LIGNUM-forest simulates a tree which grows under a light regime of a surrounding stand.
The reference tree is a member of this collective. During this work the requirement arose to investigate the behaviour of a LIGNUM tree under the light condition under a roof which is “disturbed” by a gap. In this case the reference tree can not be part of the collective of the surrounding stand. However, the ideas of light reduction calculation of LIGNUM-forest can be adapted. The light model is illustrated in figure 29. The fact that the surrounding stand belongs to a different collective of trees creates some additional requirements to parameterization. The calculation is also affected. Concerning parame-terization the values for leaf area la, height and height of crown base of the surrounding stand collective have to be provided. Furthermore the radius of the gap has to be set.
The extension of the gap is not affected by the density of the stand which forms the canopy. Table 26 gives an example for the input parameters. Technically the parameters are provided by a file. Within this example additional parameters appear. The density of the canopy is indeed given as in LIGNUM-forest. INCL, AZIM and RAD allow to parameterize the light conditions of the hemisphere. RAD is the total photosynthetically-active radiation (PAR) per growing season in southern Finland (Perttunen et al. 1996, 1998). INCL and AZIM give the number of sectors of the hemisphere “turtle”, INCL in inclination and AZIM in azimuth orientation. The values forH,Hc andLAare measured values from a site in southern Finland.
Parameter Value Unit Meaning
INCL 10.0 - number of inclination zones
AZIM 12.0 - number of azimuth zones
RAD 1200.0 [M J] total annual radiation
DENS 1000.0 [trees/ha] stand density
LA 53.3 [m2/tree] leaf area per tree
K 0.14 - extinction coefficient of the canopy
H 19.7 [m] height of canopy forming stand
HC 13.5 [m] height of the crown base of the canopy forming stand
R 10.0 [m] radius of gap
X0 0.0 [m] distance of tree base to the centre of gap
Z0 0.0 [m] elevation of reference point
Table 26: Parameters of the canopy extension of theLIGNUM light model with exemplary values.
Canopy
Sky sector
Dtr
Canopy
M D0 X0 H
Hc Hh
Figure 29: Light model extension LIGNUM-canopy. H = height of stand, Hc = crown base, Hh = height of intersection,Dtr = travel distance,R = radius of the gap,M = centre of the gap (position of the tree), X0 = horizontal distance of the reference segment to the centreM.
The remaining parameters are input values for the radiation calculation. Equations 13 and 14 show the differences in the calculation to equations 7 to 12 inLIGNUM-forest.
The distance of the tree from the edge of the gap is calculated in a more explicit way because this distances can vary from zero to twice the radiusRdepending on the direction of the light. This is specifically the case if the radius of the gap is high as e.g. in the example where the radius is 21 meters (cf. equation 14). The calculation of the height of the intersection point between the light beam and the gap cylinder is given by equation 14. It is identical to equation 10 except that here Z0 is given by the modeller.
D0 = q
R2−sin2(θ)·X02−cos(θ)·X0 (13)
Hh = Z0+D0·tan(φ) (14)
D0 = distance of tree to edge of gap,
R = radius of gap,
X0 = distance of tree to centre of gap, θ = horizontal angle of light beam.
Hh = height of intersection light beam / edge of gap, Z0 = altitude of the reference point within the gap, φ = inclination angle of the light beam.
In contrast to LIGNUM-forest this calculation is not applied for each tree segment and year. It is only determined once in the beginning of the simulation and only for one reference point. X0 is the distance from the reference point to the centre of the gap. Z0 denotes the elevation of that point. X0 is also the position of the tree within the gap.
This assumption causes an error in the calculation of D0 and Hh for each tree segment.
This differences can be expressed by
D00 = q
R2−sin2(θ)·(X0−x)2−cos(θ)·(X0−x) (15)
Hh0 = (Z0+h) +D0·tan(φ) (16)
D00 = real distance to the edge of the gap, Hh0 = real height of the intersection,
x = distance between growth unit and centre of the tree, h = height of the growth unit,
where hvaries from zero to the height of the tree andx between plus/minus the distance between the endpoint of the tree segment and the stem in horizontal direction. The function for Hh0 is not linear but depends onφ and on the result of the calculation for the distance of the edge of the gap. The values for tan(φ) vary from 0 to 1 because the angle of φ varies from 0 to 45 degrees. In the following calculations the radius R has a value of 21 meters and the tree a crown extension of around 0.7 meters, hence in the horizontal direction ∆D0 varies between zero and 1.4 meters. In the vertical direction the maximum error is exactly the height of the tree which has a maximal value of 2.7 meters.
7 Plausibility and sensitivity of LIGNUM
†The tests comprise the simulation of a tree over ten years under a strongly reduced light regime of 10000 trees/ha. The results are compared with real trees. Three types of comparison are applied: the fractal analysis, the diameter analysis after Chiba (1990, 2000) and a simulation of water flow with HYDRA (Fr¨uh 1995, Fr¨uh and Kurth 1999).
This chapter is part of a publication of Dzierzon et al. (2003).
7.1 Sample trees
As reference trees which can be compared with simulated ones, three Scots pine trees (Pinus sylvestris L.) were investigated. The trees were 8, 10 and 11 years old; they were grown on a poor sandy (medium new red sandstone) soil in a wide-spaced stand together with some aged pine trees, located in Reinhausen near G¨ottingen (Germany). The trunk and the complete above-ground branching system of each tree was mapped; lengths, diam-eters, angles and positions of insertion nodes of each growth unit were manually measured and recorded in a DTD file (Kurth 1994), together with the topological information nec-essary to reconstruct the structure of the tree crown. As we have used these trees only as examples and not to deduce general statements about Scots pine, we will present only results obtained from one of them in the following sections. The results from the other two trees were similar to the presented ones in all cases.
The appearance of the analysed trees is shown in figure 30. The real pine (left side) is the 11 years old measured one, hence we simulated a pine with a (fictitious) age of 11 years (right side). As the measured trees grew within a stand, we adopted in the simulations the light regime corresponding to the concept of LIGNUM-forest. Table 27 gives some characteristics of the analysed trees. Trees marked with bold font are used for analysis.
Parameter Unit Real pine 3 Real pine 2 Real pine 1 Simulated pine
Age [years] 10 8 11 11
Height [m] 1.380 2.034 1.155 1.706
Diameter of first element [cm] 3.12 1.91 1.80 1.74
Volume of stem [cm3] 438.58 371.58 149.75 158.47
Table 27: Some characteristics of the analysed trees.
†Dzierzon et al. (2003) slightly changed
Figure 30: The simulated (left side) and the real tree (right side) which are compared.