Have become interested in checking out dendroclimatology from the ENM point of view – particularly evaluating the model used for functional responses of alpine trees to temperature. All studies in Briffa et al. 2001 (figure below) invariably use a linear model, OLS fit of the proxy to temperature be it tree ring width (TRW) or density (MXD). It is of course not possible for tree growth to increase indefinitely with temperature increases – it has to be limited. The obvious choice for a more accurate model of tree response is a sigmoidal curve. Analysis follows…

Plate 3 from Briffa et al. [JGR 2001]. Original Caption: Plate 3. Comparison of six large-scale reconstructions, all recalibrated with linear regression against the 1881-1960 mean April-September observed temperature averaged over land areas north of 20N. All series have been smoothed with a 50-year Gaussian-weighted filter and are anomalies from 1961-1990 mean. Observed temperature for 1871-1997 (black) from Jones et al. (1999);

Unsmoothed data for the above plot of 6 climate reconstructions from tree proxies is archived here. To evaluate the potential of a sigmoidal response I fit a logistic curve to each of the 6 studies and compared the results with a linear fit on the period for which there are values of both temperature and the proxy. The results were as follows. The R script for this analysis can be found here.

Study	Linear	Logistic
1: Jones et al. (1998) Holocene	0.3519	0.3308
2: Mann et al. (1999) Geophys Res Lett	0.4316	0.4245
3: Briffa et al. (2001) J Geophys Res	0.4103	0.4215
4: Briffa (2000) Quat Sci Rev	0.2438	0.2457
5: Overpeck et al. (1997) Science	0.2537	0.2419
6: Crowley & Lowery (2000) Ambio	0.1426	0.1399

Plots of the proxy over time, the fit of proxy response to temperature, and the residuals follow:

Discussion

OK, so the logistic curve did not give a stunning increase in the R2 values — although they were comparable. I had to estimate the maximum and minimum temperatures for each proxy to fit the curve, set as 0.1 plus the max value and 0.1 minus the min value. Perhaps there is software that estimates these parameters as well and would improve the R2 statistic. I have no experience with the exotic R modules. It would also be better if the proxy data reached into the present day. ClimateAudit has referred in the past to the strange truncation of the data at 1960 in the Briffa 2000 series when the data are known to have been collected. If data were available for warmer temperatures, we might see a nonlinear curve is a better approximation. Models incorporating the known physiology of the tree response may lead to more reliable reconstructions of climate from tree ring data.