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

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