Physicist Luboš Motl of The Reference Frame demonstrates how easy it is to show that there is: No statistically significant warming since 1995
First, since it wasn’t in his original post, here is the UAH data plotted:
By: Luboš Motl
Because there has been some confusion – and maybe deliberate confusion – among some (alarmist) commenters about the non-existence of a statistically significant warming trend since 1995, i.e. in the last fifteen years, let me dedicate a full article to this issue.
I will use the UAH temperatures whose final 2009 figures are de facto known by now (with a sufficient accuracy) because UAH publishes the daily temperatures, too:
Mathematica can calculate the confidence intervals for the slope (warming trend) by concise commands. But I will calculate the standard error of the slope manually.
x = Table[i, {i, 1995, 2009}]
y = {0.11, 0.02, 0.05, 0.51, 0.04, 0.04, 0.2, 0.31, 0.28, 0.19, 0.34, 0.26, 0.28, 0.05, 0.26};
data = Transpose[{x, y}]
(* *)
n = 15
xAV = Total[x]/n
yAV = Total[y]/n
xmav = x - xAV;
ymav = y - yAV;
lmf = LinearModelFit[data, xvar, xvar];
Normal[lmf]
(* *)
(* http://stattrek.com/AP-Statistics-4/Estimate-Slope.aspx?Tutorial=AP *)
;slopeError = Sqrt[Total[ymav^2]/(n - 2)]/Sqrt[Total[xmav^2]]
The UAH 1995-2009 slope was calculated to be 0.95 °C per century. And the standard deviation of this figure, calculated via the standard formula on this page, is 0.88 °C/century. So this suggests that the positivity of the slope is just a 1-sigma result – a noise. Can we be more rigorous about it? You bet.
Mathematica actually has compact functions that can tell you the confidence intervals for the slope:
lmf = LinearModelFit[data, xvar, xvar, ConfidenceLevel -> .95]; lmf["ParameterConfidenceIntervals"]
The 99% confidence interval is (-1.59, +3.49) in °C/century. Similarly, the 95% confidence interval for the slope is (-0.87, 2.8) in °C/century. On the other hand, the 90% confidence interval is (-0.54, 2.44) in °C/century. All these intervals contain both negative and positive numbers. No conclusion about the slope can be made on either 99%, 95%, and not even 90% confidence level.
Only the 72% confidence interval for the slope touches zero. It means that the probability that the underlying slope is negative equals 1/2 of the rest, i.e. a substantial 14%.
We can only say that it is “somewhat more likely than not” that the underlying trend in 1995-2009 was a warming trend rather than a cooling trend. Saying that the warming since 1995 was “very likely” is already way too ambitious a goal that the data don’t support.
kdkd (14:12:15), “Classic “sceptic” technique of taking a bunch of information, taking bits out of context then extrapolating into areas totally irelevant to the original premise, and a gish gallop of statements with scientifically dubious provenance.”
Yet not a single fact to dispute any of the statements. In other words, a classic “warmist” argument.
kdkd (14:12:15) :
How much will the temperature go up if there is an additional 34ppm of CO2 added to the atmosphere, under the same climatic conditions as this year, in the next year?
Since July of this year we have “El Niño” again. Here in Buenos Aires it is raining every two or three days and our sommer is very fresh. The same happened in 1998.
That is perhaps the reason why now the global temperatures have increased during the last five months. When “El Niño” is over (April or May) we will able to see the global temperatures without its effect.
Richard M (05:56:25) :
For those of you who think monthly anomoly data is a valid unit … well, why not use daily data? Why not use hours, minutes, nanoseconds?
Clearly I could show any trend I wanted by making the units small enough and I could get great statistical verification.
Richard, we’re on the same side here (I think, e.g. skeptical of CO2 induced AGW) so I don’t want to see this turn argumentative. But there is no magic to any given unit of time for empirical analysis. You attempted to justify the use of annual vs. monthly, and I found the reasoning unpersuasive. Now you come back with “well, why not use daily data?”
Indeed, why not? There may well be some — many — research questions where daily data is just the ticket. Several immediately come to mind. It is not hard to imagine them.
It is not about “making the units small enough” to “get great statistical verification.” It is about using units that are appropriate for the task. For measuring temperature trends, I prefer monthly over annual because I think that it is depicts the full range of natural climate variation better than annual data. And contrary to what several have been saying (some who thought that monthly data would invalidate Luboš point, and I showed that it didn’t), it isn’t guaranteed that using monthly data will result in a better statistical result. Yes, monthly data increases the number of observations, and that’s a good thing that will improve the goodness of fit. But it also introduces a lot more volatility, and that makes it harder to find a statistically significant trend. If the monthly volatility is high enough, this could have the opposite effect of what some expect.
But the main point of my post is to emphasize that there is no magic unit of analysis for time series analysis. I think in most cases, monthly is preferable. At least for measuring temperature changes. But as I said, I can think of some cases where using daily data would be preferable. In other cases, it would be appropriate to use just portions of a year (say winter months, or a “heating season”, typically November through May, in utility usage analysis). Do not put all your eggs in the “annual data is best, and anything else must have a nefarious purpose” bag.
Here’s an interesting plot from UAH – the globe averaged monthly stratopheric temperatures:
All stratospheric results
http://img51.imageshack.us/img51/1592/uahstratospherictempsal.png
Just the global
http://img39.imageshack.us/img39/6902/uahstratospherictempsgl.png
Now, if the global data is not an artifact of the system, then there seems to be a dump of heat in 1983 and 1992.
pre 1983 temperature is basically flat
between 1983 and 1992 temperature is basically flat but 0.5 deg less than pre 1983.
after 1992 temperature is basically flat but 0.5 deg less than between 1983 and 1992.
What is this heat dump?
Answers on a postcard.
@Luboš Motl (01:24:45) :
Luboš,
To me, one of the really fascinating statistical oddities in the UAH data is that the entire “warming trend” occurs between 1995 and 2000.
There’s no warming trend before January 1995 and no warming trend after June 2000…
UAH Lower Trop
How does this guy get this bad?
Ross Gelbspan’s video on climate change and the fossil-fuel-funded disinformation campaign
http://link.brightcove.com/services/player/bcpid51061328001?bctid=52599643001
kdkd
“Based on no evidence we’d have to expect that feedback mechanisms will be neutral through random chance. However, the available evidence and underlying theory suggests that there are quite a few positive feedback mechanisms starting to operate.”
Er, uhm, ….. No.
See, the only way Hansen and his ilk can get their global warming models to work is by back-adjusting their outputs from 1970 through 1998 by ADDING in a fudge factor by artifically assigning a variable “soot level index” to the air (globally approximately the (local) European and United States-led cleanups) and then arbitrarily extending this by assuming that India/China/Brazil/Mexico/South Africa will change their soot index values (somehow) in the future.
And by multiplying the (assumed) effect of approximating CO2’s effect on the atmosphere by multiplying it by a factor of ten. (To account for CO2 increasing water vapor’s effect on greenhouse gas reflectivity – though there is no evidence that this will actually happen. And though this effect is not in proportion to any physical amounts of CO2, water vapor, or clouds actually present. And though this (assumed) extra amount of water vapor will have no other effect on the world: like increasing clouds or upper atmosphere absorption/reflection of heat/light/cosmic waves/etc.
You see, ALL of the assumed feedbacks are assumptions on your part (by Hansen and his cronies) to make the final effect what they want.
Your statement on CGM positive and negative calculation feedbacks is completely contradicted by what your people are actually doing with their calculations.
—…—
Further, there are NO observations of ANY type to suggest that ANY (assumed) positive AGW feedbacks of ANY types have been observed. And there have been several direct observations that negative feedbacks HAVE been observed (particularly in cloud reflectivity), and many calculations that show that negative AGW feedbacks SHOULD be used in any climate study.
Again, that part of your statement is completely false.
TonyB note that Helm Glacier has lost at least 30% of its volume in the last 25 years, that is impressive. As you point out the glacier was advancing in the late 1960’s, so this is not just a continuation of a long term retreat, but response to recent warming. Also note that its mass balance history looks just like all of the other glaciers reported to the World Glacier Monitoring Service. We began reporting these before this hoopla began too.
http://glacierchange.wordpress.com/2009/12/19/helm-glacier-melting-away/
RACookPE1978 (14:03:14)
Beautifully put questions. The proponents of the armageddon that AGW is supposed to present to the world have never to my mind answered these questions. Why is warming (if it is occurring) such a bad thing? As for “kdkd”, his/her insulting tone saying things like “we predict” and “classic sceptic argument” is to be expected but I note no actual answers provided to RACook1978’s questions.
Running 13 month average somehow stops or 7 months ago.
Might want to check the end-point handling on that, and/or change the caption.
If you take out the 1998 spike that is go to woodsfortrees web site and first plot the data from 1978 to 1997 you a graph that has a least squares linear fit through it with a slope of .0339 degrees / decade if again you then take out the spike and plot the data from 2000 to 2009 you get a graph with a least squares trend line through it with a slope of .0389 degrees / decade obviously the spike in the graph by the event centered on 1998 really changes the slope of the least squares fit line through the data. It would seem to me that if you treat that spike as a spurious event, then there is no difference is slope or no real change from 1978 to 2009 even though co2 has been increasing the whole time.
Er… I’m not a statistician (or a theoretical physicist) but I found this post quite compelling:
http://www.realclimate.org/index.php/archives/2009/10/a-warming-pause/
As it turns out, climatologists use better data and explain why 🙂
Your understanding of what a confidence interval tells us is flawed. Don’t worry though. Most people, even those who run a lot of very advanced models using very advanced software do not understand the concept.
That is not a valid interpretation of a confidence interval. The “true” slope of the line is just a number. As such, it is either negative or not. There is no “probability that the underlying slope is negative”.
You choose the appropriate confidence level before you run the regressions.
Confidence intervals with historical, rather than randomly selected, observations are hard to interpret.
Normally, having X% confidence means that for X% of randomly selected samples, the confidence interval calculated using this method would include the true slope.
The X% confidence is NOT the probability that the interval includes the “true” slope.
As before, the “true” slope is just a number (even though you do not know it). Therefore, it is either in the interval you calculated, or it is not.
Everything above should be interpreted within the confines of classical statistics. Bayesian stuff is slightly more interesting.
Well I’m no scientist but people manipulating statistics to further their own agenda is not news to me.I’ve wondered for many years about global warming,all the dire predictions and the alarmists comming out of the woodwork.Not surprised some manipulation of data has turned up there.
Basil (14:50:15) :
Aren’t you, at some point, just embedding the problems with averaging temperature with a simplistic calculation in the data?
(Tmin+Tmax)/2 is not the average temperature. It assumes that all temperatures exist for the same amount of time over the day. If Tmin and Tmax occur for the same amount of time, and all the points in between also do, then that would be the case, but that is almost never the case. If the temperature is 40F for seven hours, 60 for four hours, and 35F for the last thirteen, do you say the average temperature of the day was 50F? I would say it is ~41F=(40*7)+(60*4)+(35*13)/24. Is there a problem with this?
Now, I realize that there are only two samples taken, but I can’t imagine it would be a great problem to collect a sample every hour. It would require more storage space, but it would be far more accurate.
Duncan (16:20:36) :
Running 13 month average somehow stops or 7 months ago.
Might want to check the end-point handling on that, and/or change the caption.
It is a centered moving average. It has to stop 7 months before the end (leaving 6 months blank at the end, both ends, actually).
mspelto (15:34:20) :
TonyB note that Helm Glacier has lost at least 30% of its volume in the last 25 years, that is impressive. As you point out the glacier was advancing in the late 1960’s, so this is not just a continuation of a long term retreat, but response to recent warming. Also note that its mass balance history looks just like all of the other glaciers reported to the World Glacier Monitoring Service. We began reporting these before this hoopla began too.
—…—…
OK. Let us assume that glacier retreat is a “symptom” of rising global temperatures.
1) What is the actual, measured increase in (both global AND local) temperatures between (any) two dates where an AGW “expert” is claiming that “glaciers are retreating”?
2) Demonstrate conclusively – and exclusively! – that “The specific measured temeprature increase would result in that much glacier ice melting over that period of time.”
This has never been done: For example, if you want to claim that glacier retreat proves that global warming is real” then you must show that “a half of one degree temperature increase (at the measured face of the glacier) will result in 4 million tons of glacier ice melting from the face and bottom of the glacier in 20 years.
Further, you (the AGW-proponent) must show that glacier melt worldwide STOPPED in 2000 (because temperatures clearly have not risen since the year 2000 and since you claim that ALL glacier melting/retreat is due to global warming (temperature increase); therefore there can be NO glacier retreat anywhere since the year 2000.
if glaciers worldwide have continued to retreat since the year 2000 (or 1995 actually), then glacier advance and retreat must not be solely due to global warming – at the time of the retreat/advance at least.
Now, obviously, over a long period of time and many degrees of change in temperature, glacier retreat IS directly to overall global temperatures.
But the entire AGW premise is based on a 25 year change in temperatures (of less than 1/2 of one degree) that is claimed to be caused by man’s release of carbon dioxide.
If glacierretreat/advance are NOT related to short term 30 year cycles) global warming of less than 1/2 degree, then glacier retreat cannot be used as a “proof” of man-caused global warming.
Global warming of greater than 30 years (the long-term warming that IS naturally caused and that CANNOT be controlled or affected by man) does occur but CANNOT be caused by mankind.
Dave F (17:25:06) :
Well, you are raising quite a different set of questions now. Relevant and interesting, but really more of a tangent to the original discussion.
Glaciers are the easiest things in the world to cherry pick, because there are about 160,000 of them world wide. Just pick the ones that are receding, then start arm-waving and pontificating about “climate change.” It’s an easy way to scare the kids.
In general, most glaciers are receding, as they have been since the LIA. But not all. And it has nothing to do with CO2, which is the central pillar of the climate catastrophe crowd.
The alarmists can’t even get their dates straight: click. Being several centuries off casts doubt on their little remaining credibility.
Some glaciers are advancing. If CO2 was the cause of glacier retreat, all glaciers would react to it.
The basic fact of the matter is that the raw global temperature record has been so manipulated, scrubbed, fabricated, tweaked, invented/filled in and massaged, that it can not be relied on to show anything conclusively.
The only honest course of action now is to start over with well sited, reliable, regularly calibrated instruments, maintained around the globe. But honesty is very low on the government’s list of priorities. And of course ‘UN honesty’ is an oxymoron.
RACookPE1978:
Here’s your classic skeptic technique of avoiding the stuff you don’t like, and making disproportionate claims about the stuff that you do like. Personally I trust the IPCC’s work as it’s based on a wide ranging process of consensus that receives scientific then political review – it’s only flaws as far as I can see are that it tends to being more conservative than might be prudent because of the need for scientific and political consensus. I certainly don’t buy the conspiracy theories popular in these pages.
Anyway the IPCC covers a range of forcing mechanisms, but doesn’t look at feedback mechanisms that may arise from the increased forcing caused by co2.
Neil Crafter: Your tone is the insulting one here I’m afraid. I’m merely trying to use measured scientific language – modelling the kind of behaviour that I’d like to see from the “sceptic” community. Mostly I see the sceptic community as an interesting study in the group psychology of [snip].
Michael,
You might as well link to Al Gore’s new book as a reference – and if you think GISS and CRU are better measures than the satellite data, just think about it this way…
Imagine only being able to see a somewhat random subset of 1/100th maybe even 1/1000 of the pixels on your computer monitor, and then recreating/modeling the rest of your screen based on those few pixels. That is what the instrument surface temperature records are essentially doing. The satellite records are mopre akin to taking a digital snapshot.
The reason RC doesn’t reference any of the satellite data in this article is that their instrument based reconstructions still show warming where the satellite data from RSS and UAH do not. The combination of found warming and use of only their own reconstruction (Gavin is more or less in charge of GISS) as the de facto standard really are quite convenient, or quite suspicious… it’s all in how you look at ‘it I guess
kdkd,
You can ‘trust’ the IPCC all you want. But it’s like trusting a snake to not bite you. Look at this chart: click
Literally dozens of peer reviewed studies show that CO2 persistence is very short; ten years or less. But the 100% political appointees who run the IPCC don’t like CO2’s short persistence time, because it completely debunks their CO2=AGW conjecture.
To avoid that problem, the UN arbitrarily set the CO2 residence time at 100 years. And you say you trust the IPCC over all those peer reviewed studies. Why would you?
If I gave the statistical climatologists at RC this series of numbers, they would find a warming trend…
1907 -0.475528
1907.08 -0.482963
1907.17 -0.489074
1907.25 -0.493844
1907.33 -0.497261
1907.42 -0.499315
1907.5 -0.5
1907.58 -0.499315
1907.67 -0.497261
1907.75 -0.493844
1907.83 -0.489074
1907.92 -0.482963
1908 -0.475528
1908.08 -0.46679
1908.17 -0.456773
1908.25 -0.445503
1908.33 -0.433013
1908.42 -0.419335
1908.5 -0.404508
1908.58 -0.388573
1908.67 -0.371572
1908.75 -0.353553
1908.83 -0.334565
1908.92 -0.31466
1909 -0.293893
1909.08 -0.27232
1909.17 -0.25
1909.25 -0.226995
1909.33 -0.203368
1909.42 -0.179184
1909.5 -0.154509
1909.58 -0.12941
1909.67 -0.103956
1909.75 -0.0782172
1909.83 -0.0522642
1909.92 -0.026168
1910 -3.58979e-09
1910.08 0.026168
1910.17 0.0522642
1910.25 0.0782172
1910.33 0.103956
1910.42 0.12941
1910.5 0.154508
1910.58 0.179184
1910.67 0.203368
1910.75 0.226995
1910.83 0.25
1910.92 0.27232
1911 0.293893
1911.08 0.31466
1911.17 0.334565
1911.25 0.353553
1911.33 0.371572
1911.42 0.388573
1911.5 0.404508
1911.58 0.419335
1911.67 0.433013
1911.75 0.445503
1911.83 0.456773
1911.92 0.46679
1912 0.475528
1912.08 0.482963
1912.17 0.489074
1912.25 0.493844
1912.33 0.497261
1912.42 0.499315
1912.5 0.5
1912.58 0.499315
1912.67 0.497261
1912.75 0.493844
1912.83 0.489074
1912.92 0.482963
1913 0.475528
1913.08 0.46679
1913.17 0.456773
1913.25 0.445503
1913.33 0.433013
1913.42 0.419335
1913.5 0.404509
1913.58 0.388573
1913.67 0.371572
1913.75 0.353553
1913.83 0.334565
1913.92 0.31466
1914 0.293893
1914.08 0.27232
1914.17 0.25
1914.25 0.226995
1914.33 0.203368
1914.42 0.179184
1914.5 0.154509
1914.58 0.12941
1914.67 0.103956
1914.75 0.0782172
1914.83 0.0522642
1914.92 0.026168
1915 5.38469e-09
1915.08 -0.026168
1915.17 -0.0522642
1915.25 -0.0782172
1915.33 -0.103956
1915.42 -0.12941
1915.5 -0.154508
1915.58 -0.179184
1915.67 -0.203368
1915.75 -0.226995
1915.83 -0.25
1915.92 -0.27232
1916 -0.293893
1916.08 -0.31466
1916.17 -0.334565
1916.25 -0.353553
1916.33 -0.371572
1916.42 -0.388573
1916.5 -0.404508
1916.58 -0.419335
1916.67 -0.433013
1916.75 -0.445503
1916.83 -0.456773
1916.92 -0.46679
1917 -0.475528
1917.08 -0.482963
1917.17 -0.489074
1917.25 -0.493844
1917.33 -0.497261
1917.42 -0.499315
1917.5 -0.5
1917.58 -0.499315
1917.67 -0.497261
1917.75 -0.493844
1917.83 -0.489074
1917.92 -0.482963
1918 -0.475528
1918.08 -0.46679
1918.17 -0.456773
1918.25 -0.445503
1918.33 -0.433013
1918.42 -0.419335
1918.5 -0.404509
1918.58 -0.388573
1918.67 -0.371572
1918.75 -0.353553
1918.83 -0.334565
1918.92 -0.31466
1919 -0.293893
1919.08 -0.27232
1919.17 -0.25
1919.25 -0.226995
1919.33 -0.203368
1919.42 -0.179184
1919.5 -0.154509
1919.58 -0.12941
1919.67 -0.103956
1919.75 -0.0782172
1919.83 -0.0522642
1919.92 -0.026168
1920 -7.17959e-09
1920.08 0.026168
1920.17 0.0522642
1920.25 0.0782172
1920.33 0.103956
1920.42 0.12941
1920.5 0.154508
1920.58 0.179184
1920.67 0.203368
1920.75 0.226995
1920.83 0.25
1920.92 0.27232
1921 0.293893
1921.08 0.31466
1921.17 0.334565
1921.25 0.353553
1921.33 0.371572
1921.42 0.388573
1921.5 0.404508
1921.58 0.419335
1921.67 0.433013
1921.75 0.445503
1921.83 0.456773
1921.92 0.46679
1922 0.475528
1922.08 0.482963
1922.17 0.489074
1922.25 0.493844
1922.33 0.497261
1922.42 0.499315
1922.5 0.5
1922.58 0.499315
1922.67 0.497261
1922.75 0.493844
1922.83 0.489074
1922.92 0.482963
#Data ends
#Number of samples: 192
#Mean: -0.00247671
WFT
Unfortunately, the number series is a harmonic function – a Sin wave. It has no trend.
Here’s the Earth’s climate over the last 2,000 years…
Moberg & UAH
If I gave a statistician the raw numbers to the graph above, they would say that there is no warming nor any cooling… Because the linear regression is flat.
The Earth is always warming or cooling. It warmed from 1980-1942… Cooled from 1943-1976… Warmed from 1977-2003… It’s been cooling since 2003.
The episodes of warming and cooling occur along multiple cycles of varying frequency and amplitude…
UAH Spectral Decomp
All of the warming during the satellite record occurred in one 63-month period…
UAH Jan 1995
Temperatures were flat before and after that 63-month period…
UAH Dec 1978
UAH Apr 2000
Correction to: David Middleton (19:34:32)
“1980-1942” should be “1908-1942″…