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 ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
62 Chapter 3<br />
In most forest gap models Eq. 3.9 is used to predict optimum diameter growth (Shugart<br />
1984, Botk<strong>in</strong> 1993). However, <strong>the</strong> formulation <strong>of</strong> Eq. 3.8 conceals <strong>the</strong> assumptions<br />
about <strong>the</strong> “cost associated with tree size”, i.e. respiration. It can be hypo<strong>the</strong>sized that<br />
ma<strong>in</strong>tenance respiration should be proportional e.g. to stem volume or stem surface<br />
(K<strong>in</strong>erson 1975); reconstruct<strong>in</strong>g from Eq. 3.8 an equation where <strong>the</strong> formulation <strong>of</strong><br />
respiration is explicit (see Moore 1989), we obta<strong>in</strong><br />
∆V c<br />
∆t<br />
= kR · gL c – kS · V c · D c (3.10)<br />
Thus, <strong>in</strong> <strong>the</strong> conventional growth equation ma<strong>in</strong>tenance respiration is assumed to be proportional<br />
to a power higher than tree volume, which is not realistic. In view <strong>of</strong> this limitation,<br />
Moore (1989) developed an equation for tree diameter <strong>in</strong>crement from a simple<br />
carbon budget <strong>of</strong> <strong>the</strong> tree: Consider<strong>in</strong>g biomass (volume) <strong>in</strong>crement and assum<strong>in</strong>g that (a)<br />
gross photosyn<strong>the</strong>sis is proportional to leaf area gL c and (b) respiration is proportional to<br />
stem volume V c , we can write<br />
∆V c<br />
∆t<br />
= kR · gL c – kS · V c (3.11)<br />
Next we assume <strong>the</strong> follow<strong>in</strong>g allometric relationships:<br />
(c) gL c = k 1·D c<br />
2 (Whittaker & Marks 1975) (3.12)<br />
(d) gH c = 137 + kB 2,s·D c + kB 3,s·D c<br />
2 (Ker & Smith 1955) (3.13)<br />
(e) V c = k 2·D c2·gH c (<strong>the</strong> volume <strong>of</strong> a cone) (3.14)<br />
Us<strong>in</strong>g <strong>the</strong>se assumptions, <strong>the</strong> follow<strong>in</strong>g equation for diameter <strong>in</strong>crement is obta<strong>in</strong>ed (for<br />
<strong>the</strong> details <strong>of</strong> <strong>the</strong> derivation, see Moore 1989):<br />
∆D c<br />
∆t<br />
=<br />
kG s ⋅ D c ⋅ 1 - gH c<br />
kHm s<br />
2<br />
274 + 3⋅kB 2,s ⋅D c + 4⋅kB 3,s ⋅D c · ƒ(e) c (3.15)<br />
where ƒ(e) c is a multiplier used to reduce maximum growth accord<strong>in</strong>g to <strong>the</strong> environmental<br />
constra<strong>in</strong>ts described below. This equation has a form similar to <strong>the</strong> conventional<br />
equation (Eq. 3.9), but its assumptions conform more to biological expectations. Thus it<br />
is used to predict <strong>the</strong> diameter <strong>in</strong>crement <strong>in</strong> FORCLIM-P (Fig. 3.6).