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## Table II

Ten taper equations and their corresponding mathematical expressions.

Model Expression
Max and Burkhart (1976)
I + (α1z) = 1, if α1z ≥ 0        I + (α1z) = 0, if α1z < 0
I + (α2z) = 1, if α2z ≥ 0        I + (α2z) = 0, if α2z < 0
Kozak (2004) Model 01
Kozak (2004) Model 02
Q = 1 − (z)1/3       p = 1.3 / H
Bi (2000)
Zakrzewski (1999)
z1 = 1 − h/H       s = 1 + θ(H / D)
z0 = 1 − 1.3/H
Valentine and Gregoire (2001)
,
, ,
Sharma and Zhang (2004)
Sharma and Parton (2009)
Clark et al. (1991)
F = D(θ0 + θ1(5.27 / H)2)
Fang et al. (2000)
q1 = (1 − p1)(beta2β1)k/β1β2      q2 = (1 − p2)(β3β2)k/β2β3
t0 = 1t1 = (1 − p1)k/β1                  t2 = (1 − p2)k/β2z = h/H
z = h/H       k = 0.000078539
I1 = 1        if   p2zp1 ,   0 otherwise           I2 = 1 if 1 ≥ z > p2,   0 otherwise

H: Total tree height (m); D: diameter outside bark at breast height (cm); h: height above the ground (m); d: diameter inside bark at any given height h (cm); A(1.37), A(h): cross-sectional area at breast height and at height h, respectively; HCB: height to live crown base; α, β, θ, γ, δ, p: parameters to be estimated; z: h/H.