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 57<br />
3.3 Model equations<br />
For <strong>the</strong> formulation <strong>of</strong> <strong>the</strong> model equations, <strong>the</strong> follow<strong>in</strong>g notational conventions are<br />
used: First, <strong>the</strong> symbols used <strong>in</strong> <strong>the</strong> ma<strong>the</strong>matical model correspond to <strong>the</strong> identifiers <strong>in</strong><br />
<strong>the</strong> simulation model (section 3.5). Second, <strong>the</strong> first letter <strong>of</strong> a ma<strong>the</strong>matical symbol denotes<br />
its type (Swartzman & Kaluzny 1987), i.e. u stands for <strong>in</strong>put/output variables (cf.<br />
Tab. 3.1), k – model parameters, and g – auxiliary variables. State variables have no prefix.<br />
Third, <strong>the</strong> subscripts s and c are used to denote species-specific and cohort-specific<br />
variables, respectively.<br />
Tab. 3.1: Symbols used for <strong>in</strong>put/output variables <strong>of</strong> <strong>the</strong> FORCLIM model. “Eq.” denotes <strong>the</strong> number <strong>of</strong><br />
<strong>the</strong> equation where <strong>the</strong> variables are calculated.<br />
L<strong>in</strong>k Symbol Unit Explanation Eq.<br />
FORCLIM-E → P uWiT °C m<strong>in</strong>imum <strong>of</strong> current Dec, Jan, Feb temperatures 3.71<br />
uDD °C·d annual sum <strong>of</strong> degree-days 3.72<br />
uDrStr – drought stress <strong>in</strong>dex 3.75<br />
FORCLIM-E → S uAET mm·yr -1 actual evapotranspiration – 1)<br />
FORCLIM-P → S uFL i t·ha -1 three types <strong>of</strong> foliage litter (i = 1,2,3) 3.43<br />
uTL t·ha -1 twig litter 3.44<br />
uRL t·ha -1 root litter 3.45<br />
uWL t·ha -1 woody litter 3.46<br />
FORCLIM-S → P uAvN kg·ha -1 nitrogen availability 3.62<br />
1) <strong>the</strong> calculation <strong>of</strong> this variable was described <strong>in</strong> detail by Fischl<strong>in</strong> et al. (1994).<br />
3.3.1 FORCLIM-P: A forest gap model <strong>of</strong> tree population dynamics<br />
FORCLIM-P is formulated as a discrete time model with a time step (∆t) <strong>of</strong> one year<br />
(“Sequential Mach<strong>in</strong>e”, Zeigler 1976; cf. section 2.1). Each tree cohort is described by<br />
two state variables (Fig. 3.2). The dimension <strong>of</strong> <strong>the</strong> state vector <strong>of</strong> FORCLIM-P varies<br />
with time because tree cohorts are established depend<strong>in</strong>g on <strong>the</strong> environmental conditions,<br />
and <strong>the</strong>y are removed aga<strong>in</strong> when <strong>the</strong>ir last member dies. To derive an estimate <strong>of</strong> <strong>the</strong><br />
maximum size <strong>of</strong> <strong>the</strong> state vector, we generously assume that one cohort <strong>of</strong> every species<br />
is established every 10th year (cf. Eq. 3.7 and Tab. 3.12), and that <strong>the</strong> life expectancy<br />
<strong>of</strong> tree cohorts is 100 years. Thus <strong>the</strong> state vector has a dimension <strong>of</strong> not more than 20·n,<br />
where n is <strong>the</strong> number <strong>of</strong> species <strong>in</strong>corporated <strong>in</strong> <strong>the</strong> model. For European conditions<br />
where about 30 species have to be considered, <strong>the</strong> dimension <strong>of</strong> <strong>the</strong> state vector <strong>of</strong> FOR-<br />
CLIM-P may be as large as 600; however, typically it is less than 100.