Guest Post by Jeff Id:
“Tamino” has made a couple of posts on how the last 10 year drop in temperature is not statistically significant, so it isn’t real. He went too far in his last one and began claiming it was a tactic of some kind of creature called a denialist to confuse and confound the public.
Let’s see what Tamino has been saying on his blog link HERE.
Some of you might wonder why I make so many posts about the impact of noise on trend analysis, and how it can not only lead to mistaken conclusions about temperature trends, it can be abused by those who wish deliberately to mislead readers. The reason is that this is still a common tactic by denialists to confuse and confound the public.
I just hate bad science. First he points out how Bjorn Lomborg made some comments about temperature decreasing, after placing the ever more popular label of denialist on him implying Lomborg’s statements were intended to confound and confuse the public. Heres the main point of what Bjorn Lomborg said.
They (temperatures) have actually decreased by between 0.01 and 0.1C per decade.
Ok, so graphs like the one below are the reason Bjorn Lomborg is a denialist.
I copied this graph from Digital Diatribes of a Random Idiot – A great unbiased site for trends (link on the right). Note the slope of -.0082 (.01C/month units or .00098 degC/year – Thanks to digitial diatribes comment below) in the equation on the graph. Most of us know this is actual data and is correct, in fact every measure is showing similar results. The earth stopped warming- a very inconvenient truth. So Tamino what’s the argument, why are the evil and uncooperative denialists wrong?
Statistics of course.
Here comes the numbers from Tamino.
The most natural meaning of “this decade” is — well, this decade, i.e., the 2000’s. So I computed the trend and its uncertainty (in deg.C/decade) for three data sets: NASA GISS, RSS TLT, and UAH TLT, using data from 2000 to the present. To estimate the uncertainties, I modelled the noise as an ARMA(1,1) process. Here are the results:
Data Rate (deg.C/decade)
Uncertainty (2-sigma)
GISS +0.11 0.28 RSS +0.03 0.40 UAH +0.05 0.42 All three of these show warming during “this decade,” although for none of them is the result statistically significant.
Ok Tamino has calculated GISS, RSS and UAH. One ground measurement and two satellite. For those of you who don’t spend their afternoons and weekends digging into this. ARMA is a fancy sounding method for what ends up being a simple process Tamino has used to estimate the standard deviation of the temperature. Sometimes it seems the global warming guys believe the more complicated the better, but no matter. He has a 2 sigma column which represents about 95%. He then goes on to say that because of the sigma 0.28 or 0.40 is bigger than the trend, the trend is not statistically significant. He repeats the comment below.
Let’s make the same calculation using data from January 1998 to the present:
Data Rate (deg.C/decade)
Uncertainty (2-sigma)
GISS +0.10 0.22 RSS -0.07 0.38 UAH -0.05 0.38
Finally one can obtain negative trend rates, but only for 2 of the 3 data sets. But again, none of the results is statistically significant. Even allowing this dreadfully dishonest cherry-picked start date, the most favorable
Now Tamino claims to be a statistician so I can’t see how he made such a simple boneheaded error but if he wants to pitch softballs, I’ll hit em. Just to make sure he’s in good and deep here’s one more quote.
I’ve previously said “Those who point to 10-year “trends,” or 7-year “trends,” to claim that global warming has come to a halt, or even slowed, are fooling themselves.” I may have been mistaken; is Lomborg fooling himself, or does he know exactly what he’s doing?
So, Mr. Lomborg, we’re all very curious: how did you get those numbers?
Wrong turns everywhere
The first and really obvious error Tamino makes is referring to the short term variation in temperature as noise. Noise in the context of sigma is related to measurement error. How can we determine the measurement error of the three methods GISS, RSS and UAH. Well the graph of the three is below.
The first thing you notice from this graph is that the 3 measurements track each other pretty well. The signal is therefore not completely noise. Well what is the level of noise? We have above 12 measurements per year times 29 years. So we don’t need ARMA or other BS we can simply subtract the data. I put the numbers in a spreadsheet and calculated the difference between RSS and GISS, RSS and UAH and UAH and GISS. With 348 measurments for each type of instrument I was able to get a very good estimate of standard deviation of the actual measurements. Again, no ARMA, just using the difference between the graphs.
GISS – RSS one sigma 0.099 Two sigma 0.198
RSS-UAH one sigma 0.101 Two sigma 0.202
GISS-UAH one sigma 0.058 Two sigma 0.116
These are actual numbers and are substantially lower than the estimated two sigma by Tamino but still bigger than the 0.1 C per decade although the two sigma GISS – UAH is within a 90% confidence interval already!
This isn’t the end though. Tamino ended his discussion there implying shenanigans and other things of those who see a trend.
Both of our standard deviation calcs are for a SINGLE measurement NOT a trend.
This is a big screw up. How can a self proclaimed statistical expert miss this, it’s beyond me. Anyway, none of us is universally right every day but most hold their tongue rather than post a big boner on the internet. Well most scientists realize that when you take more than one measurement of a value you improve the accuracy. So being a non-genius, I used R to calculate what the statistical certainty of the slope is when taken over 10 year trends. Thanks again to Steve McIntyre for pointing me to this software. I don’t love it but it is convenient.
t=read.csv(”c:/agw/giss data/10 year variation.csv”, header=FALSE)
x = (1:length(t[,1]))
y=t[,1]
a=gls(y ~x)
confint(a)
confint(a)[2,1]-confint(a)[2,2]
y=t[,2]
a=gls(y ~x)
confint(a)
confint(a)[2,1]-confint(a)[2,2]
y=t[,3]
a=gls(y ~x)
confint(a)
confint(a)[2,1]-confint(a)[2,2]
What this script does is load the difference files i.e. GISS-UAH, fits a line to them and presents a number for the statistical confidence interval of the slope coefficient at 95 percent confidence which is about two sigma. The confidence of the slope of the trend is as follows
GISS – RSS Two sigma 0.00108 DegC/year
RSS-UAH Two sigma 0.001068 DegC/year
GISS-UAH Two sigma 0.0005154 DegC/year
Despite a standard deviation of .02 We have a twenty times more accurate slope measurement of 0.001degC/year !
Conclusions
1. We can say with a high degree of certainty that we know the trend of temperature for any ten year plot to within .01 degC/decade.
2. We can say that temperatures have dropped this past decade, just as our eyes looking at the graphs had already told us.
3. We can also say that Tamino owes a few more apologies.
He and Real Climate still don’t let me post on their blogs!
I wonder why?
YOu missunderstand what Tamino has done. His 2 sigma error is not on You are testing different hypothesis to Tamino.
In the first part of your post you calculate the error on each indevidual point by look at the standard devidation of the differences between the different data sets. Your conclusion is that the error in the measurements of the individual points is larger than the size of the trend.
In the second part you attempt to find an uncertainty on the trend. But you use the difference between the measurements… WHAT?
For example, is the GISS data and the RISS data are identical, that is the diferrence were zero at all points, that does not mean that we can be certain of the trend that results. What you have tested is if there is a trend in the differences between the different data sets. That is, do the data sets converge or diverge over time. And you find that they do not … big surprise.
Taminos approach has been to ask can we reject the null hypothesis that the trend is -0.1C per decade given the evidence presented. He tests this by using the standard hypotehsis testing procedue. First he assumes that the null hypothesis is correct – that there is a cooling trend of 0.1C. Assuming this he calculates the standard deviation of the slope of the trend, given a noise model for the indevidual points. He then asks if the real trend seen in the data is within two standard deviations of null (Lomborg’s) trend, and finds that it is not. Its not how I would have done it, but there you go.
SO what is the conclusion?
Well obviously we can say that the average temperatue of the last ten years has been lower.
We can reject the hypothesis that there is a trend of 0.1C cooling at the 95% confidence level.
There is no evidence to reject the hypothesis that the trend is a -0.01C cooling.
Similarly there is no evidence to reject the hypothesis that the trend is a 0.1C warming.
Tamino is the nom-de-plume (or should that be ‘de guerre’?) of Greg Foster, is it not?
I meant of course Grant Foster.
“Put it this way: I get a glass and fill it with water. It takes 10 seconds to fill. I then drink it in 3 seconds. Now: I could plot water in the glass over time, fit a trend line, and claim that the trendline “proves” that the glass is filling with water. But who cares? The point is that once I have drunk it, the water is gone and the glass is empty.”
Hmm… change it to beer and I begin to see what you’re talking about. But I’m not sure I agree that it is a pointless figure. Surely you have just provided the key description of the reason why I have to wait so long at the bar on a Friday night?
This is a really important finding. It indicates that for a bar to be operating properly (that is, for more glasses to be emptying than filling at any moment in time), the critical parameter is that drinks should be served in less time than it takes to drink them. Surely this research should be passed to the brewing industry immediately? Or at least my local?
The task of the sceptic of a theory is always much easier than that of the proponent. If someone proposes that all swans are black it only requires the sceptic to find one black swan to disprove the theory. No matter how many white swans are produced by the other side they cannot win the argument.
If the sceptic can show that on several of the respected temperature records there has been a slight cooling trend for over 11 years, then that serves as their black swan. For basic global warming alarmism to be true it is necessary that all periods as long as 11 years, without any extraordinary factors such as volcanoes, should have a warming trend.
Sceptics should not waste their time on responding to arguments that other, shorter periods, have warming trends. That is just as irrelevant as a white swan after the black swan has been found.
We don’t need ARMA? Hmm, the Tamino guy uses an ARMA model because the variation on the longterm trend is very much like red noise, that is noise which is auto-correlated on some typical time scale. That’s indeed a valid approach and much better than the simple-minded appraoch taken by Id. I’m afraid it’s you, Jeff who made the “big boner” here.
However, Tamino’s analysis shows no significant underlaying trend in the data used. An increase by 0.05-0.10 (predicted by the AWG hypothesis) over the time span would have stood out like a sore thumb, and therefore isn’t there. The magic flute of a warming trend is not to be found in there.
So, perhaps you are both wrong?
[…] Id Watts Up With That? Wednesday, Oct 22, […]
May I suggest a great book by Shumway and Stoffer,
http://anson.ucdavis.edu/~shumway/tsa.html
In Example 6.2. both signal and observation errors are considered as a stochastic process. Not sure if every alarmist agrees with random walk model for global temperature signal, but the analysis is very illustrating in the book. Something that combines Tamino’s and Jeff’s approaches.
“3. We can also say that Tamino owes a few more apologies.”
Hold your breath…..
Ed Zuiderwijk – You are right. The data over the last 10 years doesn’t provide the evidence to say that the underlying trend not flat, but neither does it provide data to say that we can reject that the hypothesis that the underlying trend is warming. Doesn’t provide enough data to say anything very much about the underlying trend, except that we can reject the hypothsis that the underlying trend is a 0.1C per decade cooling.
Two comments:
On the importance of picking a starting and ending date for determining trends.
If you look at the 20 or 30 year trend, everything is OK on the stock market. Just an adjustment. However, if you are an investor, you know there has been a shift in trends.
Knowing when trends have truly changed versus a minor blip is the key to understanding anything worth measuring. If you could just figure out the difference, you would be a very wealthy person in the stock market. Lots of people claim to have discovered techniques for doing so and are always peddling their software or methods or whatever. The nagging question I always have for these types of folks is: why don’t you just apply your methods to your own investments?
In any event, it is really hard to determine whether changes in data represent a change in trend or not, while we are in the period of transition. Later on, with 20/20 hindsight, we can all agree when a trend took place.
My second point, when looking at these charts I like to pretend I’m looking a chart from my stockbroker depicting my portfolio. Then I ask myself, “Is this going up or down or nowhere?” OT – I really am longing for those good old days of going nowhere.
My conclusions on temperature trends?
We most definitely have not had a warming trend over the last ten years.
IPCC and Hansen type projections for the future have already departed from observations. Others might quibble about the mathematically precise point we have to say the projections have failed, but in my mind, they have failed. I have to wonder, is it possible for these projections to ever be falsified in the minds of some?
We might have a slight cooling trend underway, but again, if the drops of the last couple of years continue, then we will most definitely say this was the turning point.
I am not a climate expert, but it seems to me that the notion of “weather noise” in a thirty-year data set is a little bit disingenuous. Over thirty years, the only thing we could possibly measure is weather. We could compare this thirty year trend to historical trends of similar length, or compare an end point to another point in the distant past to get an idea of climate. The problem with the whole AGW idea is that, in order to get people concerned about global warming, the concept has to be within the experience of living humans. Historical data can be manipulated (hockey stick) because the common man trusts his memory better than any technical analysis. It was colder 30 years ago. I remember the July 4th snow when I was in elementary school. AGW is all about the weather, not climate, so skeptics get sucked into these futile debates about short-term trends. Again, I’m not an expert, this is just my opinion.
John Phillip said
Tamino (and me) calculate the trend for the last 120 months at +0.11C but with a large uncertainty, meaning that the actual trend may be substantially different.
Check your uncertainty, If you think only stochastic you are correct however you know the slope to a high degree of certainty. (minus the corrections to the satellites and ground stations of course) The same as if you measured the same value 300 times.
Ian Sandbury
“Assuming this he calculates the standard deviation of the slope of the trend, given a noise model for the indevidual points.”
This is where Tamino didn’t finish his math. We know the slope of the line to within 0.001. Tamino didn’t do any calc of the slope and instead presented standard deviation as his proof of the null. When you actually calculate the slope confidence intervals you find a much smaller value and find to a very high degree of certainty that we have a downslope.
William
“The statistics in this post are wrong. Jeff Id has confused measurement noise (which he doesn’t really estimate 100% correctly – rather he uses the difference in different measurement series as a, probably reasonable, proxy) with weather fluctuations.”
While he is correct that my sigma isn’t 100% perfect he misses the point that I have intentionally gone out of my way to eliminate the weather noise. A common mistake in this post I’m afraid.
Regarding the statistics, my method of subtraction sig_RSS-sig_UAH overestimates the instrument error because the error from both instruments is combined.
I believe the correct val should be sig_delta = sqrt(sig_RSS^2+sig_UAH^2) but I haven’t bothered to look it up because it simply means I have overestimated my sig_delta. I have already made the point above that because of the measurement precision we know the slope well enough to show that Bjorn was correct.
Alright, one more then I need to work. There are a lot of smart people on these threads, I am a skeptic but only based on the ridiculous science and politics of this issue. I don’t claim AGW is false anywhere, some of the science is. Without specifics and unrelated to this post above I will say I believe now that some of it is done with intent. I wouldn’t have said that two months ago.
Patrick Hadley
The task of the sceptic of a theory is always much easier than that of the proponent.
I disagree with this. Certainly a skeptic can pick out a weak argument and hit it but when reasonable argument is squelched in government, media and even on some blogs (as I point out above) it makes the skeptics argument much more difficult.
” If the sceptic can show that on several of the respected temperature records there has been a slight cooling trend for over 11 years, then that serves as their black swan. ”
I don’t make the claim anywhere that this ends global warming. Only that it happened. Tamino treated it like a political issue and in his first post was reasonable yet biased but in his second he made the point the trend wasn’t statistically different from slopes of 0.4.
Since I can’t discuss it with him on his blog, I do it on mine.
And thanks to Anthony, I had a chance to do it here. I assume Tamino is welcome to post here as all people are on my blog. Is that correct?
I believe Lucia’s had some discussions about this:
http://rankexploits.com/musings/category/statistics/
Ed, indeed often it is assumed that variation on a longterm temperature trend is very much like red noise. This is of course only valid, in case there is indeed a trend during the periode of measurement. So this premiss should never be forgotten. However, ARMA could then indeed be used.
But Jeff Id’s estimate should also give a good indication at first sight. This is because the four means of measurement are reasonably independent, which is a premiss for being able to use differentials to calculate sigma. Else you’d be ignoring structurally non-constant (e.g. offsets only) errors.
However, if both methods give very big differences, one should get suspicous. Problably then, one of the two premisses will not hold.
In the end, nevertheless, not that many dispute the core-statement made by Lomorg, which is that the temperature indeed did not rise or at least not that much the last 10 years. What is disputed, whether this can or perhaps even should be seen, as natural variation or not. Tamino assumes it is natural and everybody who claims otherwise is a denier.
The truth is that Tamino could be right (except for the denier part). It could be just natural, but after 10 years of no (strong) warming and indeed having the theory predicting a trend that strong, the likelyhood of that is decreasing.
This is a bit OT but weather related. I just spent some time wandering over the new NOAA NWS maps that go with each area clicked on for the current temp. If you click on a town in Wallowa County, the temp will be somewhere around 15 to 25 degrees F right now, depending on the town you click on. But if you click in an area outside a little town circle (like in the middle of someone’s field), the temp is 43 degrees F. Every time. No matter where you click. The other thing I have begun to notice is that the automatic weather station that I check here: http://www.enterpriseweather.com/ is not updating like it used to. The temp reading right now at that weather site is from 9:00 last night.
I have also noticed that even though I am directly across from the Pendleton, Oregon airport station (its on the south facing mesa hill and I am on the other side of our little canyon on the north facing hill), the temp being recorded there ain’t nothin like it is where I am standing. I have crinkly grass under my feet and a chilly 29 degrees while the airport is recording a balmy 38 degrees F. When I get a chance, I will try to survey that station. Anthony, what do I need to do for that?
Am I alone in finding “Grant Foster” a hoot? Does your writing foster many grants, Anthony? Probably not.
Armin
There is nothing wrong with ARMA for Taminos first post. I would use it for that. In the case above we shouldn’t use ARMA because the difference gives us a method to isolate instrument variation. Still if you do use ARMA you actually get similar results when done correctly.
If you use ARMA Tamino got a sigma 2 times my sigma. This means that if he had applied slope confidence calculations he would have a result of two times my 0.001 or 0.002 deg C / year for 95% confidence.
None of this makes any conclusion about what happens next. Only that Bjorn is correct.
As a person who is neither a scientist or a mathmatician, I have a question that perhaps someone could help me with.
When someone refers to “noise” in a climate trend, it seems to me that they could be referring at least one of two things. First, they may be asserting that temperature randomly fluctuates around a given trendline. Second, they may be asserting that temperature fluctuates around a given trendline, that the fluctuation is not random, but that we lack the knowledge to determine what is causing the fluctuation.
It seems to me that Tamino is asserting that the “noise” is a random fluctuation. Does anyone know whether this true? What if the so-called “noise” has a cause that we lack the sophistication to identify?
PaulD:
The noise is chaotic not random. Yes in theory it does have a cause, but it is not predicable. Some will argue over whether chaotic systems are inherently unpredictable or if its just that we cannot predict them. The point however is that it acts as though it is random in terms of the fluctuations about the trendline.
Thanks to Anthony on behalf of those who have a good logical grip of the relevant science but are susceptible to disinformation from those who might be better mathematicians but who use their maths to obscure truth rather than to find it.
There was a time when maths was supposed to be a simple logical form of expression which from time to time could be more effective than words. That time has long gone and a good deal of modern maths usage is designed to confuse and deceive.
Noise: (noiz) n. any data in a set that either a. serves to disprove the theory upon which your grant is funded, or b. fails to prove the theory upon which your reputation is based.
Here’s my attempt at a clarifying point, as I understand it:
There is a difference between the standard deviation of the data itself that calculates a confidence around a mean value and the confidence interval of the observed trend line. The ARMA analysis originally done proves the point that actual observed data showing a negative trend can occur within a longer range set of data that has a positive trend. It does not prove that the current observations fall into that increasing trend model, only that it is possible, and a reasonable hypothesis. It doesn’t negate the hypothesis at all that the observed trend is a correct reflection of the actual trend.
The statement Tamino seems to dispute is a statement of observed fact. The observed fact is that trend lines (I’m assuming the author meant 2001-current as “this decade”) show that there has been cooling. This is not the same as saying that global warming has stopped, nor is it a statement that says this could be one of those aberrations that occur with fluctuating data. It says that, given the observed data, the trends are negative.
Tamino used a valid statistical process to make an invalid claim: that the author made an incorrect statement about the cooling trend lines. Whatever one’s thoughts about the statistical validity of a low r-squared of the trend line or high standard deviation of the observed data, the best that Tamino should have done with his point is to refer back to his ARMA presentation and remind the readers that the observed negative trend may well be the effect of what he refers to as “noise” and leave it at that.
What Jeff has done is to show that the calculated trend line, which is the best fit regardless of your comfort level with the best fit, is properly calculated – given the observed data – to a high degree of certainty. The only uncertainty with the observed data that would impact the certainty of the trend calculation then, is the measurement error in the observations.
A proxy to test this is consistency of the different sets of temperature measurements. By determining that the significance of these differences are not enough to change the trend line significantly enough to turn a negative trend into a positive trend, the conclusion is that we can be reasonably certain that the best fit trend line of temperature measurements are, in fact, negative.
The argument is simply that making such a statement is a true statement, based on observed data, and is in no way some kind of manipulation of fact by a “denialist.” It does not argue that other considerations as to why it is negative shouldn’t be considered through techniques such as an ARMA analysis.
Statistics is a shady science. This fact is easily verifiable 2-4 times a year when employment figures are released. Invariably the assumptions underlying the statistics are accused of being skewed and both political parties claim contradictory “victories” based on the same data set. Statistics have validated clinical trials that have lead to dangerous drugs being released for general consumption, only to victimize many innocents, clog our courts with lawsuits, and raise everyone’s healthcare costs. Statistics are used misleadingly to support everything racist ideals, to racism in standardized testing. Even the statistical methods used in Quantum Mechanics are believed by many to be cherry picked and self limiting in the hunt for a unified field theory. But we all know the biggest goose-egg of all statistical undertakings is weather prediction and climate science, perhaps the most inaccurate, incomplete, and most “fudged” excuse for science going on in the world today.
See statistics, like computer modeling and politics, cannot be done without some consideration of the desired outcome, and a set of human assmuptions to get there. Thus attempting to “prove science” through the use of statistics, is not only hopeless, but shows a complete lack of understanding of either. If you are capable of making accurate assumptions and handling complex mathematical calculations, then setting out to prove something statistically rather than empirically is to stray as far from doing true science as is possible. Physics/Thermodynamics holds the answers to the AGW riddle, that statistics will only serve to convolute until long after we are enslaved to legislation. Chemistry is the true SCIENCE behind the storage and transfer of heat at the molecular level, under varying atmospheric conditions. The whole of the science is built around this. Statistics’ is a footnote tool occasionally used to help clarify a point to the chemist, not the sole means to prove the point. STATISTICS NEVER PROVES SCIENCE.
It should be painfully obvious that the heavy use of statistics to support AGW theory is indicative of the disingenuous nature of the science and political effort behind it. This is why I have times over, and again now, assert that any effort to combat statistics with statistics is already a concession to bad science. It is fighting on their turf, and therefore one for the loss column. The statistics need to be rejected on the basis that even the best statistics are a far cry from scientific certainty. Meeting flawed premise with flawed premise proves nothing, nor does it advance the effort at all. Rather it sets it back, by failing to stick to the basic “Denier” assertion, that “the science needs to be better”. Statistics are never good science, so why should we attempt to dabble there too?
As much as I love seeing a “warmist” get a much needed comeuppance, I must assert that you “made” Tamino in the first place by validating his very invalid approach to “proving” global warming. That will NEVER HAPPEN through the use of statistics. You gave him is clout, you gave him his validity, so at the end of the day, you only managed to wound a monster of your own creation. Not a significant victory, enjoyable as it may be.
AGW is a very old, very well thought out, and very well funded movement. Distraction, surprise, and digression will be par for the course. To fight this fight we must do better. This entire article, is really a victory for the warmists, as a significant amount of well intentioned brain power was exhausted NOT proving a totally insignificant and diversionary point. Using methods that will never PROVE anything. Anthony, I love and respect your efforts, and all the heart and soul you put into fighting the good fight. Nobody was going to believe Taminos idiotic statistical assertions over the clearly visible trends in the data. But you lost sight of the big picture, and got locked into some “due diligence” effort over some contrived, meaningless statistics, and gave them validity where there was none. These guys fight dirty. Sometimes you gotta call a spade a spade, and a liar a liar, and move on. Your work is a threat to them. They studied you, figured out a way to draw you into their game then deployed a tactician to do just that. Tamino is that person, and he accomplished his mission. The beauty of science is never having to give the untrue or discredited a moment of consideration. Neither does a scientific blog. If (when) Tamino fails to ascribe to that, he will show his true colors and discredit himself. It’s not as fun, but that’s how you gotta play it…