Stand Density Index
Encyclopedia
Stand density index is a measure of the stocking
of a stand of trees based on the number of trees per unit area and diameter at breast height
of the tree of average basal area
. It may also be defined as the degree of crowding within stocked areas, using various growing space ratios based on crown length or diameter, tree height or diameter, and spacing. Stand density index is usually well correlated with stand volume and growth , and several variable-density yield tables have been created using it. Basal area, however, is usually satisfactory as a measure of stand density index and because it is easier to calculate it is usually preferred over SDI. Stand density index is also the basis for Stand density management diagram
s.
The maximum density line is expressed by the equation: log10N = -1.605(log10D) + k
Where N = number of trees per acre
D = dbh of the tree of average basal area
k = a constant varying with the species
When the quadratic mean diameter equals 10 inches (254 mm), the log of N equals the Stand Density Index.
In equation form: log10SDI = -1.605(1) + k
Which means that: k = log10SDI + 1.605
Substituting the value of k above into the reference-curve formula gives the equation:
log10N = log10SDI + 1.605 - 1.605 log10D
This equation can be rewritten as:
log10SDI = log10N + 1.605 log10D - 1.605
The above equation is an expression for computing the stand density index from the number of trees per acre and the diameter of the tree of average basal area.
Let's assume that a stand with basal area of 150 square feet (13.9 m²) and 400 trees per acre is measured. The dbh of the tree of average basal area D is:
Substituting this value into the stand density equation gives:
log10SDI = log10(400) + 1.605log10(8.29) - 1.605 = 2.47
SDI = 102.47
SDI = 295
The computed value of SDI is often compared to the species maximum to determine the relative "stand density" or stocking of the stand.
Stocking (forestry)
In forestry, stocking , is a quantitative measure of the area occupied by trees, usually measured in terms of well-spaced trees or basal area per hectare, relative to an optimum or desired level of density...
of a stand of trees based on the number of trees per unit area and diameter at breast height
Diameter at breast height
Diameter at breast height, or DBH, is a standard method of expressing the diameter of the trunk or bole of a standing tree. DBH is one of the most common dendrometric measurements....
of the tree of average basal area
Basal area
Basal area is the term used in forest management that defines the cross-sectional area of a tree at DBH, inside the bark.In most countries, this is usually a measurement taken at a specimen's breast height above the ground and includes the entire diameter of every tree, including the bark...
. It may also be defined as the degree of crowding within stocked areas, using various growing space ratios based on crown length or diameter, tree height or diameter, and spacing. Stand density index is usually well correlated with stand volume and growth , and several variable-density yield tables have been created using it. Basal area, however, is usually satisfactory as a measure of stand density index and because it is easier to calculate it is usually preferred over SDI. Stand density index is also the basis for Stand density management diagram
Stand density management diagram
A stand density management diagram is a simple biological model relating forest yield to forest density at any stage of a particular forest stand's development. Stand density management diagrams are used in forest management and designed to use a current stand's density to project its future yield...
s.
Calculating Stand Density Index
Plotting the logarithm of the number of trees per acre against the logarithm of the quadratic mean diameter (or the dbh of the tree of average basal area) of maximally stocked stands generally resulted in a straight-line relationship. In most cases the line was used to define the limit of maximum stocking. This negatively sloped line, is referred to as the self-thinning line or the maximum-density line.The maximum density line is expressed by the equation: log10N = -1.605(log10D) + k
Where N = number of trees per acre
D = dbh of the tree of average basal area
k = a constant varying with the species
When the quadratic mean diameter equals 10 inches (254 mm), the log of N equals the Stand Density Index.
In equation form: log10SDI = -1.605(1) + k
Which means that: k = log10SDI + 1.605
Substituting the value of k above into the reference-curve formula gives the equation:
log10N = log10SDI + 1.605 - 1.605 log10D
This equation can be rewritten as:
log10SDI = log10N + 1.605 log10D - 1.605
The above equation is an expression for computing the stand density index from the number of trees per acre and the diameter of the tree of average basal area.
Let's assume that a stand with basal area of 150 square feet (13.9 m²) and 400 trees per acre is measured. The dbh of the tree of average basal area D is:
Substituting this value into the stand density equation gives:
log10SDI = log10(400) + 1.605log10(8.29) - 1.605 = 2.47
SDI = 102.47
SDI = 295
The computed value of SDI is often compared to the species maximum to determine the relative "stand density" or stocking of the stand.