Editing Dendrochronology (section)

==Methods==
[[File:Dendrochronological drill hg.jpg|thumb|240px|Drill for dendrochronology sampling and growth ring counting]]

=== Growth rings ===
{{Redirect-distinguish|Tree ring|Tree ring (landscape feature)}}
{{Further|Wood}}

[[File:Tree secondary growth diagram.svg|thumb|left|Diagram of [[secondary growth]] in a [[tree]] showing idealised vertical and horizontal sections. A new layer of [[wood]] is added in each growing season, thickening the stem, existing branches and roots, to form a growth ring.]]
Horizontal [[cross section (geometry)|cross sections]] cut through the [[trunk (botany)|trunk]] of a [[tree]] can reveal growth rings, also referred to as '''tree rings''' or '''annual rings'''. Growth rings result from new growth in the [[vascular cambium]], a layer of cells near the [[bark (botany)|bark]] that botanists classify as a [[lateral meristem]]; this growth in diameter is known as [[secondary growth]]. Visible rings result from the change in growth speed through the [[season]]s of the year; thus, critical for the title method, one ring generally marks the passage of one year in the life of the tree. Removal of the bark of the tree in a particular area may cause deformation of the rings as the plant overgrows the scar.

The rings are more visible in trees which have grown in [[temperate zone]]s, where the seasons differ more markedly. The inner portion of a growth ring forms early in the growing season, when growth is comparatively rapid (hence the wood is less dense) and is known as "early wood" (or "spring wood", or "late-spring wood"<ref>"Early wood" is used in preference to "spring wood", as the latter term may not correspond to that time of year in climates where early wood is formed in the early summer (e.g. [[Canada]]) or in autumn, as in some [[Mediterranean region|Mediterranean]] species.</ref>); the outer portion is the "late wood" (sometimes termed "summer wood", often being produced in the summer, though sometimes in the autumn) and is denser.<ref>{{Cite book |last=Capon |first= Brian |title= Botany for Gardeners |year=2005 |pages=66–67 |edition= 2nd |isbn=978-0-88192-655-2 |publisher= Timber Publishing |location=Portland, OR}}</ref>{{better source needed|date= November 2014}}

[[File:Tilia tomentosa coupe MHNT.jpg|thumb|[[Silver lime]] cross section showing annual rings.]]

Many trees in temperate zones produce one growth-ring each year, with the newest adjacent to the bark. Hence, for the entire period of a tree's life, a year-by-year record or ring pattern builds up that reflects the age of the tree and the climatic conditions in which the tree grew. Adequate moisture and a long growing season result in a wide ring, while a drought year may result in a very narrow one.

Direct reading of tree ring chronologies is a complex science, for several reasons. First, contrary to the single-ring-per-year paradigm, alternating poor and favorable conditions, such as mid-summer droughts, can result in several rings forming in a given year. In addition, particular tree species may present "missing rings", and this influences the selection of trees for study of long time-spans. For instance, missing rings are rare in [[oak]] and [[elm]] trees.<ref>The only recorded instance of a missing ring in oak trees occurred in the year 1816, also known as the "[[Year Without a Summer]]".{{cite web |url=http://www.ltrr.arizona.edu/lorim/good.html |title= Useful Tree Species for Tree-Ring Dating |author= Lori Martinez |year= 1996 |access-date= 2008-11-08 |url-status= live |archive-url=https://web.archive.org/web/20081108094321/http://www.ltrr.arizona.edu/lorim/good.html |archive-date=2008-11-08 }}</ref>

Critical to the science, trees from the same region tend to develop the same patterns of ring widths for a given period of chronological study. Researchers can compare and match these patterns ring-for-ring with patterns from trees which have grown at the same time in the same geographical zone (and therefore under similar climatic conditions). When one can match these tree-ring patterns across successive trees in the same locale, in overlapping fashion, chronologies can be built up—both for entire geographical regions and for sub-regions. Moreover, wood from ancient structures with known chronologies can be matched to the tree-ring data (a technique called 'cross-dating'), and the age of the wood can thereby be determined precisely. Dendrochronologists originally carried out cross-dating by visual inspection; more recently, they have harnessed computers to do the task, applying statistical techniques to assess the matching. To eliminate individual variations in tree-ring growth, dendrochronologists take the smoothed average of the tree-ring widths of multiple tree-samples to build up a 'ring history', a process termed replication. A tree-ring history whose beginning- and end-dates are not known is called a 'floating chronology'. It can be anchored by cross-matching a section against another chronology (tree-ring history) whose dates are known.

A fully anchored and cross-matched chronology for oak and pine in central Europe extends back 12,460 years,<ref>{{cite journal |last1=Friedrich |first1=Michael |last2=Remmele |first2=Sabine |last3=Kromer |first3=Bernd |last4=Hofmann |first4=Jutta |last5=Spurk |first5=Marco |last6=Felix Kaiser |first6=Klaus |last7=Orcel |first7=Christian |last8=Küppers |first8=Manfred |title=The 12,460-Year Hohenheim Oak and Pine Tree-Ring Chronology from Central Europe—A Unique Annual Record for Radiocarbon Calibration and Paleoenvironment Reconstructions |journal=Radiocarbon |date=2004 |volume=46 |issue=3 |pages=1111–1122 |doi=10.1017/S003382220003304X |bibcode=2004Radcb..46.1111F |s2cid=53343999 |url=http://physics2.fau.edu/~wolf/BasicScience/Friedrich_Dendro_RC04.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://physics2.fau.edu/~wolf/BasicScience/Friedrich_Dendro_RC04.pdf |archive-date=2022-10-09 |url-status=live }}</ref> and an oak chronology goes back 7,506 years in Bohemia, 7,429 years in Ireland and 6,939 years in [[England]].<ref name="kyncl" /><ref>{{cite book |chapter-url= https://books.google.com/books?id=1rYCjUzMM3UC&q=northern+ireland+dendrochronological&pg=PT145 |chapter= 5.2.3 Dendrochronological Series |first= Mike |last= Walker |title= Quaternary Dating Methods |publisher= John Wiley and Sons |year=2013 |isbn= 9781118700099 |url-status= live |archive-url= https://web.archive.org/web/20161128050944/https://books.google.co.uk/books?id=1rYCjUzMM3UC&pg=PT145&lpg=PT145&dq=northern+ireland+dendrochronological&source=bl&ots=-83vqIKmdt&sig=gvKAhREENtGBCdVV2TK7131y92I&hl=en&sa=X&ved=0ahUKEwjR65yEzcnQAhXKCsAKHUP_CG84ChDoAQgqMAM#v=onepage&q=northern%20ireland%20dendrochronological&f=false |archive-date=2016-11-28}}</ref> Comparison of radiocarbon and dendrochronological ages supports the consistency of these two independent dendrochronological sequences.<ref>{{cite journal |last1=Stuiver |first1=Minze |last2=Kromer |first2=Bernd |last3=Becker |first3=Bernd |last4=Ferguson |first4=C W |title=Radiocarbon Age Calibration back to 13,300 Years BP and the {{chem|14|C}} Age Matching of the German Oak and US Bristlecone Pine Chronologies |journal=Radiocarbon |date=1986 |volume=28 |issue=2B |pages=969–979 |doi=10.1017/S0033822200060252 |bibcode=1986Radcb..28..969S |doi-access=free |hdl=10150/652767 |hdl-access=free }}</ref> Another fully anchored chronology that extends back 8,500 years exists for the bristlecone pine in the [[Southwestern United States|Southwest US]] ([[White Mountains (California)|White Mountains]] of California).<ref>{{cite journal |last1=Ferguson |first1=C. W. |last2=Graybill |first2=D. A. |title=Dendrochronology of Bristlecone Pine: A Progress Report |journal=Radiocarbon |date=1983 |volume=25 |issue=2 |pages=287–288 |doi=10.1017/S0033822200005592 |bibcode=1983Radcb..25..287F |hdl=10150/652656 |hdl-access=free |doi-access=free }}</ref>

=== Dendrochronological equation ===

[[File:Annual growth of the wood.jpg|thumb|A typical form of the function of the wood ring width in accordance with the dendrochronological equation]]

[[File:Annual growth of the wood (second typical form of the growth function).jpg|thumb|A typical form of the function of the wood ring (in accordance with the dendrochronological equation) with an increase in the width of wood ring at initial stage]]

The dendrochronological equation defines the law of growth of tree rings.  The equation was proposed by Russian biophysicist Alexandr N. Tetearing in his work "Theory of populations"<ref name=Tetearing2012>{{cite book|author1=Alexandr N. Tetearing|title=Theory of populations |year=2012 |page=583 |isbn=978-1-365-56080-4 |publisher=SSO Foundation |location=Moscow}}</ref> in the form:

<math display="block">\Delta L(t) = \frac{1}{k_v\, \rho^{\frac{1}{3}}} \, \frac{d\left(M^{\frac{1}{3}}(t)\right)}{dt},</math>

where Δ''L'' is width of annual ring, ''t'' is time (in years), ''ρ'' is density of wood, ''k<sub>v</sub>'' is some coefficient, ''M''(''t'') is function of mass growth of the tree.

Ignoring the natural sinusoidal oscillations in tree mass, the formula for the changes in the annual ring width is:

<big><math display="block">\Delta L(t) = -\frac{ c_1 e^{-a_1 t}+ c_2 e^{-a_2 t} }{3 k_v \rho^{\frac{1}{3}} \left(c_4+ c_1 e^{-a_1 t}+ c_2 e^{-a_2 t}\right)^{\frac{2}{3}}}</math></big>

where ''c''<sub>1</sub>, ''c''<sub>2</sub>, and ''c''<sub>4</sub> are some coefficients, ''a''<sub>1</sub> and ''a''<sub>2</sub> are positive constants.

The formula is useful for correct approximation of samples data before [[data normalization]] procedure. The typical forms of the function Δ''L''(''t'') of annual growth of wood ring are  shown in the figures.

=== Sampling and dating ===
Dendrochronology allows specimens of once-living material to be accurately dated to a specific year.<ref name=RenfrewBahn2004>{{cite book |author1=Renfrew Colin |author2=Bahn Paul |title=Archaeology: Theories, Methods and Practice |edition=4th |year=2004 |pages=[https://archive.org/details/archaeology00coli/page/144 144–5] |isbn=978-0-500-28441-4 |publisher=Thames & Hudson |location=London |url-access=registration |url=https://archive.org/details/archaeology00coli/page/144 }}</ref> Dates are often represented as estimated calendar years [[before present|B.P.]], for before present, where "present" refers to 1 January 1950.<ref name=RenfrewBahn2004 />

Timber core samples are sampled and used to measure the width of annual growth rings; by taking samples from different sites within a particular region, researchers can build a comprehensive historical sequence. The techniques of dendrochronology are more consistent in areas where trees grew in marginal conditions such as aridity or semi-aridity where the ring growth is more sensitive to the environment, rather than in humid areas where tree-ring growth is more uniform (complacent). In addition, some genera of trees are more suitable than others for this type of analysis. For instance, the [[bristlecone pine]] is exceptionally long-lived and slow growing, and has been used extensively for chronologies; still-living and dead specimens of this species provide tree-ring patterns going back thousands of years, in some regions more than 10,000 years.<ref>{{cite web|url=http://www.wsl.ch/dendro/dendrodb.html |title=Bibliography of Dendrochronology |publisher=ETH Forest Snow and Landscape Research |location=Switzerland |access-date=2010-08-08 |url-status=dead |archive-url=https://web.archive.org/web/20100804005355/http://www.wsl.ch/dendro/dendrodb.html |archive-date=2010-08-04 }}{{specify|date=March 2011}}</ref> Currently, the maximum span for fully anchored chronology is a little over 11,000 years B.P.

IntCal20 is the 2020 "Radiocarbon Age Calibration Curve", which provides a calibrated [[carbon 14]] dated sequence going back 55,000 years. The most recent part, going back 13,900 years, is based on tree rings.<ref>{{cite journal|title=The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP)|first=Paula|last=Reimer|display-authors=etal|date= 12 August 2020|journal=Radiocarbon|volume=62|issue=4|pages=725–757|doi=10.1017/RDC.2020.41|bibcode=2020Radcb..62..725R |s2cid=216215614|doi-access=free|hdl=11585/770531|hdl-access=free}}</ref>

=== Reference sequences ===
European chronologies derived from wooden structures initially found it difficult to bridge the gap in the fourteenth century when there was a building hiatus, which coincided with the [[Black Death]].<ref>{{cite book
 |title=A Slice Through Time
 |author=Baillie Mike
 |page=124
 |year=1997
 |isbn=978-0-7134-7654-5
 |publisher=Batsford
 |location=London
|author-link=Mike Baillie
 }}</ref> However, there do exist unbroken chronologies dating back to prehistoric times, for example the Danish chronology dating back to 352 BC.<ref>{{cite web|url=http://www.skalk.dk/Sider/0003wm.html |website=skalk.dk |title=WM Trædatering |language=da |trans-title=WM Tree dating |access-date=15 May 2015 |url-status=dead |archive-url=https://web.archive.org/web/20141221121805/http://www.skalk.dk/Sider/0003wm.html |archive-date=21 December 2014 }}</ref>

Given a sample of wood, the variation of the tree-ring growths not only provides a match by year, but can also match location because climate varies from place to place. This makes it possible to determine the source of ships as well as smaller artifacts made from wood, but which were transported long distances, such as panels for paintings and ship timbers.{{citation needed|date=February 2024}}

===Miyake events===
[[Miyake event]]s, such as the ones in [[774–775 carbon-14 spike|774–775]] and [[993–994 carbon-14 spike|993–994]], can provide fixed reference points in an unknown time sequence as they are due to cosmic radiation.<ref name =Maczkowski>Andrej Maczkowski et al, "Absolute dating of the European Neolithic using the 5259 BC rapid 14C excursion", Nature Communications, 2024 {{doi|10.1038/s41467-024-48402-1}}</ref> As they appear as spikes in [[carbon 14]] in tree rings for that year all round the world, they can be used to date historical events to the year.<ref>{{Cite web |last=Price |first=Michael |date=13 April 2023 |title=Marking time: Radiocarbon timestamps left in ancient tree rings by cosmic ray bombardments can date historical events with unprecedented precision |url=https://www.science.org/content/article/marking-time-cosmic-ray-storms-can-pin-precise-dates-history-ancient-egypt-vikings|website=[[Science (journal)|Science]] |quote=A previous version "Marking time: Cosmic ray storms can pin precise dates on history from ancient Egypt to the Vikings" appeared in Science, Vol 380, Issue 6641.}}</ref> For example, wooden houses in the [[Viking]] site at [[L'Anse aux Meadows]] in Newfoundland were dated by finding the layer with the 993 spike, which showed that the wood is from a tree felled in 1021.<ref>{{cite journal|url=https://www.nature.com/articles/s41586-021-03972-8.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.nature.com/articles/s41586-021-03972-8.pdf |archive-date=2022-10-09 |url-status=live|journal=Nature|title=Evidence for European presence in the Americas in AD 1021|first=Margot|last= Kuitems|display-authors=etal|date=20 October 2021|volume=601|issue=7893|pages=388–391|doi=10.1038/s41586-021-03972-8|pmid=34671168|pmc=8770119|s2cid=239051036}}</ref> Researchers at the University of Bern have provided exact dating of a floating sequence in a [[Neolithic]] settlement in northern Greece by tying it to a spike in cosmogenic radiocarbon in 5259 BC.<ref name=Bern/><ref name =Maczkowski/>

===Frost rings===
Frost ring is a term used to designate a layer of deformed, collapsed [[tracheid]]s and traumatic [[parenchyma]] cells in tree ring analysis. They are formed when air temperature falls below freezing during a period of [[cambial]] activity. They can be used in dendrochronology to indicate years that are colder than usual.<ref>{{cite journal |display-authors=etal|last1=David Montwé |title=Cold adaptation recorded in tree rings highlights risks associated with climate change and assisted migration |journal=Nature Communications |date=Apr 23, 2018 |volume=9 |issue=1 |page=1574 |doi=10.1038/s41467-018-04039-5 |doi-access=free |pmid=29686289 |pmc=5913219 |bibcode=2018NatCo...9.1574M }}</ref>