The NCI crown depth and radius relationshipsThis calculates crown dimensions as a function of tree size and local crowding. The equations are the same for crown depth and crown radius, but they each have separate parameters. NCI Crown Depth Parameters| Parameter name | Description |
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| NCI Crown Depth - Alpha | NCI function exponent. | | NCI Crown Depth - Beta | NCI function exponent. | | NCI Crown Depth - Crowding Effect "n" | Crowding effect exponent. | | NCI Crown Depth - Gamma | NCI function exponent. | | NCI Crown Depth Lambda for Species X Neighbors | The competitive effect of neighbors of species X. | | NCI Crown Depth - Max Potential Depth (m) | The maximum possible value for crown depth, in m. | | NCI Crown Depth - Max Search Distance for Neighbors (m) | The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. | | NCI Crown Depth - Minimum Neighbor DBH (cm) | The minimum DBH for trees of that species to compete as neighbors. Values are needed for all species. | | NCI Crown Depth - Size Effect "d" | Size effect function exponent. |
NCI Crown Radius Parameters| Parameter name | Description |
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| NCI Crown Radius - Alpha | NCI function exponent. | | NCI Crown Radius - Beta | NCI function exponent. | | NCI Crown Radius - Crowding Effect "n" | Crowding effect exponent. | | NCI Crown Radius - Gamma | NCI function exponent. | | NCI Crown Radius Lambda for Species X Neighbors | The competitive effect of neighbors of species X. | | NCI Crown Radius - Max Potential Radius (m) | The maximum possible value for crown radius, in m. | | NCI Crown Radius - Max Search Distance for Neighbors (m) | The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. | | NCI Crown Radius - Minimum Neighbor DBH (cm) | The minimum DBH for trees of that species to compete as neighbors. Values are needed for all species. | | NCI Crown Radius - Size Effect "d" | Size effect function exponent. |
The crown dimensions are calculated as: CR / CD = [Max CR / Max CD] * Size Effect * Crowding Effectwhere: - CR is the crown radius, in m
- CD is the crown depth, in m
- Max CR is the NCI Crown Radius - Max Potential Radius (m) parameter
- Max CD is the NCI Crown Depth - Max Potential Depth (m) parameter
Size Effect is calculated as: SE = 1 - exp(-d * DBH)where: - SE is the size effect, between 0 and 1
- d is either the NCI Crown Depth - Size Effect "d" parameter or the NCI Crown Radius - Size Effect "d" parameter
- DBH is the tree's DBH, in cm
Crowding Effect is calculated as: CE = exp(-n * NCI)where: - CE is the crowding effect, between 0 and 1
- n is the NCI Crown Radius - Crowding Effect "n" parameter or the NCI Crown Depth - Crowding Effect "n" parameter
- NCI is calculated as below
NCI is calculated as:  where: - the calculation sums over j = 1...S species and k = 1...N neighbors of each species of at least a DBH of NCI Crown Radius - Minimum Neighbor DBH or NCI Crown Depth Minimum Neighbor DBH, in cm, out to a distance of NCI Crown Radius - Max Search Distance for Neighbors (m) or NCI Crown Radius - Max Search Distance for Neighbors (m)
- α is the NCI Crown Radius - Alpha parameter or the NCI Crown Depth - Alpha parameter
- β is the NCI Crown Radius - Beta parameter or the NCI Crown Depth - Beta parameter
- γ is the NCI Crown Radius - Gamma parameter or the NCI Crown Depth - Gamma parameter
- λ ik is the NCI Crown Radius Lambda for Species X Neighbors parameter or the NCI Crown Depth Lambda for Species X Neighbors for the target species relative to the kth neighbor's species
- DBHjk is the DBH of the kth neighbor, in cm
- DBHt is the DBH of the target tree for which to calculate crown dimensions, in cm
- distanceik is distance from target to neighbor, in m
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