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 ParametersParameter name  Description 

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 ParametersParameter name  Description 

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
 DBH_{jk} is the DBH of the kth neighbor, in cm
 DBH_{t} is the DBH of the target tree for which to calculate crown dimensions, in cm
 distance_{ik} is distance from target to neighbor, in m
