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

66 Chapter 3
gL 9,c = 2.24 · 1 – e -1.136⋅(gAL gHc – 0.08) (3.23)
Finally, the light growth factor of the tree cohort (gALGF c ) is calculated by interpolation
between the above two functions, depending on kL a,s , a parameter denoting the shade
tolerance of adult trees (Fig. 3.7a):
gALGF c = MAX gL 1,c + (kL a,s –1) · gL 9,c – gL 1,c
8
, 0 (3.24)
Degree-day growth factor
The effect of degree-days on tree growth (gDDGF s ) is modelled according to the parabolic
equation proposed by Botkin et al. (1972a,b) (Fig. 3.7b):
gDDGF s = MAX 4 ⋅ (uDD – kDDMin s) ⋅ (kDDMax s – uDD)
(kDDMax s – kDDMin s ) 2 , 0 (3.25)
Soil moisture growth factor
Bassett (1964) found that the basal area increment of trees is related linearly to the amount
of drought stress they experience; thus diameter increment can be expected to be related to
drought stress (uDrStr) by a square root function. The latter relationship was incorporated
in many forest gap models in order to represent the influence of drought on tree growth
(gSMGFs, e.g. Pastor & Post 1985, Kienast 1987), taking into account the maximum
drought tolerance of the species (kDrT s , Prentice & Helmisaari 1991; Fig. 3.7c):
gSMGF s =
MAX 1 – uDrStr
kDrT s
, 0 (3.26)
Soil nitrogen growth factor
The equations by Aber et al. (1979), which are based on the fertilizer trials by Mitchell &
Chandler (1939), are used to define the influence of nitrogen availability (uAvN) on tree
growth rate (gSNGF s , Pastor & Post 1985):
gSNGF s = MAX 1 – e kN 1,kNTols · ( uAvN - kN 2,kNTols ) , 0 (3.27)
where kN 1,kNTol s and kN 2,kNTols are parameters with different values depending on
kNTol s , the nitrogen tolerance class of the tree species (Fig. 3.7d).