The Model > Juvenile Growth > Aspen


Height and Diameter Growth for Juvenile Deciduous (DBH<4 cm)

For juvenile trees, growth relationships are based on an analysis in 2004 of combined data sets. These included Alberta Agriculture and Forest SDS data updated to May 2004, WESBOGY LTS data updated to Dec 2000, and regenerated permanent sample plots contributed by Alberta forestry companies updated to Dec 2002.

Height Increment
The early deciduous height - age trajectory is initially exponential but declines toward a constant height increment. Although this is captured by the provincial and regional site index curves, their behaviour at this age was better described by a declining height increment function. MGM uses a negative exponential function with initial height as the major predictor, scaled by site index and overtopping deciduous density. Since aspen and poplar regenerate primarily by vegetative sprouts from a large root system, small sprouts appear to achieve a minimum height increment regardless of their initial height, modeled by 0.25 of the maximum height increment possible under this site index.

For juvenile aspen the annual height increment (HiAw, m/year) is represented by

HiAw = a*b + a*{1 - exp[-H/(12 a + c DecDenAbove)]}

Where: H is the height (m) of the tree at the start of the year

DecDenAbove (sph)is the density of deciduous trees taller than the current tree

SIAwis the aspen site index at breast height age 50

a=d + e SIAw

b=0.25, c=0.00175, d=-0.4 and e=0.0615

Diameter Increment

There are 3 possible cases with respect to juvenile aspen annual diameter increment predictions.

Case 1: the tree began with a height below 1.3 m and after the current annual height increment continues to be below 1.3 m. In this case

DBH is set to zero.

Case 2: the tree began with a height below 1.3 m and after the current annual height increment, has crossed the 1.3 m height threshold. DBH is predicted as:

DBHaw = MAX(-1.83 + 1.444 * Ht, 0.3)

Where: Ht is the predicted height at the end of the growth year.

It is unlikely that first year DBH will be much smaller than this, and the diameter growth function, which depends on initial DBH, performs poorly if DBH is unrealistically low. Note that this function does not work for trees older than breast height age 1.

Case 3: the tree began with a height above 1.3. In this case DBH increment is obtained from an annual basal area increment (BAI, cm2/year) model

BAI = a (BAb) (RHc) (SFDecd)

Where: BA is the basal area of the tree at the start of the year (cm2)

RH = H / Dec10H

SFDec= 1/[Dec10H*(DecDen/10000)0.5]

RH is the height of the tree relative to the juvenile deciduous canopy height (Dec10H)

H is the current deciduous tree height (m)

Dec10H is average height of tallest 10% the deciduous trees (m)

SFDec is spacing factor for juvenile deciduous trees (in tree lengths; unitless)

DecDen is deciduous tree density (stems/ha)

a=0.7898, b=0.6653, c=0.3452 and d=0.2844

SFDec is constrained to be ≤2 (i.e. at low deciduous density spacing factor begins to get very large).


Juvenile aspen mortality is predicted in three stages. The first stage is an application of an empirical mortality constant of 0.08 to the deciduous density to obtain an estimate of the final density at the end of the year. This constant is based on a re-examination of the longer term WESBOGY data as described by Bokalo et al. 2007. The second stage involves the comparison of the predicted density to the mean maximum density (MeanMaxJuvDen) defined by an average height vs. density self-thinning function (Bokalo et al., 2007)

MeanMaxJuvDen = Exp((Log(AvHtDec)) - a) / b)

Where: AvHtDec is the average height of the deciduous trees

a =8.3510 and b = -0.6767


When estimated density exceeds the mean maximum density, the density is set to the mean maximum density and the empirical mortality constant is

recalculated to match the mean maximum size density.


The third stage involves allocating the mortality among the trees in the tree list since mortality is expected to be heavier for the smaller trees in a juvenile stand. A

logistic function is used to accomplish this.


Ps = exp(c) / (1+exp(c))


Where: c = d + e HI + f RH - g DecDen

RH = H / Dec10H

DecDen is juvenile deciduous tree density (stems ha-1)

Dec10H is the deciduous canopy height (m, calculated as the average height of the tallest 10% of the deciduous trees (m)

d =-0.2472, e = 3.6967, f = 4.5031, g = 0.00000422


Note this self-thinning constraint cannot be disabled as you can for mid rotation and older trees