4 Application of a 3D-light model to the 3D-representation of beech Gr12
4.1 Methods
4.1.3 Parameterisation of STANDFLUX-SECTORS
4.1.3.1 Segmentation of leaf cloud enveloping polyhedrons
Boundaries of height layers, sectors, and sections as well as section height ranges have been chosen in order to construct compartments with as homogeneous conditions as possible, thereby explicitly representing larger gaps and inhomogeneity of the crown. This is best achieved, when the resulting compartments are either empty or densely filled with leaves. As less intersections as necessary were required on the other hand to reduce the number of compartments that have to be parameterised and calculated in the light-model.
Height layer boundaries for beech Gr12 have been chosen in an average vertical distance of around 1m with deviations due to canopy gaps. Figs. 113 a and b show the chosen sector boundaries in each height layer: 4-6 vertical intersection planes cut the polyhedrons in each layer into 3 - 12 filled sectors. The sector boundaries were chosen such that gaps in the crown may well be represented by additional cylinder shaped boundaries.
The 94 resulting sectors were cut into 410 sections using the optical representation of beech Gr12 in CRISTO (Fig. 114).
4.1.3.2 Segmentation of crown approximating polyhedrons in the stand Großebene The convex shape and gradients of leaf area density or leaf angles in the crown could be represented by division of the homogeneous tree crown approximating polyhedrons into eight 45°-sectors in the main azimuth directions and four height layers per sector. The height layer boundaries of opposite sectors are the same due to the segmentation scheme (Fig. 115):
20 20.1
20.2 20.3
20.4 20
20.2 20.4 20.6
24.5 24.6 24.7 20
20.1 20.2
20.3 20.4
19.6 19.8 20
20 20.2
20.4 20.6
24.6 24.8 25
19.6 19.8 20
1
5 4
3
2
Fig. 112: The intersection of a concave polyhedron with a vertical plane produces two incomplete polyhedrons (left side, the incomplete polyhedron which was on the left side of the intersection plane is displayed below and has been turned around). The intersection area is concave. The Delaunay
triangulation is based on the convex hull of the intersection points and therefore has to be corrected by removing the indicated triangle (below).
-5 0 5 EastHmL
-5 0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
0 - 1.05m
4.1 - 5.25m 1.75 - 2.55m
2.95 - 4.1m 1.05 - 1.75m
2.55 - 2.95m
Fig. 113a: Segmentation of height layers of beech Gr12 into sectors of the light-model STANDFLUX-SECTORS. The height range of each layer is given in m below apex.
-5 0 5 EastHmL
-5 0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
-5 0 5
EastHmL -5
0 5
NorthHmL
-5 0 5
NorthHmL
5.25 - 6.15m
10.35 - 11.5m 7.05 - 8.35m
9.35 - 10.35m 6.15 - 7.05m
8.35 - 9.35m
Fig. 113b: Segmentation of height layers of beech Gr12 into sectors of the light-model STANDFLUX-SECTORS. The height range of each layer is given in m below apex.
Height boundaries for opposite sectors (east/west, south/north, east/south-west, north-west/south-east) were drawn in the middle between neighbours in height of 4 points: 2 measured outermost border points, crown-base and apex. The horizontal extension of 45°-sectors was given by the maximum extension of a linear approximation to the crown form (Fig.
115). This kind of segmentation results in cylinders, when tree crowns are symmetrical to the stem and may represent bigger cavities along the shape of the canopy.
-5 0 5
-5 0 5
-5 0 5
1 2 3 4 5 6
-1 -0.5 0.5 1
1 2 3 4 5 6
23 23.2 23.4 23.6
SSE-Sector
Radius (m) Height (m)
Radius (m) Sector width (m)
North (m)
East (m) 1.75 - 2.55m
below apex
Fig. 114: Division of the South-South-East-sector of the third height layer of beech Gr12 into 7 sections, visually supported by an optical representation routine in CRISTO. The SSE-sector is shown from above with cylinder-shaped section boundaries (right side, above) and from the west side, where the cylinder shaped section boundaries occur as vertical lines (right side, below). The section boundaries were chosen in a way that allows to draw the height boundaries close to the border of leaf clouds, thereby enabling the representation of larger gaps.
East Apex
Crown base West
Fig. 115: Segmentation of tree crowns of the Großebene trees (vertical cross-section through the stem in west-east direction). The dotted line represents the cross-section of a tree crown approximating polyhedron with its corners at the western and eastern border points of the crown as explained above. The original crown form (thickest line) of most trees was more convex than the form of the polyhedron, which is considered in the segmentation.
Height boundaries were set in the middle between the heights of measured points. The horizontal extensions of 45°-sectors (grey fields) are given by the maxim um extension of the crown approximating polyhedron in each specific layer and direction.
4.1.3.3 Parameter determination for single compartments
Each compartment of beech Gr12 was automatically parameterised based on leaf area and volume share of included leaf cloud enveloping polyhedrons assuming volumetric homogeneity of leaf area density in the leaf clouds.
The relationship between projected wood area and leaf area of leaf clouds from Fig. 56 was employed to calculate wood area density of each compartment. The stem was considered as a cylinder with its diameter in 1.35m height, that reaches the middle height of the crown (19.75m above the floor, 5.75m below apex) and builds the central compartment of the simulated tree.
Average leaf angles of each compartment were calculated based on the average height of the compartment below apex using the relationships found for beech Bu38 (Figs. 61 and 62), which were recalculated to
in the upper part of the crown (range of 0 - 6.75m below apex) and to
in the lower part of the crown.
Branch angles in each compartment were calculated using the linear relationship from Fig. 64.
Transmissivity and reflectance were assumed to equal 10% and 6%, using the values of FALGE
(1997).
The leaf area densities of tree sectors from the surrounding stand were derived from the height dependence of leaf area density as displayed in Fig. 24. All other parameters for the surrounding tree crowns were derived in the same manner as those of beech Gr12, because specific data for Quercus petraea trees were not available. From former studies it was expected that leaf and branch angles of neighbouring trees play a minor role for the light calculation and that the main impact of the different tree species is a result of their canopy form.