Ishimori equation: Difference between revisions
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'''Stand density index''' (also known as '''Reineke's Stand Density Index'''<ref>Reineke, L.H. 1933 Perfecting a stand-density index for even-aged forest. "Journal of Agricultural Research" 46:627-638</ref> after its founder) is a measure of the [[Stocking (forestry)|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.<ref>Avery, Thomas & Burkhart, Harold. 2002. Forest Measurements 5th edition.</ref> Stand density index is also the basis for [[Stand density management diagram]]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.<ref>Nyland, Ralph. 2002. Silvicultural Concepts and Applications 2nd edition.</ref> 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: log<sub>10</sub>N = -1.605(log<sub>10</sub>D) + 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 {{convert|10|in|mm}}, the log of N equals the Stand Density Index. | |||
In equation form: log<sub>10</sub>SDI = -1.605(1) + k | |||
Which means that: k = log<sub>10</sub>SDI + 1.605 | |||
Substituting the value of k above into the reference-curve formula gives the equation: | |||
log<sub>10</sub>N = log<sub>10</sub>SDI + 1.605 - 1.605 log<sub>10</sub>D | |||
This equation can be rewritten as: | |||
log<sub>10</sub>SDI = log<sub>10</sub>N + 1.605 log<sub>10</sub>D - 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 {{convert|150|sqft|m2}} and 400 trees per acre is measured. The dbh of the tree of average basal area D is: | |||
<math>\sqrt \frac{150}{400\times .005454}=8.29</math> | |||
Substituting this value into the stand density equation gives: | |||
log<sub>10</sub>SDI = log<sub>10</sub>(400) + 1.605log<sub>10</sub>(8.29) - 1.605 = 2.47 | |||
SDI = 10<sup>2.47</sup> | |||
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. | |||
==References== | |||
{{reflist|colwidth=30em}} | |||
{{Forestry}} | |||
[[Category:Forest modelling]] | |||
Latest revision as of 18:07, 8 November 2012
Stand density index (also known as Reineke's Stand Density Index[1] after its founder) 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.[2] Stand density index is also the basis for Stand density management diagrams.
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.[3] 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 Template:Convert, 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 Template:Convert 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.
References
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