlation because, he claimed, the data wasn’t linear and therefore drawing a correlation coefficient wasn’t valid. The argument is utterly bogus, of course, but sometimes you can find interesting jewels even when rebutting the obviously silly. Here’s what I came up with: we eliminate the date from the graph and just plot CO2 against the global temperature anomaly in a scatterplot.

Now the strong linear relationship jumps out at you as big as life and impossible to miss. I like this graph so much that the next time someone tries to tell me that CO2 and temperature aren’t correlated, or that there's no proof that CO2 causes higher temperatures, this is the first graph I’m going to use. For the entire 160-year period, the Pearson correlation coefficient *r* = .89, which is highly significant.

And before anyone reading this jumps on me – yes, I realize that the relationship here is based on radiative forcing, and therefore should theoretically be logarithmic and not linear. But first, the range of CO2 values is too small here to show much of a curve; and second, forcing isn’t the only factor at work: there is also feedback to consider, which might drive the actual relationship toward linear or even worse, if for example long-term feedbacks are more positive than short term feedbacks (as seems likely). So the graphed linear relationship isn’t necessarily wrong, and certainly seems empirically justified for this range of values.

One interesting thing you can do with a graph like this is to (very roughly) estimate climate sensitivity to CO2 forcing, by finding the equation of the regression line (shown in black). The equation of that line in the graph above is: *T* = .0085*C* - 2.83. From this we can determine that the mean temperature anomaly for the pre-industrial CO2 value of 280 ppm would be ‑.46, and for the doubled CO2 value of 560 ppm it would be expected to come in at +1.92; therefore doubling CO2 should raise the Earth’s temperature by about 2.38° C. This is in the ballpark of many recent (and much more sophisticated) estimates – though perhaps a bit on the low side; most recent estimates are in the range of 2° to 4.5° C increase for doubling of CO2, though some are as high as 6° C.

But then again, we’re using HADCRUT data, which omits much of the rapidly-warming polar regions of the Earth. We can switch to NASA’s GISS dataset, which loses 30 years of early data but which includes the poles, and draw a similar scatterplot.

Here the correlation coefficient is unchanged at *r* = .89, but the regression slope is a little higher. For these data, *T* = .0096*C* - 3.05, and following the same procedure as above the regression line implies that doubling CO2 should raise global temperature by 2.68° C – which is still in the ballpark (but perhaps still a bit low). Still, not bad for a back-of-the-envelope calculation using publicly available data.

mdenisonat 08:31 AM on 7 January, 2011That CO2 and temperature appear highly correlated is a coincidence although there is an underlying explanation.Consider what would happen if a large pulse of CO2 had been added to the atmosphere. The effect would be one of increasing temperatures, rising quickly at first and then more slowly to a new stable value. The CO2 concentration would be constant with time however. ie there would be no correlation but there would be cause and effect. What would happen if CO2 then fell? There would be rising temperatures while CO2 was falling and eventually falling temperatures when CO2 was constant again. The correlation you see is in fact a coincidence due to the historical pattern of anthropogenic and natural forcing. That is temperature and CO2 concentration have changed in a similar way but for different reasons.There is no need for CO2 and temperature to be correlated for there to be cause and effect. Emphasising a coincidence at the expense of cause and effect is a mistake and does not clarify AGW arguments.This point does of course mean that those who see the apparent correlation and assume temperature must be driving CO2 are equally misguided.That the coincidence happens is because a steadily increasing forcing results in an accelerating temperature rise. CO2 additions to the atmosphere have increased exponentially but this can be well approximated by a 2nd order polynomial, as can the temperature rise. Since these are similar curves they appear correlated. That they can appear similar at all is because all the long term forcings are changing slowly and smoothly. When forcing changes abruptly correlation is lost. Had our CO2 emissions been more erratic we could still have seen a similar temperature curve and have the same total CO2 emitted but there would be poor correlation between CO2 levels and temperature. To demonstrate that the temperature rise is related to the CO2 change requires a more sophisticated analysis accounting for the many different variables and consideration of some simple physics.This correlation is coincidental. It is neither necessary nor sufficient as the basis of an argument in support of CO2 induced warming. Conversely a lack of correlation does not disprove CO2 induced warming either.keithpickeringat 09:48 AM on 7 January, 2011EliRabettat 11:38 AM on 7 January, 2011caerbannogat 12:15 PM on 7 January, 2011Marcusat 13:06 PM on 7 January, 2011muoncounterat 13:42 PM on 7 January, 2011a genuine physical causefor their similarity: increasing CO2 concentration increases CO2 forcing in a predictable way. Your argument is based on the (deliberate?) omission of this obvious fact -- and that is why it must be so tortuously circular. See CO2 effect is weak and any of the many threads on climate sensitivity to forcing. See the graph here for the relative strength of the long-term forcings; there can be no doubt that CO2 is the key.garythompsonat 16:20 PM on 7 January, 2011garythompsonat 17:04 PM on 7 January, 2011Moderator Response:[Daniel Bailey] You are almost there. Try linking to a PNG or other graphics file instead of a PDF (PDF's will not link as a visual graphic in a SkS comment window).gallopingcamelat 17:59 PM on 7 January, 2011keithpickeringat 18:10 PM on 7 January, 2011Mike Palinat 21:08 PM on 7 January, 2011JMurphyat 22:56 PM on 7 January, 2011"...it is far more prudent and cost-effective to adopt a wait-and-see approach than to spend trillions now on what may or may not be a problem.""...it would be necessary to shut down the entire global economy for a decade.""By adopting a wait-and-see approach, we still have plenty of time to address even the worst-case predictions of climate change."Pure zombie-opinion in place of facts or evidence, as usual. But there were a couple of extra zombie arguments also, that I forgot to mention :"Or, we could feed and educate everyone in the world.""Even if global warming becomes a problem, it’s going to be a problem regardless of how much we spend.""Initially I was pro-AGW, but over the years as I've witnessed the shouting down and negative labeling of legitimate scientific inquiry that questioned components of the AGW theory, my position changed. Real science is always open to refutation and revision."You often see the supposed 'concern' for the poor and starving of this world (alongside the false supposition that all problems could be solved, and that the poor and starving wouldn't continue to suffer, if only we spent all that money - money which shouldn't really be spent anyway, as far as the zombies are concerned - on food and education); as well as the shoulder-shrugging, 'so what, we can't do anything about it anyway (even if it is a problem), so why should we bother' attitude; and the 'I used to be convinced about AGW but seeing the horrid attitude to the brave deniers (as I now realise they are), I was convinced otherwise and have disregarded the science in favour of standing with the oppressed and ever-courteous Galileo-like real skeptics like, um, Watts and, er, McIntyre', and some others. Laughable, but bizarre.MarkRat 23:35 PM on 7 January, 2011Ken Lambertat 01:37 AM on 8 January, 2011keithpickeringat 02:24 AM on 8 January, 2011Yvan Dutilat 04:32 AM on 8 January, 2011Marcusat 14:12 PM on 8 January, 2011caerbannogat 04:55 AM on 9 January, 2011Albatrossat 05:04 AM on 9 January, 2011hereat Tamino's place.Rob Paintingat 21:48 PM on 9 January, 2011Klaus Flemløseat 22:49 PM on 9 January, 2011muoncounterat 02:12 AM on 10 January, 2011The most significant and best estimated effect is the dependence of temperature on the rate of increase of CO2, i.e. the change in the current value of CO2 from its value the previous year. This accounts for much of the variation of temperature about its trend. It also accounts partly for the trend in temperature, because the rate of increase of CO2 is itself increasing over the period.He also found a strong correlation between atmospheric CO2 and oil prices:Although the long term pattern of oil prices is positively correlated with (trend corrected) CO2, the spectral analysis correctly identifies the negative effect of the price increases, without which economic activity and CO2 emissions would have been even greater.What better means of establishing not just a contribution, but the anthropogeniccontrolover atmospheric CO2?Albatrossat 05:30 AM on 10 January, 2011recent paperby Kodra et al. (published in a peer-reviewed journal) demonstrates that the radiative forcing from CO2 Granger causes global SAT. They also examine the role of ENSO. They conclude that:“The results from this modified test show evidence for Granger causality from a proxy of total radiative forcing (RC), which in this case is a transformation of atmospheric CO2, to GT [globally averaged land surface temperature]. Prior literature failed to extract these results via the standard Granger causality test. A forecasting test shows that a holdout set of GT can be better predicted with the addition of lagged RC as a predictor, lending further credibility to the Granger test results.”I would not place much weight on the Soares paper given that it appears in the same journal which just published yet another sub-par paper by Douglass. In fact, it is not even clear whether or not the paper was peer-reviewed. Is the "International Journal of Geosciences" becoming the new E&E for contrarians? Perhaps someone (e.g., DeepClimate) should do some digging around and about the journal's history..... PS: The link was working a while ago, but a quick test before posting now indicated that the Springerlink site may be down.muoncounterat 06:36 AM on 10 January, 2011archiesteelat 07:04 AM on 10 January, 2011keithpickeringat 09:17 AM on 10 January, 2011monthlyvalues, a totally unsurprising result. The lag between forcing and temperature change will always be longer than that.KRat 11:05 AM on 10 January, 2011verycurious, both in article content and the mysteries of who is putting it out - previous comments have noted this as well. I would be very careful about accepting the articles based on it's (very short) history.Ken Lambertat 01:29 AM on 11 January, 2011Klaus Flemløseat 07:47 AM on 12 January, 2011gallopingcamelat 00:19 AM on 13 January, 2011