Many thanks. I’m trying to help others avoid the tedium of math analysis if some of the fubdamental inputs are doubtful. I re-read Steve’s article on station spacing (the one with the diverse map projections) and was none the wiser. We put years of computer team time into finding the right ways to interpolate ore grades and it is not a trivial subject. It has direct parallels with using paired stations to correct for surface temps and as I have been saying for a long time, you simply cannot use a search distance of 1200 km for temp work. In short, there is no global surface temperature graph, land or sea, in which I have any faith at all. You can drive a big truck through many of the assumptions and corrections.

Hans would be the person to answer these questions. I’d like to know if he did these himself or if not where he found them, as they’re very useful.

One thing I see here is that beyond about 3000 KM (27 deg), the correlations are mostly noise, so that it is better to try to constrain them to a functional form than to just take each correlation at face value. They pretty much die to 0 by 3000 KM, except perhaps for the tropics. There is a piecewise linear curve fit line if you look closely.

Another funny thing is that the northern latitude correlations converge on unity at 0 distance, while the tropical and southern ones don’t. Is this climatological, or does it just mean that tropical and southern stations often aren’t as reliable as northern ones?

Geoff is right that it might make a difference whether distance is measured NS or EW. Also, what is the frequency of this data? Daily data surely has much less correlation, so I’m guessing this is monthly or annual.

Why are there so few points nestled beside the left Y-axis? The graphs indicate that there are very few cases of comparison stations being closer than about 200 km to each other.

“Curiouser and curiouser” as Dodgson would say.

A quick look failed to find the answer to these questions.

In the series of graphs of correlation coefficient versus station separation, were the graphs conducted with a linear E-W search shape, or with some ellipsoid shape, or with a circle of up to 5000 km radius? Let’s assume the latter.

Given that a half-circumference of the earth is 20,000 km, North Pole to South, if you divide this into 7 zones shown (should be 8, but Antarctic is empty) then each latitude band is about 3,000 km wide. But the points on the graph go out to 5,000 km, so they are sampling adjacent bands. Problem?

The next problem with the graph is that the number of pairs within a latitude zone drops off with distance after a while. I would have thought that the more distant the search, the more numerous the pairs available.

Final problem, a correlation coefficient below about 0.8 gets a bit ratty when plotted. In some of the graphed latitude bands, most of the coefficients are below 0.8 by far, so I personally would not have much regard for them. In fact, I’d read very little of use into this graph other than that the tropics behave dissimilar to the poles.

Have you a reference to more of this type of work? Please don’t go to any trouble. I just seem to be missing some vital assumptions. Used to do similar things interpolating grades of ore deposits betweeen drill holes.

I haven’t parsed some of the recent discussion and will try to spend some time on it.

GISS shows temperatures from 1911-1921 between 21.5 and 26 C. The official records from 1922 show the average for that period to be much higher, at 27.3C. Also note the photograph of a well maintained and properly located station.
http://docs.lib.noaa.gov/rescue/mwr/050/mwr-050-01-0010.pdf

Interesting comparison, CVM vs. MBH algorithm. Would you prefer to eat a newspaper or drink a bottle of glue? [smile] Juckes INVR is CCE with identity S, IIRC.

I’ll take the “glue” any day! Variance Matching or “NLS” as I call it, a la Moberg et al, is statistical nonsense. The MBH data set has a lot of problems, as we are all aware, but at least their estimator, as described above, is an estimator, if only an inefficient one.

If the covariance matrix V of the first stage regression errors is known, then GLS with P = inv(V) is the efficient estimator of U. But any P, including P = I, gives an unbiased estimator. Of course, the variance of a non-GLS estimator requires knowing V, and falsely assuming that V = sigma^2 I will give you wrong answers, so you still have to come up with an intelligent estimate of V. If you have enough degrees of freedom to have reasonable confidence in this estimate of V, you may as well do GLS with it, and thereby improve your efficiency. (With small DOF, weights based on your estimate of V may be cherry picking randomly well-fitting proxies, but I’m willing to assume that away for now.)

Thanks for the Technometrics cite. I’ll take a look at it.

Hans Erren, #13 writes, re my proposal to model the correlation as a simple declining function of the great circle distance between the two sites,

But only north of 30N and south of 30S. In the equatorial region the spatial correlation is poor.

Hans has already illustrated his point with an excellent graph he posted on 2/11/08 at comment #83 of Thread 2711. The graph itself is on his site at http://home.casema.nl/errenwijlens/co2/station_correlation.gif:

The relationship is indeed tighter north of 23.6N than in the tropics or southern latitudes. An ideal model should somehow take this different behavior into account, but I think that as a first approximation, it’s better to assume that the relationship is universal than to just ignore it altogether.

The “gridding” beloved of climatologists is, if I understand it correctly, a clumsy attempt to take this correlation into account, by essentially assuming that the correlation is perfect within 5 degree gridcells (556 KM at the equator), and 0 between gridcells. MBH grid their data, I gather, presumably in an effort to “correct” for spatial correlation in this manner.

January 1938
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Dust storms
Forest fires