Statistical analysis of tree rings

Good topic Jon, This of course is the crux of the matter. Is Daniel4140 using the same as dendrochronologists, or has he made up a process he thinks is valid. There is one all ready to go at Age Correlations and An Old Earth, Version 2 No 1 that has some updated information and a slightly revised format, including more specific reference citations.Enjoy.

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And Bristlecone Pines are known for having years with no growth ring due to the extreme climate. Matching 0 widths is thus the same as matching other widths. The final correlation between the Bristlecone Pines and the two Oak Chronologies after some 8000 years of correlations is a mismatch of 37 years, with the Bristlecone Pines being "younger" - evidence of more zero growth rings than what was determined in the analysis of the data.The most recent calibration review was done in 2004, and it goes by the name of INTCAL04 (the previous, INTCAL98, was done in 1998):http://www.radiocarbon.org/IntCal04_TOC.pdf
See: INTCAL04 TERRESTRIAL RADIOCARBON AGE CALIBRATION, 0-26 CAL KYR BP
and data sets: http://www.radiocarbon.org/IntCal04.htm
from http://www.radiocarbon.org/ (Radiocarbon Journal on line archives) Volume 46 Number 3, where number 2 and 3 contain the proceedings of the conference.Notice that they did not use the bristlecone pine data, as over a period of some 8000 years covered by the tree rings in three different dendrochronologies, the data was off by 37 years to the other two chronologies:

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The replicate measurements have a mean offset of 37 6 14C yr (n = 21) from the Tucson measurements. Applying this shift to the Tucson data results in a close fit to the wiggles of the German oak, which would not occur if there were an error in the dendrochronology of either series. Because of this offset, the IntCal working group has decided not to include the BCP record in IntCal04.
(IntCal04 Terrestrial 14C Age Calibration, 0-26 cal kyr BP page 1033)

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That's an error of less than 0.5% ...In other words, the effects have been very closely studied and accounted for.This 0 growth ring problem also does not occur with the oak chronologies except for the "year with no summer" - where this shows up right on time.Year Without a Summer - WikipediaAll three chronologies correlate with this event - can you explain how this occurs if the method is fraught with problems? Which just proves that your method to "whiten" the file is false, that the variations you are eliminating are part of the data rather than noise.What you have shown is that in order for you to get rid of the correlations between samples, you have to "whiten" the file until there is no data left. That's pretty conclusive evidence that your method is false.Enjoy.Edited by RAZD, : added linksEdited by RAZD, : updated link to article for website revisionsEdited by RAZD, : no

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That was my first impression. I also see his attempt to "whiten" the data as a means to remove correct correlations and make more erroneous "correlations" possible by having fewer data points to compare.Enjoy.

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One of the places is the IntCal databases, where they have accumulated 14C matches to many other sources of measuring ages, including the tree rings. RADIOCARBON AGE CALIBRATION, 24,000-0 cal BP, RADIOCARBON, VOL. 40, No. 3, 1998, P.1041-1083, has a discussion of the methodology used and of the results for the 1998 calibration. INTCAL04 TERRESTRIAL RADIOCARBON AGE CALIBRATION, 0—26 CAL KYR BP, RADIOCARBON, Vol 46, Nr 3, 2004, p 1029—1058, has a discussion of the updated 2004 calibration and the changes made since 1998. Their data sets are at http://www.radiocarbon.org/IntCal04.htmThe problem you have is that you are fighting the correlation between a linear age counting system - the number of tree rings - against an exponential decay level of 14C inside those rings, and this presents you with an unusual problem to explain -- the different levels of 14C at different ages of the tree rings AND the similar levels of 14C for the same ages of tree rings in the three different tree ring chronologies.Carbon-14 has a half-life of 5730 years and this can be used to calculate an apparent "C-14 age" from the proportion of C-14 to C-12 in an organic sample (that derives its carbon from the atmosphere) and this "date" can be checked against known dates to determine the amount of C-14 that was in the atmosphere:

(Image based on calibration curvefrom Wikipedia(2) - Both images are in the public domain.)Note that the "C-14 age" is really a measurement of the actual ratio of C-14 to C-12 isotopes in the sample, and a comparison of that to modern day proportions.How Carbon-14 Dating Works | HowStuffWorks (5)

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A formula to calculate how old a sample is by carbon-14 dating is:

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t = {ln (Nf/No)/ln (1/2)} x t_1/2
where t is the "C-14 age", ln is the natural logarithm, Nf/No is the percent of carbon-14 in the sample compared to the amount in living tissue, and t_1/2 is the half-life of carbon-14.

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These calibration curves have been extended now to the limits of Carbon-14 dating, but it is also of interest to look at just the Carbon-14 calibration curve for dendrochronology - the results of matching tree-rings to Carbon-14 levels and their implied "C-14 age":404 Page not found (9)

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This means we can look at the "C-14 age" as a measurement of the Carbon-14 actually remaining in the samples from what was absorbed from the atmosphere at the time that the tree-rings were formed and note the following:

• If there were numerous errors in the tree-ring data caused by false rings (as you and others have proposed), then this would show up as a steep rising "C-14 age" that would be much younger than the recorded tree-ring age. This is not the case.
• The false rings would also have to be perfectly matched for each of the species used for the overall dendrochronology ages or the "C-14 age" for each one would be different and the line of calibration would be extremely blurred. This is not the case.
• The age derived from Carbon-14 analysis is consistently younger than the actual age measured by the numerous tree-ring chronologies in pre-historical times, meaning that C-14 dating underestimates the ages of objects.

This may seem off-topic to the issue of the statistical analysis of tree rings, but there is this one little factor that makes it relevant: The ages of the tree-ring data are validated by the carbon-14 levels in the samples. This a test of the methodology used by the dendrochronologists: they made their chronologies based on the tree ring patterns, and if their method were wrong there should be no correlation between age and 14C content and there should be no correlation between 14C levels for the same ages in the different chronologies.The "carbon-14 age" of a sample is really a measurement of the quantity of carbon-14 in the sample compared to the total carbon in the sample. This existing proportion of 14C/12C is just as much a part of the objective data to be matched from tree ring to tree ring as the width and density of the rings.This quantity measurement is transformed by a mathematical formula based on radioactive decay into a theoretical "age," but this "age" is really just a mathematical scale for displaying the actual amount of carbon-14 in the sample. The point here is that it does not matter what you or other creationists think about the validity of carbon-14 dating in particular, radiometric dating in general, or radioactive decay, because two samples of the same age - that lived in the same atmospheric environment and absorbed the then existing levels of atmospheric carbon-12, carbon-13 and carbon-14 (the three common isotopes) - will have the same levels of carbon-14 in the samples today.No fantastic scheme invented to change the way radioactivity works will change that simple fact, for whatever is changed in one sample is changed in all the others of the same time. Thus, when sample {A} is dated to {X} years by dendrochronology and it has level {Y} carbon-14 content, and when sample {B} is also dated to {X} years by dendrochronology and it has level {Y} carbon-14 content, the carbon-14 content validates the age - because, growing in the same environment, they could not be the same age and NOT have the same carbon-14 content.This simple fact will also refute any mismatch you propose to fit old wood to younger years.The earth is old, get used to it. You have been unable to refute the Lake Suigetsu data, your sources have been shown to provide false information on tree ring (your medical doctor's powerpoint presentation) and on the "equilibrium" of 14C in the atmosphere (see Message 159), and your method here is demonstrably questionable at best.Why do creationists need to use false information if their methods and conclusions are correct?Enjoy.

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Check out the IntCal98 information - they used a moving average (p 3/1043)

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Part of single-year Δ¹⁴C (expressed as the per mil (&permil) deviation of tree-ring 34C activity from NBS oxalic acid activity, corrected for isotope fractionation, Stuiver and Polach 1977) is tied to 11-yr-cycle solar modulation of atmospheric ¹⁴C production. Pacific Northwest single-year data (when averaged with those of a Kodiak Island tree) yield a three-year moving average for the AD 1897- 1945 interval with 11-yr-cycle Δ¹⁴C modulation averaging 2.5‰ (peak to peak) over four cycles (Stuiver and Braziunas 1998). Twenty ¹⁴C years appears to be an upper limit for single-yr ¹⁴C age change induced by the 11-yr cycle. The standard deviation introduced by 11-yr modulation around the long-term (e.g., decadal average) trend is a much smaller 8¹⁴C yr (as derived from a 2.5‰ peakto-peak sinusoidal Δ¹⁴C cycle).

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I would think you would want to use 11 year moving average to reduce the effect of an 11 year cycle, so that each averaged value would be for a whole 11 year segment.This method does not appear in the IntCal04 article, so I would assume that Daniel4140 is using the older information based on his comment of making a previous model.He may be confusing methodology for 14C with that for tree ring counting.Enjoy.Edited by RAZD, : lastPEdited by RAZD, : link

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Curiously I cannot find that statement in any of the three links Jon provided. Can you provide your source?Unpublished does not mean invalid nor does it mean that the data is not reviewed. What it usually means is that it is part of ongoing research, and the data is being made available early, which would be consistent with it being available in the data bank for you to access and critique. Where? All I see is data sets and articles that refute your position. This includes creationist articles such as: AiG article: "Biblical Chronology and the 8,000-Year-Long Bristlecone Pine Tree-Ring Chronology"

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The 8,000-year-long BCP chronology appears to be correctly crossmatched, and there is no evidence that bristlecone pines can put on more than one ring per year. The best approach for collapsing this chronology, one that takes into the account the evidence from C-14 dates, is one that factors the existence of migrating ring-disturbing events. Much more must be learned about this phenomenon before this hypothesis can be developed further.

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In other words they can find no mechanism to cause the tree ring chronology to be anything but correct.Here's another one: CreationResearch.org abstract: "Tree-Ring Dating and Multiple Ring Growth Per Year"

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There presently exist several long dendrochronologies, each comprised of about 10,000 individual growth-rings. These are examined for the possibility of multiple ring growth per year in their earliest portions due to unusual climatic conditions following the Flood. It is found that the tree-ring/radiocarbon data are contrary to the suggestion of multiple ring growth. Since it seems that the Flood must have occurred before the oldest rings of these series grew, the implication is that the Flood must have occurred more than 10,000 years ago.

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No evidence of any false correlations or mechanism to reduce the data in a way that can fit young earth scenarios.And here's another one: Biblical Chronologist.org article: "Are tree-ring chronologies reliable?"

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An Independent Check

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Early in the history of the science of dendrochronology, a tree-ring chronology using bristlecone pines from the White Mountains of California was developed. Separate dendrochronologies were then developed, also in America, using other types of trees, such as Douglas fir. These separate chronologies did not extend as far back in time because these types of trees are shorter-lived. However, they did agree with the bristlecone chronology as far back as it could be checked by the shorter chronologies. That is, rings of the same putative dendrochronological age were found to contain the same amount of radiocarbon, and to give the same pattern of fluctuations over time.

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European Tree-ring Chronology

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While American scientists were building bristlecone pine and Douglas fir chronologies, European scientists were actively building a very long tree-ring chronology using oak trees. ... The European oak chronology provided an excellent check of the American dendrochronologies. The two were obviously independent. Ring-width patterns are determined by local environmental factors, such as temperature and rainfall. The patterns in America could not bias the work on patterns in Europe, because the specimens came from two different local climates, separated by an ocean. The scientists worked independently of one another. Also, oak trees and bristlecone pine or Douglas fir trees are very different. Bristlecones, for example, are evergreens which grow very slowly, at high altitude, in a cold, arid environment, and live for thousands of years. None of these things are true of the oaks used in the European chronology. They are deciduous, grow relatively rapidly, at low altitudes, in relatively warm, moist environments, and live for only hundreds of years.

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If the science of dendrochronology was characterized by significant random error, the American and European tree-ring chronologies would certainly disagree with each other. In fact, a comparison of the European and American chronologies showed very close correlation. The pattern of radiocarbon in the rings showed a maximum divergence, even at very old ages, of only around 40 years. This objective, quantitative test of dendrochronology showed it to be reliable and accurate.

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Multiple Rings Per Year?

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These checks show that tree-ring chronologies are not subject to significant random error. However, some critics of dendrochronology go on to suggest that trees in ancient history grew multiple rings per year, perhaps due to Noah's Flood, for example. A number of evidences argue strongly against such a claim.

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Third is an argument which is perhaps the most definitive falsification of the idea that trees grew more than one ring per year in ancient history. Here is a greatly condensed version of this argument.

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Our sun occasionally goes through periods of quiescence. During these periods few sunspots are seen on the sun's surface and the solar wind is reduced. This lets more cosmic radiation into the upper atmosphere of the earth, which allows more radiocarbon to be produced in the atmosphere. These periods of quiescence occur in two varieties, one lasting an average of 51 years, and the other lasting an average of 96 years.

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How does this relate to tree-rings? During these periods of quiescence, atmospheric radiocarbon concentrations are higher. This difference in radiocarbon concentration is recorded in tree rings which are growing during the period of quiescence. If trees were growing two or three rings per year at the time one of these episodes occurred, two or three times as many rings would be affected than if trees were only growing one ring per year. In other words, if trees were growing one ring per year, a 51-year period of solar quiescence would affect 51 tree rings. If trees were growing three rings per year, a 51-year period of solar quiescence would affect about 153 rings. Thus, a record of ring growth per year is preserved in the number of rings affected by these periods of solar quiescence.

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In fact, at least 16 of these episodes have occurred in the last 10,000 years.These 16 episodes are more or less evenly distributed throughout those 10,000 years. In all cases, the number of rings affected is grouped around 51 or 96 rings. Thus it is clear that, for at least the last 10,000 years, trees have been growing only one ring per year. The suggestion that dendrochronology is invalidated by growth of multiple rings per year is thus falsified.

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It all comes back to the correlations within the data contained in the tree rings.Thus we see that the methodology used by dendrochronologists is validated by the independent data from other chronologies and from 14C/12C content within the rings.Your method has not been able to show any such correlation for verification of your methodology - why do you suppose that is? And I guess the creationists that wrote, and published, the articles above, are also part of the conspiracy?Enjoy.Edited by RAZD, : clrty

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And I assume the same correlation will hold through the Lake Suigetsu varve data as well - it would be interesting to pursue on another thread for the lake varves.Looking at just the issue of statistical analysis of tree ring chronologies, the 14C data is secondary to the initial methodology and best serves as a back-check on consistency of application of the methodology. This is due to the fact that, even without the issue of the validity of 14C dating, the actual raw data levels of 14C/12C correlate with these solar cycles as well as having the same levels across the tree ring lineages. We don't need to convert them to ages for these correlations of be important validation of the methodology of the dendrochronologists. Sorry, I'm not a "seer" (or a "biased guesser") in spite of what some people think.Enjoy.Edited by RAZD, : No reason given.

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