In my previous post I wrote about the five super-simple steps for building a hockey stick:
Step 1. Gather time series.
Step 2. Select those time series that fit the instrumental (measured) temperature record of choice. Assume that since these time series match the measured temperature in some way, then they are, in fact, temperature proxies.
Step 3. Combine the chosen proxies in some fashion and note, not surprisingly, that the combined proxies match the temperature record. (duh) Call this your temperature reconstruction.
Step 4. Call this thing made from the combined proxies your temperature reconstruction, and therefore assume that the combined proxies are also a match for the temperature that occurred prior to the temperature measurement records.
Step 5. Note that the reconstruction shows that the temperature prior to the instrumental data is relatively flat, and conclude that the temperature prior to the instrumental record changed very little.
This post is about a little subplot in gathering of time series for the Michael Mann’s 2008 version of the hockey stick (Proxy based reconstructions of hemispheric and global surface temperature variations over the past two millenia, PNAS, 2008)
Mann used 1209 proxies for this reconstruction. He explains the breakdown as follows…
We made use of a multiple proxy (‘‘multiproxy’’) database consisting of a diverse (1,209) set of annually(1,158) and decadally (51) resolved proxy series … including tree-ring, marine sediment, speleothem, lacustrine, ice core, coral, and historical documentary series. All 1,209 series were available back to at least A.D. 1800, 460 extend back to A.D. 1600, 177 back to A.D. 1400, 59 back to A.D. 1000, 36 back to A.D. 500, and 25 back to year ‘‘0’’ (i.e., 1 B.C.).
Figure 1. Northern Hemisphere proxies in alphabetical order
Mann split his analysis between the Northern and Southern hemispheres. I am going to talk about the 1,036 of the 1,209 proxies that applied to the North. The following two images show the plots of the these 1,036 proxies, just click on them to enlarge. The file sizes are less than a megabyte each and should open quickly in your browser. Figure 1 is the plots arranged in alphabetical order. If you scroll through this image you will see a lot of proxies that don’t look much like a hockey stick, and a few scattered here and there that do. However, there is a series of 71 proxies named lutannt1 through lutannt71 that look very much like hockey sticks.
These lutannt# proxies are from Pauling A Luterbacher, the researcher who “provided” them. More on this important point later
Figure 2. All Northern Hemisphere proxies in order of correlation with Northern Hemisphere instrumental temperature record.
As explained in the five easy steps for hockey stick construction, the proxies that look much like a hockey stick are likely to be weighted heavily in the final hockey stick construction. If all the 1,036 proxies are correlated (For the math inclined: see correlation formula below) with the northern hemisphere instrumental temperature record, and the plots laid out from the worst correlation to the best, it will look like figure 2. Scroll through this figure from top to bottom. You will see the worst correlations at the top and the best on the bottom. Note that the Luterbacher proxies are among the best correlated, and show up near the bottom.
Figure 3. All Northern Hemisphere proxies, except Luterbacher proxies, in order of correlation with Northern Hemisphere instrumental temperature record.
Figure 3 is the same as figure 2, but with the Luterbacher proxies removed. Scroll through, and it is quite clear that there are far fewer hockey stick-like proxies now.
The Amazing Multiplying Proxies
Remember, the point of a hockey stick is not that it goes up in the 20th century – this is a given because the hockey stick is deliberately constructed from proxies that go up in the 20th century. The real point is that it is more or less flat prior to the 20th century. (See step 5 of the super-simple steps for building a hockey stick.) The 71 Luterbacher time series are tailor-made for this purpose, because they tend to show temperature rising in the 20th century but flat prior to that. The problem with the 71 Luterbacher proxies is that they are actually not 71 separate proxies at all.
Luterbacher, et.al., (European Seasonal and Annual Temperature Variability, Trends, and Extremes Since 1500, Science, 2004) used about 150 “predictors” spread out over Europe to reconstruct European surface temperature fields. These predictors consisted of “instrumental temperature and pressure data and documentary proxy evidence.” Figure 4, taken from Luterbacher’s supplemental material, shows the geographical distribution of these predictors.
Figure 4. Luterbacher's original caption: (A) station pressure locations (red triangles) and surface temperature sites (B, red circles) used to reconstruct the monthly European temperature fields (25°W-40°E; 35°N-70°N given by the rectangular blue box). Blue circles indicate documentary monthly-resolved data, blue dots represent documentary information with seasonal resolution back to 1500. Green dots stand for seasonally resolved temperature proxy reconstructions from tree-ring and ice core evidence.
Lutenbacher used combinations of the predictors to interpolate the data to…
“a new gridded (0.5° x 0.5° resolution) reconstruction of monthly (back to 1659) and seasonal (from 1500 to 1658) temperature fields for European land areas (25°W to 40°E and 35°N to 70°N).”
Each of these grid points in the reconstruction is like one of the lutannt# graphs that show up in the list of proxies for Mann’s 2008 version of the hockey stick. Mann ends up with 71 lutannt# “proxies” by simply taking 71 points using 5° x 5° resolution from Luterbacher’s temperature field reconstruction.
Here’s the rub: Not all the predictors used to make Luterbacher’s temprature field reconstruction go all the way back to 1500. In fact, prior to about 1760 only about 10 of the total 150 predictors are used, and these predictors are primarily “documentary information.” Prior to about 1660, only about 7 are used. Figure 5, which also comes from Luterbacher’s supplementary material, shows the number of predictors used for each year to reconstruct his surface temperature fields.
Figure 5. Luterbacher's original caption: Number of predictors through time.
Figure 6 shows the location of Mann’s 71 selected “proxies” and the location of the “documentary information” sources. Not the best match in the world, is it? Amazingly, the construction of some of the proxies prior to 1750 is based on data from sources over 1000 kilometers away!
Figure 6. Blue dot show the location of Mann lutannt# "proxies." Red dots show the location of Luterbachers early "documentary information" sources.
The important point is that all the data for Mann’s 71 lutannt# “proxies” prior to about 1760 is made up of some combination of the same 10 or so “documentary information” predictors. This short list of predictors are the “Amazing Multiplying Hockey Stick Proxies.” These 10 predictors are multiplied into 71 proxies, and these proxies all rank high for correlation to the instrumental temperature record from 1850 to the present. Consequently, these 71 “proxies” likely weigh heavily in Mann’s 2008 hockey stick, and these 10 “documentary information” predictors, sometimes folded into ”proxies” over a thousand kilometers away, have an undeserved multiplied effect in making the flat part of the hockey stick prior to the instrumental temperature record.
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correlation coefficient:
where P is the proxy, and Pi is the ith year of the proxy
T is the temperature, and Ti is the ith year of the temperature
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