Tim Lambert was quick to pounce on Ross McKitrick’s programming error in calculating cosine(latitude) in a paper not involving me, so it’s ironic to see Lambert’s apparent failure to understand Mann’s erroneous use of cosine(latitude) in his temperature PC calculations, even when brought to his attention. Ed Snack has had an interesting exchange with Tim Lambert at Lambert’s blog here – see around #142. I would certainly hope and expect that, when Lambert realizes that his pronouncements on this topic have been incorrect, he will promptly correct and apologize for his error and issue a prominent denunciation of Mann’s error fully equal in ferocity to his denunciation of McKitrick’s similar error.
Mann’s calculation error was pointed out by von Storch last year in the SI to von Stoech et al [Science 2004] as follows:
Monthly nearsurface -temperature anomalies were standardized and subjected to an Empirical Orthogonal Function Analysis, in which each grid point was weighted by (cos à?”¬➩^(1/2), where à?”¬➠is the latitude (Mann et al. 1998 erroneously use a cos à?”¬➠weighting).
I’ve mentioned this a couple of times e.g. here . The error can be confirmed in the new source code release.
In response to Ed Snack raising the issue at his blog, Lambert said:
cos(lat) is going to be a good approximation of the correct weighting. Clearly sqrt(cos) is wrong. Looks like Mann is right and Ed Snack is wrong.
Later Lambert said:
Looks to me like von Storch is the one who is wrong here.
It’s pretty easy to find proof that the square root of the cosine (latitude) is the appropriate weighting in a principal components calculation. For example, J.W. Wallace says (page 14) here:
Under certain circumstances it may be advantageous to apply certain kinds of weighting to the various variables xj that enter into the EOF analysis. For example, one might want to weight the variance for each station by the geographical area that it represents. For a regular latitude-longitude grid, this could be accomplished by multiplying each gridpoint value by the square root of cosine of latitude.
If you google “wallace cosine latitude”, a number of references jump up providing further confirmation. KàÆànich et al. state here:
Prior to the EOF analysis the model data was smoothed with a binomial 30-day low-pass filter and weighted with the square root of cosine latitude.
Other examples include Wallace et al., Comments on “Northern Hemisphere Teleconnection Patterns during Extreme Phases of the Zonal-Mean Circulation, Journal of Climate 13, 1037-1039 or Limpasuvan and Hartmann, 1999, Eddies and the annular modes of climate variability, GRL 25, 3133-3136 or the description of a function here . It wasn’t very hard to find authoritative views on the matter.
I am sure that Lambert will promptly correct and apologize for his error and also issue a prominent denunciation of Mann’s error fully equal in ferocity to his denunciation of McKitrick’s similar error. In fact, I would expect that his denunciation will be even more ferocious because of Mann’s poor track record in making code available for cross-checking (obviously contrasting with McKitrick’s exemplary record.)
Update: July 24: Lambert has acknowledged the error only as comment #188 here:
So that to weight by area, the input to PCA has to be weighted by the square root of area. I retract my sugestion that von Storch might have been mistaken “¢’¬? he found an error in MBH98, though he does not seem to think that it was important.
If von Storch didn’t think that the error was important, he wouldn’t have mentioned it. It wasn’t relevant to the points being made in von Storch et al. . I am disappointed that Lambert has failed to issue a denunciation of Mann’s error equal in ferocity to his denunciation of McKitrick’s error as it shows unfortunate evidence of mere partisanship.