Once again, there is no statistically significant warming since 2000.
This is the normal situation when there is very little data. So, you might wonder why I bothered to discover this?
Here’s the story. I clicked a link at RC and arrived at Tamino’s blog. I discovered that back in August, 2007, Tamino showed there was a statistically significant warming trend since 2000. The post Garbage Is Forever very interesting, for a number of reasons:
- Tamino’s analysis was based on 7 years and 6 months of data. Tamino explained at length that one can test about hypothesis climate trends using these relatively short time spans.
- Tamino’s hypothesis test was based on a method he later said results in uncertainty bounds that are too small. If Tamino’s later claim is true, his use of too small uncertainty intervals would cast doubt on his August 2007 falsification of the “no warming this century” hypothesis in the first place. That said, these uncertainty intervals seemed good enough for him back when small uncertainty intervals seemed to disprove “No statistically significant warming since 2000”.
In any case, the post intrigued me. I thought it might be interesting to see how the falsification of the “No Warming This Century” hypothesis is holding up with time! In “Garbage is Forever”, Tamino examined HadCrut and GISS data starting from Jan 2000, through July 2007. I’ll do the same but extend through April 2008.
Application to HadCrut Data.
Applying OLS using LINEST in Excel, I calculate a trend of m= 0.4 C/century. LINEST indicates an standard error in the uncertainty interval of sm,ols=±0.5C. We really don’t need to do any more to notice that 0C/century is less than one standard error aways from 0.4 C/century. Based on HadCrut data, “No significant warming” can no longer be excluded, period.
However, to illustrate the method of falsifying to 95%, I’ll estimate the 95% confidence limits. But, it turns out the data exhibit strong serial autocorrelation. So estimate the 95% confidence limits we must correct for this feature.
But, we know this is too small, and must be adjusted. I’ll do so using the “Tamino” method as far as I can decipher it. ( Now, if you read the Tamino post I linked, you’ll find Tamino didn’t describe his technique copious details, but he’s described it in other posts, and I think this is the method he used then, and generally uses.)
Tamino generally recommends we adjust standard errors using a multistep process.
- Compute the autocorrelation in the lag 1 residuals,ρ. ( I used “Correl” in excel and got ρ= 0.63. )
- Adjust the number of degrees of freedom as Neff=N (1-ρ)/(1+ρ). The fit was based 100 months of data, and so has N= 98 degrees of freedom. I get Neff=21.96.
- Adjust the standard error by the square root of the ratio of the two numbers of degrees for freedom now estimate the standard error in the slope, m, is sm,1=0.95 C/century.
- Determine the 95% uncertainty intervals. I find the “t” value for the 95% confidence bars. To do this, I use the “TINV” function in excel, using the reduced number of degrees of freedom, 21.96. This results in t=2.08, and 95% confidence intervals of ±2.08 C/century.
- I find the 95% confidence intervals are: -1.5 C/century
So, we see the data no longer exclude the hypothesis that m=0C/century. (I don’t for a minute believe the underlying climate trend is 0C/century. But, one can’t prove this using the current HadCrut data.)
Of course, we later learned, that when Tamino finds a falsification displeasing, he suggests one must modify Neff=N (1-ρ)/(1+ρ) to Neff=N (1-ρ- 0.68/ √N )/(1+ρ+ √N).
This correction makes a bit of difference to the results. The trend in temperature is now found to fall bewteen -1.8 C/century We can repeat the whole exercise with GISS Land/Ocean. We get a best estimate of m=1.6 C/century, and 95% confidence intervals of -0.4 C/century Not much. It only means one can correctly say “There is no statistically significant warming since 2000.” This may irritate some bloggers, they may gnash their teeth and rend their garments, but based on current data, it is a factual statement. The trend from 2000 does remain positive. What doesn’t it mean? While many often assume “not falsify” means “confirmed”, this is far from true. Failure to falsify only means something when the power of a test is high. With very little data, the power of tests are low relative to any reasonable alternate hypothesis. So, what we will see is that hypotheses that are wrong will falsify, then fail to falsify, the refalsify and so on. Eventually, as more data trickles in, and uncertainty intervals shrink, the falsification will become robust. I am quite confident that 0C/century will falsify again. I’d guess when El Nino returns. That said, the fact that “failure to falsify” means very little is important to understand. One must never let oneself be tricked into believing “failure to falsify” a hypothesis means “confirmed.” It does not. In this regard, one must look at nearly every claimed validation of IPCC results critically; generally speaking, the best one can say is that a prediction failed to be falsified. But the power of the tests is often pitifully low. In this circumstance, failure to falsify means very little. In contrast, falsification, if data are not cherry picked does strongly suggest a hypothesis wrong. At a minimum, one must say the hypothesis is inconsistent with the data. Many will recall that, if we apply the method I just applied above (and a few others), the 2C/century IPCC projections for warming early this century have been, and are falsifying right now, using merged data from Jan. 2001-through April 2008.1 No. While falsifications at 95% confidence strongly suggest the 2C/century projections are wrong, and biased high, some falsifications will turn out to be incorrect. One feature of these tests is that we expect to get a 5% incorrect falsifications when we use 95% confidence intervals. Also, it’s possible the uncertainty intervals using this method are too small. I’ve been looking into that. Currently it appears that, when uncertainty intervals calculated this way are applied to periods when the stratosphere was free of volcanic dust, and the bucket-jet inlet adjustments are not suspected of creating strong biases in the trend, these uncertainty intervals seem just fine. So, one might strongly suspect the central tendency of 2C/century projected by the IPCC AR4 is high. But, as new data arrive, 2C/century may turn out to be correct. It just doesn’t seem very probable given the properties of the data measured on the real planet earth. At a minimu, one can say: If Tamino thought this method could be used to disprove 0C/century back in August, 2007, the same method gives is equally applicable to the test of 2C/century. But one never knows. Results of the hypothesis test could all change as future data arrive. Anthony Watts, David Stockwell, May are on top of the UAH data, and report May was quite a bit colder than April. —Does falsification mean something?
Are we sure 2C/century is wrong?
Updates:
(1: June 6, 2008 Edited for precisiion. See comment by Arthur Smith.)
Of course we may have to realize that if this goes on for another 2-3 years the whole AGW theory will have to go, but who will pay for the damage done? maybe if the AGW modelers changed their tactics to inventing models for reducing pollution, land usage, population etc they may save face/have a job. However CO2 models will not help in this case. Next interesting data to watch will be C02 data which we bet.. shall start receding… or is it not already? LOL
It would require more than 2-3 years of flat for the whole theory to have to go. But, if it were to go long enough, then the higher estimates of sensitivity wouldn’t be very consistent with data.
Honestly, I think this will turn around in about a year. But who knows? Maybe La Nina will last another full year, the PDO switch will slow warming down a bit and then a stratospheric volcano will go off. We are probably due for one of those.
Thought you grew up in Central America.
LA Nina, EL Nino.
🙂
Shoot! Heh.
My Spanish s*cks. My parents always spoke English at home. I learned to read in Spanish– but we moved to Buffalo NY when I was 6. Dad said my sister and I were speaking in spanish in the yard, we got teased, and I came in an announced “Spanish is ugly, I’m never speaking it again!” And then I didn’t! (Not that we did much anyway. We were living with my grandparents. My cuban grandmother spoke Spanish, but my Irish-American grandfather spoke not one word!
Now… to fix the boo-boo!
Lucia your one of the few AGW’ers who I respect highly. Your not fanatical and just present the data as “is”. However it would be nice if the satellite data was used in your falsification models instead of relying GISS which pardon me is UHI influenced?
Nicely done. This is what happens when a hypothesis of great emotional and social importance starts being revealed as inconsistent with observation. The defences get more and more ad hoc and desperate. Tamino is a good point of observation. The characteristic to watch for, which is now occurring regularly, is when the defence ends up conceding too much in another part of the wood. As when, for instance, you widen error bounds and end up conceding that the opposite of what you’re defending is also compatible with the hypothesis. As when you defend a method of PCA that will extract a hockey stick from a dead sheep.
Lucia is the following statement correct?:
“May 2008 tropics was the coldest May in the UAH record. This is where climate models say it should be warming the fastest”. (posted on Cycle 24).
Thanks for a reply if you have the time
Rex–
For the ‘main’ hypothesis test, I use A merge of 5 sources that include land and satellite data. I also show results for each group individually from time to time. (Data from all five always on the graphs.)
For this test, I used GISS and HadCrut, to parallel Tamino. He got in a bit of a snit that a nearly anonymous poster said there was “no statistically significant warming this century”. Interestingly, he “proved” there was using the exact method that he claims I can’t use to prove 2C/century is currently falsified. (That is, one can exclude it with a statistitcal significance of 95%.)
So, now, if you run around saying this, and someone points you to Tamino’s post, you can point them here and shown that “no statistically significant warming this century” is currently true.
I’m certain that eventually it won’t be. But I suspect if I tell you that, you’ll know that at least I’m willing to accept that sometimes weather noise actually does wander into regions where I have to either say: a) No, I can’t prove that yet or b) No. Right now, the data aren’t looking so great!
here is a little thought experiment. Given a hypotheis that warming is .2C per decade,
and given the noise you find in the observational record, how many months of data would
you need to establsih that the true trend was between .18C and .22C?
Tamino has been ruthless IMHO with his opinions on is blog. For instance he had a blog on Doe D’Aleo charging him with perjury because of his cherry picking of data. I tried several times to post and show Tamino’s choice of picking data points was every bit as much cherry picking compared with Joe. Let’s just say Tamino didn;t portray the “Open Mind” his blog portends.
It would be interesting to see his response to Lucia’s analysis.
steven mosher– Prospectively, you’d need tons of time. Given weather noise inherent in the transport equations, add volcano noise and add other disputed factors that may drive variability, it would take a huge amount of time to distinguish a 0.4C difference. I think I recently did this exact same analysis, and right now, to falsify 0 C/century starting at even 5 year intervals, we need to go back to 1990!
I’m going to have to do that, as it tells us something about Rahmstorf. The idea that one can even begin to say the most IPCC projections were “right” or “wrong” in any way that suggests getting the uncertainty on the slope to within 0.5C using data not collected before the projections were made is nuts. The 95% uncertainty in the slope since 1990 is about ±1C/century!
Lucia,
AGW is not a theory, as a theory by definition is a complex of interrelated hypotheses [and by extension a paradigm is a complex of interelated theories]. The single core AGW hypothesis that we have been hearing since the late 1980s posits that man-made increases in CO2 ppmv cause an increase in global mean temperatures. We are now faced with the reality that a decade or more of data from an increasingly broad set of temperature metrics [land surface, sea surface, deep ocean, lower troposphere, etc.] is in the process of falsifying this hypothesis. In order to keep the story line alive, we have over the past couple of years witnessed a defocus from CO2 alone and the casual introduction of “GHGs”, without much reference to the most potent one, water vapour, which is not “man-made”. Where things get scientifically positively dishonest is the fudge into man-made “climate change” as opposed to mere “global warming”. Science 101 teaches us that if it is not possible to demonstrate a causal relationship between A and B [as in A causes B], then it is utter nonsense to argue that A causes not only B, but causes changes in the complex B,C,D,E,F,G and H {etc.} as a whole.
Tetris–
So far, I don’t see the broad hypothesis in any particular danger. Distinct warming still remains for last century and since mid-century. Moreover, their is more warming in the second half of the 20th century than the first. These are persuasive signs that support the broad hypothesis.
I don’t have a particular problem with the switch from CO2 alone to the broader GHGs. They have radiative properties also. But, the fact that other gases cause problems complicates the solution. After all, CO2 caps do nothing for Methane.
I do agree with you there are problems with the switch to “climate change”. It’s a diffuse term, and makes everything rather confusing. To test whether a theory, set of theories, a collection of models, an esteemed panel, or a group of psychics has predictive ability, we need clearly stated quantitative predictions. With regard to AGW, that means, we need to the prediction to tell us a) what is going to change, b) where the change will happen and b) how much will whatever it is change.
With regard to AGW, at least we knew that the claim was a) global temperature would change, b) this would apply to the average surface temperature over the entire planet and c) the global temperaure would go up and amount “C” in some time “t”.
In contrast when I hear the word “climate change” I have no idea what the term is supposed to suggest.
Lucia, study the data from 1800-1900.
The trend postulated by Steven Mosher of 0.2C/d isn’t too interesting with just the recent data – which you rightly say is too little.
But the longer term trend has a lot more data anyway.
The A in AGW is all about the trend accelerating since the early 1900s. That is, there’s one more layer of obfuscation. There’s the historical climate trend, the current climate trend, the current weather “noise”, and then measurement bias, and measurement error.
If the historical climate trend is .2C/d – from data measured prior to massive carbon dioxide production – , and the current weather is pushing ‘down’ such that we’re seeing “no statistically significant warming”, what does that say about AGW?
A couple points:
1) The adjustment to the standard error of (OLS) regression noted in the text, “Neff=N (1-Ï- 0.68/ √N )/(1+Ï+ √N),” is the adjustment of Nychka et al, ” Confidence Intervals for trend estimation with autocorrelated observations,” equation (5). It is an attempt to put a better confidence interval around inefficient (i.e. highly dispersed) parameter estimates of the OLS estimation under first order autocorrelation. But why use the inefficient parameter estimate in the first place? If one doesn’t have software with time series estimating routines to estimate autoregressive and/or moving average components of the error term, one can still use a Cochrane-Orcutt or Hildreth-Lu algorithm implemented in a spreadsheet macro. These estimates have much better statistical properties under first order autoregression and somewhat better, albeit at times worse, properties under messier versions of serial correlation. Why Mr. Tamino, whoever he may be, chooses to use OLS with a correction appears to indicate either a real misunderstanding of time series estimation or an attempt to skew the results. There is free software — particularly R, but also some more specialized econometric packages — for the PC that will do pretty good jobs at time series estimation, and of course any academic has at his or her disposal all kinds of software.
Had Tamino done that, he would have found a very messy ARMA structure. My estimates of the structure for the HadCRUT3v series have the following coefficients, S.E.s, t-stats, and significance levels:
Variable Coefficient Std. Error t-Statistic Prob.
C 0.163232 0.143724 1.135731 0.2594
TIME 0.000926 0.000472 1.963259 0.0530
AR(1) 0.246250 0.129654 1.899291 0.0610
AR(2) 0.260135 0.109868 2.367713 0.0203
AR(3) -0.160860 0.092803 -1.733357 0.0868
MA(1) 0.219272 0.080283 2.731254 0.0077
MA(9) -0.267588 0.075713 -3.534243 0.0007
MA(10) -0.219605 0.077899 -2.819084 0.0060
MA(16) -0.654157 0.065740 -9.950684 0.0000
(with Newey-White HAC S.E.s for 2000:01 – 2007:07 in monthly anomalies)
Close to a rejection of no trend, but still not significant. Of course, throw in a decent explanatory variable, say the Multivariate ENSO Index, and you will get significance in the trend although not in the coefficient of the MEI(lagged once).
I am certain with a little work (i.e. cheating by specification search) I could have found a ARMA structure and estimating procedure, e.g. GARCH, that would give me a significant pure trend fit if I needed to report it. But I still wouldn’t use the Nychka adjustment because it is an adjustment on an estimating procedure I know, a priori, shouldn’t be used for significance testing of trends.
So my (multivariate statistics) moral is: Don’t encourage bad technique by repeating it. Just go a do it the best way you know how. Lucia, you know how to do Cochrane-Orcutt. Use it where you thing the AR1 coefficients are large. (OK, in this segment of data, the AR1 does not appear large, but REMEMBER the particular representation of the ARMA structure is NOT unique. With something as messy as the structure above, there are probably other just as good ways of representing it, presumably some with large AR1 values.)
2) Re comment 3220: Lucia, I am not certainty what the +/- 1C/century uncertainty refers to. Presumably that is the off-the-cuff estimate of the standard deviation of some estimate in the context of some probability model. Presumably, it is not the standard error of the trend slope (expressed in degrees per century) for the sample of monthly observations form 1990:01 to 2008:05? Could you elaborate on what the variable/model is?
Lucia,
How broad a hypothesis? The core contention in the AGW hypothesis is that whatever warming may have occurred over the past century, it has 1] been caused by CO2 and 2] that CO2 causing is man-made. As I have argued here before both points remain unproven, whereas we are faced with a clear decade long and growing disjunction between increasing CO2 ppmv numbers and global temperatures in all relevant metrics. To somehow put this on the account [as some have suggested] of a La Nina and that therefore by next year or so we will temperature trends reverse, stretches credulity to the breaking point.
How could you possibly use data from that source
http://www.theregister.co.uk/2008/06/05/goddard_nasa_thermometer/print.html
Martin —
The ±1C/century is, once again, using “The Tamino” method. I just did a quick look in a spreadsheet I was working out. The spread using this method will appear in the next post.
On the rest, I agree with you generally. If Tamino has the skill he says, one would expect he could test the statistical significance of a trend using something other than the rather obscure method discussed in the lightly cited Lee & Lund paper.
As far as I can tell from reading, Cochrane-Orcutt is better when there is a lot of red noise (even if the system is not perfectly AR(1)), and ARMA is better when the system has correlation but it’s not AR(1).
I don’t know ARMA yet. So, I normally apply C-O.
I also agree with you in principle that I should avoid flawed methods like the Nychka method (which is originally documented in a laboratory type report, and later discussed as a suggestion in Lee&Lund. Based on the 5 citations, the Lee and Lund paper has not exactly taken over the statistical world.)
Nevertheless, blog-rhetoric being what it is, the consequence of my ignoring the method entirely leads to accusations that I don’t use the method becaise ot gives results I don’t like. There are plenty out there who suggest I pick CO because it falsifies where this Nychka method would not.
As few people would understand the statistical arguments against the Tamino method, the fact is I need to respond to both prongs of the argument.
First: Tamino/Lee&Lund/Nychka method is NOT better than CO. Tamino’s method (Nychka) is an oddball, short cut method. Lee&Lund advise that it might be of value for those who don’t want to go to the trouble of doing the problem right. I’ve responded to that.
This argument should be enough for those who read and understand what the Lee&Lund paper actually says about the Nychka method. (And what they said is what managed to get through peer review at Biometrika.) But right or wrong, it’s not a persuasive argument to those who don’t understand the Lee&Lund paper.
Those people do understand the second prong of the argument which is that I use CO because the Tamino/Lee&Lund/Nychka method would not falsify 2C/century.
This is untrue. If we use the oddball Tamino/Lee&Lund/Nychka method, we also falsify 2C/century since 2001.
This particular blog post is a precursor to making the argument above. After it’s made, I can respond to people’s questions when they ask them. I am asked this all the time btw.
For the rest: better methods of hypothesis testing would be great! But for now, I do want to show a few things using the Tamino/Lee&Lund/Nychka because there are counter arguments out there. I could do the perfect tests, and I would still need to show people the results using that silly method.
tetris:
I think the temperatures will go up. But, obviously, my thoughts are not proof. We won’t know. But, you’ve switched from the theory of “AGW is falsified” to “it’s unproven.” There is a vast chasm between those two statements. Both can be true at the same time.
I think warming is certain. I think it’s proven that we caused at least some of it.
What I think we don’t know is precisely how much warming there really is, and how much we caused. But there is at least some warming, and we caused at least some.
I really doubt that’s going to reverse or be disproven.
Lucia,
I’ll leave it at this: AGW is not a theory but a tenuous hypothesis which stands on shaky scientific grounds and which remains unproven. As several observers have pointed out there has been no excess heat in the climate system for the past 10 years. In fact all relevant temperature metrics indicate that the system is shedding joules at present. Where then, would the renewed warming come from next year? The spotless sun?
The basics of the scientific method hold that if the data does not support or runs counter to the hypothesis at any time, unless the data is fundamentally flawed the hypothesis is falsified [no ifs, buts or whats]. One certainly doesn’t do what GISS does by default and modify the data. Finis.
Hi Lucia,
a point that you seem to skip over in the text here, though you clarify slightly in comment # 3229…
— the Tamino time interval is from January 1, 2000 to the present. However, the interval you’ve been working with generally up to now has been January 1, 2001 to the present. Those are quite different starting points, and a year’s worth of data between in one and not the other.
In particular, when you say here that “Many will recall that, if we apply the method I just applied above (and a few others), the 2C/century IPCC projections for warming early this century have been, and are falsifying right now, using merged data through April.” – I believe this is untrue, if you are referring to a starting point of January 2000 rather than 2001.
Which then goes to the issue of cherry-picking…
Arthur:
Yes. The start date of 2000 and 2001 makes a difference. Clearly, that is something people can consider.
It happens that I picked my start data before I was familiar with the data, and based it on publication dates of documents, what the diagrams in the AR4 show etc. I discussed the choice of the start date before I even learned how to do the corrections for AR1 noise. That said, I’m entirely aware that some don’t believe this. But I can do nothing about that.
I’ll edit the sentence– you’ll see my next post clarifies this specific point.