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The Model > Height Increment

Height Increment of Mid-Rotation and Old Growth

Mid-rotation trees have a DBH greater than or equal to 4.0 cm and that are less than 80% of their maximum height, defined by the asymptote of the height vs. DBH curve.

Old Growth trees are have a DBH greater than or equal to 4.0 cm and that are greater than 80% of their maximum height, defined by the asymptote of the height vs. DBH curve.

It is assumed that a site index-based height - breast height age curve defines the maximum increment for site trees (the thickest 100 trees/ha of that species in terms of DBH). Normally, site curves return site tree height at a given breast height age. Increment can be obtained by taking the difference of site height at the current tree age and at age+1. For trees that are thinner than the site trees, height increment is reduced by a reduction factor related to the amount of thicker competition in various species. This standard application of the site curve and reduction factor is applied to deciduous trees and pines since these are shade intolerant, and survivors are found mostly within the overstory.

Maximum Height Increment

IncMax = site height (species, SI, BHage+1)*dsc1 - site height (species, SI, BHage)*dsc0

Where: site height is the estimated height of the site trees based on species, site index and breast height age using Huang 1997 and Huang et al. 1997 regional equations.

dsc is a dominance switching correction (Feng et al. 2006) to deal with the bias introduced from using stem analysis-based height – age and site index curves.

dsc0 = 1 / (0.818 + 0.0036 * BHAge)

dsc1 = 1 / (0.818 + 0.0036 * (BHAge + 1))

Note: DSCx, is turned off  when GYPSY 2009 Site Index curves are being used.

For trees that are thinner than the site trees, height increment (HtIncr) is reduced by a reduction factor related to the amount of thicker competition.

HtIncr = RF * incmax

Reduction Factor for Aspen

The reduction factor (RFaw) is,

RFaw = exp(1.7*(exp(((-0.400*CID - 0.669*CIS – 0.230*CIP)/10000)^3)-1))


Reduction Factor for Spruce

 

Background: For shade tolerant species, such as white spruce in mixedwoods, there is a problem with this approach, since these trees can persist in the understory for years with very slow height growth, yet they still respond strongly when the overtopping vegetation is removed. Shorter trees appear to respond well to release, while taller trees less so. In other words, age does not appear to control their height growth response as much as their current size. We still need to link the potential response of these trees to site index, and we would like to use the site curve as a guide to potential growth since we have relatively little data in the mid-rotation age range. We can use the site curve to predict the maximum increment from size (total height) rather than age. 

Solution: To accomplish this, we estimate the BHage of a tree that grew as a site tree to the current total height, i.e. rearrange the site curve so BHage=f(species, SI, height). This BHage estimate can then be used in the equation above to determine the maximum increment of this tree. This means an older tree has the same height growth potential as a younger tree of the same height.


The reduction factor for white spruce (RFsw) is,

RFsw = exp (-0.119*CID +-0.229*CIS+-0.115*CIP)/10000

Where: CIx= ΣDBH*tf is the competition due to thicker deciduous, spruce-fir, and pine groups

DBH is in cm

Tf is the tree expansion factor in stems/ha (1/plot size in ha)

 

 

Reduction Factors for Pine

RFpl = Exp(-1.85 * rDGGR - 0.437 * rCGGR)

Where:

rDGGR = stDBagt) / maxBA

r CGGR = stCBagt) / maxBA

stDBagt = Ba/ha of Deciduous trees with diameter larger than subject tree

stCBagt = Ba/ha of Conifer trees with diameter larger than subject tree

MaxBA = maxDen * AreaConvConst * qmd ^ 2

AreaConvConst = 7.8537E-05 MaxDen = ((1 / qmd + 0.00865) / 0.001244) ^ (1 / 0.5225)

QMD = quadratic mean diameter

 

Reduction Factors for Black Spruce

RFsb = Exp(-(0.000147 * stCBagt^2 + 0.003023 * stDBagt^2))

stDBagt = Ba/ha of Deciduous trees with diameter larger than subject tree

stCBagt = Ba/ha of Conifer trees with diameter larger than subject tree