In my time I have seen far too many studies with cherry picked data and inappropriate statistical analysis not to spot a bad ‘un miles away. And this one stinks. Almost as bad as Hansen’s paper which suggested you can infer an entire planet’s climate from one single piece of data gathered at one point on the globe: well the other point did not agree and so had be discounted of course.

Since Doom makes good press and politically driven agendas can be boosted by spurious scientific studies, well I may not have seen it all but I have seen an awful lot of it my lifetime.

As for the poisonous academic hostility between rival schools of thought, I have seen quite enough of that too. Serious debate is one thing, fitting or inventing data and analysis to support a political agenda quite another.

Of course I may be wrong but I suspect the current quiescent period in solar activity is just about to teach us a very chilly lesson in the simple fact that great natural forces far exceed anything that humankind can manage with its puny technology. I only hope I live long enough to see it. And if so that I can afford the heating bills.

Regards A

I have replicated several of the non-ice borehole temperature reconstructions and I’ll “share” my observations. The inversion problem boils down to finding the solution to the inconsistent set of linear equations Ax~b, where A is a skinny matrix (mxn) whose columns are generated from the solution of the heat conduction equation. x is a nx1 solution vector where the first two elements are a slope and intercept and the remaining elements are the temperature reconstruction. The b mx1 vector is the borehole temperature profile. The solution is calculated using the pseudo inverse based on the singular value decomposition (svd) where A = U*S*V’ and where U (mxm) and V (nxn) are complete orthonormal basis sets. The A matrix is ill-conditioned with ratio of max to min singular value on the order of 1e6 to 1e7 on the boreholes I replicated. In the older literature only singular values of greater than 0.3 are used in the pseudo inverse, with recent literature using a ridge regression that optimizes the norm of the residual versus the norm of the solution. If you keep singular values that are less than 0.3, the reconstruction is physical unreasonable, i.e. pulses on the order of 20-40 deg K. For 500 year reconstruction and 100 year steps, the 3 smallest singular values out of the seven total aren’t used in the psuedoinverse.

So what is the problem??? The ill-conditioning of A!! For instance if A is rank deficient i.e. rank = n-1, then one has a single null vector z such that A*z = 0_mx1 and an infinite number of solutions for x. For our A, there are 3 “almost” null vectors which are the last three columns of V. So A*v(5), A*v(6), A*v(7)~0_mx1. Let x_est be the pseudo inverse solution using only singular values greater than 0.3. Let’s create a new solution x_new = x_est + 2*v(7). The individual residual changes are on the order of millikelvins. x_new “looks” substantial different then x_est but the values are reasonable. The point is that there are many x_estimates and many reasonable temperature reconstructions that have residuals that are almost identical, with differences that are less then the temperature sensor noise level.

Summarizing, the columns of the ill-conditioned A matrix are created using solutions to the heat conducting equation. x_est is one of many possible temperature histories.

As I understand it, Mann asserted non-dendro recon skill back to 1760 in MBH98. Now he is claiming skill back to 1500 under CPS or 400 under EIV.

Obviously, that should have read: Now he is claiming skill back to 1500 under CPS or 1000 under EIV.

Leif,

Here’s a good read. About 800 pages.

The Russians drilled a superdeep drill hole on the Kola peninsula, to 12.3 km depth. It was extensively studied and written up by Kozlovsky.

“The Superdeep Well of the Kola Peninsula”, edited by Yevgeny Kozlovsky, 1984, who was a former Soviet Minister of Geology. (Out of print, hard to find. Difficult English translation available.)

Inversion was used to verify geology with seismic and was found badly in error. No doubt improvements have been made since then.

Inversion of termperature data was complicated by groundwater flow when it was not expected. See reference and following quote therein -
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V72-3WRBMJ6-8&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=10&md5=d6898af2258ccc94dbb70bbf30ddc2f7

, “In particular, the largest geothermal anomaly at 0–2 km depth is caused by a downward movement of meteoric waters in the zone of active water exchange. The experimental results can be understood quantitatively if a permeability of (1 to 3) × 10−13 m2 over a 1–2 km zone of exogenic fracturing is assumed. An abrupt change of conductive HFD in the depth interval 1.7–2.2 km is attributed to a downward movement of fluids of 2–3 cm/yr along inclined zones of fracturing at the boundary between igneous and sedimentary sequences.”

Later, there was a study of geothermal gradients in Germany (the KTB project), one brief summary of which is

Finally, the potential and the limitation of the analysis of heat flows and temperature gradients are demonstrated. Heat-flow interpretations are conclusive only for nearly horizontally layered, isotropic geological units. In steeply dipping and anisotropic formations the heat-flow field is perturbed over a large distance (>1 km) around the point of interest. In such geological units only, the temperature gradient interpretation can provide reliable information on the surrounding material.

http://www3.interscience.wiley.com/journal/119221133/abstract

While these 2 quotes are not killers for shallow geothermal gradient inversion methods to study palaeoclimates, they do indicate that much care has to be taken to avoid confounding effects. Also, it is important to drill deep holes in the study area to assess the outward heat flow as it is at the base of the temperatures under study.

The rocks in Australia where I live are mostly deeply weathered and so covered with soil with different hydrologic properties to the hard rock below. It would not be wise to use the inversion method in such terrain. Indeed, it is hard to imagine a suitable place globally to conduct such studies, confident that perturbing effects were known to be negligible. There is a lot of anisotropy out there.

The “period in question” was post-1760, as I pointed out previously.

Steve: So what. Mann’s statement is not a plain disclosure of the adverse results; it’s a cunning presentation of a case that went his way.

To me, a reading of the entire text made it “plain” that MBH98 claimed skill for the complete recon back to 1400, but only back to 1760 (and not before) for the non-dendro subset. If that’s an “adverse result”, so be it, but it should have been clear to anyone who read the study.

Of course, your highly selective quotes might lead to a different impression, but that can hardly be the fault of Mann’s supposed “cunning presentation.”

Steve: Nope. It most certainly does not. Under proper disclosure, when he claimed that it didn’t matter for the period in question, he was obliged to disclose explicitly and in the same paragraph or section that this result only applied for a cherry-picked period and that it broke down for the earlier period. If you don’t understand this, I’m not going to discuss it further. Neither did he disclose the adverse verification r2 results. You show me a statement of the adverse verification r2 results. IT took an academic misconduct complaint to get Ammann to report the adverse results. TAt the NAS panel hearings, he denied even calculating a verification r2 result, making the provenance of MBH98 Figure 3 am unsolved mystery.