surface , is the optical air mass in the direction to
wards the Sun, n is the normal to the section of surface,
l is the unit vector directed towards the Sun.
The intensity of illumination by the radiation diffused
by the atmosphere depends on the extent to which the sky is
closed by the surrounding elements of the terrain, and the
reflected radiation is determined by those elements of the sur
rounding relief which can be seen from the given point 0 Hence,
in determining the diffused and reflected radiations integra
tion is performed for the open part of the sky and which can
be seen from the given point of the part of the surrounding
surface•
The values of illumination intensity and are
calculated from formulae:
27V Tl/z
= S d f f B(y, h) cos ¿ ' cosh dk (u }
where B(%E) is the function of the angular distribution of
brightness over the sky, h is the height of elementary secti
on of the sky, ^ is the azimuth of the section taken from
the Sun vertical, C is the angle of incidence of the diffused
radiation in the point of surface being considered
~ J' ®R ’ C °S L d a) (-J5 )
where is the brightness of the surface element seen under
the solid angle c/a) , i is the angle of incidence of the radia
tion reflected from it on the the section of the surface be
ing considered.
To determine the brightness of the sky B(% k) we can use
the formula obtained by Ivanov A*I* et al.(l975 ).
For numerical calculations from formulae (13 ), (1 4-) ,and( 1 5)
use is made of the approximated digital model(formula 11).Thus,
the problem is solved by the iteration method« First,the terra
in is determined on the assumption that the surface is illumina
ted only by direct rayp (i.e.it is assumed that E — E n )«
Then,from this relief the contribution of the diffused and ref -
lected surfaces is determined and the brightness is calculated
resulting from the direct radiation alone , which allows the re
lief to be found in the second approximation,and so on. In prac
tice, two iterations are sufficient for obtaining satisfactory
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