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Obstruction of the sky by trees--Algorithm 1.44

Tree crowns partially obscure the sky. Their luminance is a function of the illuminance on the foliage, the reflectance of the foliage, the amount of sky visible within the envelope of the crown, and the sky luminance.

a. Luminance of tree crowns

Input Mean illuminance on tree crown, Ef
Mean reflectance of crown, rf
Fraction of sky visible through crown, ps
Luminance of sky behind crown, Ls

Equation
The effective luminance of the tree crown is

Note
The crown reflectance varies with the angle of view and is less than the reflectance of individual leaves. For most purposes, the crown reflectance may be taken as 0.1 and the illuminance taken to be the value on a vertical surface.

Source
General photometric theory

b. Luminance of tree crowns under CIE overcast sky

The following equation gives the luminance of a tree crown as a fraction of the luminance of the overcast sky obscured.

Input
Mean reflectance of crown, rf
Reflectance of ground, rg
Fraction of sky visible through crown, ps
Mean altitude of sky behind crown, g

Equation

Note
For an angle of view just above the horizon, when rg=0.2 and rf=0.1,

This is an adequate approximation for most purposes where the reflectance and sky fraction parameters of the trees are not known in detail.

Source
General photometric theory
c. Typical values of sky cover fraction for individual mature tree crowns

species ps summer ps winter
Oak .17 .50
Sycamore .18 .54
Birch .24 .54
Lombardy poplar .13 .50
Lime .11 .54
Beech .19 .47
Hawthorn .22 .44
Alder .24 .49
Scots pine .27 .30
Ash .22 .53
Horse chestnut .19 .52

Source
Wilkinson, (1)

References

  1. Wilkinson D M Modelling light attenuation by urban trees PhD thesis, Manchester Metropolitan University (1992)

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