Allometry
In this document:
Allometry parameters
Canopy depth 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
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.
Allometry parameters
- Adult Height-Diameter Function The allometric relationship used to relate DBH and height for adult trees. Each of the choices is described in detail below.
- Adult Linear Function Intercept The intercept of the adult linear function for DBH and height. Any species not using that function can omit this value.
- Adult Linear Function Slope The slope of the adult linear function for DBH and height. Any species not using that function can omit this value.
- Adult Reverse Linear Function Intercept The intercept of the adult reverse linear function for DBH and height. Any species not using that function can omit this value.
- Adult Reverse Linear Function Slope The slope of the adult reverse linear function for DBH and height. Any species not using that function can omit this value.
- Canopy Height Exponent The exponent in the equation for calculating canopy height. Used by all species.
- Canopy Radius Exponent The exponent in the equation for determining the canopy radius. Used by all species.
- DBH to Diameter at 10 cm Ratio The ratio of the DBH, in cm, to the diameter at 10 cm height, in cm, in small trees. Used by all species.
- 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.
- Ratio of Canopy Radius to DBH The ratio of the radius of the tree canopy, in m, to the DBH, in cm. Used to relate DBH to canopy radius. Used by all species.
- Sapling Height-Diameter Function The allometric relationship used to relate DBH and height for saplings. Each of the choices is described in detail below.
- Sapling Linear Function Intercept The intercept of the sapling linear function for DBH and height. Any species not using that function can omit this value.
- Sapling Linear Function Slope The intercept of the sapling linear function for DBH and height. Any species not using that function can omit this value.
- Sapling Reverse Linear Function Intercept The intercept of the sapling reverse linear function for DBH and height. Any species not using that function can omit this value.
- Sapling Reverse Linear Function Slope The slope of the sapling reverse linear function for DBH and height. Any species not using that function can omit this value.
- Seedling Height-Diameter Function The allometric relationship used to relate diameter at 10 cm and height for seedlings. Each of the choices is described in detail below.
- Seedling Linear Function Intercept The intercept of the seedling linear function for DBH and height. Any species not using that function can omit this value.
- Seedling Linear Function Slope The slope of the seedling linear function for DBH and height. Any species not using that function can omit this value.
- Seedling Reverse Linear Function Intercept The intercept of the seedling reverse linear function for DBH and height. Any species not using that function can omit this value.
- Seedling Reverse Linear Function Slope The slope of the seedling reverse linear function for DBH and height. Any species not using that function can omit this value.
- Slope of Asymptotic Canopy Depth Slope of the equation for determining canopy depth. Used by all species.
- Slope of Asymptotic Height Exponential decay term in the adult and sapling standard function for DBH and height. Any species not using that function can omit this value.
- Slope of Height-Diameter at 10 cm Relationship The slope of the seedling standard function for diameter at 10 cm and height. Any species not using that function can omit this value.
Canopy depth and width relationships
In general, canopies 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 canopies. Saplings and adults (and, in some cases, snags) all use the same relationships to describe canopy shape.
Canopy radius is calculated as:
canrad = C1 * DBH a
where:
- canrad is the canopy radius, in meters
- C1 is the Ratio of Canopy Radius to DBH parameter
- a is the Canopy Radius Exponent parameter
- DBH is the tree's DBH, in cm
Canopy radius is limited to a maximum of 10 meters.
Canopy height is calculated as
canopy height = C2 * height b
where
- canopy height is the distance from the top to the bottom of the canopy cylinder, in meters
- C2 is the Slope of Asymptotic Canopy Depth parameter
- height is the tree's height in meters
- b is the Canopy Height Exponent parameter
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
where
- DBH is the DBH in cm
- diam10 is the diameter at 10 cm height, in cm
- R is the DBH to Diameter at 10 cm Ratio parameter
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:
- 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
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:
- height is tree height, in m
- a is the appropriate linear intercept parameter (either Adult Linear Function Intercept, Sapling Linear Function Intercept, or Seedling Linear Function Intercept)
- b is the appropriate linear slope parameter (either Adult Linear Function Slope, Sapling Linear Function Slope, or Seedling Linear Function Slope)
- diam is DBH (in cm) for saplings and adults, or diam10 (in cm) for seedlings
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:
- height is tree height, in m
- a is the appropriate reverse linear intercept parameter (either Adult Reverse Linear Function Intercept, Sapling Reverse Linear Function Intercept, or Seedling Reverse Linear Function Intercept)
- b is the appropriate reverse linear slope parameter (either Adult Reverse Linear Function Slope, Sapling Reverse Linear Function Slope, or Seedling Reverse Linear Function Slope)
- diam is DBH (in cm) for saplings and adults, or diam10 (in cm) for seedlings
Last updated: 28-Apr-2005 10:19 AM