Editing Dendrochronology (section)

=== 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.