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Source of fishy odor confirmed: Rahmstorf did change smoothing.

29 June, 2009 (10:09) | Data Comparisons Written by: lucia

Those following the fishtale of m=11 smoothing to test the TAR projection will be interested to learn that Stefan Rahmstorf confirms what we, in the more “excitable” part of the blogosphere, suspected: He has abandoned m=11 year smoothing to test observations against models. He now uses m=15 years. JeanS shows the difference in trend projections back when Rahmstorf et al was published in 2007 and now, using both m=11 years and m-15 years:

Figure 1: Comparison of change due to smoothing.

Figure 1: Comparison of change due to smoothing.

A little history

Back in 2007, Rahmstorf and 6 co-authors published a paper in Science in which they smoothed temperature data using m =11 years, and told the world:

The global mean surface temperature increase (land and ocean combined) in both the NASA GISS data set and the Hadley Centre/Climatic Research Unit data set is 0.33°C for the 16 years since 1990, which is in the upper part of the range projected by the IPCC. Given the relatively short 16-year time period considered, it will be difficult to establish the reasons for this relatively rapid warming, although there are only a few likely possibilities. The first candidate reason is intrinsic variability within the climate system. A second candidate is climate forcings other than CO2: Although the concentration of other greenhouse gases has risen more slowly than assumed in the IPCC scenarios, an aerosol cooling smaller than expected is a possible cause of the extra warming. A third candidate is an underestimation of the climate sensitivity to CO2 (i.e., model error).”

In comments here today, JeanS suggested the obvious fourth candidate (which did not occur to Rahmstorf at the time), “Of course, the fourth candidate might have been simply the “trend” calculation method they used.”

Flash forward to 2009

Ramstorf published an updated figure which indicated he added data, but still used m=11. Jean S posted a question asking whether m=11 was correct, if he had changed to m=14.

Stefan now says:

[Response: Almost correct: we chose M=15. In hindsight, the averaging period of 11 years that we used in the 2007 Science paper was too short to determine a robust climate trend. The 2-sigma error of an 11-year trend is about +/- 0.2 ºC, i.e. as large as the trend itself. Therefore, an 11-year trend is still strongly affected by interannual variability (i.e. weather). You can tell from the fact that adding just one cool year - 2008 - significantly changes the trend line, even though 2008 is entirely within the normal range of natural variability around the trend line and thus should not affect any statistically robust trend estimate. -stefan]

Hindsight? Hindsight?!

The discovery that Stefan’s method was flawed may have occurred to Stefan Rahmstorf, his many illustrius coauthors and peer reviewers for Science in hindsight, but “The Blackboard” readers will recall that the method Rahmstorf used was criticized in the blogosphere immediately after publication. The main reason: Outside the climate community, it is widely known that testing theories by smoothing data and eyeballing the curve is an abysmally poor method to test any scientific theory or model.

That is: the method Rahmstorf used has been known to be a very poor method for testing projections.

Period.

This has been known for eons. For this reason, few would bother to submit a peer reviewed paper on the subject because the discovery of how bad the method is not new. (Peer reviewed articles are supposed to present something new information. So, the the paper would, justifiably be rejected on the basis of simply rehashing widely known information.)

It is well also known that “Rahmstorf” method is particularly bad near endpoints, and this is true for any and all choices of smoothing, including both m=11 years and Stefan’s current choice of m=15 years. For those wondering which data are near endpoints: when using Rahmstorf’s method, the “end” region is the region within m/2 years of the final data point. So, using m=15 years, the temperature in the region within 7 1/2 years of the end point is sensitive to the addition of a new data point. So, if “robust” means we will conclude the same thing next year we do this year, using m=15, “robust” comparison of any sort can only be made between projections and smoothed data prior to 2001, which is the year the projections were made. (In 2007, Rahmstorf used m=11, but data end in 2006. That meant that the “robust” portion of his comparison as, once again, periods before 2001!)

So, the short criticism of Rahmstorf’s method: Stefan used a bad method (smoothing) and then applied it in the region where it is especially bad. He continues to use the method, evidently believing he can “fix things up” by changing m=11 to m=15. He “discovered” this problem when new data trickled in and no longer gave the answer some believe Stefan is inclined to believe to correspond to “truth”.

As a method to test projections, the method Rahmstorf selected remains a foolish choice.

As there is no existing statistical principle dictating any correct or best choice of “m”, there will be some who suspect Rahmstorf’s choices have been unintentionally influenced is by confirmation bias. It is plausible to suspect his choice of “m=11″ in 2007 was unintentionally influenced by his tendency to believe the higher trends associated with the model projections in the AR4 are more likely correct than those in the TAR. His improved “hindsight” dictating his current choice of m=14 might be similarly influenced by a belief the current flat trend cannot be correct, combined with a wish not to admit that the his of “slide and eyeball” methodology was obviously foolish in 2007 . Rahmstorf’s choice of method remains foolish to this day.

To show that the problems with the method were not discovered in “hindsight”, it’s worth nothing that David Stockwell , Ian Castles who was particularly vocal in my comments (and I believe he wrote letters to the Australian government) and I all criticized the method for various different flaws.

Some readers will be interested to read the David Stockwell not only commented back in 2008, but took the step of writing a formal article showing how the results and conclusions of in Rahmstorfs 2007 paper changed with the addition of new data. David has now published a note in Energy and Environment (ee-20-4_7-stockwell2) . David’s note discusses the peer reviewed article appear in Science IPCC by lead authors Rahmstorf, S., Cazenave A., Church J.A., Hansen J.E., Keeling R.F., Parker D.E., and R.C.J. Somerville. David’s abstract explains:

The non-linear trend in Rahmstorf et al. [2007] is updated with recent global temperature data. The evidence does not support the basis for their claim that the sensitivity of the climate system has been underestimated.

 

Mind you: one might suggest that, to some extent the method Rahmstorf selected and conclusions are now shown to be wrong only because the temperature in 2008 fell. He’d be looking ok if weather noise had one a different way and temperature had remained level or risen. But, in that case, his method would happen to have given the ‘correct’ answer by accident. That is the way with statistical analysis of stochastic systems. Sometimes, results based on bad methodologies turn out to be right by accident. In fact, because all statistical tests reject hypotheses only at a particular confidence level sometimes, results obtained using correct methods are shown to be outliers later. (That is: things that happen only 5% of the time when a hypothesis is true, will happen 5% of the time!)

But the fact is, Rahmstorf method of testing models was obviously flawed back in 2007 when first published.

Consequently, it was little surprise the results did not hold up when data from 2008 were added to the “analysis”. Not surprisingly, to prevent his original method from showing a flattening of the temperature trends, Rahmstorf needed to “tweak” his arbitrarily chosen parameter of m=11 when later data arrived. Even tweaking, the Rahmstorf method still overturns his main conclusion in Rahmstorf 2007: with both m=11 and m=14, the observed temperature anomalies since 1990 do not fall in the upper range of the TAR projections.

So, using Rahmstorf method (which in my opinion is a silly error prone method, the observed temperature anomalies fall pretty well in the center of the TAR projections.

What of the more recent AR4 which projects more warming than the TAR? A similar analysis applied to the AR4 would indicate that temperature anomalies fall below the multi-model mean trend in the AR4. However, making conclusions based using this method based on the current comparison to the AR4 would be just as foolish as Stefan making conclusion based on the results he showed in his 2007 paper.

Whatever Stefan may currently believe, his premature conclusions in 2007 were not based on using m=11 rather than m=15. Stefan was led astray by trying to “analyze” data using smoothing, which is a very bad method of testing hypotheses. The fact that the change in smoothing was inadvertently not disclosed to readers, and was also not explained in “The (Copenhagen) Synthesis Report” is unsettling.

Readers who are now aware of the change will anticipate that the trend at the end point will continue to oscillate. Since 2009 will likely be warmer than 2008 and we are due for an El Nino, I don’t anticipate Stefan discovering the value of “m” needs to increase to 17 next year or even the year after. But who knows what will happen when the next La Nina hits!

Written by lucia.

Comments

Jorge (Comment#15444)

Fishy odour!

It is now very clear that it was a dead fish, a rotten fish, in fact, a putrid fish. A fish so tainted that it was unfit for human consumption.

I am sure the Hadley defence will be used again. It would have been misleading to show the trend had turned down just because the temperature in 2008 was unusually cool.

I cannot begin to voice my disgust at this sort of behavior. This is not science but looks much more like the slanted output of a shabby propaganda factory.

Chip Knappenberger (Comment#15445)

Well put, Lucia!

lucia (Comment#15446)

Jorge–
At least Hadleys solution is to just de-emphasize the trend in the “not-robust” region by dashing the line

This helps people understand that smoothed ‘data’ in the dashed region are going to change when the future is actually observed.

Andrew_FL (Comment#15447)

Scandalous! Hehe, well, goes to show that smoothing is a dangerous game.

Jorge (Comment#15449)

I give Hadley some credit for that. Naturally, they did not show dashed lines when the trends were still going up. In fact, the original Hadley mistake was even more stupid than you can imagine because they treated the first few months of a year as if it would be true for the rest of the year. It was this transient value that then got repeated 10 times in the 21 point binomial weighting.

There really does not seem to be a good answer to the treatment of the endpoints as it is a battle between timely information and accurate information. This is apart from choosing the frequency cut-off point of your filter. It seems that if weather turns out to have lower frequencies than expected it is quite ok to adjust the filter in conformance with the new found idea that climate has to be measured over even longer periods.

One really is left with the suspicion that a temperature signal can only be climate if the signal is going up. Otherwise it is weather.

lucia (Comment#15450)

Jorge–

There isn’t any good answer to best treatment of endpoints. But, if “m” is going to be tweaked, ideally, the specific criterion for selecting any value should be documented when that criterion is first applied. Then, later, if m is changed, we can see whether the new value m arises from application of the criterion using new data or whether the new value arises from reasonsing that goes like this:

“After looking at the answer I got using m=11, my gut said, ‘Urp! Let’s try another value! After looking at a range of number, my gut felt least queezy when I saw the curves for m=14. Then I thought about it, and came up with an idea that explains why m=14 is actually better than m=11. ‘”

Right now, it looks like the “criterion” is the rumblings in stefan’s gut.

steven mosher (Comment#15452)

Damn Girlfriend, you kick the boys and make them cry. Keep up the good work. and don’t suffer fools.

Scooter (Comment#15453)

the method Rahmstorf has been known

You might want to rephrase that sentence. I don’t think Rahmstorf is a method. You use several better phrasings elsewhere, including “Rahmstorf’s method”.

Andrew_FL (Comment#15454)

“Right now, it looks like the “criterion” is the rumblings in stefan’s gut.”

Yeah I once ate some data that didn’t agree with me. I too got indigestion! Hehe…

lucia (Comment#15455)

Thanks scooter.

Les Johnson (Comment#15456)

Lucia: your

Hindsight?!
The discovery that Stefan’s method was flawed may have occurred to Stefan…
…it is widely known that testing theories by smoothing data and eyeballing the curve is an abysmally poor method to test any scientific theory or model.
Consequently, it was little surprise the results did not hold up when data from 2008 were added to the “analysis”. Not surprisingly, to prevent his original method from showing a flattening of the temperature trends, Rahmstorf needed to “tweak” his arbitrarily chosen parameter of m=11 when later data arrived. Even tweaking, the Rahmstorf method still overturns his main conclusion in Rahmstorf 2007: with both m=11 and m=14, the observed temperature anomalies since 1990 do not fall in the upper range of the TAR projections.
That is: the method Rahmstorf used has been known to be a very poor method for testing projections.
Rahmstorf’s choice of method remains foolish to this day.
But the fact is, Rahmstorf method of testing models was obviously flawed back in 2007 when first published.
…just as foolish as Stefan making conclusion based on the results he showed in his 2007 paper.
…his premature conclusions in 2007 were not based on using m=11 rather than m=15. Stefan was led astray by trying to “analyze” data using smoothing, which is a very bad method of testing hypotheses.

Don’t hold back, Lucia, and don’t tip toe around. What do you really think of Rahmstorf 2007?

lol

MikeC (Comment#15458)

Dang girlie… I’m gone for a month and get back to an article like this. It was deeeeefinitely worth the read, even tho I had to squint to read the letters on the left where they are in the blue frame. By the way, this kinda scientific behavior gives old, been layin round the dock too long, stinky fish a bad name. See ya when I get to the next wifi hot spot

clivere (Comment#15463)

Lucia – an entertaining analysis.

Perhaps this is the one that will get Anthony to recognise your worth!

BTW – agree with MikeC the annoying grey bar on the left is very very annoying when trying to read using IE unless you compress the favourites centre

lucia (Comment#15464)

Hmmm.. Now I have to go back to that site that shows the blog in all browser to see what you are seeing. then I can fix it!

lucia (Comment#15465)

I’m running a test at http://browsershots.org/http:/.....m/musings/ That should let me see what people are seeing on different browsers. (I thought I had the browser issue licked last November… but evidently not)

clivere (Comment#15466)

The problem is quite recent. Particularly bad in lower resolutions when the first 2 or 3 characters on each line are obscured.

lucia (Comment#15467)

clivere–
I can adjust the css to make shift the text. It’s annoying that IE keeps changing their mind about how to implement css instructions, and the various browser manufacturer don’t all agree. (I am not going to write style sheets for each and every browser type, so the alternative is mostly to wast a little screen space.)

lucia (Comment#15468)

Browsershot indicates the blog looks bad on lots of windows machines. I’ll have to fix that tomorrow. Now that I now just HOW it looks I think I can do it.

Niche Modeling » Recent Climate Observations: Disagreement With Projections (Pingback#15469)

[...] Update: Lucia does a fine job of explaining the history and issues in Source of fishy odor confirmed: Rahmstorf did change smoothing. [...]

stan (Comment#15478)

That Rahmstorf screwed up royally is unfortunate. That the world of climate scientists/alarmists did not see fit to take issue with his foolishness speaks volumes about the quality of science that informs public policy.

Perhaps the problem is one of competence. Perhaps the problem is one of corruption. [my vote is both] Either way, we shouldn’t allow their problems to be the cause of our problems.

tetris (Comment#15479)

Stan,
Maybe it is a matter of competence: as fish rot they increasingly smooth out and become harder to handle. Then again it may be a matter of corruption: “fish rot from the head down”.

cal browser (Comment#15480)

Nice job. You or Jean S should email one or more of the authors of the synthesis informing them of the error. Listed as Chair of the authors (whatever that means) is Professor Katherine Richardson (Chair), Vice Dean of the Faculty of Science, University of Copenhagen. I would send the email with a link to your original post and a simple statement that the m=11 is should be corrected to m=15 per the rc comment of Rahmstorf. They are, I think, obligated to fix it via either an erratum or revised report and should reference you as the source of the correction. Keep up the pressure by posting your email here. Clearly Rahmstorf didn’t tell them what he did or he told them and they thought they could get away with the error. They are pretty pathetic for either not noticing or going along with the wrong info. The fact that they compare to TAR and not the more recent AR4 is rather amazing, given that this was supposed to include the most up-to-date information. When the more recent predictions yield worse comparisons (than obtained using TAR) and they still use TAR it makes them look, frankly, not serious (at best). Sadly, most scientists just aren’t paying enough attention to any of this.

Nick Stokes (Comment#15482)

Lucia,
To be fair, I think the main reason for the declining slope is not the change in smoothing interval, but the fact that the 2009 plot includes 2008/9 data. These were cool years, and would have shifted the slope down even if the smoothing interval had not changed. Because of the smoothing, the curve from about 2002 onwards would be affected.

Charlie (Comment#15485)

Nick, there is a nicely done GIF that shows the effect of adding 2007 and 2008 data to the plot,with both M=11 and M=15 smoothing over at The Blackboard. http://rankexploits.com/musing.....smoothing/

Stefen did respond to my first ever comment on Real Climate, with a response that sounds like he was unaware of the error in the Figure 3 caption, but a second comment by me over at Real Climate seems to be stuck in the moderation queue:

“Charlie Says: Your comment is awaiting moderation.
28 June 2009 at 7:01 PM
Inline comment to #363: “Not sure why a small technical error in the caption would give ammunition to anyone except conspiracy theorists: ”
If you look at the URLs below, it is obvious that changing the smoothing period and end conditions radically changes the trend line of Figure 3 in the Copenhagen report.
See http://landshape.org/enm/anoth.....#more-2459 and
http://rankexploits.com/musing.....is-report/
The Copenhagen report was intended to show the affect of more recent data and studies. In keeping with that philosophy it would perhaps been better to leave the smoothing at the same 11 year setting that was chosen for the original report.
The only apparent advantage of changing the data smoothing is that it causes the trendline to continue without the more recent data having any significant effect on the plot. See the above URLs to see the changes.”

Nick Stokes (Comment#15486)

Charlie,
Yes, in fact it’s the same as the one on this post. I missed that you can see the effects of both the extra data and the shift from m=11 to m=15, although the motion is confusing. If you focus on, say, the blue curves, their common motion, which predominates, is the effect of the 2007-8 data; the difference in their motion is the effect of the change in smoothing length.

These plots always have issues with the end condition, due to the dilemma which Jorge noted above. The apparent end slope depends on guesses you make about the next m/2 years. Rahmstorf uses MRC, which takes the most recent reading and projects with an estimated slope. It’s as good as any, but has the fault that the most recent value is replicated m/2 times in the data – ie it has an artificially amplified effect. So if you finish on a cold month or year, the graph goes way down, as we see here. Increasing m to 15 increases the amplification, and this jiggling gif reflects exactly that. Most other guessing systems do the same.

lucia (Comment#15487)

Nick-
Of course the reason for the decline in slope is because the temperature fell instead of rising.

This notion is captured in this bit above

Mind you: one might suggest that, to some extent the method Rahmstorf selected and conclusions are now shown to be wrong only because the temperature in 2008 fell. He’d be looking ok if weather noise had one a different way and temperature had remained level or risen. But, in that case, his method would happen to have given the ‘correct’ answer by accident.

If the temperatures had not fallen, then by a happy (for Rahmstorf) accident, the slope would not bend over at the end. Diagnosing anything withing N/2 of the endpoints using the method he selected is still bad because the uncertainty in endpoints is always enormous. Still, if there was very little “weather noise”, things would have worked out for him. That would have been luck.

Larry T (Comment#15488)

We will have 2 more years of colder than normal data by 2011. Will he will change m = 15 or 17 so that he again removes the effect of the end points?

Charlie (Comment#15489)

My perspective on this epside is that it doesn’t really tell us much about the underlying science or facts, but it does say a lot about the parties involved.

It makes one wonder if Rahmstorf’s primary commitment is to science and facts, and whether his preference for a certain outcome is affecting his “professional” judgment.

I recall reading about a famous incident where several researchers were able to repeat and confirm an experiment, but later it was shown that the true answer was quite different. What had happened is that the experiment was difficult and prone to lots of subtle errors. Each experimenter kept finding and removing errors when their results differed from the expected results, but stopped looking for problems once they got the “proper” result.

Does anyone remember such an example in the history of science? The incident I vaguely remember reading about was not a recent event, but more likely something in the 1800’s or early 1900’s.

lucia (Comment#15491)

LarryT

We will have 2 more years of colder than normal data by 2011. Will he will change m = 15 or 17 so that he again removes the effect of the end points?

Who knows? Maybe, at some point, he or the broader climate science community will realize the notion of using smoothing to test models is unwise (aka “foolish.)

Jonathan (Comment#15492)

Lucia, having spent an hour or so reading about smoothing with a minimum roughness criterion at the end points I’m getting a little confused about what is being described here.

My understanding of minimum roughness is that it minimises the second derivative at the end, and that it does this by reflecting earlier years around the endpoint, as described in Mannomatic Smoothing and Pinned End-points. For most plausible choices of filter function this has the effect of forcing the line to pass through the endpoint, whatever the filter length, and so the m=11 and m=15 lines should coincide at the end. Which they don’t.

Nick Stokes (Comment#15486) then describes “MRC”, but appears to describe what I would call minimum slope.

So, are these graphs minimum roughness, or minimum slope, or something else entirely? Or am I just horribly confused?

lucia (Comment#15493)

Charlie

Not sure why a small technical error in the caption would give ammunition to anyone except conspiracy theorists:

I don’t think there is any conspiracy. I think Stefan is subject to confirmation bias, as are all people.

That said, I think Stefan is either being disingenuous or he is entirely incapable of seeing how this “type” looks to outsiders.

He characterizes his blunder as nothing more than a technical error in the caption. But there are other issue being discussed elsewhere, which anyone equipped with more than a brain stem can grasp.

First, the methodology itself was changed and the motivation for the change appears to be based on the actual data that arrived after the Rahmstorf’s 200y report was published. This opportunistic changewould have raised eyebrows even if the caption had correctly indicated “11 years”.

Second: the body of the report did not mention the method was changed and provided no justification for the change. Had the reported mentioned the change and explained why, a reviewer would have noticed the typo saying ‘11 years’ instead of ‘15 years’ in the caption and that would have been corrected.

But, as it stands, there was nothing in the text to indicate the Rahmstorf had changed the method from the cited paper. Stefan and the other authors of the Copenhagen report know there are people who think they are spinning like tops. (In fact, they think there is a conspiracy devoted to causing people to believe this.)

Since he know there are people who suspect a group of climate scientists sometimes does not act in good faith, why does he make disingenuous claims that he doesn’t know why “the typo” results in people thinking there is a conspiracy theory?

If he and other climate scientists don’t want to feed conspiracy theories, they should be pro-active and actively disclose when he (or they) changed methods for diagnosing whether models are on track or off track.

lucia (Comment#15494)

Jonathan–
You are right; Nick is wrong.

Jean S (Comment#15495)

Charlie and others, I have an additional story to add for consideration.

When the Science-paper appeared and Lucia and others criticized it, a problem they faced was that Rahmstorf was not giving any code or data for replication. An answer David Stockwell essentially got for his critique was that he was doing replication somehow “wrong”. In other words, that there were no problems with the paper itself, but in people’s replication.

Last autumn, when I decided to take a closer look, I contacted Rahmstorf through two different contacts (another one being a scientist and another one a journalist). Neither of them received neither code nor any data! Rahmstorf essentially claimed that he did not own a copyright, so he could not pass either the code or data!!! I was then lucky enough to obtain, a way I do not want to disclose, the smoothing routines used by Rahmstorf. Using those it was easy to replicate the results from the Science paper. I then replicated and updated the result using the preliminary 2008 data for a Finnish TV-documentary, the graph is here:
http://ohjelmat.yle.fi/files/o.....mstorf.jpg
The journalist behind the documentary sent my graph to Rahmstorf for a comment before the program was aired, but he never replied. So I kind of concluded that my replication was correct as I suppose he would have objected if there was a mistake. So we know for sure Rahmstorf knew already last autumn, at latest, what happens to his graph when it is updated to include 2008 data. I also made new graphs for David Stockwell (for his upcoming E&E paper) when the final values of last year were available.

Anyhow, this is how I knew how the updated graph should look like, and was able to spot the change in the Synthesis Report when Lucia posted the figure. I’m also convinced that, if I had not been able to do exact replication, Rahmstorf would never have admitted the change.

I’ve put quite a few hours to this thing, and as everyone understands, it is only because Rahmstorf has consistently refused to give away the code. In my opinion, as a scientist myself, that’s the main “misconduct” from Rahmstorf’s part as a scientist in this matter: one tries actively prevent others from replicating one’s results. That is something whose odor made me to investigate this matter more closely in the first place. On the other hand, I like doing this kind of “puzzles”, and the only additional negative experience in this replication matter is the behaviour of people like “Deep Climate” who, without properly investigating matter, are quick to jump to conclusions that my graphs are incorrect and hinting what ever motives for me doing this (see Tamino’s place).

Jean S (Comment#15496)

Jonathan, it’s minimum roughness. Here’s the Matlab script how it’s done in the original code:

idx=(1:mp)’;
pleft=polyfit(idx,x(idx),1);
epleft=sqrt(max(sE_x(idx))^2+std(detrend(x(idx)))^2);

idx=(n-mp+(1:mp)’);
pright=polyfit(idx,x(idx),1);
epright=sqrt(max(sE_x(idx))^2+std(detrend(x(idx)))^2);

paddedX=[polyval(pleft,(-(M-1):0)');x;polyval(pright,n+(1:M)')];

paddeX is then filtered with the standard filter-command.

I would otherwise post all the code for public consumption, but, as I said earlier, I do not want to disclose the source I obtained the codes, and there may be some small hints in the code I have. If someone really wants these codes, please contact the original author Aslak Grinsted
http://www.glaciology.net/
and ask him to put the code (ssatrend.m and related files) on-line. I’ll then put the rest of the replication code available.

PaulM (Comment#15497)

I recall that on David Stockwell’s blog, Rahmstorf was repeatedly asked how he did his endpoint smoothing, and refused to answer the question. Instead, he just referred to a file called ssatrend.m that was (and still is) not available.
Does he really use the absurd Mannian ‘minimum roughness’ endpoint padding,
apad=2*indata(nn)-indata(nn-ipad);
which gives a huge weighting to the final gridpoint indata(nn)?
I think not, because that forces the smoothed curve to go through the final point, which it doesnt seem to.

Given his record I am not at all surprised to see Rahmstorf change the smoothing period to obtain the required result.

So to summarise, the caption to figure 3 of this influential synthesis report is incorrect, is that right?

Jonathan (Comment#15498)

Jean S (Comment#15496), many thanks. His thesis (pdf) is quite helpful on the outline method, where he says on page 20

Two useful boundary conditions are the minimum slope and the minimum roughness conditions (Mann 2004). The minimum slope condition minimizes the first derivative, and minimum roughness
minimizes the second derivative at the boundary. Mann (2004) implements the minimum roughness condition by padding the series with the time series mirrored around the end
point (both horizontally and vertically), and the minimum slope by mirroring horizontally. Here, I will use a variation of the minimum roughness criterion where the series is padded with a linear extrapolation based on the m preceding points.

There is also a picture (but not a definition) of his smoothing function on page 19.

PaulM (Comment#15499)

Jean S, thanks for posting that code snippet.
I don’t think you need to post more of it, that’s the essence of it.
For those who are having difficulty interpreting it (it took me a while)
x = original data
n = length(x)
M = number of padding points needed (eg 7 for 15-point smoothing).
What the code then does is tack on M extra points at each end that lie on straight lines. These straight lines are found from a fit of the first (or last) mp points of the original data x. (As explained by Grinsted in the passage quoted by Jonathan).

But this is not ‘minimum roughness’ as originally proposed by the great Mann himself, which reflects the data horizontally and vertically about the final point, forcing the smoothed version to go through the last grid point (although Mann did not seem to realise this until it was pointed out by McIntyre). At first glance it seems more sensible than minimum roughness, although I am sure you can find examples where it gives bizarre results.

Jean, what value of mp is used? mp = M?

lucia (Comment#15504)

If you firmly believe the data consists of a trend plus noise, the Grinstead method has got to be better. But if you applied it to a sinusoid, and computed the trend based on earlier data points, it will hide changes in the trend.

Predicting the future is hard. That part wouldn’t bother me so much. It’s convincing yourself you can treat “data” that is computed based on a predicted future as observations and then using these to test theories that I dislike. (Dispensing with uncertainty intervals makes things worse.)

lucia (Comment#15507)

Paul M–
I redid my Mannian smooth graphs. The Mannian smooth graphs show the current 11-year smooth about to penetrate the TAR lower bounds.

Bob Koss (Comment#15518)

Charlie (Comment#15489)
John Brignell has a personal anecdote about the effect of bias when doing science.
http://www.numberwatch.co.uk/then_and_now.htm

David Stockwell (Comment#15519)

Bob: That is a great read, thanks. “and often referred to poor John Brignell, who never got his PhD because of low results, yet was probably right.” At least I believed in the system long enough to get my PhD. It became apparent to me that people will use whatever means at their disposal to promote their own pet theories – so what is the point of super-computers and mega-databases? All you are doing is selling computers for IBM. I went back to simple theoretical models and classical statistics.

Galloyd (Comment#15528)

Lucia
I can’t pretend to have a strong knowledge of statistics but, given his undeniable excellence as a climate scientist and his flawless use of statistics, does Gavin Schmidt’s use of a 5 year smoothing period in the chart on page 22 of his book (Climate Change) mean that Rahmstorf and Mann should be using 5 years.
By way of disclaimer I was browsing the book in a bookstore and decided my money was better spent on Ian Plimer’s “Heaven & Earth”

Nick Stokes (Comment#15529)

A response and a comment;

Jonathan–You are right; Nick is wrong

Yes. I was following David Stockwell’s implementation (see Fig).

But one can get too caught up in how these formulae are derived – extrapolations etc. They all in the end give smoothed values as a weighted sum of neighboring values. Internally, the weights are usually the same as you move along, but near the ends they have to change to accommodate the limits on the data.

The weights have to be such that a constant function smoothes to the same constant, which means they must sum to 1. You would also expect that a linear function should be unchanged by smoothing. Symmetric weights will ensure this on the interior. One way to ensure that this remains true near the ends is to construct the weights as the interior weights applied to some linear extrapolation, since a linear function will extrapolate as itself. Both MRC and the Grinsted method do this.

There’s not much more you could ask from a smoothing function of this general form. The remaining criticism of MRC is that it heavily weights the last term. This makes the result very sensitive to current information, which may be seen as a virtue, although it is less stable.

Ian Castles (Comment#15532)

Re #15528.

Professor Phil Jones, Director of the CRU and IPCC Coordinating Lead Author, also appears to have given support to five-year smoothing. He told BBC News Online’s environmental correspondent in 2003 that:

“Globally, I expect the five years from 2006 to 2010 will be about a tenth of a degree warmer than 2001 to 2005″(‘Heat high for 2003 but no record’, published at http://news.bbc.co.uk/2/hi/sci.....325033.stm ).

With the CRU anomalies up to May 2009 now published (41 of the 60 months of the 2006 to 2010 period), the average monthly anomaly from January 2006 to May 2009 has been .07 C BELOW the average for the years 2001 to 2005.

In order to reach the same average for 2006-10 as for 2001-05, the average anomaly during the 19 months between June 2009 and December 2010 would need to rise by .23 C.

For the 2006 to 2010 average to exceed that for 2001 to 2005 by one tenth of a degree, as Professor Jones expected, the average for June 2009 to December 2010 would need to exceed the average from January 2006 to May 2009 by .76 C.

Jean S (Comment#15535)

PaulM, yes, you are right, it’s the “variation of minimum roughness criterion” (by Grinsted) not the “minimum roughness” by Mann, I should have been clearer about that. David had it correctly implemented in his replication:
http://landshape.org/enm/anoth.....ort-error/
Yes, mp=M. That’s actually set in the code just right before switch-command selecting between minimum roughness and minimum slope.

One more thing to clarify. I may have been part of making this confusion (sorry for that), but M parameter is the padding period and the actual filter length is 2M-1. So when Rahmstorf et al are speaking about “11-year smoothing” it is actually “21-year smoothing”. If someone wants to give a try, here are the actual (symmetric) filter coefficients for M=11 (HadCRUT3, –>2006; others almost the same): 0.0073 0.0152 0.0235 0.0321 0.0410 0.0499 0.0587 0.0674 0.0758 0.0837 0.0910 0.0837 0.0758 0.0674 0.0587 0.0499 0.0410 0.0321 0.0235 0.0152 0.0073
and for M=15: 0.0037 0.0077 0.0119 0.0164 0.0211 0.0259 0.0308 0.0357 0.0406 0.0455 0.0502 0.0548 0.0591 0.0631 0.0668 0.0631 0.0591 0.0548 0.0502 0.0455 0.0406 0.0357 0.0308 0.0259 0.0211 0.0164 0.0119 0.0077 0.0037

PaulM (Comment#15537)

Jean S, wow, that’s another important revelation. I guess that should have been clear to me from comparing the code snippet with Rahmstorf’s reply. It also explains why you were talking of an even number (14) which seemed odd to me.

lucia (Comment#15550)

Jean S–

Wow!
So… in fact with ‘11-year’ smoothing, when Rahmstorf’s compare between ’smoothed observations’ and projections every single one of his “smoothed” data points involve both guessed data and data known before the report was published (i.e. 2001). Plus, smoothed data from 1990-2000, was computed using data known even before the claimed “freeze” date for the projections (i.e. 1990)! Fifteen years is even worse.

Jean S (Comment#15555)

Yes, you can actually spot the filter length from the animated GIF if you look it very carefully: the first value which is not changing at all for the blue solid line is for year 1996 (notice that I forgot to offset the trend lines by half a year as I did for the actual values as it was done in the original graph).

MikeN (Comment#15565)

That is two charts in the Copenhagen Report confirmed to have bad captions(the other is the comparison of CO2 emissions to scenarios).
Perhapos the whole report needs to be put up for critical review?

Carrick (Comment#15659)

Lucia:

Diagnosing anything withing N/2 of the endpoints using the method he selected is still bad because the uncertainty in endpoints is always enormous.

Wouldn’t you agree that this is an argument for dropping N/2 from the front and end of the detrended series?

This is what I do except in cases where (for purely mathematical reasons), I need the final series to be of the same length as the original.

lucia (Comment#15664)

Carrick–

Wouldn’t you agree that this is an argument for dropping N/2 from the front and end of the detrended series?

Sure. But we have data back to 1900 and even earlier. So, that doesn’t end up being important in the climate-blog-war debate.

Carrick (Comment#15667)

Sure. But we have data back to 1900 and even earlier. So, that doesn’t end up being important in the climate-blog-war debate.

Well, it kind of does, because Rahmstorf includes the end-points in their figure.

If they go from N=11 to N=15 in going from their 2005 figure to their 2007 figure, and they had dropped the last N/2 points, wouldn’t they have stopped at the year 2000 in both cases?

Also the prior to 1900 isn’t even an issue here, because nobody is debating the Earth is warming. The only question in hand is how much of it is from anthropogenic activity.

If you look at the combined effects of CO2 (warms) and sulfates (cools) from anthropogenic activity, most models don’t show much net impact from human impact till circa 1980. (I use the criteria a net 0.1C increase for the “much” qualifier.)

See, e.g., this figure.

(See the wikipedia figure and caption for more details.)

lucia (Comment#15671)

Carrick–
Yes. If we indicated the end region in Rahmstorf, it would start at 2008-(15-1)/2 = 2001.

The Blackboard » Interesting Quote from GRL Paper (Pingback#15787)

[...] like changing the characteristics of their smoothing filters without notifying readers. (See (1), (2), and (3).) Until that time, a not-insignificant number of people who believe model [...]

Charlie (Comment#16096)

The figure in this post is enlightening, but shows only the effect of the filtering. As noted http://www.climateaudit.org/?p=6513 “Rahm-Centering: Enhancing ‘Successful’ Prediction”, the rhetorical effect of the figure is also significantly changed by single year centering of the model on the 1990 Rahmstorf-filtered value.

What would the figure at the top of this post look like with a more widely accepted centering, such as 1961-1990 reference period?

Or asked a slightly different way, what would Figure 3 of the Copenhagen report look like if done using more generally accepted methods of centering and filtering?

lucia (Comment#16097)

Charlie–
I’ve often discussed the issue of selecting baselines on these sorts of tests and agree with Steve that the centering issue matters. This is particularly true when the modelers test their models by centering based on recent time period and eyeball anomaly graphs.

The reason I prefer to examine trends is that the choice of baseline matters less.

Charlie (Comment#16098)

Obviously there are many more powerful statistical tools for testing hypothesis and models than simply plotting and eyeballing. Even a non-statistician like me has bumped into things like Student’s T, Chi-squared, etc and I have no doubt that there are others much more appropriate for testing the various hypotheses, often implicit, of the models.

My interest is in the public policy impact. I see figure 3 in the Copenhagen synthesis report as kind of like a mini-version the hockey stick, whose pubic policy impact far exceeded its scientific value.

Niche Modeling » Rhamstorf Reamed (Pingback#29735)

[...] search Niche Modelling, and see ClimateAudit, the Blackboard, as well as many other posts from these and other statistical blog [...]

 

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