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.
From the looks of what I found over at GreenieWatch, the stooges at CRU make Moe, Larry and Curly look like rocket scientists.
http://69.84.25.250/blogger/post/ClimateGate-Data-Series-Part-5-A-break-down-of-large-data-file-for-manipulating-global-temperature-trends-from-2006-2009.aspx
Anyway, if the data’s all wrong to begin with, what’s the point of arguing over what it means, at least until we can get a correct data set, that is?
Jim (20:07:59) : “Those issue were preemptively dealt with -”
I assume you are referring to the statement: “The furnace has a scheduled maintenance each Nov, the same two people live in the same house and the thermostat settings have not changed.”
The annual maintenance would only prove the furnace was running within certain parameters not necessarily at the exact same efficiency. Likewise with the thermometer. The point I was making was that a mix of many causes could be responsible for increased fuel usage, not just cooler weather. So the science wouldn’t be settled in that case just as it isn’t settled with climate change.
I read through this a couple of times, and I found myself wondering why you chose 1995. I think that it might be because that is when the oscillation makes its home, so to speak, above the line representing the mean, but I am not sure. Why 95?
Also, enjoyed the piece on Motl’s blog about the Wunderkind. If anyone hasn’t been, check it out.
http://motls.blogspot.com/
Since the current warming has taken us no farther than the peak of the last warming, 60 to 70 years ago, looking at the actual temperature data, rather than the value added data, I don’t see what all the fuss is about.
Curiousgeorge (16:52:20) : “Anthony, as a statistician you should know better. With enough data points, anything can be “statistically significant”.”
not really
kdkd – thanks for the paper!
One extract from the introduction:
“Linear trends are the simplest way to assess climate change, and are
used in the IPCC reports and most of the trend studies cited in the introduction, among many others. Linear trends also have the advantage that confidence intervals are well defined, which aids in interpretation. Calculating such linear trends overcomes issues due to subjective interpretation of noisy data and the arbitrariness of various methods of smoothing the data, especially at the end points”
I’m sure there are lots of people smarter than me that know much more about climate science and statistics who think this approach is valid, but this paper tells me the same as all the other places I have seen these kind of analyses.
“It’s customary”
Maybe a different question to ask would be “Is climate chaotic?”
Or, “If climate is chaotic can we learn anything (useful) from linear trends and confidence intervals?”
Thanks again for the link to the paper.
cohenite (20:25:57) :
Lubos has picked 1995 and most critics are referring to 1998 being an outlier; that’s ironic because if 1998 is an outlier than by including it Lubos is actually tilting the scales towards a warming trend.
No, since 1998 occurs before the halfway point it tilts away from a warming trend. Whether to include/exclude 1998 comes down to cherry picking.
Richard M (18:29:19) :
“…Even years are probably too fine (a better unit might be PDO full cycles).”
Icarus (19:04:39) :
“Actually 30 years is what is ‘put forth’ by climate scientists, and with good reason…”
I strongly agree with Richards point, that everything below a full 60-70 years ocean cycle is misleading.
On the other side, if realclimate “scientists” chose to put forth 30 years, i.e. exactly the warming half of a full natural cycle, their “good reasons” appear to be “good” in an odd and now familiar way.
The solution to this dilemma and the loss of trust in CRU, NOAA and GISS temperature records should be to correct UAH values for ocean current cycles just as they are corrected sometime for El Nino/La Ninas and volcanoes.
An ocean cycle correction should remove most if not all of the warming since 1979, and with respect to the warming due to land use changes, the question arises, if global cooling did not already start in the 1930s or 1940s.
Tenuc (17:57:39) :
That has always puzzled me a bit too. Why not just eliminate even carving out a mean for the data? Why not just throw it all against the wall and see what sticks? If it sticks, it is done! Seriously, though, why not just analyze the entire temperature set, every single point? Then you don’t have to deal with the logistical headaches of transporting a temperature to the next closest station. The way I understand radiative forcing, and anyone feel free to correct me if I am wrong, the temperatures should be Higher highs and higher lows, so the entire dataset should exhibit an upward trend, right? So, I say make pasta. Throw it against the wall and see what sticks.
scienceofdoom:
All non-linear regressions do is use an appropriate mathematical function to transform a non-straight line into a straight line. In the case of the paper I posted, I think (from memory) they used a sinusoidal function to straighten the line up. Other than that the techniques are the same. And yes, the climate system is chaotic, but this just means that there’s a lot of variability that we can’t properly account for among the significant amount of variability that we can account for.
Michael Jankowski:
[ So which temperature data set shall we use for the 200 year period? ]
Well to be honest the best approach is to use as many sources as possible into an aggregate data set. Relying on a single data source is generally to be avoided.
[ And since CO2 has been increasing and is supposed to account for “80% of the observed warming in the late 20th century/early 21st century,” then I assume it should be easiest to spot even in a subset of, say, the most recent 15 years? ]
No. This is because although the magnitude of the decadal trend is about the same as the year on year variability, so the long term trend doesn’t really become apparent until the long term trend exceeds the short term variability by quite a lot. So the technique I used to ascribe the proportion of co2 associated with the temperature anomaly reading only works well over time periods of at least 30-50 years.
As a few others have mentioned, you do yourself no favours by taking yearly data when monthly are available. When the same analysis is done for the larger (monthly) data set sd´s fall and t-values (significance) increase.
Having said that, I tend to take an engineering apprach to graphs like this before I apply stats. Step back, look at the graph, and ask yourself, what does the data appear to tell you?
IMHO I see data with longish fluctuations of 2-3 years with enough variation to from year to year that forcing a linear trend on the data would be folly. It tells you nothing of real significance.
As humans we are very adept at pattern recognition as we devote a major portion of the brain to it. In that sense everybody is equally capable of looking at the first graph and “seeing” patterns if there are any.
To my mind there is very little to see there other than the regular oscillations and one or two stand outs. Firstly El Nino of 1998 stands out because it is a larger oscillation than the rest, and secondly the period from 2001 to 2007 looks a little odd because of the lack of variation compared to the previous couple of decades.
However, the last two paragraphs are based on focusing on the 13-month moving average. Shortening the term of the average to 5 months or so would introduce more amplitude in the oscillations and change the impressions somewhat.
I believe Aesop was attributed to saying something along the lines of:
“We can easily present things as we wish them to be.”
Statistics weren´t even around in his day… smart man that.
kdkd (20:12:57) :
(e.g. in the early 20th century, co2 levels accounted for about 25% of observed warming whereas in the late 20th century/early 21st century, co2 accounts for ~ 80% of observed warming – now correlation is not causation, but it is rather suggestive given the cohesive body of scientific theory associated with this information).
How much does this scientific body of literature say the temperature will 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?
Hi Leif … good to see you around 🙂
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.
That really seems a sleight of hand, though. If the yearly anomaly is not a statistic composed of the monthly anomalies, what is it? So aren’t the monthly anomalies contained in the yearly anomalies? Hell, we could break it down to daily anomalies if you would like, but aren’t you really just adding data points for the sake of adding data points? The more I think about the anomaly as a means of measurement, the more I dislike it.
kdkd (20:12:57) :
in the late 20th century/early 21st century, co2 accounts for ~ 80% of observed warming
Without reference to studies please don’t make statements like this.
We’ve all been in the circles these type of statements make before.
So references please?
The sun’s variance is only .1% our of which we would receive only a quarter portion of that.
Isn’t that at the surface of the Earth? What about UV variation at the top of the atmosphere which I believe is way more than the TSI variation. And the UV is mostly absorbed at the top of the atmosphere.
Last I heard the effect of UV in the models is parameterized. i.e. based on assumptions rather than explicit physics.
kdkd (20:12:57) :
the current warming which appears to be caused by the burning of fossil fuels.
Supply all the references for this statement. Otherwise please don’t play this game here.
‘Appears’ is a word that doesn’t count in science.
But it does count in sophistry and propaganda.
kdkd (20:12:57) :
the current warming which appears to be caused by the burning of fossil fuels.
——————————————–
Stamp prices have gone up at the same time as temperatures have gone up. So it appears stamp prices control temperature.
Leif: 2 points; as is indicated in the linked paper, 199[7] is NOT a cherry pick because it is supported by prominent climate events and a likely PDO phase shift; other break papers by such authors as Tsonis and Swanson;
https://pantherfile.uwm.edu/kswanson/www/publications/2008GL037022_all.pdf
argue for a break around this time, although S&T select 2002 as the regime shift date; other phase change or step papers are;
http://www.arl.noaa.gov/documents/JournalPDFs/Seidel&Lanzante.JGR2004.pdf
http://www-eaps.mit.edu/faculty/lindzen/203_2001GL014074.pdf
Secondly, in respect of 1998 adding to a warming trend, I guess I was thinking of a running mean.
David Starr, instead of taking the time to type out all those rhetorical questions, you could have just looked at the website for yourself:
http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps
If I were less cordial, I could have referred you here
his is because although the magnitude of the decadal trend is about the same as the year on year variability, so the long term trend doesn’t really become apparent until the long term trend exceeds the short term variability by quite a lot.
Well then. Since the daily variation is on average in the 10 deg. C (or more) range…..
Or take the mid latitude Summer vs Winter variation of 20 deg C (or more)….
We can’t know how much “observed warming” there is because the record is so bad. The statement of 80% of “observed warming” might turn out to be very little at all.
How much warming has there been since the 1930’s? What about temperatures of the MWP? What is responsible for the cooling since then? Why are todays temperatures cooler than the MWP in spite of more CO2? Why did temperature rise from 1830 to 1930 outpace later rise when CO2 was not rising nearly as fast?
Any linkage of climate warming and CO2 is pretty much a guess and nothing more.
@ur momisugly Jeff L (13:01:52) :
GISTEMP:
http://data.giss.nasa.gov/gistemp/sources/
CRU:
http://www.metoffice.gov.uk/climatechange/science/monitoring/subsets.html
It means that the probability that the underlying slope is negative equals 1/2 of the rest, i.e. a substantial 14%.
So those claiming “global cooling” are betting on the 14%.
Good to know.
I appreciate several things on the above comments–First, Eve’s list of home fuel consumption by year and their indication of an increasing trend from 1997 to 2008. Of course there can be a number of things that might cause this but most of the objections are minor compared to the actual heat balance indicated. (I mean really, how many of you have seen the windows of your house fall apart or the seal on the doors fall off within 10 years, or the insulation get eaten up by termites, or so on and so forth. Certainly these should be considered but in the houses I’ve lived in, they are very minor aspects.)
So I entered the data into Excel and did a simple plot and eye-balled it for trend line (no need going any further than that). It looked like some of the temperature graphs for the same time period–imagine that!
Where I do take great issue with these “climate scientists” was mentioned in a post above with this sentence:
“Then you don’t have to deal with the logistical headaches of transporting a temperature to the next closest station.”
My expertise happens to be in 3-dimensional statistics, something called kriging, an invention of mining. In that science, the position of a data point has meaning as well as the value of the data point. Never, EVER could I ever justify moving a data point from one place to another regardless of any adjustment factors–what’s required is getting that data point from sampling. Simply adjusting a data point so you can put it someplace else is absurd beyond imagination. It’s beyond a logistical headache–it’s simply a NO-NO!
Of course, where I’ve used three-dimensional statistics before is in reserve estimations and models of mineral deposits–particularly gold and silver. If part of the model has unacceptable estimation variances (based on what’s considered proven, probably, and possible), one simply drills and gets the data. And because nature is unpredictable, there is no justification under the sun for simply inventing data points (which is what moving a data point from one place to another actually is– FALSIFICATION OF DATA)
Admittedly, my example of obtaining data can’t be applied to climate science since temperatures are obviously time related. However, temperatures are also position related, so again, shifting data from one location to another simply boggles my mind. I am beginning to believe that “climate scientist” is another word for “charlatan” or “witch doctor” or “lazy programmer” or “political activist” and a dozen other unflattering terms. The deeper I dig into what these “climate scientists” do, the more disillusioned I become. Much of their methodology wouldn’t be acceptable where I’ve worked in the past, and certainly wouldn’t warrant investing significant capital based on their results.
I believe there is a very good reason they don’t want to show anybody what they do–we’d be having a pitch fork party with lots of tar and feathers. And until they come clean, show us all their data and methodology, I’m afraid we can’t make any significant conclusions about earth’s climate. Garbage in, garbage out.
I think our efforts should concentrate on pressing FOIA requests to successful conclusion, both in the US and in the UK. In the meantime, we can quell all arguments AGWers might make with the pointed fact that they are hiding the science.
Show us the data, discussions and methodologies. All of it!
Rob Vermeulen (14:22:28) :
That really seems a sleight of hand, though. If the yearly anomaly is not a statistic composed of the monthly anomalies, what is it? So aren’t the monthly anomalies contained in the yearly anomalies? Hell, we could break it down to daily anomalies if you would like, but aren’t you really just adding data points for the sake of adding data points? The more I think about the anomaly as a means of measurement, the more I dislike it.
———————————
Yes and no. The yearly averages are certainly comprised of the monthly averages but you lose 11 pieces of information by using only the annual data.
For example, if I gave you the annual averages only and asked you to back out the data for the monthly temperature anomolies you would look at me as if I had two heads. The information simply isn´t there anymore.
For exactly this reason any statistic, like a linear trend, derived from annual averages over a time period is less significant than a trend calculated from monthly data over the same period because the annual trend took less pieces of information into account.
Statisticians will talk of degrees of freedom and the like, but I hope the above explains it well enough.
Another way of thinking about it would be like averaging colours across pixels in a computer image. Eventually, if enough pixels are averaged, the picture is no longer recognisable. Eventually you would have a single brown (or whatever colour) pixel… no way you could back out the image from that single average pixel.
Statistics is a black art really… we try to separate out the noise to find a signal. The problem is that it is very easy to “perceive” things that are not there. Perhaps that is the downside to the human pattern recognition ability – we find it very easy to see patterns in random clusters. Think of spotting familiar shapes in clouds, for instance. The cloud certainly did not deliberately align to make that specific shape… you merely imagined it to be there.
How one looks at data depends on what one is looking for. It is always a balanncing act between the fine detail (and increased noise) and the more general holistic picture. It´s a question of whether we are interested in the wood or the trees.
Time to go ski on some of that global warming >.>
… delete if replicated