Environmental Engineering Reference
In-Depth Information
emerging from n are taken into account. Similar queries can be used to calculate the
biomass or the stored carbon in compartments of plants or in whole individuals. An
ecosystem simulation at a higher level could use these data to assess the carbon flow
through the system.
11.7 An Eco-Physiological Model of a Coniferous Tree Stand
Formalisms like L-systems or RGG can be used for functional-structural plant
models (FSPM). Such models combine structural and functional features of plants
or plant populations in one coherent formal framework. As an example we will
sketch a model of trees competing for light and a small part of its implementation in
the XL language. This eco-physiological growth model is taken from Lanwert
(2007). For the modelled competing conifers, only the above-ground part is repre-
sented in the model. For reasons of efficiency, the structure of the individual trees is
simplified.
The model uses a spatial approach based on biomass and photosynthetic capacity
which are assumed to be the main factors which control growth (Pfreundt 1988;
Pfreundt and Sloboda 1996). The individual trees are modelled as one-dimensional
entities, i.e. no branching is represented. The segments of the trunk axis carry all
relevant information, including certain properties of the crown. The calculation of
the basic processes such as photosynthesis, respiration, allocation and of growth is
carried out in annual steps. First the biomass of the needles is allocated vertically
along the trunk axis using a beta distribution.
Photosynthetic performance is calculatedinrelationtothemaximumphoto-
synthetic capacity in unshaded conditions at the tree top and depends on the
corresponding weighted needle mass above the calculation point as an input
quantity of a Beer-Lambert function (Monsi and Saeki 1953). Respiration is
calculated separately for the five tree compartments: “needles”, “branches”,
“trunk”, “coarse roots” and “fine roots”. After subtracting the maintenance respi-
ration from gross assimilation, the remaining net assimilation pool forms the basis
for growth.
After considering the mortality rates for roots, branches and needles and sub-
tracting the proportional cost rates for needle, branch, root and height growth, the
remaining pool of assimilates determines the secondary growth of the trunk. Height
growth of the individual tree is calculated using a function relating height to age
with a stochastic and rank preserving correction component.
After completion of growth, the new needle densities are calculated for the next
year. This is carried out separately for each needle-age cohort. The new tree height,
the death rates of the old needles, the newly formed needle mass as well as an
upshift of the crown base is taken into account.
The implementation of the model follows an object-oriented approach
(cf. Chaps. 4 and 12). A tree consists of segments whose properties, such as
