Mortality for Mid-Rotation and Old-Growth Aspen
For deciduous trees with DBH>4cm, annual survival probability (Ps) is predicted using a logistic model:
Pslogistic = exp(c) / (1+exp(c))
Where: c = b0 + b1*DBH + b2*DBH2 + b3*DI + b4*DBH2*BAGT
DBH is in cm
DI is the current diameter increment (cm/y)
BAGT is the basal area in thicker trees (all species) (m2/ha)
b0 = 2.20, b1 = 0.207, b2 = -0.00286, b3 = 0.659, b4 = - 0.0000778
It was confirmed in 2006 the the function above underestimated mortality by approximately 1%. The following adjustment was added.
SRF0 = (0.98 + 0.02 * (1 - stDBagt/stBaDec))
For very large, old trees and stands there are two additional mortality penalties, designed to account for wind damage to large trees, increased mortality in
heavily stocked stands, and the dieback of old, slow growing trees (Yang 2002):
These are active when MAFlag is selected (checked)
1) If the quadratic mean DBH of the aspen in the stand (QMDaw) exceeds 26cm and the current tree is thicker than the QMDaw, survival of the tree is reduced by
a similar factor as for white spruce
Z = (QMDaw - 26) ^ 2 / 100
SRF1 = (1 + Z * QMDaw / DBH) / (1 + Z)
2) If the stand basal area exceeds 55 m2/ha in mixed stands (BAaw/BAtotal<0.8), or 40 m2/ha in aspen dominated stands, survival of all aspen trees is reduced
SRF2 = ((BAtotal - 55) / 80) * Ps for mixedwoods
SRF2 = ((BAtotal - 40) / 80) * Ps for deciduous-dominated
3) Lastly, if the aspen are within 3m of the aspen top height (average height of the thickest 100/ha) or taller, and their height growth has dropped below
0.003*aspen site index, their survival is decreased by 10%, SRF3=0.9.
If unmodified by the criteria above, all SRFx=1. The adjusted annual survival probability, applied to the tree expansion factor is:
Psadjusted = PSlogistic * SRF0*SRF1*SRF2*SRF3
A final mortality factor was imposed to limit the densities below an empirical size-density line. This is typically only invoked for initially dense, vigorously growing stands in the stem exclusion phase (Oliver and Larsen). Users can tum this on by entering a 1 in the Aw species field in the MaxDcnAdj box. The maximum size-density relationship is
Nmax=((1 / qmd + 0.00865) / 0.001244) ^ (1 / 0.5225)
And is based on an update of Yang’s (2002) analysis, containing older juvenile data. This equation is applied when stand density (stDen; including all species’
groups) exceeds Nmax.
Ps = Ps * (DBH / maxDbhspp) * Nmax / stDen) ^ 0.2
Where maxDBHspp is the maximum DBH found in that species group. The exponent (0.2) softens the mortality penalty, so that Nmax is achieved in about 5 years.