Ground truth · dendrochronology

Every Tree Wrote the Same Bad Year

You cannot date a piece of wood by counting its rings. What you do instead is find the year the weather went wrong and look for it in everything else that was standing. This page carries 45,411 published ring measurements from 109 cores in three collections, and no dates are used until you ask for them. Slide a core against a chronology and watch a year lock on. Then run the tests that say whether to believe it.

In 1929 the whole of Ancestral Puebloan archaeology had no calendar. Ruins across the Colorado Plateau were ordered by pottery style and guesswork, and the guesses ran centuries apart. Then a charred roof beam pulled out of a wall in Show Low, Arizona, was matched against a sequence of tree rings, and a stretch of prehistory acquired exact years. Not a range. Years.

The claim is extravagant. A piece of wood, no label, no context, and a laboratory returns a single calendar year for its outermost ring. The reasonable response is to ask how anyone could possibly check that. So this page checks it, in front of you, on real data, and then keeps going until it finds the places where the method is weaker than its reputation.

1. The lock

Here are two Douglas-firs. One grew at Navajo National Monument in northern Arizona, cored by the archaeologist Jeffrey S. Dean. The other grew at Mesa Verde in Colorado, cored by Edmund Schulman. The sites are 187 km apart. Nothing connects the two trees except the weather over the Colorado Plateau.

Drag the lower trace, or use the slider. Every position is a guess about what year the first ring of the lower core belongs to. Watch what the two traces do to each other.

At almost every position the two traces are unrelated scribbles. At one position they are the same scribble. The eye finds it before the arithmetic does, which is the whole trick: a dry year narrows the ring in every tree on the plateau at once, so a run of good and bad years is a barcode that the region prints simultaneously into everything growing in it.

2. What the arithmetic is, exactly

The number in the readout is the one the field has used since 1973. Mike Baillie and Jon Pilcher, at Queen's University Belfast, published a short paper with a FORTRAN listing in it, and the program has outlived the machine it ran on. It does two things.

First it filters. A tree gets wider rings when it is young and narrower ones as it ages and thickens, and that trend is the tree's own biography, not the weather's. So each ring width is divided by the average of the five rings centred on it, which throws away everything slower than about five years and keeps the jitter:

The program carries out a simple standardization where each ring width is converted to a percentage of the mean of the five ring widths of which it is the centre value. In this form the data varies about a mean of 100 but is not normally distributed. Normalization is achieved by taking log to base e of the percentage figures. Baillie & Pilcher 1973, p. 11

That is one line of their FORTRAN, and it is the line this page runs: A(I) = ALOG(500 * A(I+2) / (A(I)+A(I+1)+A(I+2)+A(I+3)+A(I+4))). Then it correlates the filtered series against the chronology at every possible position and converts each correlation to Student's t. Bigger overlap and higher correlation both push t up.

And then there is the number everybody quotes. A match with t ≥ 3.5 is treated across the discipline as significant. Here is where that number comes from, in the authors' own words, in the section of the paper that describes what the program prints:

At the end of the table of t values there is a summary of all values greater than an arbitrary preset value of 3.5. Baillie & Pilcher 1973, p. 11. The FORTRAN comment on the previous page reads "VALUES OF 'T' ARE SCANNED FOR ANY OVER A PRESET VALUE OF 3.5".

An arbitrary preset value, in a print routine, to keep the output short. It was never a critical value from a table. Hold on to that, because section 5 measures what it is worth.

3. Date a core with its dates taken away

Pick any of the 48 cores from the Arizona collection. The page builds a chronology out of the other 47, discards the chosen core's dates entirely, and tries it at every position with at least 100 years of overlap. Nothing about the true answer enters the search.

One core is an anecdote. Run all of them.

4. Against a stranger's trees

The first experiment has an obvious weakness, and it is worth naming before the numbers arrive. The 48 Arizona cores were dated together, by one person, as one collection. Asking whether 47 of them can date the 48th is asking whether a collection agrees with itself.

So the second experiment hands the same cores to a chronology they have nothing to do with. Mesa Verde is 187 km away in another state, was cored by a different scientist a generation earlier, and shares not one tree with Navajo National Monument. If the barcode is really the region's weather and not an artefact of one collector's habits, it should transfer.

It does. Every one of the 48 Arizona cores lands on its published year against the Colorado chronology, and the weakest of those 48 correct matches still reaches t = 7.21.

5. Now the control, and what the threshold is worth

A method that says yes to everything is worthless, so the third experiment gives it something that cannot possibly match. Herring Alpine is a western hemlock stand on the coast of Alaska: a different genus, a wet maritime climate, 3,718 km from Arizona. No Arizona core has any business matching it.

None of them do. Zero of 48 land on the right year. But look at what they land on instead, because this is the part the textbooks state as a warning and never quantify:

Roughly half the cores produce a "significant" match at a date that is certainly wrong. The strongest of them is stronger than the threshold by a comfortable margin. That is not a flaw in the arithmetic; it is what happens when you take the best of several hundred tries and then apply a cutoff designed for one try. Baillie and Pilcher's own paper has the warning, two sentences after the formula:

Even when the computer indicates a high degree of confidence in the crossdating, this must still be checked visually. Baillie & Pilcher 1973, p. 11

And yet the method is not in trouble, which is the second half of the finding and the part that surprised us. Put the two distributions side by side. The best false match anyone can squeeze out of 3,718 km of irrelevance is 5.17. The weakest genuine match against an independent chronology is 7.21. There is clear air between them. The conventional threshold sits well down inside the noise, and the real signal is not near it at all: it is two to ten times higher.

This is not a hypothetical worry, and the discipline is not hiding from it. In 2009 Carol Griggs and Sturt Manning went back to a published Anatolian chronology from Tille Höyük and took it apart:

a few of the short overlaps (~30 yr) critical to the construction of the original chronology, were based on false, but highly positive, statistical values plus good visual correlations. This often occurs in matching tree-ring patterns with short overlaps, and is a problem well-recognized in dendrochronology. Griggs & Manning, "A Reappraisal of the Dendrochronology and Dating of Tille Höyük (1993)," Radiocarbon 51(2), 2009, p. 711

False, but highly positive, and the eye agreed with the arithmetic. The two building phases survived the reappraisal; their order in time did not. Note who found the error: the same laboratory that had published the chronology, using an independent method that did not share the first one's assumptions. That is the shape a healthy check has.

6. The move that founded the field, redone

Everything so far dates one core against a chronology that already exists. The harder problem, and the one that made 1929 matter, is what to do when nothing is dated at all.

The Arizona collection contains four cores from wood that stopped growing long before the collectors arrived: they end in 1555, 1614, 1699 and 1919. Treat them as archaeology. Strip every date. They are now four sticks with no calendar.

The procedure is Douglass's. Crossdate the sticks against each other until they form one long sequence with internal years but no external ones, a chronology that floats. Then, and only then, slide the whole float against wood that carries a calendar from outside the wood. That outside anchor is the one thing in the whole edifice that pattern matching cannot supply, and Douglass names it in his first book:

The fundamental starting-point in all identification is the ring partially formed at the time of cutting the tree. Douglass 1919, Climatic Cycles and Tree-Growth I, p. 15

Somebody stood in front of a tree in a year they wrote down. Every date below descends from that, and nothing on this page can audit it.

The popular version of 1929 says a beam bridged a gap between a dated chronology and a floating one. The popular version is wrong, and Douglass says so himself. What beam HH-39 actually did was settle a doubt:

We had not a gap to bridge, as we had thought, but one we had closed without knowing it! Our two chronologies had covered an overlapping period. But those rings of the old series which overlapped the new at 1260 had been gathered from such small fragments that I had never been willing to accept their evidence. A. E. Douglass, "The Secret of the Southwest Solved by Talkative Tree Rings," National Geographic 56(6), December 1929, pp. 736-770

The overlap was already there. Douglass had refused to publish on evidence he did not trust, and went on refusing for two years. The historian of the field, Stephen Nash, went through the records and found that Douglass had privately closed the gap in 1927 and said nothing. What HH-39 gave him was not the join. It was permission to believe the join.

7. One ring that is not there

Now the failure the whole method exists to survive. In a dry year a conifer can lay down no ring at all along part of its circumference, or lay down two. A locally absent ring is not rare in the American Southwest, and it is invisible: there is nothing to see where nothing grew.

Counting rings cannot survive this, and the man who founded the discipline is the one who measured how badly. Douglass had originally put the error in simple counting at two per cent. Then he invented crossdating and checked:

Superficial counting of rings is subject to errors due to omission and doubling of rings. In the first investigation of trees at Flagstaff it was supposed that the results were subject to an error of 2 per cent, most of which arose from double rings near the center of the tree. But the discovery and application of the method of cross-identification revolutionized the process of ring identification, and it was proved that the error of unchecked counting in the Arizona pines was 4 per cent and lay almost entirely in the recent years. Douglass 1919, Climatic Cycles and Tree-Growth I, p. 15

Four per cent of a five-hundred-year-old tree is twenty years, and you would never know. Crossdating survives it, and the way it survives is worth watching.

The whole-core date comes out wrong, and it comes out wrong in a specific way: the match splits the difference, aligning either the part before the deletion or the part after it, never both. Meanwhile the segmented test (this is what Richard Holmes's COFECHA program does) breaks into two blocks that disagree by exactly one year, and the boundary between them is where the ring went missing. The method does not just fail. It says where.

The deleted ring above is ours, but the failure it simulates is not. In 2025 Marta Domínguez-Delmás re-measured two oak panels behind Rembrandt portraits that Peter Klein had dated in the 1990s, and found this exact class of error sitting inside a published result:

The series of the GNM panel seems to have one ring too much (either the ring corresponding to the year 1426 or 1427 was measured or annotated twice) and one too few. Marta Domínguez-Delmás, "A replication study in dendrochronology: revisiting the panels of two portraits of Rembrandt," Humanities and Social Sciences Communications 12 (2025), article 1778

One ring counted twice and one missed. The two cancel in length, so the ends of the series still fall where they should, but they do not cancel in pattern: everything between them is displaced by a year. What that produced was not a wrong date. It was a correct date carrying a weaker statistic than it should have had, which the original study reported without knowing why. The conclusions survived, and the paper is explicit that the conclusions surviving is a separate fact from the measurements being right.

8. How many trees

One core is a tree's opinion, and trees have private opinions: a rock under the roots, a neighbour that fell. Averaging cancels the private part and keeps the shared part. The standard measure of when you have averaged enough is the expressed population signal, EPS = N r̄ / (1 + (N-1) r̄), where r̄ is the mean correlation between cores.

The Southwestern sites need almost nothing, because the drought signal is so loud that any few trees agree. The Alaskan site needs several times more for the same nominal quality, and a wet temperate site with no single limiting climate factor can need dozens.

Where this bites is not at the site, it is at the joins. A chronology is only as good as its thinnest year, and the thin years are usually where two pieces of wood were spliced. In 2016 Sturt Manning and colleagues withdrew a set of published crossdates that had been carrying Bronze Age Anatolian chronology, and the reason was arithmetic about sample depth, not about statistics:

the part of the chronology linking Gordion and Porsuk contains very low sample depth, with just 1 or 2 trees in the Gordion chronology, too few for any secure crossdating following standard dendrochronological methods, which makes the best available match, whether statistical, visual, or both, highly tentative at best. Manning et al., "Integrated Tree-Ring-Radiocarbon High-Resolution Timeframes to Resolve Earlier Second Millennium BCE Mesopotamian Chronology," PLOS ONE 11(7), 2016, e0157144. Their figure captions read "the original, now withdrawn, positions".

One or two trees, in the years that joined two chronologies together, holding up a date that a great deal of archaeology then leaned on. The paper's own summary of the cause is worth reading twice: "fundamental problems with key dendrochronological crossdates due to small sample numbers in overlapping years and insufficient critical assessment."

9. What the filter throws away

Return to the five-year running mean in section 2. It is what makes dating work: it deletes the tree's slow biography so that only the region's fast jitter is left to match on. But a filter cannot know why a signal is slow. Anything slow goes, including the climate.

The Mesa Verde collection reaches back to 1176, which means it covers the drought that Douglass himself identified in the 1920s and that has been argued over ever since: the long dry stretch at the end of the thirteenth century, contemporaneous with the depopulation of the Colorado Plateau. Standardise the cores with a stiff curve that keeps slow variation and the drought is the worst multi-decade stretch in eight centuries. Run the same cores through the crossdating filter and it is not there at all.

This is the trade at the centre of the discipline, and it has a name. Cook, Briffa, Meko, Graybill and Funkhouser called it the segment length curse: the low frequencies you can recover are bounded by the length of the individual pieces of wood you standardised, not by the length of the chronology you built out of them. Their own statement of the limit is stricter than the version usually repeated:

In the time domain, this is equivalent to a sine wave with a wavelength of n years. So for a 300-year chronology, it is possible in principle to identify a climatic fluctuation or cycle of that duration in the data (in fact, the realistic frequency limit is probably more like 3/n, or 100 years in this case). Cook, Briffa, Meko, Graybill & Funkhouser, "The 'segment length curse' in long tree-ring chronology development for palaeoclimatic studies," The Holocene 5(2), 1995, p. 230

So a date and a climate history are extracted from the same wood by filters that are close to opposites, and a chronology built to be excellent at one is not thereby good at the other. The dating is not in question here. What is in question is the temptation to read a dating-grade chronology as a climate record.

10. What a date actually dates

The last thing to be honest about is the smallest and the most often lost. Crossdating returns the calendar year of a ring. It does not return the year the tree was felled unless the bark is still on the sample, and it does not return the year the building went up.

Wood is stored, reused, salvaged, and trimmed. If the outer rings have been cut away in shaping the beam, the date recovered is a boundary and not an event. What survives on the sample decides which of four quite different statements you are entitled to make:

The three lower rows are the ordinary case in archaeology. The bottom row is the one that gets flattened in retelling, because "dated to 1486" reads the same on the page whether it means a felled year or a floor. The distinction, and the roughly ten-year figure for oak sapwood, are set out in Tegel, Muigg, Skiadaresis, Vanmoerkerke & Seim, "Dendroarchaeology in Europe," Frontiers in Ecology and Evolution 10 (2022), article 823622, doi:10.3389/fevo.2022.823622, which is open access.

And then felling is still not building. A beam can season, sit in a yard, be carried across a country, or be pulled out of an older structure and used again. Every honest tree-ring report says which of these steps it has evidence for and which it is inferring. Our own instruments above date the first ring present in a core and nothing else, which is why they say exactly that in the readout rather than announcing a felling year they cannot know.

Sources

1. Baillie, M. G. L. & Pilcher, J. R. 1973. "A simple crossdating program for tree-ring research." Tree-Ring Bulletin 33: 7-14. repository.arizona.edu/handle/10150/260029. Open access; the quotations above were read from the PDF at /server/api/core/bitstreams/91f4f9cd-2926-4fd3-bd29-6655d779ebac/content.
2. Douglass, A. E. 1929. "The Secret of the Southwest Solved by Talkative Tree Rings." The National Geographic Magazine 56(6): 736-770. Scan of the offprint: ltrr.arizona.edu.
3. Douglass, A. E. 1919. Climatic Cycles and Tree-Growth, Vol. I. Carnegie Institution of Washington, Publication 289. archive.org. The opening of the introduction states the motive: the work "was approached by the author from the standpoint of astronomy and a desire to understand the variations of the sun."
4. Nash, S. E. 2016. "HH-39: Why Good Science Doesn't Need Eureka Moments." SAPIENS, 17 May 2016. sapiens.org. Nash's book-length treatment is Time, Trees, and Prehistory (University of Utah Press, 1999).
5. Haury, E. W. 1962. "HH-39: Recollections of a dramatic moment in southwestern archaeology." Tree-Ring Bulletin 24(3-4): 11-14. hdl.handle.net/10150/259283. Haury flags his own famous version of the scene as reconstructed from memory.
6. Cook, E. R., Briffa, K. R., Meko, D. M., Graybill, D. A. & Funkhouser, G. 1995. "The 'segment length curse' in long tree-ring chronology development for palaeoclimatic studies." The Holocene 5(2): 229-237. doi:10.1177/095968369500500211. Freely readable copy: st-andrews.ac.uk.
7. Buras, A. 2017. "A comment on the expressed population signal." Dendrochronologia 44: 130-132. doi:10.1016/j.dendro.2017.03.005.
8. Wigley, T. M. L., Briffa, K. R. & Jones, P. D. 1984. "On the Average Value of Correlated Time Series, with Applications in Dendroclimatology and Hydrometeorology." Journal of Climate and Applied Meteorology 23(2): 201-213. doi. The source of the EPS formula. Paywalled; not read here.
9. Wigley, T. M. L., Jones, P. D. & Briffa, K. R. 1987. "Cross-dating methods in dendrochronology." Journal of Archaeological Science 14(1): 51-64. doi:10.1016/S0305-4403(87)80005-5. Paywalled; not read here. Its abstract states that all the methods compared "are sometimes found to produce spurious dates or to fail to identify a known correct match."
10. Griggs, C. & Manning, S. W. 2009. "A Reappraisal of the Dendrochronology and Dating of Tille Höyük (1993)." Radiocarbon 51(2): 711-720. doi:10.1017/S0033822200056046. Freely readable at the publisher; the quotation above was read from that PDF.
11. Manning, S. W. et al. 2016. "Integrated Tree-Ring-Radiocarbon High-Resolution Timeframes to Resolve Earlier Second Millennium BCE Mesopotamian Chronology." PLOS ONE 11(7): e0157144. doi:10.1371/journal.pone.0157144. Open access.
12. Domínguez-Delmás, M. 2025. "A replication study in dendrochronology: revisiting the panels of two portraits of Rembrandt." Humanities and Social Sciences Communications 12: article 1778. doi:10.1057/s41599-025-06066-2. Open access.
13. Tegel, W., Muigg, B., Skiadaresis, G., Vanmoerkerke, J. & Seim, A. 2022. "Dendroarchaeology in Europe." Frontiers in Ecology and Evolution 10: 823622. doi:10.3389/fevo.2022.823622. Open access; the source for the felling-date ladder in section 10.
14. Buras, A. & Wilmking, M. 2015. "Correcting the calculation of Gleichläufigkeit." Dendrochronologia 34: 29-30. doi:10.1016/j.dendro.2015.03.003. Paywalled; not read here. The corrected form this page implements, in which an interval where both series are flat scores full agreement rather than half, is the one carried by the current released source of the R package dplR, which we did read.
15. Holmes, R. L. 1983. "Computer-assisted quality control in tree-ring dating and measurement." Tree-Ring Bulletin 43: 69-78. The COFECHA segmented diagnostic that instrument 6 reimplements. hdl.handle.net/10150/261223.
16. The measurement files: NOAA National Centers for Environmental Information, International Tree-Ring Data Bank, measurements/northamerica/usa/ (az023.rwl, co021.rwl, ak001.rwl).