ClimateBallers are extremely suspicious of the MM05 simulation methodology, to say the least. A recurrent contention is that we should have removed the climate “signal” from the NOAMER tree ring network before calculating parameters for our red noise simulations, though it is not clear how you would do this when you not only don’t know the true “signal”, but its estimation is the purpose of the study.
In the actual NOAMER network, because of the dramatic inconsistency between the 20 stripbark chronologies and the 50 other chronologies, it is impossible to obtain a network of residuals that are low-order red noise anyway – a fundamental problem that specialists ignore. Because ClimateBallers are concerned that our simulations might have secretly embedded HS shapes into our simulated networks, I’ve done fresh calculations demonstrating that the networks really do contain “trendless red noise” as advertised. Finally, if ClimateBallers continue to seek a “talking point” that “McIntyre goofed” because of the MM05 estimation of red noise parameters from tree ring networks, an objective discussed at the ATTP blog, they should, in fairness, first direct their disapproval at Mann himself, whose “Preisendorfer” calculations published at Realclimate in early December 2004, also estimated red noise parameters from tree ring networks, though ClimateBallers have thus far only objected to the methodology when I used it.
For example, ATTP here: (I was unaware of this question until my recent examination of ClimateBall blogs):
as a physicist, I just find it very odd that M&M would use the MBH data to produce the noise. Surely you would want to make sure that what you were using to produce the noise had no chance of actually having hockey sticks.
So, my basic question to either Stephen McIntyre or Ross McKitrick is did you properly remove any underlying hockey stick profile from the data you used to produce the red-noise that you used in your 2005 paper.
or by one of ATTP’s readers who added:
2) His [McIntyre’s] random noise was badly contaminated with “hockey-stick” signal statistics (i.e. he didn’t filter the hockey-stick out of the tree-ring data before he used it as a template for his random noise).
ClimateBallers, including ATTP, mostly express disdain for the underlying issues of these reconstructions, but hoped that they could generate a talking point that I had “goofed”:
Perhaps a talking-point like “McIntyre goofed — he generated red-noise that was contaminated with hockey-stick signal *statistics*” would work. The talking point makes it clear how McIntyre messed up with his noise model without propagating the erroneous notion that his red noise was not actually trendless.
How Would You “Remove the Climate Signal” Anyway?
While it may seem obvious to ATTP that one ought to remove the “signal” before building “noise” models, no one knows what is “noise” and what is “signal” in the NOAMER tree ring network. Or whether the stripbark growth pulse is temperature “signal” or some sort of complicated “noise” arising from mechanical deformation or some other bristlecone peculiarity. Specialists prior to Mann et al 1998 had stated that the strip bark pulse was not due to temperature. Even coauthor Hughes stated that the bristlecone growth pulse was a “mystery”. It cannot be simply assumed that the bristlecone HS growth pulse is “signal” – this has to be demonstrated. Indeed, the majority of the focus of MM05_EE was exactly on this issue.
Even if ClimateBallers discount my position on the stripbark growth pulse, they need to recognize that both Briffa and Esper espoused positions on strip bark in 2006 that were almost identical to positions subsequently advocated at Climate Audit after our sampling at Almagre. Briffa expressed his concern about mechanical deformation and related issues in a Climategate thread with his coauthors of Juckes et al 2007, with Briffa warning them that they risked opening “Pandora’s box” if they opened up the connection between mechanical deformation and strip bark. The topic remained safely undiscussed in Juckes et al and, for the most part, in subsequent academic literature. The 2006 exchange arose from concerns over the NAS panel recommendation that stripbark chronologies be “avoided” in temperature reconstructions, a recommendation which, if followed, would appear to make Mannian-Stokesian arguments about lower order PCs completely moot. However, while Mann and others have paid lip service to the NAS panel report, they ignored its recommendation on strip bark chronologies, the use of which actually increased after the NAS panel -the paleoclimate community thumbing its nose at outsiders, so to speak.
Finally and arguably most problematically, the inconsistency between the stripbark chronologies and the rest of the NOAMER network (e.g. cypress and other chronologies which have negligible centennial variability) make it impossible that the network is “signal” plus low-order red noise. This fundamental problem is never confronted by paleoclimate specialists, and ATTP can hardly be blamed for being obtuse on an issue that the specialists evade.
Most statistics operates through the analysis of residuals. In the present case, let’s suppose, for argument’s sake, that the network of tree ring chronologies is a temperature “signal” plus low-order red noise. Forward model the signal – be it hockeystick or Lamb or red noise – to the network of tree ring chronologies and examine the residuals, as one would presumably do in physics or any “normal” science. If the “true signal” is a bristlecone-ish HS, then the residuals for the other 50 or so series in the NOAMER network – none of which have an HS shape – will consist of a low-order red noise series minus some multiple of a HS-shaped signal, i.e. the residuals will have a strong HS shape, violating the premise that the “noise” itself is low-order red noise. It doesn’t matter what temperature “signal” one hypothesizes, the network of residuals is not going to be low-order red noise. So ATTP is asking something that, in my opinion, is impossible for the NOAMER tree ring network. (His question isn’t foolish, but the answers of the ClimateBallers are.)
Arfima and Strip Bark
ClimateBallers have additionally expressed concern, not always politely, that the supposed “trendless red noise” of MM05 had somehow surreptitiously imported HS patterns and that the MM05 histograms and related results were an artifact of these imported patterns, a claim sometimes asserted with considerable conviction. The MM05 simulations used the hosking.sim function of Brandon Whitcher’s waveslim package; this function requires a long autocorrelation function and the ClimateBallers were suspicious that empirical acf’s calculated from HS-shaped bristlecone chronologies would somehow secrete HS-patterns in the simulations. Alternatively, nearly all ClimateBallers are convinced that the autocorrelation of these networks makes the noise too “red”.
A couple of responses. First, if the strip bark growth pulse (as much as 6 sigma in some trees) is related to mechanical deformation (as Pete Holzmann, myself and seemingly Keith Briffa and Jan Esper believe), it is “noise” (not signal), but not noise that can be modeled as AR1, and, perhaps not even as arfima (though arfima is better at capturing some of the variability.) In some instances, there is elliptical deformation, with the growth pulse being a change from the short part of the ellipse to the long part. It seems to me that arfima is better than AR1 for this sort of problem, though even arfima has important shortcomings in the exercise. But be that as it may, the arfima networks show the existence of an important bias in Mannian principal components. In our 2005 articles, having established the existence of the bias, we turned our attention to its impacts.
“Trendless Red Noise”
To further re-assure suspicious ClimateBallers that the MM05 simulated networks did not secretly embed HS patterns, I re-executed the MM05 script to generate new 1000 tree ring networks in MM05 style. For each network, I did the first step of a simple CPS calculation, in which I normalized each series and calculated the average of each network (the underlying series were close to mean 0, sd 1 in any event and a simple average would be immaterially different.) In Figure 1 below, I plotted all 1000 averages in light grey, with the overall average plotted in red. There is obviously no trend and negligible variation (sd=0.0035) in the overall average, supporting the description of these networks as “trendless red noise”. I also wanted to extract a set of simple averages to compare to centered PC1s, as the validity of even centered PC1s needs to be demonstrated, rather than asserted. This proves to be an interesting comparison, which I will discuss soon.
Figure 1. 1000 simulations using MM05 script. Grey- average for each network; red – overall average; black – 97.5 and 2. quantiles by year.
Mann’s Simulations Also Used Empirical Coefficients
But before ClimateBallers get too excited about our calculation of noise parameters from the empirical NOAMER network without first removing a “signal” that is not only unknown but the end-product of the calculation, they should first recognize that Mann also estimated noise parameters from the empirical NOAMER network (without such prior removal) in an important calculation.
In December 2004, in one of the earliest Realclimate pages (here), Mann reported the results of simulations using red noise series of the “same lag-one autocorrelation structure as the actual ITRDB data”:
Shown also is the null distribution based on Monte Carlo simulations with 70 independent red noise series of the same length and same lag-one autocorrelation structure as the actual ITRDB data using the respective centering and normalization conventions (blue curve for MBH98 convention, red curve for MM convention). In the former case, 2 (or perhaps 3) eigenvalues are distinct from the noise eigenvalue continuum. In the latter case, 5 (or perhaps 6) eigenvalues are distinct from the noise eigenvalue continuum.
In other words, Mann estimated his red noise parameters directly from the tree ring network – the same supposed offence that the ClimateBallers accused us of – but, needless to say, the ClimateBallers do not mention this. Nor was this a trivial calculation on Mann’s part. This was the calculation in which he purported to mitigate his erroneous PC methodology by arguing for the use of 5 PCs in the AD1400 NOAMER, an increase which enabled him to increase stripbark bristlecone weight through the backdoor.
Did MBH98 Use His Empirical Preisendorfer Calculation?
By (perhaps inadvertently) drawing attention to Mann’s 2005 “Preisendorfer” calculation, ATTP has raised an issue that is highly relevant to Steyn’s allegations of fraud and which ought to be minutely examined by Steyn and others. Indeed, this is one of the issues on which discovery might turn up something interesting.
Prior to our 2004 submission to Nature, there wasn’t a shred of evidence that Mann had done a “Preisendorfer” calculation for tree ring networks, though there was evidence that he done such a calculation on temperature networks. In 2005, Mann produced source code showing the calculation on temperature networks, but produced no such code for tree ring networks, even in response to a request from a House Committee. My own present surmise is that Mann didn’t use a “Preisendorfer” calculation for tree ring networks in MBH98, but was driven to this calculation in order to mitigate problems arising in 2004 from our exposure of Mann’s defective principal components method. Supporting this surmise is the impossibility of reproducing the actual pattern of retained PCs in MBH98 using the “Preisendorfer” calculation first attested in 2004. I believe that Mann was scrambling in 2004 to figure out some way of trying to mitigate his erroneous PC method and that his “Preisendorfer” calculation for tree rings was first used in 2004, not 1998.
If I were in Steyn’s shoes, I would require meticulous disclosure of the original calculations, which are totally undocumented. I would also be surprised if such discovery requests yields documents showing that Mann actually used the Preisendorfer Rule for PC retention in tree ring networks in MBH98.