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 69<br />
Stress-<strong>in</strong>duced mortality<br />
Analogous to <strong>the</strong> age-related mortality, <strong>the</strong> <strong>in</strong>creased mortality rate <strong>in</strong>duced by environmental<br />
stress (gP m2,c ) is based on <strong>the</strong> assumption that only a small fraction <strong>of</strong> trees will<br />
survive a given number <strong>of</strong> years when <strong>the</strong>y are subject to such stress (Shugart 1984,<br />
Pastor & Post 1985, Kienast 1987, Solomon & Bartle<strong>in</strong> 1993):<br />
gP m2,c =<br />
kSlowGrP SGr c > kSGrYrs<br />
0 else<br />
(3.31)<br />
where SGr c is <strong>the</strong> <strong>the</strong> number <strong>of</strong> consecutive years <strong>the</strong> cohort's diameter has <strong>in</strong>creased<br />
less than 10% <strong>of</strong> <strong>the</strong> maximum diameter <strong>in</strong>crement (kM<strong>in</strong>RelInc) or less than 0.3 mm<br />
(kM<strong>in</strong>AbsInc). Hence, SGr c provides a memory for past environmental stress; <strong>the</strong>refore<br />
it is a state variable (Eq. 3.32):<br />
SGr c (t+1) =<br />
SGr c (t) + 1 ƒ(e) c < kM<strong>in</strong>RelInc ∨ ∆D c<br />
∆t<br />
0 else<br />
< kM<strong>in</strong>AbsInc<br />
(3.32)<br />
where t denotes <strong>the</strong> discrete time <strong>in</strong> years.<br />
Disturbance-related mortality<br />
As noted <strong>in</strong> section 3.1, <strong>the</strong> disturbance-related mortality is formulated <strong>in</strong> a simple manner,<br />
i.e. <strong>the</strong> probability that <strong>the</strong> trees on <strong>the</strong> patch are killed by a disturbance is regulated<br />
by <strong>the</strong> model parameter kDistP (Eq. 3.33):<br />
gP m3 = kDistP (3.33)<br />
Overall mortality probability<br />
Eq. 3.34 describes <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> overall mortality probability for each tree and<br />
each year (gP m ). The trees are subject to <strong>the</strong> disturbance-related mortality first (gP m3 ); if<br />
<strong>the</strong>y survive, <strong>the</strong>y may die from <strong>the</strong> age-related mortality (gP m1,s ) and, f<strong>in</strong>ally, from <strong>the</strong><br />
stress-<strong>in</strong>duced mortality rate (gP m2,c ). In <strong>the</strong> simulation model, <strong>the</strong> overall mortality<br />
probability (gP m ) is determ<strong>in</strong>ed for each tree us<strong>in</strong>g Monte Carlo techniques.<br />
gP m = gP m3 + (1 – gP m3 )·(gP m1,s + [1 – gP m1,s ]·gP m2,c ) (3.34)