Briffa’s Tornetrask temperature reconstruction is done by regression analysis. Previously I reported that Briffa purported to justify his upward adjustment of 20th century MXD chronology (and downward adjustment of MWP reconstruction) by a very slight improvement of R2 (going from 0.503 to 0.553 – see Clim. Dyn 1992). I’ve attempted to replicate these regression calculations — I show an R2 using unadjusted data of 0.555 and with adjusted data of 0.558 (both using Briffa’s 1876-1975 reference period). With a reference period of 1851-1980, the corresponding unadjusted R2 is 0.571 (adjusted 0.572). As mentioned before, my RW chronology calculations are based on the 65-core dataset used in the MXD calculation.
As I noted a few posts ago, the discrepancy between 20th century RW and MXD series in the 20th century may very well derive from "Modern Sample Bias", where the minimum core diameter in modern trees eliminates slower growing trees from the distribution. This pretty much eliminates any quasi-justification for the adjustment. Even the very weak justification in terms of R2 cannot be justified. (BTW Briffa and co-authors are co-authors of the Rutherford et al 2005 diatribe against R2 statistics.)
Another curiosity of the Briffa regression is the retention of insignificant regressors. Briffa did an “inverse regression” of April-August temperature (AA) against 4 regressors: rw, mxd and next year’s rw and mxd (on the basis that the following year’s rw and mxd are influenced by prior year’s temperature).
|Value||Error||t value||Pr > |t||
Residual standard error: 0.6124 on 95 degrees of freedom
Multiple R-Squared: 0.558, Adjusted R-squared: 0.5394
F-statistic: 29.98 on 4 and 95 DF, p-value: 3.956e-16
Three of the 4 regressors — rw and the two lag variables — are insignificant. It is hard to understand why these insignificant regressors would be retained. The insignificance of the t-statistic for the rw regressor make the adjustment described previously even more bizarre. More Hockey Team oddities.
I’ve provided a textfile here tornetrask.dataframe.txt with my estimates of his underlying temperature and tree-chronology dataset hecking. The temperature data are July-August (JA) and April-August (AA) averages from gridcells described in Briffa et al [Nature 1990 page 435 col 1] using a contemporary gridcell dataset, which is as close to the one that he used as I can find (downloaded from http://cdiac.ornl.gov/ftp/ndp020/ndp020r1.txt.) Briffa has not archived any chronologies. I’ve included my emulations of his chronology versions, mxd nomenclature shown here, with corresponding rw versions (except for adjusted): mxd.spline – standardized by spline equal to 2/3 core length; mxd.RCS – standardized by linear age model; mxd.RCS.adjusted - post-1750 values “adjusted” as discussed before.