Stand density management diagram

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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. [1] Stand density management diagrams are used in forest management and designed to use a current stand's density to project its future yield. [2] One major reason for the effectiveness of density management diagrams is the relatively low effect of site variance on the diagram’s shape. Density management diagrams have transformed ideas long held in traditional stocking diagrams. In 1967, Samuel F. Gingrich published his idea of comparing basal area per acre, trees per acre, and quadratic mean diameter in one graph. He called this the stocking diagram. [1] These same principles are used to make the stand density management diagram work. [3] Basal area and density are plotted against one another and quadratic mean diameter lines are plotted through the plot.

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in the social sciences.

Forest dense collection of trees covering a relatively large area

A forest is a large area dominated by trees. Hundreds of more precise definitions of forest are used throughout the world, incorporating factors such as tree density, tree height, land use, legal standing and ecological function. According to the widely used Food and Agriculture Organization definition, forests covered 4 billion hectares (9.9×109 acres) (15 million square miles) or approximately 30 percent of the world's land area in 2006.

Diagram plan, drawing, sketch or outline to show how something works or the relationships between the parts of a whole

A diagram is a symbolic representation of information according to visualization technique. Diagrams have been used since ancient times, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram.

The diagram itself is a plot of the natural logarithm of the volume or yield against the natural logarithm of stems per acre. Just like a stocking diagram, the A-line, B-line, and C-line are plotted. In addition, the -3/2 rule maximum density line is plotted just above the A-line. [1] The diagram works well for even aged, single cohort stands. However, it is not as effective with uneven-aged stands. [2]

Logarithm family of functions for which the image of a product is the sum of the images

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. The logarithm of x to baseb is denoted as logb (x) (or, without parentheses, as logbx, or even without explicit base as log x, when no confusion is possible). More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm for any two positive real numbers b and x where b is not equal to 1, is always a unique real number y. More explicitly, the defining relation between exponentiation and logarithm is:

Volume quantity of three-dimensional space

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space.

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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 (DBH) of the tree of average basal area, also known as the quadratic mean diameter. 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 diagrams.

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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. A desirable level of stocking is often considered that which maximizes timber production, or other management objectives.

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References

  1. 1 2 3 Kershaw, J. A., and B.C. Fischer. 1991. A stand density management diagram for sawtimber sized mixed upland central hardwoods. pp. 414-428 in McComick, L.H. and Gottschalk, K.W., eds. Proceedings, 8th Central hardwood forest conference.
  2. 1 2 British Columbia Ministry of Forestry. How to use a stand density management diagram. Published 1997. Accessed 17 March 2008.
  3. Fischer