# Geochronology/Dendrochronology

Dendrochronology is the science or technique of dating events, environmental change, and archaeological artifacts by using the characteristic patterns of annual growth rings in timber and tree trunks.
Dendrochronology is used in radiocarbon dating to calibrate radiocarbon ages.

## Tree rings

A new layer of wood added in each growing season, thickening the stem, existing branches and roots, to form a growth ring.
The outer portion is the "late wood" and has sometimes been termed "summer wood", often being produced in the summer, though sometimes in the autumn and is denser.
Missing rings are rare in oak and elm trees.
The only recorded instance of a missing ring in oak trees occurred in the year 1816, also known as the Year Without a Summer.
Each ring marks a complete cycle of seasons, or one year, in the tree's life.
A fully anchored and cross-matched oak and pine chronology in central Europe extends back 12,460 years, and an oak chronology goes back 7,429 years in Ireland, and 6,939 years in England.
The consistency of these two independent dendrochronological sequences has been supported through comparison of their radiocarbon and dendrochronological ages.
Another fully anchored chronology that extends back 8500 years exists for the bristlecone pine in the Southwestern United States (White Mountains of California).
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.
The oldest tree-ring measurements in the Northern Hemisphere are a floating sequence extending from about 12,580 to 13,900 years.
This dendrochronological equation defines the law of growth of tree rings in the form:
$\Delta L(t)={\frac {1}{k_{v}\,\rho ^{\tfrac {1}{3}}}}\,{\frac {d{\bigM^{\tfrac {1}{3}}(t){\big )}}{dt}},$
where $\Delta L$ is width of annual ring, $t$ is time (in years), $\rho$ is density of wood, $k_{v}$ is some coefficient, $M(t)$ is function of mass growth of the tree.
With the neglection of natural sinusoidal oscillations in tree mass, the formula of the changes in the annual ring width is:
$\Delta L(t)=-{\dfrac {c_{1}e^{-a_{1}t}+c_{2}e^{-a_{2}t}}{3k_{v}\rho ^{\tfrac {1}{3}}(c_{4}+c_{1}e^{-a_{1}t}+c_{2}e^{-a_{2}t})^{\tfrac {2}{3}}}},$
where $c_{1}$, $c_{2}$, and $c_{4}$ are some coefficients, $a_{1}$ and $a_{2}$ are positive constants.
The formula is useful for correct approximation to data before data normalization procedure.
The typical forms of the function $\Delta L(t)$ for the annual growth of a wood ring are shown in the figures.

## Dates

Dendrochronology makes available specimens of once-living material accurately dated to a specific year. Dates are often represented as estimated calendar years B.P., for before present, where "present" refers to 1 January 1950.
For the period back to 12,400 B.P., the radiocarbon dates are calibrated against dendrochronological dates.
European chronologies derived from wooden structures initially found it difficult to bridge the gap in the 14th century when there was a building hiatus, which coincided with the Black Death, however there do exist unbroken chronologies dating back to prehistoric times, for example the Danish chronology dating back to 352 BC.

## Art

Unlike analysis of samples from buildings, which are typically sent to a laboratory, wooden supports for paintings, or panel paintings, usually have to be measured in a museum conservation department, which places limitations on the techniques that can be used.
Wooden supports other than oak were rarely used by Netherlandish painters.
Since panels of seasoned wood were used, an uncertain number of years has to be allowed for seasoning when estimating dates.
Panels were trimmed of the outer rings, and often each panel only uses a small part of the radius of the trunk. Consequently, dating studies usually result in a "terminus post quem" (earliest possible) date, and a tentative date for the actual arrival of a seasoned raw panel using assumptions as to these factors.
As a result of establishing numerous sequences, it was possible to date 85–90% of the 250 paintings from the 14th to 17th century analysed between 1971 and 1982; by now a much greater number have been analysed.
A portrait of Mary, Queen of Scots, in the National Portrait Gallery, London, was believed to be an 18th-century copy. However, dendrochronology revealed that the wood dated from the second half of the 16th century. It is now regarded as an original 16th-century painting by an unknown artist.
On the other hand, dendrochronology was applied to four paintings depicting the same subject, that of Christ expelling the money-lenders from the Temple. The results showed that the age of the wood was too late for any of them to have been painted by Hieronymus Bosch.
While dendrochronology has become an important tool for dating oak panels, it is not effective in dating the poplar panels often used by Italian painters because of the erratic growth rings in poplar.
The 16th century saw a gradual replacement of wooden panels by canvas as the support for paintings, which means the technique is less often applicable to later paintings.

## Buildings

The dating of buildings via dendrochronology requires knowledge of the history of building technology.
The Fairbanks House, Dedham, Massachusetts, had long been claimed to have been built circa 1640 (and being the oldest wood-framed house in North America), core samples of wood taken from a summer beam confirmed the wood was from an oak tree felled in 1637–8. An additional sample from another beam yielded a date of 1641, thus confirming the house had been constructed starting in 1638 and finished sometime after 1641 as wood was not seasoned before use in building at that time in New England.
The burial chamber of Gorm the Old, who died c. 958, was constructed from wood of timbers felled in 958.

## Radiocarbon activity

"Tree ring studies from the last two centuries show that the radiocarbon activity in wood grown in AD 1950 (before nuclear weapons testing) is lower than in samples grown in AD 1850 (prior to the internationally accepted boom in fossil fuel combustion from the industrial revolution) despite the radioactive decay of 14C that has occurred in the latter (Aitken, 1990)."
"Tree ring studies attempting to quantify the Suess effect have shown a strong offset for the period 1890 to 1950 of ∆$^{14}$ C = -20‰ for the Pacific coast of the United States (oceanic air) (Levin and Hesshaimer, 2000) and a further c. 10‰ depression in ∆$^{14}$ C observed in Dutch oak trees (De Jong and Mook, 1982)."
"Calibration using dendrochronologically dated, continuously overlapping tree-ring sequences has proven to be the most successful method since the production of the first calibration curves (Stuiver and Suess 1966, Suess 1979). Dendrochronological (calendar) dates can be matched with $^{14}$ C dates, using $^{14}$ C age measurements made on annually ringed tree samples to construct a calibration curve for atmospheric/terrestrial biospheric $^{14}$ C dates. Use of this curve allows calibration of $^{14}$ C ages to calendar years. Beyond the limit of the absolutely dated tree ring sequence, calibration becomes more problematic (Reimer et al., 2009; Bronk Ramsey et al., 2006; Mellars, 2006a; Mellars, 2006b; Turney at al., 2006; Blockley and Housley, 2009). The most recent publication of the atmospheric calibration curve is INTCAL09 (Reimer et al., 2009) which superceded the previous dataset, INTCAL04 (Reimer et al., 2004)."

## Little Ice Age

The Little Ice Age (LIA) appears to have lasted from about 1218 (782 b2k) to about 1878 (122 b2k).
The second image down shows the $^{14}$C data obtained from tree rings. The lower the solar activity, the higher the cosmic radiation, which determines the isotope content. The periods of highest $^{14}$C production as measured from tree rings coincide with the periods of highest cooling during the past 1200 years.
In 1859, the German-American Jacob Kuechler (1823–1893) used crossdating to examine oaks (Quercus stellata) in order to study the record of climate in western Texas.

## Medieval Warm Period

The Medieval Warm Period (MWP) dates from around 1150 to 750 b2k.
"A proof-of-concept self-calibrating chronology [based upon the Irish Oak chronology] clearly demonstrates that third order polynomials provide a series of statistical calibration curves that highlight lacunae in the samples."
As indicated in the figures, the data used in the plots comes from radiocarbon dating of Irish Oaks.
Gaps occur near the 1070s and 1470s b2k during the rising Δ$^{14}$C values.
"The number of suitable samples of wood, which connect Antiquity and the Middle Ages is very small [shown in the third figure on the left]. But only a great number of samples would give certainty against error. For the period about 380 AD we have only 3, for the period about 720 AD only 4 suitable samples of wood (Hollstein 1980,11); usually 50 samples serve for dating."
"The center of the graph [in the fourth image on the left] shows the time axis of conventionally dated historical events. Upper and lower coordinates show reconstructed time tables. The black triangles mark the phantom years."
"In Frankfurt am Main archaeological excavations did not find any layer for the period between 650 and 910 AD."

## Imperial Antiquity

"The Strood causeway to Mersea Island was thought to be Roman, built in the 1st c. AD. It leads to Mersea’s Roman burial mound (barrow) where a typical Roman lead covered box with a no less typical Roman glass urn (tentatively dated between 100 and 120 AD) was retrieved [in the image on the right]. Oak piles in typical Roman cut were discovered in 1978. Up to the 1980s it was never doubted that the dam was built by Romans in the 1st c. AD to reach their settlements on the Island."
"Scientific dating methods have been applied to some substantial oak piles discovered beneath the Strood in 1978, when a water-main was being laid. They indicate that the structure was probably built between A.D. 684 and 702. The piles were discovered at the south end of the causeway where the trench was at its deepest—they were about 1.6m below the present ground level and were sealed by a series of road surfaces. Seven piles were recovered and samples were submitted to Harwell laboratory for radiocarbon dating to get a rough idea of the date. Samples from four of the piles were sent to the University of Sheffield for tree ring dating (dendrochronology). The remaining three piles are now in the Colchester and Essex Museum. The dating of the construction to AD 684 to 702 was regarded as conclusive."

## Iron Age

The iron age history period began between 3,200 and 2,100 b2k.
The Greek botanist Theophrastus (ca. 371 – ca. 287 BC) first mentioned that the wood of trees has rings.
"Moreover, the wood of the silver-fir has many layers, like an onion; there is always another beneath that which is visible, and the wood is composed of such layers throughout."

## Boreal transition

"In recent years, the German oak chronology has been extended to 7938 BC [9938 b2k]. For earlier intervals, tree-ring chronologies must be based on pine, because oak re-emigrated to central Europe at the Preboreal/Boreal transition, at about 8000 BC [10,000 b2k]."
"The age range, 7145-7875 BC [9145-9875 b2k], is represented by the oak chronology, 'Main9'."
"The age range, 7833-9439 BC [9833-11439 b2k], is covered by the 1784-yr pine chronology."