I observed yesterday that I had been unable to replicate the archived version of Kaufman’s Hallet Lake series – something that I thought was due to a change in the archived version (since the NCDC archive noted that a new version had been archived in Nov 2008.) This turns out not to be what happened.
Kaufman archived BSi (%) at NCDC and I innocently assumed that this was what was used in Kaufman et al 2009. It appears that, instead of using the archived BSi%, Kaufman used (a version of ) the temperature reconstruction from BSi flux developed using a “classical logarithmic” regression by one of Kaufman’s students.
I thought that CA readers would be intrigued by the “classical logarithmic” regression. The thesis of Kaufman’s student says:
Quantitative summer temperature reconstruction: BSi flux increases exponentially with temperature over the calibration period (figure 19). A classical logarithmic regression was used to develop a transfer function.
The “classical” logarithmic function is then shown in full as follows (url pdf page 34):
I don’t feel quite so bad for not being able to figure out this “classic” functional form from the information in Kaufman et al 2009 and NCDC.
I tested the above formula against the archived temperatures in McKay A-6 and replicated these temperatures almost exactly. The reconstruction uses BSi flux, not BSi %, BSi flux being (conventionally) defined as follows in the McKay thesis as follows:
BSi concentrations (%) were converted to flux (mg cm-2 yr-1) by multiplying %BSi by total flux (the product of bulk density and sedimentation rate).
The use of 1.000626 as a base in the logarithm seems a little exotic and it’s unclear why this unusual nomenclature was used. The form itself can be somewhat simplified (with one less free parameter) to the following (still not the most elegant functional form in the world) – the estimation of the parameters remains unclear.
Temperature = 12.79*( 0.765718 +log(BSi_flux))^(1/3)-1.082
In other words, temperature is said to be proportional to the cube root of flux_all times BSi.
They go on to say:
To minimize the effects of point-to-point variability, and to emphasize longer-term changes in temperature, a 50-year Gaussian-weighted low-pass filter was applied to the high-resolution record of BSi flux before using the transfer function to reconstruct summer temperatures for the past 2 kyr. The BSi flux-inferred summer temperatures for the past 2 kyr range from 9-14°C; the average of the unfiltered data for the past 2 kyr is 10.6°C (10.7°C for the filtered data), nearly 2°C cooler than the modern average temperature (12.4°C) (figure 21); here defined as 1976-2005, the period of continuous measurement during the current AL regime. Comparisons of the observed and predicted values, along with the residuals show that the transfer function tends to slightly underestimate the highest and lowest temperatures (figure 19).
Earlier today, I thought that I’d managed to replicate the Kaufman 2009 version from the temperature recon in the McKay thesis, but as of now, I’m still stumped as to the provenance of the Kaufman version. Here’s what I get, kaufmanizing the McKay temperature reconstruction:
The NCDC version is the same as the thesis version, but says that a new version was provided in Nov 2008. Perhaps Kaufman used an old version of this series. Another Team mystery.
BSi flux and BSi-flux reconstructed temperature are shown against depth in the McKay Thesis Appendix A-6, with temperatures expurgated below 192 cm. (These would be high temperatures in the early Holocene according to the McKay formula.) The BSi% measurements can be matched to the BSi% measurements at NCDC for all but three years (three high years expurgated from the NCDC record.) The NCDC record is indexed by year rather than by depth. The two records can be spliced to yield an age-depth relationship that (annoyingly) is not otherwise archived.