On the Ecology of Mountainous Forests in a Changing Climate: A ...
On the Ecology of Mountainous Forests in a Changing Climate: A ...
On the Ecology of Mountainous Forests in a Changing Climate: A ...
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The forest model FORCLIM 67<br />
Growth reduction by unfavorable environmental conditions<br />
In section 3.1 it was noted that both <strong>the</strong> multiplication <strong>of</strong> all <strong>the</strong> growth factors with each<br />
o<strong>the</strong>r (e.g. Botk<strong>in</strong> et al. 1972a,b) as well as “Liebig's Law” (Kienast 1987) are partly unsatisfactory<br />
for calculat<strong>in</strong>g <strong>the</strong> overall growth reduction <strong>in</strong> forest gap models. Ideally,<br />
such a procedure should fulfil <strong>the</strong> follow<strong>in</strong>g requirements:<br />
1) The numerical value <strong>of</strong> each s<strong>in</strong>gle growth factor should affect tree growth, not<br />
only <strong>the</strong> rank<strong>in</strong>g <strong>of</strong> <strong>the</strong> growth factors; too much <strong>in</strong>formation on <strong>the</strong> environmental<br />
conditions is lost if only <strong>the</strong> smallest growth factor is considered.<br />
2) Tree growth should not converge to zero when an <strong>in</strong>creas<strong>in</strong>g number <strong>of</strong> nonzero<br />
growth factors is considered.<br />
Nei<strong>the</strong>r <strong>the</strong> multiplicative nor Liebig's approach fulfil both requirements. As an alternative,<br />
<strong>the</strong> geometric mean could be used to comb<strong>in</strong>e <strong>the</strong> growth factors. However, this<br />
measure has a strong smooth<strong>in</strong>g effect; specifically, low growth factors are smoo<strong>the</strong>d too<br />
much. For example, three growth factors with a value <strong>of</strong> 0.5 each and one factor with a<br />
value <strong>of</strong> 0.01, i.e. almost zero growth, result <strong>in</strong> an overall growth factor still amount<strong>in</strong>g<br />
to 0.19, which is too high. Thus a modified geometric mean as given <strong>in</strong> Eq. 3.28 was<br />
formulated; it conforms to <strong>the</strong> above two requirements, but it smoo<strong>the</strong>s <strong>the</strong> growth factors<br />
less than <strong>the</strong> unmodified geometric mean:<br />
3<br />
ƒ(e) c =<br />
gALGF c · gDDGF s · gSMGF s · gSNGF s<br />
(3.28)<br />
Besides <strong>the</strong> third root, <strong>the</strong> square root was evaluated as well. The FORCLIM-P model appeared<br />
to be little sensitive to <strong>the</strong> choice <strong>of</strong> <strong>the</strong> square or third root. Thus Eq. 3.28 was<br />
used <strong>in</strong> <strong>the</strong> model.<br />
TREE MORTALITY<br />
As stated above, FORCLIM-P models <strong>the</strong> establishment and growth <strong>of</strong> tree cohorts, not <strong>of</strong><br />
<strong>in</strong>dividual trees. However, <strong>the</strong> mortality functions described below are evaluated for each<br />
member <strong>of</strong> each tree cohort <strong>in</strong>dividually, i.e. <strong>the</strong> mortality probability does not refer to all<br />
<strong>the</strong> members <strong>of</strong> a tree cohort simultaneously. The symbols used <strong>in</strong> <strong>the</strong> mortality submodel<br />
are given <strong>in</strong> Tab. 3.4.