Allometry

In this document:
Allometry parameters
The "standard" crown height and width relationships
The "Chapman-Richards" crown height and width relationships
DBH - diameter at 10 cm relationship
The "standard" diameter-height relationships
The "linear" diameter-height relationship
The "reverse linear" diameter-height relationship
The "power" diameter-height relationship

Allometry is the relationships between various aspects of a tree's size and shape. A tree may use different relationships for different life history stages.

You can choose the relationship used by each life history stage of each species. These can be freely mixed-and-matched.

Definitions: DBH (diameter at breast height) is the diameter of a tree trunk at 1.35 meters above the ground. Diameter at 10 cm, or diam10, is the diameter of a tree trunk 10 cm above the ground.

In general, crowns are modeled as cylinders, with a radius and a height. Specific behaviors may make different assumptions but if so they should be clearly stated in that behavior's documentation.

Seedlings in SORTIE-ND do not have crowns. Saplings and adults (and, in some cases, snags) all use the same relationships to describe crown shape.

Allometry parameters

The "standard" crown height and width relationships

Crown radius is calculated as:

rad = C1 * DBH a

where: Crown radius is limited to a maximum of 10 meters.

Crown height is calculated as

ch = C2 * height b
where

The "Chapman-Richards" crown height and width relationships

The Chapman-Richards equation for calculating crown radius is:

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

The Chapman-Richards equation for calculating crown height is:

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

DBH - diameter at 10 cm relationship

Seedlings use the diameter at 10 cm as their primary indicator of size, and have no DBH. Saplings use both DBH and diam10. The use of both measurements by saplings helps to maintain continuity between the seedling and adult life history stages. Adults use only DBH.

DBH and diam10 are related as follows:
DBH = (diam10 * R) + I

where

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.

The standard sapling and adult DBH - height function is:

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

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:

The "linear" diameter-height relationship

The linear diameter-height relationship is the same for all life history stages, but each stage can use a different set of parameter values.

The linear diam - height function is:

height = a + b * diam
where:

The "reverse linear" diameter-height relationship

The reverse linear diameter-height relationship is the same for all life history stages, but each stage can use a different set of parameter values. The name comes from the fact that it is almost the same as the linear function, but with height and diameter switched. In other words, in the linear function, height is a linear function of diameter. In the reverse linear function, diameter is a linear function of height.

The reverse linear diam - height function is:

height = (diam - a) / b
where:

The "power" diameter-height relationship

The power diameter-height relationship relates height and diameter with a power function. Since it uses diameter at 10 cm, NOT DBH, it is active for saplings only.

The power diam - height function is:

height = a * d10 b
where:


Last updated: 25-Jan-2006 03:17 PM