page_title: Dendrochronology
section_title: Dendrochronological equation
hierarchical_section_title: Dendrochronology / Dendrochronological equation
caption_attribution_description: English: A typical form of the function of the wood ring width in accordance with the dendrochronological equation.
context_page_description: Dendrochronology is the scientific method of dating tree rings to the exact year they were formed. As well as dating them this can give data for dendroclimatology, the study of climate and atmospheric conditions during different periods in history from wood. Dendrochronology derives from Ancient Greek dendron, meaning "tree", khronos, meaning "time", and -logia, "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.
context_section_description: 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 (in years), ρ is density of wood, kᵥ 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:
  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(t) of annual growth of wood ring are  shown in the figures.
caption: A typical form of the function of the wood ring width in accordance with the dendrochronological equation
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