A Sunny Crown Profile Equation for Hinoki Cypress based on the Height Increment

Abstract

The power equation r =azb is often used to represent the sunny crown profile of conifers, where r is the crown radius (m) at distance z (m) from the tree apex, and a and b are parameters. When parameter b is invariant between trees, parameter a is the only independent variable that determines the sunny crown profile. Assuming that parameter b is invariant between trees, this study derived a sunny crown profile equation for Hinoki cypress (Chamaecyparis obtuse ENDL.) based on the power equation from the relationship between parameter a and the annual height increment HI (m/year): a =c HId where c and d are parameters. First, we derived the relationship a = c HId. Next, we evaluated the efficacy of the equation r =c HIdzb at representing the sunny crown profile of Hinoki cypress. Data were obtained from 112 trees in six pure stands of even-aged Hinoki cypress. The fit of the equation a =c HId to the data was good. The equation r =c HIdzb made more precise predictions than the equation r =azb assumed that each of parameters a and b is common to all trees. The values of parameters b, c, and d estimated from the sample trees were 0.686, 0.401, and -0.299, respectively. The integration of the sunny crown profile equation r =c HIdzb with a tree growth model, including the total height growth and the sunny crown length estimations, enables prediction of the sunny crown profile and its change with growth for Hinoki cypress.