Lognormal with exponential shade reduction

This behavior does either diameter or height growth as a function of tree size and GLI.

Parameters for this behavior

Parameter name	Description
Lognormal - Diam Effect of Shade (c)	Effect of shade, for diameter growth.
Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a)	Annual growth increment at diameter 36, in mm/yr, for diameter growth.
Lognormal - Diam Shape Parameter (b)	Shape parameter, for diameter growth.
Lognormal - Height Effect of Shade (c)	Effect of shade, for height growth.
Lognormal - Height Growth Increment at Diam 36, in cm/yr (a)	Annual growth increment at diameter 36, in cm/yr, for height growth.
Lognormal - Height Shape Parameter (b)	Shape parameter, for height growth.

How it works

This behavior calculates annual diameter or height increases as:

where

Y = amount of diameter increase, in mm, or the amount of height increase, in cm
a = Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) parameter (for diameter growth) or the Lognormal - Height Growth Increment at Diam 36, in cm/yr (a) parameter (for height growth)
b = Lognormal - Diam Shape Parameter (b) parameter (for diameter growth) or the Lognormal - Height Shape Parameter (b) parameter (for height growth)
c = Lognormal - Diam Effect of Shade (c) parameter (for diameter growth) or the Lognormal - Height Effect of Shade (c) parameter (for height growth)
GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)

For diameter growth: Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments.

For height growth: In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.