Monday, August 16, 2010

The Tiljander Data Series: Data and Graphs

I have compiled the information from the Lake Korttajarvi borehole varved sediments record that was characterized in Tiljander03, and then used in the multiproxy paleoclimate reconstruction Mann08.

The Excel file containing this data can be downloaded from this archive. The name of the 1.5MB file is Tiljander-Mann08-proxies-data+graphs.xls. The name of the 1.8 MB file is Tiljander_proxies_dataset_graphs.xls .

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.

Typically, data is log-transformed for one of a few reasons:

* 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.
[Update 18 Aug 2010: I struck the previous few sentences: log transformation of varve data seems to be an accepted practice in paleolimnology. See the Update at the end of the post -- AMac]

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 Darksum, XRD, higher values correspond to cooler periods, reflecting a mix of Darksum and Lightsum.

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  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.


  1. Here, I am showing data rather than coming to conclusions.

    I'd invite you to consider the following.

    1. The Tiljander proxies cannot be meaningfully calibrated to the instrumental temperature record (1850-1995) due to any climate signals in these proxies being overwhelmed by local factors (e.g. peat cutting).

    2. Tiljander03 explicitly proposes particular temperature signals for Darksum, Lightsum, and XRD in the pre-1720 era. The evidence for a temperature signal of this kind in those proxies appears to be weak. (For example, consider the modest extent of the traces' inflections during the Medieval Warm Period and the Little Ice Age.)

    3. Mann08 implicitly accepts Tiljander03's temperature signal for Darksum, implicitly proposes an opposite signal for Lightsum and XRD, and implicitly proposes a novel signal for Thickness. Mann08's authors offer no justifications for these assignments.

    4. Among them, Darksum, Lightsum, and XRD cannot have more than two degrees of freedom, at most. Mann08's use of these as three independent proxies appears to be in error.

    5. The Tiljander data series appear to be unconnected to temperature, and especially to 19th and 20th Century temperature: correlations to temperature seem to be "spurious" or "nonsense" in type. In this light, it is notable that the use of the Tiljander data series "validates" Mann08's non-dendro reconstructions before 1500. This result calls the meaning of terms such as "validate" into question.

  2. Good content, man. Will read and bloviate obvious thoughts later tonight (at least it helps me digest your insights). Gotta get a lift in. Darn climate wimps are pissing me off. I'm actually getting more interested in work than in the dramah. Not even irked that others don't see it as me. Just honestly bored. But you rolling out real content is a nice break from the Neverending Audit.

  3. Amac: FWIW reactions to your work (reading order, not synthesized):

    1. Not a "borehole". That's for stuff like mining and ice cores where a temp profile is kept in the hole (at least in normal usage).

    2.How often does he do this extrapolation forwards. We know he did it at least on one occasion backwards, in MBH. Interacting with this is even issues like series selection. In addition to getting all the representative series, are we getting all the "exception series" that we can. There is a downside and upside for doing stuff like this. Upside is getting more series, more chance for a better Bayesian guess. Downside is more danger of overfitting. It's definitely not a conservative step and ought to be highlighted (not just in the SI, but he has a bad habit of making the paper about the headline and not the methods).

    3.(out of sequence): Seems like M08/9 versus M98/99 differs in both data input and in method. could even add a third factor in terms of extra years of recent time. Would be interesting to see the full factorial and compare the different method-network combinations, in output (hindcast) as well as RE/CE. IOW, how much is different from the data, how much the method. Shame that he does not disaggregate these things.

    4. (out of sequence): more I see Tjilander, the more trouble it is. Recent series added to new method (point 3), flipping, lognormalizing, caveats of the collector, discussed in SI rather than in paper, extraplation forwards (missing post 85 values), weakness of the Tjilander paper itself, non-independance of the series, lack of phsycial insight into what DS and LS are. (I was going to put an etc., but I think those are all of them.)

    5. (out of sequence) I do wonder if we picked at some random series, would we find all the same issues or not? IOW, is Mann calm about Tjilander as all the kids are he is used to ugly kids? So he just collects and puts up with ugly kids?

  4. 6. Log normalizing. Hm...was this disclosed? What other stuff does he do it for? I could see it making the recent runup more reasonable-looking and handle-able. B Log nromalizing would also implicitly help settle down some of the supervarve outliers. ut that is not nescessarily a reason for doing it (little bit opportunistic). I guess there are physical things like particle size that have known physical log distributions. But not sure where in the conventional varve literature that this is advocated or justified. I would think something like thickness would be linear like a tree...but I'm not an expert. I don't have as good a feel for XRD as it would seem to be a measure of composition. LS and DS as transforms of the X ray measurments may have some inherent rationale forthe log transform (but I hate LS and DS untill someone shows me a paper justifiying their use...even from medicine or something).

    7. Or lightsum plus darksum = thickness. I thought of lightsum as the area of white and darksum as the area of dark. Wasn't sure if there were any noncounted pixels. Guess not. Also, I guess you have to convert area measurement to linear, but it looks like this is done before we call it LS or DS. So LS and DS are really LS'/width and DS'/width. BTW, was this your "aha" that this neat formula applies? It didn't seem that well explained in the paper and I know I was kind of cogitating around on this issue, but I didn't have it all figured out. IOW, is this just news to me or would it be news to Mann and McI, etc.?

    8. I assume XRD (which I think has to do with percent transmittance) is also related to LS or DS (can't remembber which is which with the photo negative). IOW X -rays pass through the sample and that means 100% transmittance (I'm unsure the units for XRD though, but it's realated to % transmittance, perhaps with a transform via Beers law to absorptoin (which would implicity include all modes of scattering, etc. that are not transmission). But anyhow, the light or is it dark pixels also relate to wehther the X rays got through to the film.

  5. 9. How do you feel about Tjilander's rationale for direction pre-1700. Both in and of itself (as proven in the paper) and in that it seems to have changed in 1700 and she doesn't really seem to have proven that landuse changed (perhaps it did, but she hasn't nailed it quantitaively).

    I sorta slacked off once you got gentle with me. But reading back into her paper and looking at some of the magnetic suscpetibility and ashing might give more insight into the material nature of the core at least. I didn't get the impression that she had any calibration to show that warm winters wash less minerals or the like. But maybe she has a reference to a paper where someone else shows this??

    10. There are two things that make LS or DS go up. One is thickness of the layer itself, and one is mineral content (related to XRD, I'm sure). I guess in a simple sense, you could think of LS as the light part of the varve and DS as the dark part (or does it reverse, can't remember). Of course there is a mixing zone. But I guess that is kind of Tiljander's intuition. that the varve can get thicker (overall) because of either more minerals (winter washin) or more organic (summer algea). So she feels sort of justified in differentiating the two. It would be interesting to see or think about how this really plays out. To what extent even in the instrumental record are cold summers and winters correlated? And is it really right to think about the two as sort of independent things, really two sublayers within the layer? Or better to think about overall thickness (And what drives that) versus overall mineral content and what drives that. For instance, when we have a "thick year" is it usually the LS that drives it or the DS (or either)?

    Looking at you figure, it seems like DS drives the bus a little more. I mean it is bigger than LS overall (although not far off). You can see some interesting things going on post 1900 when LS twice rises above DS, which it never did before. Could be the modern land use/contaminaiont (or could be climate perhaps, for instance if LS more affected by climate). Also looking at some of the peak years, there are interesting behaviors. Like at 600, 650, the spikes seem to be more driven by DS than LS. Arguable 1330 is driven by both. Interesting to see how many peaks seem to be driven by both, though. LS and DS do not seem very decoupled from each other. Maybe a plot of thickness and % LS would be interesting.

    I'm rambling and what started as a critical comment, kinda has me evolving my thinking. I did like her micrograph pictures of the little rock grains inside the layers. :)

  6. 11. The bridge is interesting. Seems like one could maybe excise that year or two. also, to the extent thatit affects flow and that affects sediment...maybe that is an insight into what happened previously as well. Maybe when a tree falls across the river one year you have differnt flow into the lake that next year. Maybe there was a mideival mill (I just read Chricton's Timescape) on the river from 1000-1700. I donno...

    12. the confounding of precip issues with temp signals is interesting. I wonder if looking at the instrumental record might help us bound this confounding issue. Like do they generally trend togother in a manner that would help us (in extracting signal) or do they trend apart or just independent? IOW are cooler winters normally wetter anyhow and warmer summers wetter also? That would be nice...

    13. XRD is interesting. Only one without a huge ramp. I kind of think of it as % LS or % minerality. sorta makes sense that is more behave, I guess. Boy thiks would have been much simpler and more defeinsible if all he had was the thickness! ;)

  7. 14. Just checking, you used tha ctuall dat for the average and standard deviation, right? Not the smoothed stuff?

    15. DS doesn't actualy look that crazy. I mean if you accept a warmer 20th century. Yeah, you're not seeing MWP, exactly, but you can kinda make out a LIA and it's a plausible looking little hockey stick.

    16. LS is a little crazier looking.

    17. Thicnkess: no comment. Not indpenedant.

    18. Wait...kind of a slight increase in minerality (do I have directions right) in last few years. Does higher XRD mean less transparent to X rays which means more rocks, less plant poop? I need to break down and figure out what XRD means. anyhow...if he had just used this as his hockey stick, no one would have noticed and been on his ass. It pretty much looks like an anamoly plot of temp, no?

  8. 19. Intersting insight on the 18th century vice 19th and 20th. I wonder if we have Helskini data in early 1800s or even nearby country? If we had to make a guess based on instruments, what kind of curve for Finland would we get 1750-2000 and how does that correspond to the varves? Especially is the high 19th century plausoible temp wise? Or an indicator of land use or something.

    20.'re doing it. I'm read it, now. cool!

    21. Correlation plots are helpful, as it looks to the eye like the temp is more flat until 1900, then up. Perhaps a twosegment line or parabolo would show temp more reasabbly. Anyhow, the correlation shows ti all. A little smoothing might be justified if you're concerned about dating error on the varves I think Tiljander does mention this, and has a plot of how many years could be off for the varve layers. maybe some fancier regression that takes this uncertainty into account would be justified. Seems like a weak relation in LS, DS, thickness and none in XRD, whih is what the eye sees. I wonder what kind of relationshop would be extpected to ve valid. Is this enough?

  9. 2. Extrapolation forwards -- The only advantage I see to this is that it lets you run a standard procedure where the necessary data points aren't there. Whatever the method is, it's just a fancy way of guessing. Seems particularly inapt for setting up a calibration step--calibrating to your guesses.

    4. IIRC, it is mentioned in the paper…

    6. I've found a few papers on varves, but behind paywalls. There's a new Tiljander one for Lake Korttajarvi that I listed in the "Primary sources" post. Printed but not read yet; she does some 13-C and 2-H isotope measurement on the sediments. I don't know what I think about log normalizing, yet. Not necessarily bad. Perhaps the worst is that it makes things more "mathematical," a string of numbers rather than an actual physical measurement. Something that's 0.8 millimeters of fine silt is harder to make silly, fantistic ideas about than a set of strings of digits.

    7. I read somewhere that Lightsum is measured, and thickness is measured, as "with a caliper," and that Darksum is the difference. Tiljander03? Anyway just adding the columns in Excel makes it totally obvious. The graphic makes it totally^2 obvious. Interestingly, (infilled Thickness) - (infilled Lightsum) = (infilled Darksum). By intent (ie with understanding), or courtesy of blindly precise formulas?

    8. I'm pretty sure this is how XRD works, X-Ray-dense material of a prescribed thickness would be placed over the film (Kodak XAR-5 or equivalent). Then the film is exposed to a preset dose of X-Rays (e.g. an X-Ray source from a medical machine), then developed. The film will be grey, except where the X-Rays were blocked by the sample. The film is then scanned at 600 nm or so, such that dark is a high number and transparent is a low number. Probably absorbance (logarithmic) rather than transmittance (linear).

    --- continues ---

  10. --- continuing ---

    9. For Tiljander's rationale: it makes sense, *I guess*. Probably this is the way varvologists think, "everybody" in paleolimnology seems to have accepted her interpretation no sweat. But there just isn't much there there, in these Korttajarvi core results. I would guess her interpretation is weakly right… but mostly it isn't precipitation/temperature related signal that is interpretable in a straightforward way. As to quantitation, how could she? Quantitate to what? Chicken and egg.

    10. I'm not sure about those things. It'll take more reading of varve papers to figure it out.

    11. Funny, I was thinking that Lightsum (mineral) was the bigger contributor. Transcription error (urk)? Checking… no, you are right. It's Darksum (organic) that's usually the bigger number. In the newer paper, TIljander points out that they drilled in the southern basin of the lake which is fairly isolated from the main northern one. In particular most of the inflows are to the northern part. So dammed rivers, mills, etc. are less likely, based on how they sited their spot.

    12. I dunno, I wondered that too (if there's enough data). There is good temp and precip data from the nearby weather station since ~1890, seasonal averages etc--it's Fig 2 IIRC of Tiljander03. But seemingly not online.

    13. Thought of that too, haven't played. Download the Excel file from Bitbucket, it is set to go for that.

    14. Actual numbers for means and sds, not smoothed.

    15. Darksum as a climate proxy -- totally no sale. Look at the wacky 20th Century swings. This is eutrophication and roadbuilding and…

    18. Not buying for XRD either. It looks only somewhat-bad compared to the others. That means, kinda like noise. Or, kinda like flattish noise that trends upwards starting aroung 1850… goody! Sobering, though--if Mann et al. had just used that, *nobody* would give my comments any credence at all. So he had to do something *really* noxious to finally get a reaction.

    21. The spreadsheet has it set to do correlations on smoothed etc. data too. You can try your own idea and see if it gooses up the R^2. Unsurprisingly given the nature of the time series, the thing that *really* pushes the R^2 up is if you smooth the proxy data *and* smooth the temperature data. But I don't think Mann08 did that. Philosophically, better to use the 5x5 gridcell anomaly calculations, or to use local data when available (as it is here, ~1890-on)? If you believe in teleconnections (e.g. Gulf Stream affecting Baltics, maybe hemispheric cooling causes more Gulfiness thus more Finnish precip thus more Lightsum) -- maybe stick wth CRUTEM. If you are looking for temperature qua temperature, reliable local records would seem like a much better bet.

    Thanks for giving it a look.

  11. By the way, the "R^2" values Excel gives for its linear regression should be the square of "r" as used in Mann08. RomanM says it gets more complicated where more than one dependent variable is at play, but here it seems to be the simple case of {proxy vs temperature}.

  12. I'm not crazy about smoothing the series and then doing correlations. You want to be able to prove this is a proxy by showing that it tracks year to year variations.

    I do think some kind of fancier regression (not sure the formula) that allows for a year of dating error (or whatever she had in her paper, there was a figure on it) might be justified. I' definitely not the one to know how to do that though. And I'm pretty lazy. Prefer to read and comment than actually do analysis.

  13. What are the other series in M08 that are varves? Could we learn something from them? Perhaps see a stronger textbook signal, better calibration, etc?

  14. The more I think about it, the more I dislike the log transformatoion. That really does seem like fishing for the "right" kind of time series vice taking the data. Unless, this is a common practice in varvelogy, this seems very wrong to me. I know it sounds minor, but it kind of bugs me a this shows real looking at the series to try to get them to work. Not just feeding into the proxy hopper and having the defense that it was just another series.