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.
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O/T Hansen has a book to sell.
http://www.latimes.com/entertainment/news/la-ca-james-hansen27-2009dec27,0,5460299.story
“”Storms of My Grandchildren: The Truth About the Coming Climate Catastrophe and Our Last Chance to Save Humanity” by James Hansen
Did he miss the christmas gift market or is the critic late? it says 27th Dec.
Think it’s about time that the precautionary principle was resurrected.
I and many others, in the uk, not only survived the searing summer of 76 but rather enjoyed it!
No doubt that,at that time, many were worried about Global Cooling. Forget the feeble, history re-writers, the next ice age was the biggest threat to mankind ever. Those whom say that this was not what science said at the time are as guilty of revisionist history as the current Iranian leader and his drinking buddies.
Climate confounds the senses, climate cabals confuse the science and politicians carry on doing what they’ve always done.
Adding to the paradox that gave us hot summers during the seventies, I or is that we, got cold, icy winters.
We/I/us survived! Open fireplaces upon which we combusted anything combustible gave us heat and light. And at prices we, the financially disadvantaged, could afford.
Not now. When the electricity and the gas stop, thousands will die. Not of drowning, heat prostration or computer predictions but of cold-induced metabolic disfunctioning!
To any politicos who may be out there, get a grip guys, a reducing population will diminish the tax returns, cut down deadly pollutants, provide more Lebensraum for Tuvaluans and Scuba- dressed Maldivians but is that how you want to be remembered?
Coming back to the precautionary principle, if the Scientific Consensualists turn out to have been wrong or frauds and we’re taking precisely the wrong measures then how are you going to explain that to your grandkids?
I have yet to informed why an increase in CO2 to cause a zero order increase in global temperature. The idea that one can just fit a straight line without having an underlying hypothesis is nonsense. You do not fit to the line which gives you the best R2 value, if that were the case everything would be fitted to polynomial’s, no you fit to a modeled relationship between X and Y. CO2 increases are not linear, therefore the line shape of temperature should not be linear, instead plot temperature against [CO2] or log[CO2] or at least some function of [CO2]; anything else is bollocks. The whole point of the excercise to to find any relationship between [CO2] and Temp, please, please, do not take your eye of the ball.
Paul (15:39:43) :
I believe that this posted analysis is flawed. You cannot apply this type of simple linear trend analysis to serially correlated data, since the precision of the parameter estimates is strongly a function of the autocorrelation in temperature data.
In this case, not strongly enough to change the outcome. Using a robust method for computing standard errors, the confidence interval still includes 0: -0.55 to 2.45 C per century. The standard deviation drops from 0.0084 to 0.0069, raising the t-ratio from 1.13 to 1.37, but still far from indicating a trend significantly different than zero.
Ok the critic was late. Now that’s dumb. Promoting the book after it’s intended market window. Maybe there were too many leftovers in the shops.
Anthony, as a statistician you should know better. With enough data points, anything can be “statistically significant”. Besides that, it’s a subjective comment anyway.
I have a MS in stats. That doesn’t make me an expert or anything, but I do know a little about stat methodology. The analysis above is very simplistic for the following reasons:
1. It fails to consider the measurement error. Each data point is accepted as “true” and without error. That’s a giant leap of faith and unsupported by the evidence.
2. The analysis includes a calculation of parametric error based on the Normal (Gaussian) distribution. The data are not normal, not independent, and are not the product of infinite replications.
3. The analysis fails to consider probabilistic (Bayesian) error.
Since all those varieties of error exist and are not accounted for, the precision and accuracy are much, much less than assumed. Hence the real confidence intervals are much, much wider.
As Dr. Briggs [http://wmbriggs.com] likes to say, people are way too certain of themselves!
In response to Icarus’s challenge to compare 1979-2009 and 1995-2009, I’ve plotted it.
1995-2009 has a lower slope. Rate of increase in temparature since 1979 is slowing.
http://www.woodfortrees.org/plot/uah/from:1979/to:2009/plot/uah/from:1979/to:2009/trend/plot/uah/from:1995/to:2009/trend
Many Christmas thanks to Anthony Watts and Luboš Motl, Steve McIntyre and all other defiant free thinking global warming skeptics and global warming debunkers. You all can proudly tell your grandchildren that you made a difference. A very big difference
You have exposed a lie that’s more dangerous than the Lysenko lie because this one is global
Plus seasons greetings and eternal gratitude to the CRU leaker cum whistle blower
Even if trying to follow the math gives you a headache then just watch the weather on tv. There’s been longer winters the last 3 years around the world. These were never predicted by the global warming scientists.
For example: this past week from Dec 19–25 there were 846 snowfall records in the lower 48 of the U.S. And winter is just getting going.
Much ado about nothing from them scientists!
Clear description of analysis — CHECK
Analysis code provided — CHECK
Data used adequately identified — CHECK
Clearly not the work of a Professional Climate Scientist so it can be safely ignored.
Why not just graft this on to the GISS figures starting in 1979. The only problems is Hansen will keep adjusting the prior figures down to fabricate an upward trend.
I believe Tamino did this exact ‘trick‘ a few weeks ago (and received *praise* for it) –
– Does this/would this caveat apply to him as well?
i.e., his posted analysis was flawed: … cannot apply this type of simple linear trend analysis to serially correlated data, since the precision of the parameter estimates is strongly a function of the autocorrelation in temperature data.
Comment?
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niphredilflower: You wote, “How long a period are we blamed for effecting the climate? I heard recently that CO2 is only blamed for the last 20 years…”
It really depends on the study and who’s trying to prove what. I’ve also recently run across studies citing anthropogenic influence since the mid-1800s. And I can recall one that attempted to show man’s influence for 1000s of years.
Icarus (13:33:14) :
The long-term warming trend is around 0.13C per decade according to the entire UAH record. What you should be calculating is whether there is any statistically significant deviation from that warming trend – otherwise you’re just grasping at straws.
——————————————————-
No Icarus, 15 years in which temperature has not responded to increasing levels of CO2 is contrary to the Hypothesis of AGW…… The 0.13c per decade for the 30 year UAH satellite record is well within range of Natural temperature variation…… AGW hypothesis is flawed.
johna1800 (16:53:04) :
In response to Icarus’s challenge to compare 1979…
—————————————-
Talk to Icarus about the Medieval Warm Period. He wants longer data sets. 1000 year data set should do the trick.
Rob Vermeulen (14:22:28) :The trend is non-significant only because the poster used the average yearly anomaly. Taking every month into account, the trend becomes statistically more significant.
Very right. Our goal here should be to understand, not try to advocate for one position or another.
David Starr (14:04:33) :
“Have satellite readings been calibrated against earth based instruments?”
that is an interesting question. are satellite data in any way contaminated by a calibration to ground based data ?
does poor ground based data adjustment, station cherry picking, possible fabrication, warming biasing in data set splicing or lack of UHI adjustments also contaminate satellite readings ?
kadaka (14:21:52) : You asked, “And what do things look like without the 1998 spike?”
You can’t really remove it, though many have tried. There are multiyear aftereffects of the 1997/98 El Nino.
http://bobtisdale.blogspot.com/2009/11/more-detail-on-multiyear-aftereffects_26.html
and:
http://bobtisdale.blogspot.com/2009/12/more-detail-on-multiyear-aftereffects.html
You asked, “How much of the heating of the Pacific Ocean is due to underwater volcanic activity?”
Little. Refer to Emile-Geay and Madec (2009).
http://www.ocean-sci.net/5/203/2009/os-5-203-2009.pdf
They write, “Of course, the deep ocean is subjected to another heatsource: the geothermal flux due to lithospheric cooling. Yet the latter is usually neglected in oceanographic studies, primarily because it amounts to less than 2% of surface heatfluxes (Huang, 1999) – a total power of 0.03 PW and a meanflux of ∼88 mW m−2 (Stein and Stein, 1992), while surfacefluxes are on around 30 to 250Wm−2, larger by three orders of magnitudes.”
Following on from DocMartyn..
Looking for statistical significance between CO2 and temperature according to say a log function (or whatever it exactly is) would have a point. But even to the modelling community with a huge confidence in their models (vast overconfidence I believe) it isn’t a simple relationship because of all the feedbacks in the climate system.
I agree with DocMartyn’s main point – you need a hypothesis to test against. Just plotting a graph and fitting a linear trend is a pointless exercise.
I believe this crazy concept has come about because of the idea that “natural variation” is “noise”. Therefore, we are trying to see the “signal” without the “noise”.
In this case – flawed beyond belief – it makes sense to try to find the real signal.
But where’s the body of evidence and testable theories that build the case that year to year changes in the earth’s temperature (and more importantly, heat) are “noise”?
I’m not a climate scientist so maybe I missed it.
Rule of thumb when spending your own money: Keep the money in your pocket unless there’s a 99% confidence in the desired outcome by spending the money.
Rule of thumb when spending somebody else’s money: 50:50 sounds like a good idea.
“Tilo Reber (15:47:08) :
Lubos should post his results at Tamino’s place, since Tamino is so much in love with statistical sophistry.”
——————————————————
Good one.
Tamino would either:
(a) not allow it to be posted
(b) allow it to be posted, come up with some reason to blindly dispute the results (e.g., suggest the period was cherry-picked), and keep Lubos or anyone from defending it all the while getting his chorus of flute blowers
grumpy old man (17:21:10) :
Rob Vermeulen (14:22:28) :The trend is non-significant only because the poster used the average yearly anomaly. Taking every month into account, the trend becomes statistically more significant.
Very right. Our goal here should be to understand, not try to advocate for one position or another.
Luboš was probably just trying to be as simple and straight-forward as possible. In any case, the argument that taking monthly data into account would make the trend become “statistically more significant” is without merit. It is still not significantly different than zero. Using monthly data, the trend is 0.93 (in C per century), with a 95% confidence interval of -0.22 to 2.08.
Eve (14:08:45)
Maybe you are just getting older. I notice that I need more heating in my old age.
the 846 snowfall records referred to before:
http://mapcenter.hamweather.com/records/7day/us.html?c=snow