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2014-03-16 12:49:46 UTC
http://answers.yahoo.com/question/index?qid=20140315181904AA5PLeF
pegminer and Hey Dook --
I hope this is useful and answers your questions. If not, drop me a note.
[NOTE: Out of habit - I realize that I mostly refer to tree-rings in the following discussion even though Mann used a multi-proxy data set. It doesn’t matter because the pre-1400 data are dominated by the tree-ring data and the regression analysis uses the tree-ring data (the reason Michael used the tree-data is because it is the only proxy record with annual resolution and he needed that resolution in order to run the regression analysis).]
[NOTE: The biology and math for all of this was established by Hal Fritts. Hal is the only person I know who invented a scientific discipline all by himself. For that reason, I used to call him, “Big Daddy.” http://www.ltrr.arizona.edu/~hal/hal1.html]
Here is a down & dirty version:
The principle that allows us to decompose signals from tree-ring series is based on a model where tree-ring growth for year t, [R(t)] = B(t) + C(t) +D1(t) + D2(t) + E(t); where [B] is the genetic / biological / physiological growth component, [C] is climate, [D1] and [D2] are local and regional disturbances, and [E] is everything else (random…noise…error…whatever).
The challenge is to control / eliminate everything except climate (e.g., precip, temp, drought). Tree stands where climate variables limit growth are typically found at a species’ extreme distributional boundaries (i.e., upper treeline and lower forest border stands on steep slopes with minimal soil development). Mann’s dilemma with the 1,000-year long reconstruction was caused by thin sample depth prior to AD 1400 that was leveraged by a PC dominated by upper elevation bristlecone pine series containing a growth trend beginning in the mid-nineteenth century that is greater than can be explained by temperature, alone.
It has been suggested that this is the result of CO2 precipitating out of the atmosphere at high elevations and increasing the water-use efficiency in some trees. Regardless of what it IS – it IS NOT temperature – and it needs to be removed before building the reconstruction. It needs to be removed because the reconstruction equation is developed using regression techniques over the common time period for both the tree-rings and the climate data – in this case, the historic temperature record.
This is called the calibration period and in Mann’s study it was 1902 – 1980. Using (1) the historic temperature record and (2) the tree-ring record from 1902-1980, you build a regression equation (that describes the climate-tree growth relationship). This equation is called a transfer function because it converts proxy data into temperature data. You then take the full set of tree-ring (proxy) data from 1000-1998 and run it through the regression equation (i.e., transfer function) – and you end up a reconstruction of temperature from 1000-1998.
Now, here is the reason Mann needed to adjust the data. If you leave the CO2 signal in, it gets included in the regression analysis and contributes to defining the parameters in the transfer function. Therefore, your transfer function does not describe the relationship between historic temperature data and proxy temperature date – it describes the relationship between historic temperature data and a proxy record that is some unknown combination of temperature and CO2.
This creates two problems (in addition to the big problem of not knowing what your data represent): (1) because there is a relationship between CO2 and temperature, you are in some sense counting the same thing twice – and, therefore, artificially inflating the correlation in you regression analysis, and more importantly; (2) you are imposing the recent CO2 effect on the whole length of record – which means that, especially for the period from 1000-1400, the reconstruction contains (is contaminated by) a CO2 signal that did not exist from 1000-1400.
Michael addressed the problem by creating a residual series – which contrary to McIntyre’s whining, is not difficult or impossible to figure out – simply by subtracting the proxy data unaffected by CO2 from the PC containing the upper elevation tree-ring data. I’m not sure that I would do it that way, but in Michael’s defense he explicitly states that he is only concerned about the low-frequency signal.
Michael understood what was going on and recognized the problem – something that McIntyre never saw. McIntyre may have some math skills, but he does not know shlt about this stuff – or scientific research, in general.