Since I showed the effect of smoothing on the relationship of Dunde to temperature, I thought that it would be useful to post up a table showing the Jones et al  proxy correlations to temperature versus my calculations using HadCRU2.
This table shows: col 1- my calculated correlation for 1881-1980 using HadCRU2 (I haven’t tested why they used 1881-1980); col 2- correlation as reported in Jones et al ; col 3- original reported correlation, according to Table 4 of Jones et al ; col 4- t-statistic from obtaining the correlation by a regression model (which matches the usual calculation). I’ve not attempted to deal with spurious t-statistics issues here. In a number of cases, Jones et al  already reported lower correlations than the original publication, e.g. Jacoby treeline; Lenca and Rio Alerce; Galapagos corals. In some cases, my calculations using HadCRU2 are much lower again, with the differences sometimes being substantial. For example, the correlation for the Jacoby NH treeline study is reduced here to 0.07, down from the original 0.72 (Jones – 0.37) . Likewise for the Rio Alerce and Lenca series. A few series show higher correlations e.g. Svalbard melt.
Jones says (p. 461) :
"The most surprising correlation in Table 4 is for ENG. The value is relatively low because the gridbox series (50-55N, 0-5W) incorporates up to 10 station records and some SST data while ENG is based on only 3 inland stations."
It is surprising that the reconstruction of gridcell temperature from Tornetrask tree rings (this includes the "adjustment" discussed before) is supposedly more accurate than the Central England temperature version is to the HadCRU2 gridcell. This seems unlikely and suggests that some portion of this high correlation may be spurious. A t-statistic seems to me to be a more sensible approach, but there are no surprises in the t-statistics here. Relative to the usual 2.96 benchmark, 5 of 7 SH series are insignificant and 3 of 10 NH series.
Report (Jones 98)
|Great Barrier Reef (5)||0.19||0.18||0.31||1.86|
Jones et al  Table 4 shows "decadal" correlations which are supposedly measuring "low frequency" effects. I’ve spent quite a bit of time recently pondering statistical issues of handling "low frequency" and they are by no means easy, if you’re trying to do it in an advanced way. In this table, col 1 – my calculation of the correlation: I made decadal averages for both proxies and temperature (not by smoothing); col 2- reported inJones et al ; col 3- OLS t-statistic.
The Law Dome statistic here is meaningless as it based on 3 decades ( i.e.the correlation results from 3 values) which are hardly enough to ground a reportable correlation statistic. There are a couple of significant decreases: the Polar Urals decadal correlation declines from 0.92 to 0.23 (whereas Tornetrask is unchanged). I’m not sure why. It might be due to changes in the HadCRU2 version. The decadal correlation in the Svalbard melt series improves. I’ve noticed major changes in Greenland temperature series in HadCRu editions and maybe htere was a change in Svalbard here. Jones et al  mentions as a caveat that inaccurate temperature series may contribute to low correlations.
The t-statistics here show the impact of the reduced number of values used in the correlation calculations. Despite the seemingly high decadal correlations, only 4 series have significant decadal OLS t-statistics (let alone t-statistics allowing for spurious significance issues). The four are: the Central England series – hardly a "proxy" for temperature; the Central Europe historical series; Svalbard melt % and the Tornetrask reoonstruction. The Svalbard melt series is hugely non-normal. I’ve been meaning to check to see the effect of normalizing this series. The Tornetrask series was "adjusted". This may have an effect. Again, it is disquieting that this reconstruction is "more accurate" than the CEng series.
|Kameda.melt||-0.40||- 0.28||- 1.24|