I’ve done a data analysis that simply looks at the addition of thermometers to airports, by latitude, over time. Your point is well made. Not only is the AHI important, but it grows dramatically over time in the bulk record as more and more of the thermometer records come from airports (and more of them in the Tropics).

http://chiefio.wordpress.com/2009/08/26/agw-gistemp-measure-jet-age-airport-growth/

What I didn’t get from Steve’s #82 is that a large number of Monte Carlo replications of the data set are generated with unit variances and zero correlations across series, so that the true eigenvalues for each replication are equal and the computed eigenvalues differ only randomly. Then if the actual first eigenvalue (with normalized data) is greater than the 95th monte carlo percentile, it is retained for further investigation. If then the second is greater than its (slightly lower) monte carlo percentile, it is retained, and so forth until the eigenvalues are no longer significant by this test.

Preisendorfer points out that a correction must be made if the series are in fact serially correlated, since this reduces the effective independent sample size. Rather than make his indirect sample size correction, it would seem easier just to generate series with the empirical autocorrelation whatever that may be.

I would quibble with Preisendorfer on three small points.

The first is that he in fact says to retain all eigenvalues that are greater than their respective 95th percentiles. But under the null of equal (and therefore uninteresting) eigenvalues, about 5% of the eigenvalues should be greater than their 95th percentiles, so that with eg 100 series, this rule might randomly pick eg PC4, 39, 52, 63, and 92. The rule I set out above would not stoop to PC92 (or PC4 for that matter) unless all of PC1 – PC91 (or PC1 – PC3) are also significant.

Of course having passed Rule N just means that the PC should be considered in a next step calibration equation, and does not imply that it will have any significance correlation with temperature or whatever.

My second quibble is that he doesn’t direct you to normalize the replications to unit sample variance. Even though they were drawn with unit population variance, they will never have unit sample variance, and therefore will have different properties than your sample under the null, if the sample has been normalized.

My third quibble is that he erroneously states that with say 100 replications, the 95th largest realization should be your 95% critical value. In fact, this is the 95/101 critical value. To obtain a true 95% critical value without interpolating, you should use say 99 replications, and then take the 95th of these as the 95% critical value. Under the null, your sample is then the 100th realization of the process, and the probability is exactly 5% that it is one of the 5 largest draws, ie greater than the 95th largest of the 99 artificial samples. Jean-Marie DuFour at U. Montreal is very fond of this point.

(In fact, DuFour insists that you only need to take the largest of 19 replications. It’s true this gives an exact 5% test size, but it lacks the desirable property of replicability. I would instead go for at least 999 replications, and take #950.)

It’s unclear where the name “Rule N” comes from, since his sample size is n, not N.

JFK or ORD and the like have ASOS stations arguably located in the middle of 24/7/365 blast furnaces. But as you correctly point out the instrumental record is probably as accurate as you are going to get. That would make these sites suitable longinatudally as long as you acknowledged that airport heat island effects are baked into the nominal temperature record. ASOS also would allow you to compare ASOS TAN (Taunton MA), a prop job daylight onesy-twosey airstrip to nearby KBOX (NWS Taunton) to nearby BOS and PVD. With a little work, you might tease out a valid AHI factor. It is the absence of conventions in measurements and phony baloney adjustment factors that have transformed the entire ground level temperature exercise into a huge waste of time money oxygen and bandwidth. There are alot worse starting points than ASOS. Maybe that’s why they are the stations making into the grids.

In fact, when one re-examines the chronology of when Rule N was first mentioned in connection with tree rings, it is impossible to find any mention of it prior to our criticism of Mann’s biased PC methodology (submitted to Nature in January 2004)

Yet in MBH 98 (p. 786, column 1 near middle), they wrote, “Preisendorfer’s selection rule ‘rule N’ was applied to the multiproxy network to determine the approximate number N_eofs of significant independent climate patterns that are resolved by the network…”

So I think it can be said that rule N was at least on the table as early as 1998. (Of course, this is not to say that they really used it, or that they used it correctly, etc.)

Steve: Hu, I’m aware of that comment and I think that I’ve quoted it in the past. This comment describes how they determined the number of temperature PCs to reconstruct. This step can be seen in the source code. This is a different step than the determination of retained PCs in tree ring networks,. where the only thing that they say was:

Certain densely sampled regional dendroclimatic data sets have been represented in the network by a smaller number of leading principal components (typically 3–11 depending on the spatial extent and size of the data set).

This particular statement doesn’t preclude the use of PReisendorfer’s Rule N, but Rule N has nothing to do with “spatial extent” and indicates that something else is involved. But perhaps not. Mann didn’t produce the relevant section of source code for tree ring networks so no one really has any idea right now how the calculation was actually done and, as noted elsewhere, it seems impossible to figure out a rule that yields both AD1600 Vaganov and AD1750 Stahle SWM retentions. I’d

It’s not this is a bad procedure for exploratory purposes. My issues are: 1) that I am unconvinced that it was actually used in MBH. Perhaps they now wish that they’d used it, but the evidence is against its actual use; 2) passing a Rule N test is the beginning of scientific testing, not the end. Bristlecones are a distinct pattern in the NOAMER network; that doesn’t mean that they can detect worldwide temperatures.

If there are N unit variance series, the N eigenvalues must sum to N. Does Preisendorfer’s rule call for excluding all PC’s but those whose eigenvalues exceed 1/N of the total variance, ie all but those whose eigenvalues exceed 1?

Steve: My calculations are here: http://data.climateaudit.org/data/mbh98/preisendorfer.info.dat . The column headed “preis” shows what results from my Preisendorfer Rule N calculation. The third column shows the MBH number. Nothing matches. Actually even the AD1400 example at realclimate doesn’t precisely match.

Good to see another part of the perpetual bob and weave about MBH98 bite the dust. Rule N wasn’t used. Simple as that.

w.