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The Model > Diameter Increment > Old Growth Diameter Increment

Old Growth Diameter Increment

Aspen and Spruce

For tall trees that approach the constant asymptote of the height – DBH curve, diameter increment begins increasing rapidly for the same height increment. However, the site index curve continues to increase in height. In this sense, these curves are incompatible; however, an H-D curve with height continuing to increase with large DBH could not be fit to this data. To avoid the instability this constant H – D asymptote causes, we switch to a constant tree-level basal area increment (BAI) for site trees trees taller than 80% of the H-D asymptote for its species. The DBH increment is determined for a hypothetical site tree which has just reached this 80% point, using the equations described above for mid-rotation trees. This is then converted to a BAI.

BAI80% =π / 4 * [(DBH80% + DI80%)2 – DBH80%2]

This constant BAI is applied as the tree continues to grow. For each year (t), the thickest tree gets the diameter increment DImaxt:

DImaxt = SQR(4 /π * BAI80% + Dt2) - Dt

Consequently, as these “old-growth” trees put on growth around an increasing stem perimeter, the DBH increment declines. Trees which are thinner than the thickest tree (and meet the “old-growth” height criterion) have this maximum DBH increment reduced for:

Aspen - by the same reduction factor as the mid-rotation trees.

Spruce - by:

RFsw = exp (-0.07449*CID + -0.41993*CIS + -0.07046*CIP)/10000

Where:

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

Lodgepole Pine

DBHIncr = HtInc / Exp(-0.331 + 1.263 * rDGGR + 3.34 * rSWGGR + 2.061 * rPLGGR)

Where:

HtInc = height increment for the current tree

rDGGR = stDBagt) / maxBA

rSWGGR = trSWGGR) / maxBA

rPLGGR = trPLGGRCol) / 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 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

 

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 deciduous trees with diameter larger than subject tree

max100SF = is the stand spacing factor. maximum spacing factor is 50