Rob Wilson wrote in today pointing out that D’Arrigo et al 2006 had obtained a correlation to gridcell temperature of 0.58 for the Jacoby Mongolia site chronology, working from original data and not relying on hand-me-down data from Mann and Jones. This is actually higher than the 0.25 reported by Mann and Jones for annual correlation, which, regardless of whatever is the "correct" answer, is a disquieting difference for a simple calculation between a gridcell temperature series and a tree ring site chronology – a calculation which should reconcile exactly.
However, it turned out that this correlation was not to the actual gridcell containing the Sol Dav site (48N, 98E) but to the northeast contiguous gridcell 100-105E, containing Irkutsk, Russia. So this rises an interesting question about the effect of "picking" from 9 candidate gridcells, as the results vary dramatically from gridcell to gridcell.
Secondly, although Jacoby has not archived an RCS chronology (or any other chronology for the extended Sol Dav collection archived in July 2004 and published in GRL 2001), he did archive a chronology for the shorter collection published previously, which I’ve considered here. I’ve also done my own RCS calculation (which is very trivial mathematically) – so we’ve got three tree ring chronologies to compare against 9 gridcells. I’ll show these correlations for the 1881-1997 (although all 9 contiguous gridcells are only really represented in the 1936-1997 period) and then show details for the northeast gridcell and central gridcell.
Figure 1. Barplot showing correlations of Site Chronologies to Gridcells 1881-1997
As you can see, one can derive a correlation exceeding 0.5 between the RCS chronology and the northeast gridcell (more or less as reported in D’Arrigo et al.) However, the seeming significance of this relationship must surely be qualified by the negligible correlations of the RCS and crn chronologies to the other 8 contiguous gridcells, includinga negative correlation for the actual gridcell (5). Ths possibility of a spurious correlation to the northeast gridcell must be considered.
Next here are some details of the gridcell series from the northeast gridcell and the actual gridcell (top and middle panels.) The bottom panel shows the Mann-Jones archived chronology as compared to the Jacoby archived mong003 short chronology (which was actually used in MBH98 and presumably familiar to Mann) and in Briffa 2000 (and familiar to Jones coauthor Briffa).
Figure 2. Top gridcell 50-55N, 100-105E; middle gridcell 45-50N, 95-100E; Bottom – Mann and Jones chronology compared to mong003.crn
The deficiencies in Mann’s scanning process are evident here as the entire Mann and Jones chronology appears a couple of years out. The RCS chronology (not shown here) tracks the crn chronology reasonably but has additional upward drift. The "decadaly smoothed" chronology has a correlation of 0.53 to the northeast gridcell and -0.17 to the actual gridcell. So the gridcell selection "matters". Now the northeast gridcell is available for a longer period. However if the 1936-1997 common period is used, the relationships are about the same – a correlation to the northeast gridcell and negligible correlation to the actual gridcell.
Some Time Series Properties
Before venturing into thinking about regression significance, it is prudent to examine the ARMA character of the series. Millennial climate scientists have got into (in my opinion) a very bad habit of using AR1 models as a benchmark, when the series are nearly always strongly ARMA(1,1) or probably some very high form or persistence.
Gridcell 50-55N 100-105E has very high and highly significant ARMA(1,1) coefficients : AR1 0.9817 (se- 0.0175) and MA1 -0.8032 (se – 0.0527). The actual gridcell has similar properties. This series has an AR1 coefficient almost equal to that of a random walk and, in econometric terms, is almost integrated. With the high MA1 coefficient, it is a combination that is "almost white almost integrated" – which poses difficult significance tests. I’ve commented on this from time to time – see comments on Vogelsang, Deng on Ferson etc. The AR1 coefficient in a mis=specified AR1 model is only 0.50, giving a false idea of the degree of persistencei n a mis-specified model.
The DW statistic is valid only for AR1 errors and is not sensitive to ARMA(1,1) as here. However, even here the DW statistic for the relationship between the RCS chronology (my version) and the northeast gridcell is 0.67 – which is well below the 1.5 minimum. Rob Wilson has reported a much different value.
Hockey talk always leads to interesting little by-ways. Rob mentioned Irkutsk; this is located at 52.3N, 104.3E in the contiguous northeast gridcell. This turns out to be a site studied by Warwick Hughes here. Warwick’s website show the figure below, with a bewildering variety of station data, leading to a very different outcome than the HAdCRU gridcell.
Figure 3. Irkutsk variations from Warwick Hughes