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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13<br />
2 . Analysis <strong>of</strong> exist<strong>in</strong>g forest gap<br />
models<br />
This chapter starts with an analysis <strong>of</strong> <strong>the</strong> model formalism <strong>of</strong> forest gap models (section<br />
2.1). Section 2.2 presents simulation studies with <strong>the</strong> FORECE model, which are used to<br />
exemplify <strong>the</strong> type <strong>of</strong> basic simulation results produced by forest gap models and to<br />
analyse some <strong>of</strong> <strong>the</strong>ir statistical properties. These considerations provide <strong>the</strong> basis for an<br />
ecological analysis <strong>in</strong> section 2.3: First, <strong>the</strong> sensitivity <strong>of</strong> <strong>the</strong> FORECE model to structural<br />
simplifications is <strong>in</strong>vestigated <strong>in</strong> order to derive a m<strong>in</strong>imum set <strong>of</strong> ecological factors that<br />
are necessary to model forest dynamics <strong>in</strong> <strong>the</strong> European Alps (section 2.3.1). Second, <strong>the</strong><br />
set <strong>of</strong> climate-dependent factors rema<strong>in</strong><strong>in</strong>g after <strong>the</strong> simplification procedure is analysed<br />
for its sensitivity to alternate formulations (section 2.3.2).<br />
Throughout <strong>the</strong> <strong>the</strong>sis, <strong>the</strong> nomenclature <strong>of</strong> <strong>the</strong> European tree species follows Hess et al.<br />
(1980). Their scientific and common names are listed <strong>in</strong> Appendix I.<br />
2.1 Model formalism<br />
Zeigler (1976) dist<strong>in</strong>guished <strong>the</strong> follow<strong>in</strong>g categories <strong>of</strong> model formalisms: Differential<br />
Equation System Specifications (DESS), Discrete EVent System Specifications (DEVS),<br />
and Sequential Mach<strong>in</strong>es (SM, i.e. discrete time models). It is <strong>of</strong>ten difficult to specify to<br />
which <strong>of</strong> <strong>the</strong>se three formalisms complex models belong, because <strong>the</strong> ma<strong>the</strong>matical equations<br />
are not published <strong>in</strong> detail, <strong>the</strong> various submodels may be based on different formalisms,<br />
or <strong>the</strong> formalism used for <strong>the</strong> ma<strong>the</strong>matical model does not correspond to <strong>the</strong><br />
one used <strong>in</strong> <strong>the</strong> simulation model, i.e. <strong>in</strong> <strong>the</strong> computer code. For example, <strong>the</strong> tree growth<br />
equation <strong>of</strong> forest gap models most <strong>of</strong>ten is described as a differential equation (DESS,<br />
Botk<strong>in</strong> et al. 1972a,b, Shugart 1984), while <strong>the</strong> descriptions <strong>of</strong> tree establishment and<br />
tree death suggest that <strong>the</strong>se processes are simulated us<strong>in</strong>g a discrete event model<br />
(DEVS). However, forest gap models typically are implemented as discrete-time models<br />
(SM) with an annual time step. Hence, <strong>the</strong>re arises <strong>the</strong> question to which formalism <strong>the</strong>se<br />
models conform.