Mar 31 2008
Using an Accurate Global Temperature Index to Diagnose Global Climate Change
Please note that this post was part of an April Fools Day Experiment. Comments have been turned off. If you wish to comment, please read the thread April Fools, Skepticism, and Climate Change and comment there. The original post follows.
When discussing global climate change, it is necessary to degrade the overly-complex to simple metrics. This is especially true when the conversation involves the lay public. Thus, we often hear scientists exclaim that the global temperature has risen by 1 degree Celsius in the last few years. This is unfortunate because it conceals the details that often are counter-intuitive.
Global Temperature Index
When diagnosing global climate change, a temperature index is often used that is derived from the lower troposphere. This is no coincidence since we live in the lower troposphere, and its temperature is innately important for our survival. However, it is not a good metric for global climate change studies. When carbon dioxide (CO2) is added to our atmosphere, radiative transfer models predict that the temperature in the lower troposphere will increase. However, they also predict that the temperature in the stratosphere will decrease.
The global stratospheric temperature since the beginning of the satellite era can be compared to the global lower tropospheric temperature. In the figure above, the blue line is the familiar lower tropospheric temperature that shows a small trend in surface temperatures. Notice the large variations due to natural variability such as the perturbation in 1998 caused by the El Nino - Southern Oscillation (ENSO).
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The green line above shows the stratospheric temperatures. In contrast to the blue line, the green line has a slight negative trend. This seems to confirm the predictions from radiative transfer models that suggest stratospheric temperatures have decreased because of the increased level of CO2 in our atmosphere. However, this temperature time series is contaminated by large natural fluctuations in 1983 and 1991. These were caused by increased levels of aerosols in the stratosphere. Because the beginning of the time series has a positive bias, it is necessary to apply corrections to the data before finding the temperature trend.
Corrections to GTI
First, the global temperature index (GTI) must be calculated. This is the most straightforward step in the process of determining an accurate global temperature. The uncorrected GTI is calculated by simply subtracting the stratospheric temperature from the tropospheric temperature. As suggested above, this temperature still has large biases that need to be corrected before proper analysis can be performed.
The large natural variation is sometimes referred to as “noise”. This is to distinguish it from the supposed global warming “signal”. In this instance, the increased level of aerosols in the stratosphere is noise because it represents a natural variation that does not correspond to a global warming signal.
The 1998 ENSO event is also represents a large natural variation that must be corrected. Luckily, it is possible to accomplish both of these corrections using the same technique. The correction factor is found by looking at the extremely long time-scale events; over 2 years in duration. A Gaussian filter with a full-width half max (FWHM) of 2.5 years was applied to the uncorrected GTI. 2.5 years was chosen instead of 2 because the orignal data was monthly and a 2 year filter could not be applied.
The results of this correction can be seen in the figure below. The black line is the uncorrected GTI. The two large natural volcanic eruptions caused a significant decrease in the GTI prior to 1995. The red line is the correction factor as explained above. When the GTI is corrected for known natural variations, we obtain the blue line.
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Before interpreting the results from the aerosol and ENSO correction, another correction must be applied. These temperatures were calculated from satellites that rotate around the Earth. Because of various problems, the orbits decayed. The original intent was to have the satellite cross over the same site at the same time of day. This is known as a sun-syncronous orbit. Prior corrections have either under-estimated or over-estimated this error. (e.g. Randall and Herman, 2008; Gaffen et al., 2000)
Randall and Herman found that the error due to the orbital decay was better corrected in the calculations done at the University of Alabama, Huntsville (UAH). The Remote Sensing Systems (RSS) correction, initially calculated because of suspected errors in the UAH dataset, actually over-corrected for the orbital error.
In this analysis of a true Global Temperature Index (GTI), I apply the correction suggested by Randall and Herman. This is the green line in the above graph. As can be seen, this results in a small correction to the blue line, but is mostly a shift to larger values.
The analysis above shows that for a true GTI, there is no trend from the late 1970s through the present.
Correlation with Corrected Sunspot Numbers
While the correct GTI found above does not have a trend, it does show a remarkable similarity to natural variations in the sun. The solar cycle is approximately 11 years. From inspection, it does not appear that there is a strong solar signal in the GTI. However, this is because of the way in which the graph was presented. Below is the same GTI in blue, and the number of sunspots in orange.
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The sunspot number may not appear the same as previous diagrams because it too has undergone a correction. I wished to find a number representative of several aspects of solar variability. Therefore, I created an index that combines characteristics of the total solar irradiance (TSI), solar heat flux (SHF), cosmic ray flux (CRF), and sunspot number (SSN).
The correlation coefficient between the corrected sunspot number and the global temperature index is 0.81 (R2=0.655). This is statistically significant at the 99% level after accounting for serial correlation.
Conclusions
When a true global temperature index is used to diagnose global climate change, it is clear to see that there has been no trend in temperatures since the beginning of accurate satellite measurements. While the temperatures in the lower troposphere, as measured by both surface-based thermometers and remotely sensed thermometers, have increased, there has not been a corresponding decrease in the stratospheric temperatures. When one visually inspects the uncorrected stratospheric temperatures, there does appear to be a decrease in temperatures. However, after the correction is applied for aerosol this trend vanishes.
When the true global temperature index (GTI) is compared to the variation in the sun, there is an extremely high, statistically significant correlation. The implications for this are vast. This shows that the temperature variations as measured by surface stations are actually measuring changes in the solar cycle and not changes due to to so-called anthropogenic global warming.
References
Gaffen, D. J., B. D. Santer, J. S. Boyle, J. R. Christy, N. E. Graham, and R. J. Ross, 2000. Multidecadal Changes in the Vertical Temperature structure of the Tropical Troposphere, Science, 287 (5456), 1242, doi: 10.1126/science.287.5456.1242.
Randall, R. M., and B. M. Herman, 2007. Using Limited Time Period Trends as a Means to Determine Attribution of Discrepancies in Microwave Sounding Unit Derived Tropospheric Temperature Time Series, Journal of Geophysical Research, doi:10.1029/2007JD008864.
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19 Responses to “Using an Accurate Global Temperature Index to Diagnose Global Climate Change”
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Why the
at the end?
Hmmm humor huh? Well then you’d best change the date to April 1 rather than March31.
There’s some problems with the Randall and Herman paper that would be too difficult to explain for this blog. Readers who have understood the paper should know what I’m referring to.
If the Randall/Herman paper was intended to be the target, then why is the entire article tagged as “Climate change, humor”?
[Reply: Randall and Herman wasn't the target. I'll elucidate in a post tomorrow.]
“Randall and Herman wasn’t the target.”
Yeah, I kind of figured that.
Atmoz,
Very interesting. Just a quick question, though, about the R-squared. How did you control for serial correlation? Is some, even a lot, of the R-squared the result of a lagged error term?
You know, when first learned stat nearly two full Hale cycles ago, it was drilled into me not to fixate on R-squared, that even a regression with a low R-squared may be revealing something significant, and what mattered were the standard errors and t-stats of the regression coefficients. Alas, R-squared is a lot easier to explain to a layperson than a t-statistic. And when the R-squared is low, that’s an easy way to take a cheap shot at someone’s statistics.
So if the R-squared of the OLS regression is much lower, and a lot of the R-squared in the corrected regression comes from a lagged error term, I’m not going to fault anyone for that if the regression coefficients remain statistically significant.
Incidentally, I don’t know if they still teach this or not, but I was even taught that if the t-statistic was greater than 1, but not at the level normally associated with, say 95% confidence, the variable still “explained more variation than it contributed to the model.” I wonder what the IPCC terminology is for that level of “certainty?”
Basil
[Reply: Depending on the number of degrees of freedom, for a t statistic of 1, the IPCC terminology would be "more likely than not" or "likely".]
Looks like you have your fish!
-W.
Bravo. I’d rank it up there with http://www.realclimate.org/index.php/archives/2007/04/the-sheep-albedo-feedbacki/ as one of the most profound climate change articles I’ve ever read.
On a more serious note, there is a disturbing propensity for people to see complex arguments that they do not understand the math or reasoning behind and agree to them simply because they sound good. There needs to be more of a push to encourage people to rely on the peer reviewed literature, which has a reasonably good (albeit not infallible) system to check the veracity of analysis, rather than the latest spurious solar correlation posted on their favorite blog.
10 words in I knew you were kidding.
“degrade” was the wrong word. “reduce” would have kept your pretense alive.
Otherwise, this was a nice job. Moshpit seal of approval.
Ya Zeke the sheep albedo piece was funny as well, but I think ATMOZ beat it fair and square… with my one little quibble
After I read your post, I had to walk the dog before I figured out what you did. I don’t want to ruin the joke, but will you eventually post the, uh, “uncorrected” version, or is it the”corrected” version?
[Reply: Feel free to ruin the joke. But if you think there is an "uncorrected" or "corrected" version, you probably didn't get it.]
The orthodoxy of the alarmist camp must be pretty severe if they have to go through such contortions in order to prove AGW. As a former modeler of chemical systems, this behavior is typical when you cannot advance a model any further. In other words, it becomes easier to start manipulating the data to fit the model than it is to fix the model. It is clear to me that AGW climate modelers have given up trying to understand our climate and instead have switched to data manipulation. At some point, the dissonance is going to be too great to ignore.
I don’t know about others, but I caught a number of problems before seeing the comments about this post being about humor and April fools. The assumption that stratospheric temps only reflect aerosols, somehow combining stratospheric and tropospheric temperatures to obtain some kind of temperature index, no foundation for the blue line in the solar graph and somehow obtaining a large fluctuation in temperatures due to solar considering how the oceans dampen that signal. The first thing that came to mind was; this is the same kid that used 13-year-old meta data to analyze a current temperature station. Hopefully your point tomorrow will not be based on rhetoric or faulty logic because your stock value will plummet more than it already has.
well at least for an AGW’er you seem to have a sense of humour. Well done!
Best be careful - I’m wondering how many links to this post you’re going to end up with from the deniers. LOL…
Well done…
Nice one - and, reading the comments, it’s the gift that keeps on giving! Happy April Fool’s.
Its a fine joke, but nothing in climate science will ever equal the one perpetrated on April 1 1998 by Mann Bradley and Hughes. I don’t know how many people remember the story. They made so many egregious errors it was hilarious. First they took some trees which measured rain and said they measured temperatures. Then they did some stats which require the mean to be used, and used some other numbers. Then they claimed to have abolished the MWP and Little Ice Age! They actually took in a UN body if I heard correctly. It was truly wonderful.
Like all truly great April 1 jokes, that one just ran and ran, and you will still find people today referring to it perfectly seriously.
So yours was a nice effort, but one fears the standards in this field have been set very very high, and you will have to do better to reach the high points of your predecessors.
Still, nice try. Good luck with the next one.
Okay, I get the joke now. A second look and some background reading was required. To take your joke a little further, how do you “correct” for production of man-made aerosols and particulate matter (pm) since the fall of the Soviet Union and the modernization of China. I know the perception is that China is adding to the world’s pollution by building coal-fired power plants on a weekly basis, but have you ever been to rural China in the winter? They burn all sorts of ag waste to generate heat. The NOx and pm in the air is palpable. Urbanization and the construction of modern power plants is an improvement in my opinion over past rural practices with regard to pm. Thus, how much cooling of the stratosphere (and conversely heating of the troposphere) is due to less pm in the atmosphere (stratosphere specifically)? And, if real, what is the time lag between less pollution on the earth’s surface and its effect on the stratosphere? Or, have climate modelers assumed that man-made production of pm has not changed (or even increased) over the past 20 years?
Chris I don’t think much pm from burning ag waste gets into the stratosphere to cool it. Burning ag waste is likely to produce a fair bit of black carbon which will directly warm the troposphere somewhat reducing the cooling effect of other aerosals like SO2.
[...] of a typical April Fools Joke, I decided yesterday to do a sort of April Fools Experiment. The goal of the post was to take something completely made up, pepper it with scientific lingo and [...]