To Tell The Truth: Will the Real Global Average Temperature Trend Please Rise?
Part III
A guest post by Basil Copeland
Again, I want to thank Anthony for the kind invitation to guest blog these musings about what is going on with global average temperature metrics. It has been a most interesting, and personally rewarding, experience. My original aim was quite modest, but I fear that the passion that many feel for this issue prevented them from seeing that. So in this final part to this series, I want to try to make my aim more clear, and to show how a lively exchange of ideas can lead to new insights.
The IPCC has made the earth’s global average temperature trend a central focus in the debate over anthropogenic global warming. In the AR4 report of Working Group 1, they state:
The range (due to different data sets) of global surface warming since 1979 is 0.16°C to 0.18°C per decade compared to 0.12°C to 0.19°C per decade for MSU estimates of tropospheric temperatures. (Chapter 3, Page 237)
Similar, if not the same, estimates are reported in Table 3.3, Page 61, of the Synthesis and Assessment Product 1.1 of the U.S. Climate Change Science Program (accessible here: http://www.climatescience.gov/Library/sap/sap1-1/finalreport/sap1-1-final-all.pdf ). Presumably, these estimates provide some kind of basis for the IPCC SRES scenarios that assume 0.2C per decade warming over the next two decades.
Figure 1
From what I can tell in reading the representations of the sources for these estimates, they are based on a straight-line linear regression that includes corrections for serial correlation. In other words, regressions that look something like what are shown in Figure 1. The trend at the top is from Appendix A, Page 130, Figure 1, of the U.S. Climate Change Science Program report just cited. The second is taken from the RSS website (http://www.remss.com/data/msu/graphics/plots/sc_Rss_compare_TS_channel_tlt.png accessed on March 15, 2008). Both show a warming trend of 0.17C/decade since 1979.
Are these “good” estimates of the historical trend since 1979? Forgive me, but I refuse to accept them as authoritative ex cathedra, nor will any true scientist expect me to. Bear in mind, I’m taking the data for what it’s worth, and am overlooking any questions about the reliability of the surface record, such as what Anthony is looking into (or Steve Mcintyre at www.climateaudit.org), or the kind of urbanization and land use effects reported by Ross McKitrick and Patrick Michaels. My concern is solely with the technical procedures used to estimate the “trends” that are commonly cited for evidence of global warming. Bottom line? There are problems with the way those trends are computed that overestimate the degree of global warming since 1979 by 16.3% to 41.3% (based on results presented below).
In Part II I attempted a demonstration of this using what might be considered to be rather a rather blunt or brute force approach — a test of whether there was a significant “structural break” (the way we describe it in my field of study) after 2001, along with whether or not linear trends are distorted by the effect of the 1998 El Nino. Nothing in the comments that followed the posting of Part II fundamentally undermined the validity of my conclusions. The chief concerns seemed to be that my decision to test for a structural break (or “change point”) at the end of 2001 was arbitrary (it wasn’t), or whether one could say anything meaningful about a cyclical system like climate from linear trend lines. Well, with respect to the latter, that horse is out of the barn, and we’re being told — by supposed authorities — that there has been X degrees of global warming per decade since 1979 on the basis of linear trend lines. If they can use linear regression to claim that global warming is proceeding apace, well please excuse me for doing the same in questioning them.
Still, the comments were provocative, and encouraged me to dig further into my toolbox of econometric techniques to see if I might be able to come up with something that would alleviate some of the concerns commenters had about what I did. So it occurred to me that I might treat the weather like a “business cycle” and model it with Hodrick-Prescott smoothing. (If you want an explanation of what that is, look here: http://en.wikipedia.org/wiki/Hodrick-Prescott_filter ). The results are presented, for the four global average temperature metrics we are using, in Figures 2 through 5.
Figure2 – click for a larger image
Figure3 – click for a larger image
Figure4 – click for a larger image
Figure5 – click for a larger image
Those who think we should let the data tell us where the “change points” are should find this approach more appealing, as well as those who believe we should be modeling the data with non-linear techniques. But in the end, the point is the same: the “real trend” over the 29 years we are looking at is substantially less than we get using straight-line regression. With the exception of GISS, Hodrick-Prescott smoothing results in even lower estimates of the degree of global warming over the past 29 years. As shown in the following Table 1, compared to the two methods I’ve employed, the straight line regression method relied upon by IPCC and the U.S. Climate Change Science Program overstates global warming since 1979 by anywhere from 16.3% (using GISS) to 41.3% (HadCRUT).
No one should be offended by what I’ve done, or what I’m saying. True science is always open to the possibility of refutation. Given the policy implications that hang on conclusions about the degree of global warming that has occurred in recent decades, we should take a closer look at what the supposed authorities are telling us, and see if there are not perhaps some significant short-comings in the way they have calculated the degree of global warming in recent decades.
Just a quick addition. It occurs to me that the confidence interval I calculated in my last response to Lee may not be what people think it is. It is what I represented it to be, which is a confidence interval for the mean first difference from the smoothed HadCRUT series. It is not a confidence interval that infers anything about how well the smoothed series fits the raw data. Now the smoothed series fits the raw data better than a straight linear regression, so a confidence interval based on that should be less than a confidence interval based on a straight line regression. But as a practicioner rather than a theoretician or professional statistician, I’m always cautious about claiming statistical significance when using techniques that do not have standard metrics for statistical inference associated with them. It is a cautiousness sort of like not wanting to make claims about PC’s that might prove bogus, if you know what I mean. 🙂
Incidentally, as a practicioner, it has been my experience that practicioners often have a different perspective on things than academics, and can sometimes see things that the academics miss, or have insights that the academics do not. In my own narrow little field of expertise, I have had some modest success in successfully challenging the way academics look at things. I think it notable that it appears that meteorologists, as a group, are more skeptical about the claims of AGW than climate scientists. I’m not surprised, though. And I don’t think their insights, or perspective, are any less valuable that what gets published in peer-reviewed journals. Having published in peer reviewed journals, and having been a referee for a couple of them — something pretty uncommon for a non-academic lacking a Ph.D., I think — I know well both the strengths and limitations of peer review.
So take what I’ve been saying in my blog posts and the dialog in comments with however many grains of salt you wish. I have no axe to grind, or hidden agenda. There’s no question that there’s been “global warming,” especially since the beginning of the instrumental record, which roughly corresponds with the earth coming out of the Little Ice Age. The questions are “how much?” and “why?” I’m not saying anything at all about “why” because that is outside my domain of expertise or practical experience. But as to the question of “how much,” I’m comfortable making some modest claims to expertise based on my past academic training and 30 years of experience as a professional economist and economic consultant. If I bring to the task of looking at “how much” a perspective that is different than the conventional wisdom, and yields some insights perhaps missed by the conventional wisdom, it will not be the first time.
Of course, as to the “why” of the earth warming in the 20th century, I’d consider myself a curious layperson with a kind of well-informed and rational skepticism about the claims of AGW. But that’s not what I’ve been blogging about.
Hello, I’m new here and have been looking for information the might relate to these two links below. They are not peer reviewed papers but I think they highlight important data that was ommited by IPCC. First link on water vapor gives radiative forcing of 131 w/m^2, and much more. Second link claims CO2 only absorbs 8% of long wave radiation. Taken together makes IPCC claims look very suspect. Please delete my comment if I am intruding.
http://www-ramanathan.ucsd.edu/FCMTheRadiativeForcingDuetoCloudsandWaterVapor.pdf
http://www.nov55.com/ntyg.html (CO2 Absorption Spectrum)
Richard
Basil,
Thanks for taking so much time with these posts and responses. One of your comments above caught my eye – I have a question out of ignorance of the smoothing method you used.
You mentioned the avg monthly first difference of 0.00086229, and a confidence interval (I believe for this avg) of +/-0.001. That gives a range of 1.86229 to -0.13771. What, if anything, should I conclude from that (esp. that the range takes in 0)?
Fitting monthly or yearly temperature data with a linear regression
is just plain stupid. That’s a theorem somewhere. ok, it’t not stupid.
It’s easily communicated.
I’m less certain about alternatives. A piecewise linear ( say Tammy) is a cheap
and easy fix. Basils approach, I havent got to the bottom of. Beware the cookbook chaps. However, eschew the cookbook at your peril Dr. Mann.
I’d prefer to model the system and devise a technique to detect trend changes
in that system. hmm
Atmoz has an interesting post on Short term cycles ( like ENSO) and the trend excusions you see during these periodic episodes.
At the bottom. This cooling weather phase is probably a very good thing for climate science. Why?
TCO: I may be a good example of those affecting the ‘pomposity’ you loathe, but we as a group find Basil’s seamless use of ‘ex cathedra’ amusing and deft.
Regardless of our individual levels of success those who aspire to word-smithery do so to communicate well. It’s a work-in-progress.
I find your tendency toward criticism of your cohort, “people on our side”(here and in adjoining threads), PC.
Might I suggest ‘Eeyore’ as a more fitting, exuse the pun, nom de plume?
Basil, it seems to me that when all is said and done Lee is correct; all you are ultimately doing is doing a curve fit that, if you were to do a linear regression on, merely shows the same trend as before the curve fit. It also seems that what you have done is — again as he points out — merely manipulated what you call the trend TODAY based on the endpoints.
As mosher points out a regression is probably the worst way to do this except for all of the other methods.
That being said, bear in mind that although I disagree with your conclusions, I applaud the post series. Certainly, by looking at the data from a different persepctive, this gives food for thought… meaning you have made your point, even if I figure you are wrong. This is reminiscent of Edison in a way; he said he’d discovered 2000 ways to not make light bulbs but never once failed.
Congratulations on a thought provoking series!
Thank you for posting this. I found it enlightening. I would like to see similar statistical analyses of other climate data.
A potpourii of replies
Paul Clark,
I don’t know the answer to your question. I would be surprised, though. Roger Pielke Jr. has a little write up today over at http://www.icecap.us on what Lucia is doing to validate some IPCC projections. If you haven’t been following what she’s doing, head over to her web site (http://rankexploits.com/musings/) and take a look.
JamesG,
I understand your point. When I teach anything having to do with statistics, I usually begin “If you torture the data long enough it will confess, even to crimes it did not commit.” I’m sure that’s what Lee thinks I’m doing here, but I’m not. I’m asking some questions of the data that don’t appear to have occurred to many, but not for the purpose of forcing it to confess to any preconceived notions of what it should be saying.
Stan Needham, Gary Gulrud, Josh, Enochson,
Thanks for the kind words. Gary, your comment (“I especially respect your limiting the discussion to features of the data rather than leaping ahead to causation which statistics seldom informs.”) especially made my day when I first read it.
jd,
Yes, it has been going up. But by how much, “on average?” That’s obviously a question that a lot of people are interested in, and I don’t think the answer is as simple as what you get from fitting a straight line through the data.
Stephen Mosher,
“Fitting monthly or yearly temperature data with a linear regression is just plain stupid. That’s a theorem somewhere. ok, it’t not stupid. It’s easily communicated.”
I wouldn’t call it “stupid,” but it is often done to data that don’t deserve it, or which should be analyzed more carefully before concluding too much from the slope of a straight line trend.
Ian,
The .001 is applies to the decadal form of the estimate. Take 0.00086229 and multiply it by 120, and you have 0.1034748. The latter is what the .001 applies to.
randomengineer,
Is that what they call damning with faint praise? 🙂 I appreciate the attitude, but you are still not getting it.
Let’s you (and Lee) put aside the smoothed series in Part III for a moment, and think back to the linear trends estimated in Part II. How do you propose calcuating the “average” trend for a trend line which slopes up modestly for a while, shoots sharply up and back down before resuming the modest trend, then jumps up and begins to trend down after 2001? Everybody knows how to read the trend of a straight-line regression. How do you read the “average” trend of a trend line that varies like the trends plotted in Part II? Don’t suggest that I fit a straight line trend through the trend (which is basically what you are proposing for the smoothed series in Part III).
I took a short cut and calculated it from the delta in the end points. But let’s do for the trends in Part II what I did for Lee on the smoothed lines in Part III: first difference the trend, and take the average of the first differences. For HadCRUT in Part II, this produces an “average” trend, per month, of
0.00093967
This compares to the straight line linear trend of
0.00132630
The first number is lower than the second number because of the declining rate of growth at the end of the series. Multiply these numbers by 120 for decadal equivalents. BTW, in my reply to Lee where I calculated the equivalent HadCRUT number for the smoothed series,
0.00086229
I said “Now multiply it by 349, and divide it by 120, and see what you get.” That was incorrect. For these numbers, we just multiply by 120. We divide by 349 when using the delta from the endpoints, which should just give us the same numbers we have above. I.e., if we do the math right, it makes no difference whether we compute the average from the end points, divided by 349, or from the average of the monthly first differences. The numbers should be the same.
Everybody understands the 0.0013230 from a straight line regression, because that is what it is, and can be read from the output of a statistical regression. That doesn’t make it a better, or more correct number than the other two, which I think people are having a hard time grasping because of the novelty of the technique used to derive them. But the technique is sound, and nobody has yet to show otherwise.
In the end, the “trend” is no more meaningful than the delta from the end points. One is simply an estimate of the average monthly change, and the other is a measure of the cumulative change. Choosing which model is “best” has nothing to do with how I’ve calculated the cumulative or monthly or decadal change.
[…] Temperature Trend Please Rise? Posted on March 18, 2008 by tommoriarty I appreciate the detailed write-up that Basil Copelanddid for Anthony Watts’ “Watts Up With That” over the last several days. However, […]
I reproduced Basil’s smoothing using the Hodrick-Prescott filter. I also repeated the smoothing by ending three months early (Nov. ‘07), six months early (Aug. ‘07), nine months early (May ‘07), and 12 months early (Feb. ‘07). The results can be seen here
This simply demonstrates that this smoothing technique, like most others, can be quite unstable near the beginning and end of a time series.
By the way, I made a donation to Watts’ tip jar , today and recommend that readers give what they can.
REPLY: Thanks Tom!
basil,
I think we are in violent agreement. The descriptions I hear from climate scientists lead me to believe that the underlying model ( reality) is not
linear. So, fitting the temps to a linear trend is excel easy and not very
informative. That said, I scratch my head when pressed for an alternative.
Corrections for serial correlation are a good start..
I liked your approach, I just need to wrap my skull around it.
Basil,
Thank you. I have enjoyed this read… Please forgive me for what I am about to post if I am wrong about what you are trying to say.
Basil is simply saying that a straight linear progression maybe leaving out possible information about a larger overall trend. To be honest we do not know what this larger overall trend portains to, but in looking a a smoothed dataset you can see where the nuiances of said trend maybe occuring rather then looking at the trend as a whole.
Look at the DOW over the last year. If this where the average temperature the trend on linear regression would be positive. This is true even though we are now basically at the same amount of money that the DOW is now vs a year ago. Now if you were to look at this as a smoothed trend you would see that it was positive, and now it is negative. You get a bettter idea of what is going on really by the smooth trend.
Again sorry if I am speaking out of turn, just trying to help explain what is going on by attempting to give an outside example that may not have people as biased in thier thinking… If that is what is going on.
Tom,
I’ve replied to you over on your own web page.
Basil
As the discussion draws to its close, I want to thank everyone who responded, even Lee! Exposing one’s view of things to criticism and the possibility of refutation is the essence of objectivity and critical thinking. While Lee, and perhaps others, remain unconvinced that there is utility at looking to the cumulative change implied by various trending or smoothing methods, I’m still convinced that there is.
But in all the discussion of whether it makes any sense to imply a trend from the average cumulative change of a series, or concern about too much weight being given to the downturn at the end of the period of analysis, a significant observation made in Part II has largely gone overlooked. There I noted:
“Incidentally [a lower implied decadal average than what results from a , this not entirely owing to fitting a downward trend through the data since 2001. Separate slope and constant dummy variables are also included for the 1998 El Nino, and this accounts for some of the difference. In fact, somewhat surprisingly, when a constant dummy is added for the 1998 El Nino, it reduces the slope (trend) for the non-El Nino part of the time series through 2001. We usually expect a constant dummy to affect the model constant term, not the slope. But in every case here it reduces the slope in a significant way as well, so some [maybe most?] of the difference in the “dT” and the result we’d get from a straight trend line owes to the effect of controlling for the 1998 El Nino.”
For anyone still interested in trying to learn something from all of this, I invite you to look carefully at the following chart, for HadCRUT, which superimposes all three trending/smoothing methods on the data, paying particular attention to around 1995 and 1996, in the months before the 1998 El Nino:
http://i26.tinypic.com/51cwaw.jpg
First, note how poorly the HP smoothing captures what is happening at that point: it begins trending upward while the actual anomalies are moving downward before they begin the rapid climb to the 1998 peak. In the same way, the straight linear trend, that so many seem convinced is the only way to do this, is well above the x-axis at a time when the anomalies are moving downward below the x-axis. Both the straight line trend, and HP smoothing, are excessively influenced by the 1998 El Nino, i.e. “pulled upward” by it, in a way that is unjustified by the data.
Of the three techniques, only the one that models 1998 El Nino as a shock (and “change point” also), avoids this bias and accurately measures the straight line trend in the period prior to the break point used to control for the 1998 El Nino. And that trend, taken directly from my regression output, and not some “dodgy” number I’ve calculated from endpoints (though it would be exactly the same, rendering moot the concerns or criticisms about my “dodgy” technique), converted to decadal form, is 0.118C/decade, well below the 0.159C/decade derived from the straight line for the entire period. The latter is unduly influenced and biased by the 1998 El Nino.
Here’s a prediction for the future. As we move forward in time, the trend from a straight line regression through the data since the beginning of the satellite period, 1979, will drift downward as we move away from 1998 El Nino. When the El Nino becomes part of the earlier half of the data series, those looking for evidence of AGW will finally see the wisdom of controlling for it somehow, because at that point it will actually become a negative influence on the overall trend, being on the other side of the fulcrum point as it were.
Again, thanks for all the dialog.
Basil, I wasn’t damning you with faint praise. I simply didn’t agree with your conclusion. This is an example of what I meant by your stuff being interesting. Superimpose your HP plot on this —
http://www.climateaudit.org/?p=2868#comment-225274
— and you appear to have invented the cosmic ray detector that can be seen in temp data. Seems to confirm that temp cycles look to be the same as cosmic ray cycles… then again it could also be that cosmic ray detection equipment is temp sensitive… whoops. 🙂
(Here’s a prediction for the future. As we move forward in time, the trend from a straight line regression through the data since the beginning of the satellite period, 1979, will drift downward…)
Well… Duh. I could tell you that without the fancier versions of showing statistical trends. I’d guess though that you could treat 1998 as an outlier and ignore it and conclude similarly. Or.. you could calc 2nd derivatives and plot regressions on that; it would do the same thing, especially if you tossed 1998 as an outlier. I merely wanted to point out that your plots didn’t add any more than what I already knew or could derive using simpler means.
On the other hand refer back to the cosmic ray and neutron plots and now you have a statistical tool that tells me something I didn’t already know.
basil,
In fact they are waiting for the next El nino to bring the “trend” back to the
norm.
There is no climate trend. there is the mean of a calculation. we never observe
the climate. It does not exist.
The phase transition at the end of 2001, noted in this excellent series, is also evident in the data of the International Satellite Cloud Climatology Project. Any connection?
REPLY: We’ll take a look. – Anthony
Randomengineer,
I’m looking at using LAD (least absolute deviation) to do the regressions. This will produce a straight line, which everybody seems to be able to understand, but will not be as influenced by outliers the least squares regression is. I may return to the use of it with the same four metrics this discussion has focused on, but right now, I’ve turned my attention to the IPCC’s claims about what has happened over the hundred year period 1906-2005.
Steven Mosher,
🙂
[…] and reality, as diagnosed by surface air and tropospheric temperatures (e.g. see, see and see) and upper ocean heat content (i.e. see), Climate Science is reposting a weblog from 2006 titled […]
“I’m taking the data for what it’s worth, and am overlooking any questions about the reliability of the surface record,”
Then why do you constantly point to those questions?
The usual – the primary – assumption with any data series is that a.) it will have errors, and b.) those errors will be randomly distributed.
Every analysis made on this site is based on those assumptions. The statistical techniques waved at every opportunity here as some sort of Better Business Bureau badge of approval, just flat out don’t work without the assumption of random distribution of errors. That is a fact of life.
But for apparently agenda related reasons, you – and others – constantly insinuate that the errors are systemic – in one direction only, rather than having the random character assumed in your own analysis. Yet you use bogus application of statistical techniques to support those insinuations.
A claim of unidirectional error in all data series – that all errors in the measurement of temperature are positive, with none negative – is an extraordinary claim, and you better supply extraordinary evidence. Muttered insults aren’t going to cut it.
If you believe there are systemic errors you should make that case, not just say ‘abracadabra’ with statistical magic and predigestation, while stroking your beard in false concern.
You can’t have it both ways. You can’t on the one hand make arguments from data, and then hint that the data is suspect. Make an honest argument from the data available, or alternatively question – with real argument, not just concern trolling – that the data should not be relied on.
Otherwise you’re just substituting major league noise and nitpicking for honest discourse.
Basil,
Thanks for an interesting analysis of the recent temperature data. My only comment is for people like Lee: Please tell us when a temperature trend is long enough/clear enough to infer that the trend is real. There is no statistically significant trend in average global temperature since 2001. How long would the current lack of statistically significant warming have to continue before it would be reasonable for someone to doubt IPCC’s 2007 projections of warming (and resulting environmental disruptions) due to carbon dioxide over the coming two decades? 3 more years? 5 more years? 20 more years? Under what circumstances could people reasonably conclude that the IPCC projections of 0.2C per decade are simply wrong? Would a falling temperature trend for the next 5 years be enough?
The researchers at the Hadley Center have demonstrated the courage of their convictions, and have predicted no warming until the end of 2009 (due mostly to ENSO), followed by a return to “rapid warming” in 2010 and beyond.
This prediction by the Hadley Center is enormously helpful, for it begins to place the climate modelers in the same boat as everyone else who works in science: good science makes accurate predictions, while bad science makes incorrect predictions. With the Hadley Center on record about the next several years, reasonable people will be able to evaluate the validity of the climate models the Hadley Center is using to make their predictions.
If there are no circumstances under which we can conclude from incorrect predictions that the models are wrong, or if the modelers simply refuse to make or be judged by the model predictions, then the modelers have left the field of science and entered the field of theology….. and they should just be ignored by scientists (and everyone else).