Mid-Rotation Diameter Increment
Aspen and White Spruce
MGM predicts annual height increment (HI) first, then links this to diameter increment (DI) through a height - DBH curve fit to site trees. Like height increment, this maximum increment is then reduced by the amount of competition, though this is a stronger effect than it is for height.
A height – DBH curve was fit to site trees (100 thickest/ha) from permanent sample plots. This equation is a cumulative Weibull distribution with parameters specific to Alberta natural subregions (for white spruce) as shown in the equation below and Table 1:
H = a*(1-exp(-((DBH / b) ^c ))
Table1. Regional parameters for height – DBH equations.
*Natural Regions Committee 2006. Natural Regions and Subregions of Alberta. Compiled by D.J. Downing and W.W. Pettapiece. Government of Alberta. Pub. No. T/852.
The derivative (f’ ) of this function relates height increment (HI) to diameter increment (DI) at any DBH.
HImax / DImax = f ' (DBH)
The maximum diameter increment is then
DImax = HImax / f ' (DBH)
Where HImax is the height increment of a site tree, obtained from the slope of the height vs. age and site index curve. DImax is then reduced by competition.
DBHIncr = DImax*RFspp
Where the reduction factor for deciduous species (RFaw) is
RFaw = exp (-0.285*CID -1.071*CIS - 0.129*CIP)/10000
And for white spruce, RFsw is
RFsw = exp (-0.150*CID -0.390*CIS -0.159*CIP)/10000
As for height increment,
CIx= ΣDBH*tf is the competition due to thicker deciduous, spruce-fir and pine species groups
DBH is in cm and tf is the tree expansion factor in stems/ha
DBHIncr = HtInc / Exp(-0.331 + 1.263 * rDGGR + 3.34 * rSWGGR + 2.061 * rPLGGR)
HtInc = height increment for the current tree
rDGGR = stDBagt / maxBA
rSWGGR = trSWGGR / maxBA
rPLGGR = trPLGGR / maxBA
trSWGGR = Ba/ha of white spruce trees with diameter larger than the subject tree
trPLGGRCol = Ba/ha of lodgepole pine trees with diameter larger than the subject tree
st DBagt = Ba/ha of deciduous 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
DBHIncr = HtInc * (1.142535 * Exp(-(0.099215 * Caggr + 0.102159 * Daggr)))
Caggr = stCBagt / max100SF
Daggr = stDBagt / max100SF
stC Bagt = Ba/ha of coniferous trees with diameter larger than subject tree
st DBagt = Ba/ha of deciduaous trees with diameter larger than subject tree
max100SF = is the stand spacing factor, maximum spacing factor is 50