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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What’s nice about this post – both the data & methods are posted for everyone to see & verify – wouldn’t it be nice if the CRU & GISS would do the same – like real scientists doing real research would do so that it can be verified (& if decisions are made on the basis of the analysis, those decisions can be made with confidence)
This *should* be filed under things everyone knows. Sadly thanks to climate hysterics very few do know of it because it undermines the “right” policy conclusions.
Whats worse than that though is that an article such as this presenting undeniable facts in a concise and easy to follow manner isn’t likely to make a dent in the problem.
Still the effort is greatly appreciated all the same. The truth will eventually prevail.
I am far from expert in statistics, but is this really valid? By including the obvious outlier of 98 (El Nino) the SD is increased so widening the confidence intervals. While I should agree that in the long run the 98 jump is just a part of the variability, over this restricted timescale it is a major anomaly.
But then what do I know?
Says nothing about what humans might have caused. Totally meaningless imo.
I am betting on galactic cosmic rays, thank you very much.
Heh, love it. Nice one Luboš.
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.
http://www.woodfortrees.org/plot/uah/from:1979/to:2009/plot/uah/from:1979/to:2009/trend
Seems like I heard it from the AGWers that 15 years without warming would falsify the hypothesis. Of course, they would claim that the greater probability of warming is enough.
Whatever the direction, the magnitude is much lower than IPCC forecasts.
http://www.bbc.co.uk/sn/hottopics/climatechange/climate_challenge/aboutgame_2.shtml
If The Nobel Prize winners were correct, temperatures should have risen over half a degree since 1995.
Why start at 1995 instead of 1979?
Why not use monthly data?
Melly Kalikimaka and a hearty thank you to Anthony and all his merry elvises who do such a great job at this crossroads of knowledge. Thanks for bringing us such nice lumps of carbon rich reading. Wishing you a great and prosperous New Year. Keep up the good work.
Good
You are so mean to use facts to go up against emotional arguments. The polar bear extinction alone is over the top for data.
Ah yes, let’s predict the future based on past data.
Firstly you have give us some reasons to believe that your data is meaningful. Where does your satellite data comes from? What sensor does the satellite use? Have satellite readings been calibrated against earth based instruments? Does the satellite read surface temp? Tropospheric temp? Stratospheric temp? Top of the atmosphere temp? Temp at noon? Temp at midnight? Or just temp at any old time? How do you know ? How do the satellite readings change as the satellite sensors age? How many satellites are in your data? One? More? If more than one, how closely do the readings from the various satellites agree with each other?
Then we want to know the average and standard deviation of your data. How much noise (standard deviation is a measure of noise) is in your data? Is the noise level higher than any trend you might be seeing?
Looking at your code, it seems your are asking Mathematica to do a least squares straight line fit to your data. If we believe a straight line is a good approximation , then we can take to slope of the best fit straight line as a trend.
Then you have to explain why you picked 1979 as a start point. Suppose I pick 1998 as a start point? I can get any answer I like if I can pick my start year. If I pick 1998, then I can say temperature has been declining since then. You have to explain your choice of start year.
My heating fuel usage shows that there has been cooling since 1997, which is the oldest data I have. I will show fuel usage in Litres per year. I do not heat the house when it is warm therefore each year after 1997 must have been cooler. The furnace has a scheduled maintenance each Nov, the same two people live in the same house and the thermostat settings have not changed.
1997-2767.20 Litres
1998-3057.50 Litres
1999-4009.30 Litres
2000-3874.70 Litres
2001-3586.70 Litres
2002-3752.20 Litres
2003-3634.50 Litres
2004-4072.50 Litres
2005-3293.50 Litres
2006-4276.70 Litres
2007-3700 Litres
2008-4476.20 Litres
How long a period are we blamed for effecting the climate? I heard recently that CO2 is only blamed for the last 20 years… and the 1998 peak was due to an El Nino… If this is the case then surely we are only being blamed for a tenth or so of warming, of which is showing signs of returning.
If we return to temperatures of pre-blame… does that prove the build up of heat is gone? Or can they still claim that we have reduced cooling that would have occurred to a greater degree? – What happens if the heat in the climate system is not measured or has reversed in the next few years?
Get rid of the Hadly, CRU, MET, NASA, GISS, NOISE and whala….. Static normal cycle……
Whoda thunk it…?
– addition: tenth of a degree
They will probably say that this decade is the warmest ever by a significant amount, that is if you cut off the data somewhere after the 1930’s.
Also, Piers Corbyn is talking about a dangerous system developing that could be even worse than the one still rolling in the United States on Dec. 28-30.
http://www.iceagenow.com/Notably%C2%AD_dangerous_warning_for_28-30_Dec.htm
Despite Okla. City getting slammed hard, Wichita got off easy on that system, Weather Underground already has two days in a row with snow chances before New Year’s in their forecast column, we can’t dodge the worst parts of these snow storms forever.
And a scientist who shares his methods and equations…
Haven’t seen that from any of those so called scientists who scream the earth is melting…..
Hey man, don’t you know that the issue is settled? Al Gore told me so, so it must be true. The fact that he owns a piece of the largest carbon trading firm, and is actively pushing for cap and trade is not a conflict of interest, because he’s thinking of the children (and the polar bears).
I am constantly dismayed by the “use” of statistical significance and relationship correlations in the media and by the public.
Even a 90% significance is weak by statistical standards. (95% is just enough to be reasonable.)
When a coefficient of correlation (linear regression) is less than 0.9, there is barely more than a “trend” established. When they start to use log plots, almost anything starts to look like a straight line relationship.
Forget about causation. Correlation means that factors demonstrate similar effects. Not that one causes the other.
Forget about cropping and truncating the graphs or picking a range of data that only looks at a short (for the event) time-frame.
When you start to throw in “adjusted” data that mysteriously suits an agenda…
Samuel Clemens had it right. Lies, damn lies and statistics….
Which is why people who want to spin the numbers are now saying that the last decade is the warmest on record, rather than temperatures are getting hotter.
You can spin almost anything using statistics. It’s nice to see them being used properly for a change, though the title of the article is spin because it implies there’s no warming trend. The closing statement of the article isn’t that definite. It merely says that we can’t say that a warming trend is “very likely”.
I believe the issue is clouded by earlier analysis that proved there _was_ statistially significant warming for a time interval ending in 2000. Menzie Chin, an economist who publishes on the site Econbrowser replicated that math. He’s something of a Democratic partisan, but surely has command of the math.
Like all of these experiments, the results depend on what data you choose to work with.
And what do things look like without the 1998 spike?
How much of the heating of the Pacific Ocean is due to underwater volcanic activity? After all Al Gore informed us it is millions of degrees just a few kilometers down so volcanic activity must be a potentially significant source of heat. The global warming theories are concerned with how CO2, with the positive feedback mechanisms, traps solar energy. Shouldn’t heating from below the surface then be discounted somehow when figuring warming based on atmosphere-based reasons? Thus if El Nino is tied to such from-the-Earth heating, shouldn’t 1998, involving a strong El Nino event, be discounted when calculating the trends?
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.