The Excel file containing this data can be downloaded from this BitBucket.org archive.
Some observations and some graphs follow.
The data sets accumulated by Mia Tiljander and coworkers were deposited at NOAA by Prof. Mann's group, along with all of the other proxies they used in Mann08. Once unzipped, the files can be seen to be in two sets of four text files. The four are the Darksum, Lightsum, Thickness, and X-Ray Density data series. The two are the "Original" and the "Infilled" versions. Tiljander's data apparently ends in 1985. To extend it to the end of the screening period used in Mann08 (1850-1995), the final 9 years were "infilled" -- actually, extrapolated, by RegEM (I believe). This nine year period accounts for 6% of the full screening period; obviously a somewhat greater proportion when it is split into calibration and validation sub-periods.
Mann08's authors transformed all four of the data series by taking their natural logarithms. Presumably this is how they were screened and calibrated.
* There is an a priori physical reason to expect an exponential relationship between the data set, and other variables.
* The data has a log-normal (or near-log-normal) distribution, rather than a normal (Gaussian) one.
* It is more convenient to use log-transformed data.
I know of no evidence that either of the first two conditions holds.
Darksum, Lightsum, and Thickness are all measurements of varve thickness in millimeters, though Darksum and Lightsum are expressed as tenths of microns (i.e. as a 10,000x larger number). Darksum is derived from a very simple relationship:
Darksum = Thickness - Lightsum
[Illustration added 8/17/10; click to embiggen]
From this, it is obvious that there are at most two degrees of freedom among the three data sets. Mann08's authors were arguably in error to use all of them in their reconstructions.
What follows are a series of traces generated by Excel, one for each of the four Tiljander proxies, with limited commentary. The following should be kept in mind:
According to Tiljander03's claims:
Prior to about 1720, climate signals are present in these three data series: Darksum, Lightsum, and X-Ray Density. Tiljander03 doesn't interpret Thickness.
For Darksum, higher values correspond to warmer and wetter summers with longer growing seasons.
For Lightsum, higher values correspond to cooler and wetter winters with more pronounced spring snowmelt.
For the pictures that follow, I haven't adhered to Tiljander03's interpretation--it is simpler to graph everything such that larger values are up, whatever the climactic meaning of rising signals may be. For further perspective, see the discussion between scientist/TCO and me, at this post (warning, it is a long, two-part exchange).
After about 1720, the Lake Korttajarvi sediments became progressively more contaminated as a result of local human activities. These included farming, roadbuilding, peat cutting, eutrophication, and bridge reconstruction.
Also (not in Tiljander03), the Geological Survey of Finland noted that the water level of the lake was altered by farmers, sometime after 1700. The account is in Finnish, and lacks detail.
First, here are the four proxies, from 200 AD to the near-present (Mann08's infilled values 1986-1995 are used). The red and green traces are the annual varve data, while the centered black line is the same data, smoothed with an 11-year rolling average (my choice of filter). The scale for the Thickness, Darksum, and Lightsum have been kept comparable -- in these three cases, "millimeters of varve thickness" is being graphed. (You may have to scroll to the left or increase the size of your browser window to get a complete view of these first two graphs.)
In the second set of charts, I have simply calculated the mean and standard deviation of the data series (millimeters of varve thickness; arbitrary units for XRD) by century from the 3rd Century on, as a measure of variability. "Standard deviation" has limits in this setting, as these time series are likely autocorrelated to some extent--but it is an acceptable first shot, I think.
Notice the pattern that holds through the 18th Century, before changing in the 19th and then quite drastically in the 20th (through 1995, including the infilled values).
In all four cases, the 18th Century appears to have characteristics that resemble earlier periods more than the 19th and 20th Centuries. Thus, to get a sense of what a "normal" century looks like next to the "unusual" period that includes the 1850-1995 interval, I graphed each data series from 1700 through 1995, along with the synthetic temperature-anomaly reconstruction that Mann08's authors used for CPS. This is the 5-degree by 5-degree gridcell for Southern Finland that includes Lake Korttajavi. Details at this post. (There is a local weather station with records dating back to the 1890s whose data are depicted in Tiljander03. That is probably a better representation of local climate; it appears to trend more-or-less stably over the 20th Century, with less upward trend than the gridcell shows. I haven't located that information, though.) Note that raw data (millimeters of varve thickness, or arbitrary grayscale units (XRD)) are used here, rather than the log-transformed variants.
Finally, here are graphs showing my attempt to show the correlation between proxy and temperature over the entire 1850-1995 period. For this series, unsmoothed log-transformed data is used--although an 11-year trailing rolling average provides a modest boost in R^2 (charts of "ln(proxy)(11-yr-avg) vs time" and of correlations with 11-year smoothed log-transformed data are provided in the Excel file at BitBucket.org). A caveat: note that Mann08 uses the metric "r", while Excel -- and thus I -- have used "R^2".
As promised: lots of data, with little editorializing!
[UPDATE 18 Aug 2010 -- Two good comments on the subject of logarithmic transformation of varve data were left at the Air Vent's post MW10 -- Some thoughts. Reproduced below. -- AMac]
#4 -- BobN -- August 18, 2010 at 11:31 am
It is my experience looking at lots of environmental data (e.g., groundwater contamination, natural distribution of elements in the environment, river flow data) that many such data are better describer as log-normal than normal distributions. So it may be the case with varves.#6 -- Doug Proctor -- August 18, 2010 at 12:12 pm
BobN suggested “varves” may be better described by log-normal than normal distributions from his work.
Varve thickness is controlled by two variables:
1. effective runoff time length, and
2. sediment load.
The effective runoff time, i.e. the length of time sediment-carrying waters entered the catchment basin, is itself a function of temperature during the melting or rainfall period of the year, AND the rate of discharge. Below a locally critical rate virtually no sediment will enter the basin even though the streams are running and it is warm. The sediment load is controlled by source area and discharge rate, both affected by temperature, plant growth and precipitation. Bare, cold, dry areas of dirt will make periodic muddy streams when warm, plant covered areas will lead to clear streams. Or warm and dry areas can give periodic muddy streams, and so on.
The variables show that there is no unique solution to varve analysis. At the same time, each of those variables is definitely not linear. Temperature and precipitation in the watershed are clearly cyclical but there are step-functions for both. Strong events are periodic but also neither random nor predictable. We are dealing with weather, not climate in the study of varves (similarly tidal cycles have strong weather signatures on top of the lunar cycles).
You see periodicity in varve changes, which over time is climate. Linearity is not to be expected, but if it occurred would be a nice indication that only one variable was being changed. It would then be up to other lines of thinking to figure out which one it was.
Engineers find geology crazy-making. All data is soft, and few problems have single solutions.
[UPDATE 2 14 Aug 2011 -- At Bart Verheggen's blog post How science does and does not work (and how skeptics mostly fall in the latter category), commenter Luminous Beauty critiqued the scatterplots in this post:
Your simple statistics are not so simple. Being able to plug & play into Excel doesn’t necessarily mean you know what you’re about. Log normalization, if implemented properly, is a calibration step, which you keep claiming is impossible. What it does is make the two data sets to be compared orthonormal, or in simple language, proportionately equal, i.e., calibrated to the same scalar mean. Just glancing at your scatter plots indicates ur doin’ it rong.As I understand it, Luminous Beauty's criticism is that the scatterplots should plot the logarithm of each Tiljander data series against temperature anomaly.
I don't think it makes much difference -- these plots are mainly visual aids, and the observed correlations are spurious in any case. Revisiting the issue, I note that the scatterplots already plot the natural logarithm (ln) of each data series against CRUTEM3v.
However, XRD is already a logarithmic scale -- "absorbance", not "transmission". Thus, that plot should not have XRD log-transformed. A revised scatterplot follows.