Height and diameter growth for juvenile pine
For pine annual height growth for seedlings (height<1.3m) is predicted based on preliminary relationships fitted to the Alberta LFS SDS and MP data (Yao PhD thesis 1995). This function predicts height growth using primarily total age; only very slight impacts for density and species composition are present. Site index and other competing vegetation has no effect on the predictions.
HiJvpl = jHtpl(Age + 1) - jHtpl (Age)
Where: HiJvpl is the pine height increment
jHtpl = 1.385364 * Exp(0.164135 * Health + (-0.0000039035 * stTotDen) + (0.623597 * trSc) + (0.243658 * sitecls) + (0.626597 * DW)) * (Exp(0.355587 * Age) - 1) / 100
Health = 1 if healthy and 0 if damaged, defaults to 1
stTotDen = stand total density
trSc = relative total density of pine
sitecls = is set to 0 if site index is <= 18 and set to 1 if site index > 18
DW = drainage 1 if well drained and 0 if poorly drained, defaults to 1
Age = tree age
Height growth for saplings (height ³1.3m, DBH<4 cm) of these species is based on the increment predicted by the regional site curve, given the breast height (BH) age of the tree. Annual diameter growth of saplings is the difference in diameters predicted from the regional height-diameter relationships using present and future tree height.
HiJvpl = siteHt(spp, BHAge + 1, site) - siteHt(spp, BHAge, site)
siteHt is height predicted by the regional site index curve
BHAge is breast height age
Site is the pine site index
Diameter growth for juvenile pine
DIncr = prDBH(spp, Ht) - prDBH(spp, Ht - HtInc)
where: prDBH is the predicted DBH
if Ht <=1.3 m then prDBH = "-1" dbh does not exist
else "case where Height > 1.3 but less than asymptote of diameter height curve"
prDBH = Log(1 - ((Ht - 1.3) / A) ^ (1 / A(C))) / A(B)
A, B, C = are coefficients from the AESRD height diameter model
Diameter Increment Reduction Factor for high density stands
The reduction factor reduces the diameter increment by a factor of 1.0 to 0.5 as density increases from 20,000 to 70,000 stems per hectare.
DIncr = redFact * DIncr
redFact = 0.5 * (stTotDen - 20000) / 50000), Maximum reduction is 0.5
where: stTotDen = stand total density
Survival probability (Ps) for juvenile pine (DBH<4 cm)
For juvenile pine, annual survival probability (Ps) is predicted using (1) a logistic model fitted to the AFF monitor plots (Yao 1996) and (2) limited by a maximum size-density function (Yang 2001).
(1) Ps = exp(c) / (1+exp(c))
Where: c = d + e TAge + f H + g ln(H) + h ln(TotDen) +k*ln((PlDen)+ i PlDen/TotDen + j Site
TAge is tree total (root collar) age, H is tree height, PlDen is pine density (stems ha-1)
TotDen is total density (stems ha-1)
Site=1 if the pine site index is ≥18m, Site=0 otherwise.
Juvenile Ps predicted by this function is constrained to a maximum of 0.98.
d=12.0637, e =0.44474, f=0.2761, g=0.5476, h=2.393, i=5.057, j=0.742, k=1.7123
The diameter-based self-thinning function is
(2) MaxDen = ((1 / qmd + 0.00865) / 0.001244) ^ (1 / 0.5225)
QMD is the stand quadratic mean DBH (all species).
Note this is always on (not affected by MAFlag or MaxDensityPIAdj flag)
In pure Pine stands. if the Stand BA exceeds 40, Ps will be decreased to achieve 40. This is alays on(o't • affected by MAFlag)