20. EXPERIMENTAL STUDY OF STATISTICAL
CHARACTERISTICS OF PLANT CANOPY RADIATION REGIME
197
Let us assume that
corresponds to the maximum of the IPDF in
umbra, and that
corresponds to the maximum of the IPDF in sun flecks.
The IPDF in umbra
is then characterized by a normal distribution,
determined with the mean value
and a dispersion
By analogy, the
IPDF in sun flecks
is characterized by a normal distribution determined
with the mean value
and a dispersion
In penumbra, the fitted beta
distribution is constrained by two parameters, v and
The characteristics of these IPDFs depend on solar elevation h and on the
depth of canopy, expressed by the downward cumulative leaf area index L.
These characteristics can be replaced by a joint parameter, the sunray’s path
length expressed as the leaf area
Fig. 9 expresses the distribution of the umbra, penumbra and sun flecks
fractional areas at different depths within the willow forest. Sun flecks exist
only in the upper part of the forest (where the path length
and rapidly
decrease with depth. The proportion of penumbra area increases
correspondingly, and is dominating in the middle layers. Starting from a
depth of
the umbra area linearly increases with depth and is dominating
in the lower layers.