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Table II
Ten taper equations and their corresponding mathematical expressions.
| Model | Expression |
|---|---|
| Max and Burkhart (1976) |
|
| I + (α1 − z) = 1, if α1 − z ≥ 0 I + (α1 − z) = 0, if α1 − z < 0 | |
| I + (α2 − z) = 1, if α2 − z ≥ 0 I + (α2 − z) = 0, if α2 − z < 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)(beta2 − β1)k/β1β2 q2 = (1 − p2)(β3 − β2)k/β2β3 | |
| t0 = 1t1 = (1 − p1)k/β1 t2 = (1 − p2)k/β2z = h/H | |
z =
h/H
k = 0.000078539 |
|
| I1 = 1 if p2 ≥ z ≥ p1 , 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.