Not Spaghetti

[UPDATE - June 24, 2010: the following text has been slightly modified following some discussion at ClimateAudit and in particular a detailed explanation from Steven Mosher of what he did wrong. Changes are indicated by strikethrough for deletions and bold for additions].

When people are obviously wrong it doesn't take much time or effort to dismiss their claims. When Joe Barton apologizes to BP we know he's spouting nonsense. When Gerhard Kramm gets simple integrals and averages confused it doesn't take much effort to convince anybody other than Kramm where he went wrong. When Tom Fuller blusters about quantitative meta analysis, Gish Gallops, and alternate universes you can tell he has trouble with logical coherence.

But the tricky cases are those who are much more subtle in their nonsense. Making stuff up is easy. Making stuff up that on the face of it looks somewhat plausible does take a bit more skill. Figuring out that the "plausible" stuff is just as much nonsense as the obviously wrong takes considerably more work, and some of these actors tend to make a lot of work for those of us trying to defend real science. One of the most skilled in creating plausible nonsense is Christopher Monckton. Prof. John Abrahams is the latest of us to take on Monckton's fabrications, and collectively thousands of hours have surely been spent tracking down the ways in which Monckton has misrepresented science.

Brian Angliss has recently put a lot of effort into tracking down the basis of some of the claims regarding "climategate", in particular looking at the implications of malfeasance on the part of the scientists whose emails were stolen. Many of these the conclusions Angliss examined were claimed at the website ClimateAudit, and in particular in a book published by Steven Mosher and Tom Fuller. There followed an extensive thread of comment including from Fuller and Mosher, and a response from Steve McIntyre at ClimateAudit that clarified some of the claims prompting Angliss to revise his article to attempt to correct his own mistakes.

The first discussion point in Angliss' review of the claims and in the ClimateAudit back and forth with Mosher and Fuller is the meaning of the "trick" to "hide the decline" phrase found in the stolen emails. This has been adversely interpreted in a couple of different ways but the actual meaning has been clearly identified as the process of creating graphs that do include tree-ring-based temperature "proxy" data only up to 1960, or 1980, a point where they start to diverge from temperatures measured by instrumental thermometers. There is nothing scientifically nefarious or "wrong" about this - the "divergence problem" has been extensively discussed in the scientific literature including in the text of the most recent IPCC report. If you have reason to believe a particular collection of tree ring data is a good measure of temperature before 1960 but for some still uncertain reason not after that point, then it's perfectly legitimate to create a graph using the data you think is reliable, particularly if these choices are all clearly explained in the surrounding text or caption.

Figure 2.21 from IPCC TAR WG1

Figure 6.10b from IPCC AR4 WG1

What's definitely not legitimate is presenting a graph that is specifically stated to be showing one thing, but actually showing another. That might happen just by accident if somebody messed up in creating the graph. But the ClimateAudit discussion and Mosher/Fuller book appeared to claim that in one figure in the 3rd IPCC report (TAR WG1 figure 2.21, 2001) and in one figure in the 4th report (AR4 figure 6.10b, 2007) there was a real instance where "the scientists had actually substituted or replaced the tree ring proxy data with instrument data" deliberately, for the purpose of "hiding the decline". As Angliss cited, McIntyre definitely uses the word "substitution" (but Angliss was apparently wrong that McIntyre did this in the IPCC context), and Fuller highlighted a portion of the Mosher/Fuller book using the word "replaced". McIntyre later clarified that his claim was not related to these IPCC figures but rather something else. However, Steven Mosher in comment #7 on Brian's article at June 8, 2010 at 12:34 pm stated very clearly that he knew what the trick was and that this substitution/replacement was used for the IPCC figures:

you wrote:

"Looking closely at the graph shows that the tree ring data was neither replaced nor substituted. The zoomed-in version of IPCC TAR WG1 Figure 2.21 at right shows that the instrument data starts around 1900 (red line, red arrow added) while the tree ring data ends at around 1960 (green line, green arrow added). If the tree ring data after 1960 were simply substituted or replaced as McIntyre and Fuller claim, then the instrument data would have been appended to the end of the tree ring data or the instrument data would be shown in green in order to maximize the potential for misinterpretation. Neither is the case."

The TAR is the third Report. We are talking about the FAR. figure 6.10. But I can make the same point with the TAR was with the FAR. You clearly don’t know how the trick works. Let me explain. The tree ring data POST 1960 is truncated. That is step 1. That step is covered in the text of chapter 6 ( more on that later ) The next step is to SMOOTH the data for the graphical presentation. The smoothing algorithm is a 30 year smooth. Whats that mean? For example,
if you have data from year 1 to year 100, your first data point is year 15. Its value is the combination of the 15 PRIOR YEARS and the 15 Following years ( for illustration only to give you an idea how centered filters work) your LAST year is year 85. This year is the combination of the prior 15 years of the record and the last 15 years. year 86 has no value because there are not 15 following years. So with a record that goes to 1960 your SMOOTH with a 30 year window should only display up to 1945. The problem of end point padding ( what do you draw from year 1945-1960) has extensive literature. So for example, there is extending the means of adjacent values at both ends of the smooth. ( the proceedure used in Ar4 ch06) In the case of Briffa’s curve, this procedure was not used. It was used for all the other curves, but in Briffa’s case it was not used. To fill out the filter, to supply data for 1945-1960, the INSTRUMENT SERIES was used.
This has been confirmed by replication. So still, after all this time people do not understand the trick because they have not attended to the math.

1. the series is truncated at 1960.
2. a smoothing filter ( typically 30 years) is applied.
3. To compute the final years of the smooth ( half the filter width) the temperature series is used.

That procedure is the trick. in a nutshell. If you want directions read Jones’ mail.

So Steven Mosher here claims that the "trick" was to use the instrumental data for "end point padding" in the 1960-truncated Briffa (2001) series used in IPCC AR4 Figure 6.10b (and presumably in the similar series in the TAR figure 2.21 Brian Angliss looked at). So that, despite claims to the contrary, in the IPCC reports Mosher claims they really did substitute/replace tree ring with instrumental data. And in a way that was concealed to the public - in particular, the caption of figure 6.10b specifically states what the end-point padding was:

“All series have been smoothed with a Gaussian-weighted filter to remove fluctuations on time scales less than 30 years; smoothed values are obtained up to both ends of each record by extending the records with the mean of the adjacent existing values.”

Similarly in TAR figure 2.21 the end-point padding is stated as:

“All series were smoothed with a 40-year Hamming-weights lowpass filter, with boundary constraints imposed by padding the series with its mean values during the first and last 25 years.”

Mosher is claiming a very specific procedure was used for smoothing that differs from that stated in these figure captions. I asked what the basis was for this claim, but no particular email from the scientists emerged to explicitly support Mosher's claim, and the closest thing to any analysis of the problem were pointers to this thread at ClimateAudit where, if the above endpoint padding procedure was examined, it's certainly not clear from the discussion.

One of the commenters pointed to the difference between the Briffa 2001 curve in the AR4 Figure 6.10b figure and in this NCDC page on the reconstructions:

Briffa 2001 reconstruction with others from NCDC

And indeed you see the Briffa curve (light blue) drops down a bit precipitously in the NCDC figure close to its endpoint in 1960, while the IPCC AR4 figure doesn't drop nearly so far - here's a closeup of the IPCC version:

Figure 6.10b from IPCC AR4 WG1 - closeup on the endpoints

So why are these different? While the differences in the individual curves common to both figures seem rather minor visually, there definitely looks like a problem with handling of smoothing near the Briffa 2001 end point in 1960. But note that the NCDC figure actually doesn't specifically state what endpoint padding was used for its graphs - it only says "All series have been smoothed with a 50-year Gaussian-weighted filter". Perhaps Mosher is right, that the NCDC figure uses the nearby-mean endpoint padding that the IPCC figure claimed to use, while the IPCC figure uses the instrumental data for padding, contrary to its specific claim about padding with the mean? If Mosher is right, that means the scientists really did conceal what they were doing here, and the figure caption for figure 6.10b (and presumably for the TAR figure as well) was a lie.

A commenter (Glen Raphael, #112) at Angliss' post thought proof of Mosher's point was that nobody had debunked it yet:

Perhaps an even stronger bit of evidence is that we haven’t seen Mosher’s claims “debunked” by any of the usual suspects. If his account were incorrect and there were some innocuous alternative way to generate the same graphics, don’t you think we’d have heard about it by now? Wouldn’t a rebuttal have shown up in gloating posts or comments at Deltoid, DC, RealClimate, Tamino, or all of the above? I think it’s safe to say *if* these claims were false they’d be easy for somebody with access to the data to debunk and it’s also safe to say that if they *could* be debunked that would have been done

Well, maybe nobody has actually seen Mosher state what he's talking about so clearly before. But now that he has, yes, it should be easy to debunk. Let's take a look.

The raw data for the NCDC graph is available for download via the page linked above. And here's what it looks like:

Raw (unsmoothed) NCDC data (R code here)

Now let's apply a Gaussian smoothing filter with nearby-mean endpoint padding as both the NCDC and IPCC AR4 figures claimed - though I don't know exactly the parameters or equation they used, I found a functional form that seems to roughly reproduce the main features of the curves in those figures:

NCDC data with Gaussian smooth (10-year) + padding with mean of first/last 15 years (R code here)

The Briffa 2001 curve (blue, ending in 1960) looks remarkably like the curve in the IPCC AR4 Figure 6.10b above. Let's look at close-ups near the end-point:

Magnified view of smoothed NCDC curve, and IPCC AR4 Fig 6.10b (R code here)

The Briffa 2001 curve is blue on the left (from NCDC data) and light blue on the right (IPCC). While the right-hand light blue curve is a little hard to see under all the others, it seems to peak at very close to zero, slope down and then tail off to flat right around -0.15 in both cases. Comparing to the Briffa 2000 curve (green on the left, darker green on the right) the Briffa 2001 endpoint is just a little above the bottom of the valley of the Briffa 2000 curve in both cases. I.e. a pretty good match.

But then, what explains the NCDC figure which had the Briffa 2001 data definitely heading rapidly downwards at the end? As I mentioned, the NCDC page doesn't say how endpoints were handled in that figure, so we'll need to do a bit of guessing.

The first natural possibility is that the endpoints were padded with the very last (or first) point in the series - rather than taking the mean of 15 or 25 points near the end, using the very last point alone. Doing that with the raw NCDC data gives this figure:

NCDC data with Gaussian smooth (10-year) + padding with first/last year data (R code here)

Oops! That looks even less like the NCDC graph, and not like the IPCC graph either - here's a close-up on the end:

Magnified view of smoothed NCDC curve with endpoint padding, compared with nearby mean padding (R code here)

The Briffa 2001 data now has a new valley at about -0.1 and then curves up - the reason for this is that the 1960 endpoint has a value of 0.076, much higher than the typical (negative) values in earlier years. So that one endpoint pulls the whole curve up when you pad and smooth in this fashion.

So clearly the NCDC graph didn't use the IPCC padding or simple endpoint padding for the Briffa 2001 data. One likely alternative was that they used the original Briffa 2001 data extended beyond 1960 for padding, despite the fact that the scientists had concluded it was no longer a valid temperature proxy after 1960. The NCDC data doesn't include the post-1960 Briffa 2001 data, and I couldn't find it in a quick search, but looking elsewhere it appears the data quickly falls to somewhere around -0.4 degrees temperature anomaly. So I took the simple expedient of padding the Briffa 2001 curve with -0.4's:

NCDC data with Gaussian smooth (10-year) + padding (Briffa 2001 only) with -0.4 (R code here)

and here's a comparison of the endpoint region:

Magnified view of smoothed NCDC curve with -0.4 padding (for Briffa 2001), compared with nearby mean padding (R code here)

This indeed looks very much like the original NCDC figure. So the unstated padding in that figure that brought the Briffa 2001 curve down so much was very likely use of the original Briffa 2001 curve beyond 1960, while chopping off the smoothed curve in 1960. That's perhaps justifiable, but a little inconsistent with the statements concerning the source of that data.

So it's pretty clear that the difference in endpoint smoothing between the NCDC and IPCC figures does not require grafting the instrumental data onto the tree-ring data as Steven Mosher claimed. But what do the graphs look like if you do that grafting?

NCDC data with Gaussian smooth (10-year) + padding (Briffa 2001 only) with instrumental data (R code here)

and comparing the endpoints region again:

Magnified view of smoothed NCDC curve with instrumental padding (for Briffa 2001), compared with nearby mean padding (R code here)

While the difference is small, you can see that the instrumental-padded curve flattens out more quickly than the mean-padded curve, and never goes much below -0.1 in temperature anomaly, while the mean-padded curve does go lower. Only the mean-padded curve matches the behavior of the IPCC AR4 WG1 Figure 6.10b illustrated above.

So, conclusively, despite Mosher's claims of certainty on what the scientists did, he was wrong.

But it sure takes a lot of effort to prove that one claim wrong, doesn't it?