# Growth - structural

 FORGEM

Structural features simulated by the ForGEM model are stem volume, tree height, stem diameter, crown diameter and crown length. Empirical equations are used for volume, diameter, and height. The coefficients of these equations are indicated as ${\displaystyle C_{n}}$, with ${\displaystyle {n}}$ a numeric identifier. See structural growth parameters for the values of ${\displaystyle C_{n}}$ for different tree species.

## Contents

### stem volume

${\displaystyle {\frac {dV}{dt}}={\frac {f_{st}}{\rho _{st}}}\cdot NPP}$

With:

V: volume (m3 tree-1)
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$f{}_{st$

allocation of NPP to stem
${\displaystyle \rho _{st}}$: wood density
NPP: primary production (kg tree-1 d-1)

### height

${\displaystyle H=H_{\max }\cdot \left(1-e^{C7\cdot t}\right)^{C8}}$

${\displaystyle \Rightarrow {\frac {dH}{dt}}=C7\cdot C8\cdot H\cdot \left({\frac {e^{C7\cdot t}}{1-e^{C7\cdot t}}}\right)}$

with:

H: tree height (m)
t: tree age (yr)

### stem diameter

${\displaystyle V=D^{C1}\cdot H^{C2}\cdot e^{C3}}$

${\displaystyle \Rightarrow {\frac {dD}{dt}}={\frac {D}{C_{1}}}\cdot \left\{{\frac {1}{V}}\cdot {\frac {dV}{dt}}-{\frac {C_{1}}{H}}\cdot {\frac {dH}{dt}}\right\}}$

with:

V: volume (dm3 stem-1)
D: stem diameter at breast height (cm)
H: tree height (m)
e: exponent of the natural logarithm.