Dendrochronology

Dendrochronology is the scientific method of dating tree rings to the exact year they were formed in a tree. As well as dating them, this can give data for dendroclimatology, the study of climate and atmospheric conditions during different periods in history from the wood of old trees. Dendrochronology derives from the Ancient Greek , meaning "tree", , meaning "time", and , "the study of".
Dendrochronology is useful for determining the precise age of samples, especially those that are too recent for radiocarbon dating, which always produces a range rather than an exact date. However, for a precise date of the death of the tree a full sample to the edge is needed, which most trimmed timber will not provide. It also gives data on the timing of events and rates of change in the environment and also in wood found in archaeology or works of art and architecture, such as old panel paintings. It is also used as a check in radiocarbon dating to calibrate radiocarbon ages.
New growth in trees occurs in a layer of cells near the bark. A tree's growth rate changes in a predictable pattern throughout the year in response to seasonal climate changes, resulting in visible growth rings. Each ring marks a complete cycle of seasons, or one year, in the tree's life. As of 2023, securely dated tree-ring data for Germany, Bohemia and Ireland are available going back 13,910 years. A new method is based on measuring variations in oxygen isotopes in each ring, and this 'isotope dendrochronology' can yield results on samples which are not suitable for traditional dendrochronology due to too few or too similar rings. Some regions have "floating sequences", with gaps which mean that earlier periods can only be approximately dated. As of 2024, only three areas have continuous sequences going back to prehistoric times, the foothills of the Northern Alps, the southwestern United States and the British Isles. Miyake events, which are major spikes in cosmic rays at known dates, are visible in trees rings and can fix the dating of a floating sequence.

History

The Greek botanist Theophrastus first mentioned that the wood of trees has rings. In his 1651 Trattato della Pittura, Leonardo da Vinci was the first person to mention that trees form rings annually and that their thickness is determined by the conditions under which they grew. In 1737, French investigators Henri-Louis Duhamel du Monceau and Georges-Louis Leclerc de Buffon examined the effect of growing conditions on the shape of tree rings. They found that in 1709, a severe winter produced a distinctly dark tree ring, which served as a reference for subsequent European naturalists. In the U.S., Alexander Catlin Twining suggested in 1833 that patterns among tree rings could be used to synchronize the dendrochronology of various trees and thereby to reconstruct past climates across entire regions. The English polymath Charles Babbage proposed using dendrochronology to date the remains of trees in peat bogs or even in geological strata.
During the later half of the nineteenth century, the scientific study of tree rings and the application of dendrochronology began. In 1859, the German-American Jacob Kuechler used crossdating to examine oaks in order to study the record of climate in western Texas. In 1866, the German botanist, entomologist, and forester Julius Theodor Christian Ratzeburg observed the effects on tree rings of defoliation caused by insect infestations. By 1882, this observation was already appearing in forestry textbooks. In the 1870s, the Dutch astronomer Jacobus Kapteyn was using crossdating to reconstruct the climates of the Netherlands and Germany. In 1881, the Swiss-Austrian forester Arthur von Seckendorff-Gudent was using crossdating. From 1869 to 1901, Robert Hartig, a German professor of forest pathology, wrote a series of papers on the anatomy and ecology of tree rings. In 1892, the Russian physicist wrote that he had used patterns found in tree rings to predict droughts in 1882 and 1891.
During the first half of the twentieth century, the astronomer A. E. Douglass founded the Laboratory of Tree-Ring Research at the University of Arizona. Douglass sought to better understand cycles of sunspot activity and reasoned that changes in solar activity would affect climate patterns on earth, which would subsequently be recorded by tree-ring growth patterns.

Methods

Growth rings

Horizontal cross sections cut through the 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 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 seasons 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 zones, where the seasons differ more markedly. The inner portion of a growth ring forms early in the growing season, when growth is comparatively rapid and is known as "early wood" ; the outer portion is the "late wood" and is denser.
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.
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. 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, 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 whose dates are known.
A fully anchored and cross-matched chronology for oak and pine in central Europe extends back 12,460 years, and an oak chronology goes back 7,506 years in Bohemia, 7,429 years in Ireland and 6,939 years in England. Comparison of radiocarbon and dendrochronological ages supports the consistency of these two independent dendrochronological sequences. Another fully anchored chronology that extends back 8,500 years exists for the bristlecone pine in the Southwest US.

Dendrochronological equation

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" in the form:
where ΔL is width of annual ring, t is time, ρ is density of wood, k_v is some coefficient, M 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:

where c₁, c₂, and c₄ are some coefficients, a₁ and a₂ are positive constants.
The formula is useful for correct approximation of samples data before data normalization procedure. The typical forms of the function ΔL 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. Dates are often represented as estimated calendar years B.P., for before present, where "present" refers to 1 January 1950.
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. 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. 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.