By William M. Briggs, professional statistician
“J’accuse! A statistician may prove anything with his nefarious methods. He may even say a negative number is positive! You cannot trust anything he says.”
Sigh. Unfortunately, this oft-hurled charge is all too true. I and my fellow statisticians must bear its sad burden, knowing it is caused by our more zealous brethren (and sisthren). But, you know, it really isn’t their fault, for they are victims of loving not wisely but too well their own creations.
First, a fact. It is true that, based on the observed satellite data, average global temperatures since about 1998 have not continued the rough year-by-year increase that had been noticed in the decade or so before that date. The temperatures since about 1998 have increased in some years, but more often have they decreased. For example, last year was cooler than the year before last. These statements, barring unknown errors in the measurement of that data, are taken as true by everybody, even statisticians.
Th AP gave this data—concealing its source—to “several independent statisticians” who said they “found no true temperature declines over time” (link)
How can this be? Why would a statistician say that the observed cooling is not “scientifically legitimate”; and why would another state that noticing the cooling “is a case of ‘people coming at the data with preconceived notions’”?
Are these statisticians, since they are concluding the opposite of what has been observed, insane? This is impossible: statisticians are highly lucid individuals, its male members exceedingly handsome and charming. Perhaps they are rabid environmentalists who care nothing for truth? No, because none of them knew the source of the data they were analyzing. What can account for this preposterous situation!
Love. The keen pleasures of their own handiwork. That is, the adoration of lovingly crafted models.
Let me teach you to be a classical statistician. Go to your favorite climate site and download a time series picture of the satellite-derived temperature (so that we have no complications from mixing of different data sources); any will do. Here’s one from our pal Anthony Watts.
Now fetch a ruler—a straight edge—preferably one with which you have an emotional attachment. Perhaps the one your daughter used in kindergarten. The only proviso is that you must love the ruler.
Place the ruler on the temperature plot and orient it along the data so that it most pleases your eye. Grab a pencil and draw a line along its edge. Then, if you can, erase all the original temperature points so that all you are left with is the line you drew.
If a reporter calls and asks if the temperature was warmer or colder last year, do not use the original data, which of course you cannot since you erased it, but use instead your line. According to that very objective line the temperature has obviously increased. Insist on the scientificity of that line—say that according to its sophisticated inner-methodology, the pronouncement must be that the temperature has gone up! Even though, in fact, it has gone down.
Don’t laugh yet, dear ones. That analogy is too close to the truth. The only twist is that statisticians don’t use a ruler to draw their lines—some use a hockey stick. Just kidding! (Now you can laugh.) Instead, they use the mathematical equivalent of rulers and other flexible lines.
Your ruler is a model Statisticians are taught—their entire training stresses—that data isn’t data until it is modeled. Those temperatures don’t attain significance until a model can be laid over the top of them. Further, it is our credo to, in the end, ignore the data and talk solely of the model and its properties. We love models!
All this would be OK, except for one fact that is always forgotten. For any set of data, there are always an infinite number of possible models. Which is the correct one? Which indeed!
Many of these models will say the temperature has gone down, just as others will say that it has gone up. The AP statisticians used models most familiar to them; like “moving averages of about 10 years” (moving average is the most used method of replacing actual data with a model in time series); or “trend” models, which are distinct cousins to rulers.
Since we are free to choose from an infinite bag, all of our models are suspect and should not be trusted until they have proven their worth by skillfully predicting data that has not yet been seen. None of the models in the AP study have done so. Even stronger, since they said temperatures were higher when they were in fact lower, they must predict higher temperatures in the coming years, a forecast which few are making.
We are too comfortable with this old way of doing things. We really can prove anything we want with careful choice of models.
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Yanno, a lot of grad school guys try to model stock prices in similar, simplistic ways. They quickly learn better, if they want to stop losing money for themselves or their clients.
Interestingly, a lot of aggressive speculators are also fascinated by weather and prediction. I don’t think that this is coincidental. The climate prediction and “modeling” and the stock market prediction and “modeling” games are very similar.
The big difference is that there’s very real and immediate pecuniary reward and punishment in the stock market prediction game. In the climate game? Well, it seems to me that there’s little relationship between accuracy and pecuniary reward, unless it is an inverse one.
From my position, if global temperatures were a market that I would trade on price (temperature data) alone, I’d view it as having broken up the uptrend unambiguously by 2001. I’d be looking to short rallies since then, but I’d not be making big, long term bets on the down side just yet. I’d view temperature as rangebound but vulnerable to further declines.
I think that most of my profitable peers would be looking at this data the same way (if temperature were price).
The average price for a gallon of gas $2.99.34689734221. Where can I get gas at this price?
A) The price of gas has gone down over time.
B) The price of gas has gone up over time.
C) Both.
D) Neither.
E) All of the above.
True or False : I can use data to show you gas prices are always going down.
You didn’t know there’d be a pop quiz, did you!
” Rob Vermeulen (08:03:16) :
the problem is that it is well known in dynamical theory that negative feedbacks, when coupled to positive feedbacks, can lead to instabilities as well.”
Point to the significant positive feedback. The one that is certainly present is quite small, pretty monotonic, and well bounded. The AGW models aren’t based on chaos theory instabilities. They’re based on the non-existence of any significant cooling systems – which would cause fatal warming from the addition of any net increase in warming.
The shortform simplification of AGW is:
1) An increase in atmospheric carbon dioxide causes a quite small direct net retention in heat. This warming – in itself – isn’t directly relevant. (We can calculate the direct greenhouse effects directly, and even an overwhelming amount of carbon dioxide isn’t exciting directly. Even amazing levels of carbon dioxide don’t cause us to “Go Venus.” (Or we would have before the oceans even cooled off enough to liquify.) But…
2) The fact that the atmosphere is slightly warmer means there is more water vapor due to equilibrium with the oceans.
3) More water vapor means more clouds.
4) Clouds act as a strong radiation blanket causing more warming.
5) Return to #2 – with amplification. Strong amplification.
Looking at the well understood #1, there is a hefty chunk of unexplained warming remaining. There’s only one other spot to assign the apparent warming to in this model. So when you -fit- this model, you calculate a strong positive feedback from cloud cover.
What Lindzen is saying is: When one actually puts satellites up and observe step four directly, as opposed to projecting via models – one finds that step four should read “4) Clouds insulate the ground from the incoming radiation substantially better than they retain the existing heat. Thus they cause a net cooling.”
More CO2 -> More heat -> More Clouds -> More cooling isn’t a runaway feedback loop. Well, unless the first step is wrong. But we have the physical chemistry for that step pretty well nailed down. The entire reason we were looking for a positive feedback loop in the first place was that the quite solid science of the “More CO2 -> More Heat” steps was dramatically failing to answer why, precisely, we were getting more heating than that.
This fundamental parameter “How much warming does an increase in cloud cover cause?” is one of the inputs in the circulation models. Extensive computer modeling occurs here – with the basic assumption that clouds are a net warming effect.
What a clever, witty, piece. Why do we elect politicians (and even some scientists ( not all ) who have not learned to think in such obvious ways of logic, such as this excellent article suggest we do. Sadly. plain common sense seems to be the main victim every time a politician gets elected, and claims to be a success.
Bernie (10:12:47) :
But perhaps he already knew exactly what the statisticians would have to say given his poorly articulated charge.
That and,
perhaps he thought saying “the National Oceanic and Atmospheric Administration and NASA” would be enough to settle it and keep people from looking at the other data sets. Because after all “the National Oceanic and Atmospheric Administration and NASA”, well, how could they be wrong. 😉
Good one, thanks Mr Briggs.
However, so what? Temperatures go up and down, we live in a fluid dynamic environment. Does it say anything about the difference between mans influence and that of nature? Not that I can see.
The AGW disseminators say we control our weather much like the Victorians thought they could conquer it. It seems to me both were/are wrong. Heck, most people I talk to do not understand where the carbon comes from in organic life!
“First, a fact. It is true that, based on the observed satellite data, average global temperatures since about 1998 have not continued the rough year-by-year increase that had been noticed in the decade or so before that date.”
When you say a “decade or so”, you actually mean 2 years don’t you?
http://data.giss.nasa.gov/gistemp/graphs/Fig.A2.lrg.gif
Do you think a statistical significance test yields a statistically significant cooling temperature trend between 1998 and present. It certainly doesn’t and the entire premise of this article is flawed.
The human body has it’s own statistical memory. It knows, for example, if the weather has been getting warmer or colder year-on-year. The warmist statisticians and marketeers try to overwhelm this human memory, but they succeed only in alienating as the memory of what is happening grows stronger.
Hysteria goes so far and no more, as does emotional drive.
Ask a football coach how long and far that type of game plan will last.
Well the good Dr Statistician puts it about in perspective. Part of the fault must lie with the mathematics (of statistics, that is).
I can create a set of data (numbers) which have the property that not one of those numbers bears any relationship to anything real; I simply make them up in my head, and write them down on the list as they come to mind; in no particular order.
Now I can present my data set to a statistician; well why not Dr Briggs’ set of statisticians; and I can ask them; “what do you make of this data ?”
Each of them can now apply the mathematics of statistics to my set of data; and produce means and medians and standard deviations; and any or all of the trappings of statistical mathematics; and their results are as valid as if I took a sequential set of readings of the official NIST Atomic clock time Standard, and gave them those numbers instead.
And therein lies the rub. The mathematical processes may be faithfully carried out; but give no assurance that the result actually means anything. Which means I can do the same analyses on the numbers in a telephone book, and extract the same amount of nonsense.
So Dr Briggs has an adorable straight line ruler. It might be quite useless, since no such thing as a straight line exists anywhere in the universe; that is simply a figment of our imagination, as is all of mathematics.
So what about the polynomial fit to the data; how many real physical processes actually follow a polynomial theoretical model. Well there are some that come close to doing that. I know that the mechanical resonant frequencies of some cuts of quartz crystal resonators, change with temperature in polynomial fashion such as parabolic; but then only over certain temperature ranges.
One is much more likely to encounter an exponential function in nature than a polynomial one. Radioactive decay for example, would give you a headache trying to fit a polynomial expression to measured data; exponential decay is much more common.
Statistics is supposed to give us “better” answers for experiments that are repeated many times; and the more the merrier; if Statisticians are as emotional as Dr Briggs suggests.
I still love the example of the first SSS Draft Lottery where calendar birth dates for conscription were selected by lottery. Overzealous statisticians immediately declared the result of that lottery to be not random, and therefore unfair; because more earlier calendar dates were selected , than later ones. I maintain that the draft lottery could have come up; Jan1, Jan2, Jan3…..Dec 29, Dec 30, Dec 31 ; a result which is no more unlikely than the result they actually got, which was one out of 366! (factorial) possible results.
But I submit that Dr Briggs concerns are somewhat irrelevent; because the real problem is in the data sampling methodology.
The theory of Sampled Data Systems, and the reconstruction of continuous functions from sampled data, is very well understood, and well developed. Our entire modern data communication, and telephone communication; as well as all our digital recording of music or images; even movies, is all dependent on sampled data theory.
And the most fundamental theorem of Sampled Data Theory, is the Nyquist Sampling Theorem; which establishes the requirement for adequacy of sample spacing, in order for the sampled function to be properly reconstructed. The theory goes on to explain the aliassing noise, errors that arise, and the creation of false in band error signals that corrupt the reconstruction irretrievably. No filtering process can completely remove aliassing noise errors, without also removing valid signal information which also corrupts the reconstruction.
So all the statistical manipulation is irrelevent Dr Briggs, because the data itself is pure garbage; just like the random stream of consciousness data set I wrote down as it occurred to me.
Global temperature data is a continuous function of two variables; time and space, and the Nyquist theorem requires that to correctly map that function in a retrievable fashion so the data can be processed to yield a global long term mean temperature; requires that the timing and spatial separation of sampling locations conforms to the Nyquist Criterion, that requires at least one sample taken for each half cycle of the highest frequency present in the presumably band limited function. Failure to do that by a factor of two or more means that aliassed noise will occur at the zero frequency which is the average that is being sought.
The min/max twice daily temperature sampling method in wide use for land based stations, already fails that test, since the diurnal temperature cycle is NOT a pure sinusoidal waveform; nor is it even time symmetric on a 24 hour basis, and that means even the daily time average is unrecoverable for any single site. The spatial sampling fails the Nyquist test by orders of magnitude, so that is simply a joke; to suggest that GISStemp or HADcrut is related with any accuracy to the mean global temperature of the earth.
The satellite measurments might be doing better on that score; but even that system has its problems.
So take heart Dr Briggs, you statisticians are not the only varmints in the pantry; the data gatherers are guilty of egregious errors.
And the computer modellers don’t seem to understand the garbage in; garbage out relationship.
George
Mark Young (10:38:30) :
The climate prediction and “modeling” and the stock market prediction and “modeling” games are very similar.
Making it look like a stock is going up and temperatures are going up can be the same :
http://www.thedailyshow.com/watch/thu-march-12-2009/jim-cramer-extended-interview-pt–2
The video will continue to a part 3 at the end of part 2
There’s no doubt that the satellites give a cooling trend by linear regression e.g. from 1998 and many other moments including 2001 – beginning of the century. Wolfram Alpha is enough to check it.
It can also be demonstrated that one gets warming with different choices, especially of the initial moment.
More importantly, most of these trends up to 15-year-long intervals are not statistically significant.
At any rate, it’s bizarre to fight against a “global cooling” straw man. As Roy Spencer correctly said, wasn’t this discussion about global warming as opposed to cooling? The absence of statistically significant cooling doesn’t imply the presence of warming.
Dr. Briggs is always a fun read, and always an educational read as well. His nmberwatch site is in itself a great education as to the wiles of those who play around with numbers.
What these warm-mongers are doing is exactly what my professors in college when I majored in physics lo those many years ago warned me specifically to not do.
Oh well, those whiz kids made all of the financial computer models which extrapolated past data bet our bankrolls on their future extrapolations. Disaster has been the result.
Well, according to my “model,” the AP will be going out of business shorty.
Maybe the answer to what has been going on is a lot simpler. Maybe GIStemp has been dropping cold stations and adding/keeping warm ones. Then gridcells with no stations are interpolated/filled in from other (warmer?) stations. All but one station north of 65 degrees in Canada have apparently disappeared. Only coastal stations remain in California (the inland and mountain ones are apparently gone). Similar issues apparently show up in Australia and Brazil (stations further away from the Equator have been dropped). The stuff is still preliminary but very interesting. See http://chiefio.wordpress.com/.
Mark Fawcett (10:35:57) :
Great article.
Sorry for the OT – what’s happening back at the science museum “prove it” survey? It’s now (5:35 PM GMT) reading 771 in, 5249 out?
Cheers
Mark
Maybe they are using only votes that have comments?
anyway now it is
# 773 counted in so far
# 5279 counted out
Personally I love bicubic splines, you can prove anything with those.
Jeff in Ctown (Canada) (09:35:52) :
“Good analysis. I imagin a 10 year moving average would indeed hide the last 7 years cooling fairly well.”
That is because a 10 year moving average has a 5 year group delay. You would not even begin to see the change until then, and it would be smoothed out.
Alan S. Blue (10:44:33) :
” Rob Vermeulen (08:03:16) :
the problem is that it is well known in dynamical theory that negative feedbacks, when coupled to positive feedbacks, can lead to instabilities as well.”
I don’t know from which board this came. I guess Alan had multiple windows open. But, this is certainly not well known, or at least, the problem needs to be defined more carefully. Assuming a series plant, the basic rule is that the gain of the negative feedback must be greater than the positive feedback gain to stabilize the mode. I.e., the bandwidth of the negative feedback must be greater than the frequency of instability. In this case, increasing negative feedback always improves stability. On the other hand, the bandwidth of the negative feedback must be less than the frequency of non-minimum phase zero dynamics, or it will induce instability.
This is something which bothers me about the entire analysis enterprise to date. I have seen lots of assertions of positive feedbacks which are, in fact, zero feedbacks (pure integrators). I have never seen any discussion of the zero dynamics. In fact, I am doubtful that the climate modelers are that advanced in their understanding of feedback theory. But, I have a hunch the existence of NMP zero dynamics within the bandwidth of known negative feedbacks could invalidate some of the models, since it would have led to instability in the past.
Don’t take this as an assertion that there are such deficiencies. I don’t have the time to expend any of my own effort in this direction and have not done so. But, maybe, someone else will have an inspiration to try it.
Alan Cheetham (09:39:10) :
The global temperature was not increasing in the satellite era prior to the 1997/98 El Nino. And it has not been increasing since that El Nino. The El Nino resulted in a net change of about 0.3 degrees.
http://www.appinsys.com/GlobalWarming/GW_Summary_files/image004.jpg
An interesting step change caused by an El Nino?
Total OT, belongs to an older topic:
From Greenie-Watch: http://antigreen.blogspot.com/
The museum’s Prove It! website, which is designed to influence politicians at the Copenhagen climate summit in December, allows members of the public to pledge their support, or lack of it, to the environmentalist cause. But so far those backing the campaign are out-numbered nearly six-to-one by opponents.
By Saturday, 2,385 people who took the poll said “count me out” compared to just 415 who said “count me in”, after being asked whether they agreed with the statement: “I’ve seen the evidence. And I want the government to prove they’re serious about climate change by negotiating a strong, effective, fair deal at Copenhagen.”
LarryOldtimer (11:28:54) said:
Unfortunately, Oldtimer you have a case of mistaken identity:
Number Watch John Brignell
http://www.numberwatch.co.uk/number%20watch.htm
William M. Briggs
http://wmbriggs.com/blog/
BOTH are excellent reads. Dr Brignell has given us the list of all the things caused by AGW. Dr Briggs has given us several chapters of a useful introductory text on statistics.
best wishes
anna v:
I voted, prompted by the mention of the survey here. The numbers are astounding. Given the obvious bias of this Prove It posting, namely pro-CAGW, the results will be embarrassing in the extreme. I somehow doubt that we will hear much about these results come December.
You do have to identify yourself with a valid email address for them to count your vote.
Politicians use statistics like a drunkard uses a lamp-post – not for illumination but for support…!
“If your experiment needs statistics, you ought to have done a better experiment.”
Ernest Rutherford
Hey, today is Climatefoolsday:
http://climatefoolsday.com/
Here is the confernce program:
http://climaterealists.com/attachments/database/Climate%20Fools%20Day%20List%20of%20Speakers.pdf
Ever notice when a reports come out that shows earth is cooling ,which it is just geting started,or when the report that showed where the global temperature had dropped by 1 degree that the global warming crowd tries to find ways to discredit the report.Now i’m wondering if where they show a record high temp or back in 2007 when the ice was suppositly at lowest level ever in the Artic do they try to find out if it is true or,do they just accept it as FACT????? My guess is they will never try to dispute warmer temps or less ice and just accept that as gospel.