The standard diameter-height relationships

"Standard" is one of the names used to describe a set of allometric functions relating height to diameter. There is one for adults and saplings, and one for seedlings. These are called "standard" because they were the original SORTIE functions and until recently were the only choices.

Parameters

Parameter name	Description
Maximum Tree Height, in meters	The maximum tree height for a species, in meters. No tree, no matter what allometric function it uses, is allowed to get taller than this. Used by all species.
Slope of Asymptotic Height	Exponential decay term in the adult and sapling standard function for DBH and height.
Slope of Height-Diameter at 10 cm Relationship	The slope of the seedling standard function for diameter at 10 cm and height.

The standard sapling and adult DBH - height function is:

height = 1.35 + (H₁ - 1.35)(1 - e^-B*DBH)

where:

height is tree height in meters
H₁ is the Maximum Tree Height, in m parameter
B is the Slope of Asymptotic Height parameter
DBH is tree DBH in cm

In some articles, B (Slope of Asymptotic Height) is a published parameter. Other articles instead use H₁ and another parameter, H₂, which was called the DBH to height relationship. In this case, B can be calculated from published values as B = H₂/H₁.

The standard seedling diam₁₀ - height function is:

height = 0.1 + 30*(1 - e^{(-α * diam₁₀)})

where:

height is tree height in meters
α is the Slope of Height-Diameter at 10 cm Relationship parameter
diam₁₀ is tree diameter at 10 cm height, in cm