The non-spatial density dependent crown depth and radius relationships

The density dependent equations for crown radius and crown depth use non-spatial measures of density to influence crown radius and crown depth. Density is measured across the plot as a whole, not locally (thus "non-spatial").

Crown Radius Parameters

Parameter nameDescription
Non-Spatial Density Dep. Inst. Crown Height "a" The "a" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "b" The "b" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "c" The "c" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "d" The "d" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "e" The "e" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "f" The "f" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "g" The "g" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "h" The "h" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "i" The "i" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Density Dep. Inst. Crown Height "j" The "j" term in the instrumental crown depth equation, used to calculate crown radius
Non-Spatial Exp. Density Dep. Crown Radius "D1" The "D1" term
Non-Spatial Exp. Density Dep. Crown Radius "a" The "a" term
Non-Spatial Exp. Density Dep. Crown Radius "b" The "b" term
Non-Spatial Exp. Density Dep. Crown Radius "c" The "c" term
Non-Spatial Exp. Density Dep. Crown Radius "d" The "d" term
Non-Spatial Exp. Density Dep. Crown Radius "e" The "e" term
Non-Spatial Exp. Density Dep. Crown Radius "f" The "f" term

Crown Depth Parameters

Parameter nameDescription
Non-Spatial Density Dep. Inst. Crown Radius "a" The "a" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "b" The "b" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "c" The "c" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "d" The "d" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "e" The "e" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "f" The "f" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "g" The "g" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "h" The "h" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "i" The "i" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Density Dep. Inst. Crown Radius "j" The "j" term in the instrumental crown radius equation, used to calculate crown depth
Non-Spatial Log. Density Dep. Crown Height "a" The "a" term
Non-Spatial Log. Density Dep. Crown Height "b" The "b" term
Non-Spatial Log. Density Dep. Crown Height "c" The "c" term
Non-Spatial Log. Density Dep. Crown Height "d" The "d" term
Non-Spatial Log. Density Dep. Crown Height "e" The "e" term
Non-Spatial Log. Density Dep. Crown Height "f" The "f" term
Non-Spatial Log. Density Dep. Crown Height "g" The "g" term

In addition to the use of density variables, the density dependent equations for crown width uses an estimate of crown depth as a dependent variable (and vice versa). This estimated value of crown width and crown depth (radi and chi) used in the density dependent equations come from the instrumental variable equations. Calculating the instrumental variables equations avoids "uncoupling" the crown radius - crown depth relationship.

The non-spatial exponential density dependent crown radius function is:

rad = D1 * DBH a * Height b * chi c * STPH d * BAPH e * BAL f

where:

The instrumental equation for calculating chi is as follows:

chi = a + b * DBH + c * Height + d * DBH 2 + e * Height 2 + f / DBH + g * STPH + h * BAPH + i * BAL + j * (Height / DBH)

where:

The non-spatial logistic density dependent crown depth function is:

Non spatial logistic density dependent crown depth function

where:

The instrumental equation for calculating radi is as follows:

radi = a + b * DBH + c * Height + d * DBH 2 + e * Height 2 + f / DBH + g * STPH + h * BAPH + i * BAL + j * (Height / DBH)

where: