SORTIE-ND
Software for spatially-explicit simulation of forest dynamics

The NCI crown depth and radius relationships

This 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 nameDescription
NCI Crown Depth - AlphaNCI function exponent.
NCI Crown Depth - BetaNCI function exponent.
NCI Crown Depth - Crowding Effect "n"Crowding effect exponent.
NCI Crown Depth - GammaNCI function exponent.
NCI Crown Depth Lambda for Species X NeighborsThe 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.

Parameter nameDescription
NCI Crown Radius - AlphaNCI function exponent.
NCI Crown Radius - BetaNCI function exponent.
NCI Crown Radius - Crowding Effect "n"Crowding effect exponent.
NCI Crown Radius - GammaNCI function exponent.
NCI Crown Radius Lambda for Species X NeighborsThe competitive effect of neighbors of species X.
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 Effect

where:

• 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