On the Ecology of Mountainous Forests in a Changing Climate: A ...

The forest model FORCLIM 67
Growth reduction by unfavorable environmental conditions
In section 3.1 it was noted that both the multiplication of all the growth factors with each
other (e.g. Botkin et al. 1972a,b) as well as “Liebig's Law” (Kienast 1987) are partly unsatisfactory
for calculating the overall growth reduction in forest gap models. Ideally,
such a procedure should fulfil the following requirements:
1) The numerical value of each single growth factor should affect tree growth, not
only the ranking of the growth factors; too much information on the environmental
conditions is lost if only the smallest growth factor is considered.
2) Tree growth should not converge to zero when an increasing number of nonzero
growth factors is considered.
Neither the multiplicative nor Liebig's approach fulfil both requirements. As an alternative,
the geometric mean could be used to combine the growth factors. However, this
measure has a strong smoothing effect; specifically, low growth factors are smoothed too
much. For example, three growth factors with a value of 0.5 each and one factor with a
value of 0.01, i.e. almost zero growth, result in an overall growth factor still amounting
to 0.19, which is too high. Thus a modified geometric mean as given in Eq. 3.28 was
formulated; it conforms to the above two requirements, but it smoothes the growth factors
less than the unmodified geometric mean:
3
ƒ(e) c =
gALGF c · gDDGF s · gSMGF s · gSNGF s
(3.28)
Besides the third root, the square root was evaluated as well. The FORCLIM-P model appeared
to be little sensitive to the choice of the square or third root. Thus Eq. 3.28 was
used in the model.
TREE MORTALITY
As stated above, FORCLIM-P models the establishment and growth of tree cohorts, not of
individual trees. However, the mortality functions described below are evaluated for each
member of each tree cohort individually, i.e. the mortality probability does not refer to all
the members of a tree cohort simultaneously. The symbols used in the mortality submodel
are given in Tab. 3.4.