SORTIE-ND
Software for spatially-explicit simulation of forest dynamics

# The Chapman-Richards crown depth and radius relationships

### Crown Depth Parameters

Parameter nameDescription
Chapman-Richards Asymptotic Crown HeightThe asymptotic crown depth (or length), in m, of the Chapman-Richards crown depth equation.
Chapman-Richards Crown Height InterceptThe intercept of the Chapman-Richards crown depth equation. This represents the crown depth, in m, of the smallest possible sapling.
Chapman-Richards Crown Height Shape 1 (b)The first shape parameter, b, of the Chapman-Richards crown depth equation.
Chapman-Richards Crown Height Shape 2 (c)The second shape parameter, c, of the Chapman-Richards crown depth equation.

Parameter nameDescription
Chapman-Richards Crown Radius InterceptThe intercept of the Chapman-Richards crown radius equation. This represents the crown radius, in m, of the smallest possible sapling.
Chapman-Richards Crown Radius Shape 1 (b)The first shape parameter, b, of the Chapman-Richards crown radius equation.
Chapman-Richards Crown Radius Shape 2 (c)The second shape parameter, c, of the Chapman-Richards crown radius equation.

The Chapman-Richards equation for calculating crown radius is:

rad = i + a (1 - e -b * DBH) c

where

• DBH is the tree's DBH, in cm
• i is the Chapman-Richards Crown Radius Intercept parameter, which represents the crown radius of the smallest possible sapling
• a is the Chapman-Richards Asymptotic Crown Radius parameter
• b is the Chapman-Richards Crown Radius Shape 1 (b) parameter
• c is the Chapman-Richards Crown Radius Shape 2 (c) parameter

The Chapman-Richards equation for calculating crown depth is:

ch = i + a (1 - e -b * H) c

where

• ch is the distance from the top to the bottom of the crown cylinder, in meters
• H is the tree's height, in m
• i is the Chapman-Richards Crown Height Intercept parameter, which represents the crown depth of the smallest possible sapling
• a is the Chapman-Richards Asymptotic Crown Height parameter
• b is the Chapman-Richards Crown Height Shape 1 (b) parameter
• c is the Chapman-Richards Crown Height Shape 2 (c) parameter