Height-GLI Weibull Mortality with Browse

This behavior calculates the probability of mortality using a Weibull function of tree height and GLI (light level). It can also simulate the effects of herbivory by using different parameters for browsed and unbrowsed trees.

Trees killed by this behavior will have a mortality reason code of "natural".

Parameters for this behavior

Parameter name	Description
Height-GLI Weibull - a	The "a" parameter in the Weibull function for calculating annual mortality.
Height-GLI Weibull - b	The "b" parameter in the Weibull function for calculating annual mortality.
Height-GLI Weibull - c	The "c" parameter in the Weibull function for calculating annual mortality.
Height-GLI Weibull - d	The "d" parameter in the Weibull function for calculating annual mortality.
Height-GLI Weibull - Max Mortality (0 - 1)	The maximum mortality probability for a species, expressed as a proportion between 0 and 1.
Height-GLI Weibull - Browsed a	The "a" parameter in the Weibull function for calculating annual mortality for a browsed tree.
Height-GLI Weibull - Browsed b	The "b" parameter in the Weibull function for calculating annual mortality for a browsed tree.
Height-GLI Weibull - Browsed c	The "c" parameter in the Weibull function for calculating annual mortality for a browsed tree.
Height-GLI Weibull - Browsed d	The "d" parameter in the Weibull function for calculating annual mortality for a browsed tree.
Height-GLI Weibull - Browsed Max Mortality (0 - 1)	The maximum mortality probability for a browsed tree, expressed as a proportion between 0 and 1.

How it works

The same function is used to calculate the probability of mortality for both browsed and unbrowsed trees, but the parameters are different. The function is:

p = M_max * exp(-a * H ^b - c * GLI ^d)

where

p - annual probability of mortality
M_max - the Height-GLI Weibull - Max Mortality (0 - 1) or Height-GLI Weibull - Browsed Max Mortality (0 - 1) parameter
a - the Height-GLI Weibull - a or Height-GLI Weibull - Browsed a parameter
b - the Height-GLI Weibull - b or Height-GLI Weibull - Browsed b parameter
c - the Height-GLI Weibull - c or Height-GLI Weibull - Browsed c parameter
d - the Height-GLI Weibull - d or Height-GLI Weibull - Browsed d parameter
H - tree height in meters
GLI - light level, between 0 and 100% of full sun

If the timestep length is not one year, the actual probability of mortality for the timestep is calculated as p' = 1 - (1 - p)^T, where p is the annual probability of mortality, p' is the timestep probability of mortality, and T is the number of years per timestep. Once the mortality probability for the timestep is known for a tree, then a random number is compared to this probability to determine if the tree lives or dies.

Light levels can come from any of the light behaviors that directly assign a tree its light level. It is expected that this is a GLI value, from 0 to 100% of full sun.

Whether or not a tree is browsed is determined by the Random browse behavior. If the Random browse behavior does not apply to a tree, or is not present in the run, the unbrowsed parameters are always used. The other parameters can be ignored.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. You must also use a light behavior. If you wish to include the effects of herbivory, also include the Random browse behavior in the run.