The Model > Diameter Increment > Mid-Rotation Diameter Increment

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


Black Spruce

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