User's Guide ______________________________________________________________________
76 __________________________________________________________________ M210482EN-B
obvious that the denser a cloud is, the stronger the reflection will be.
The relationship can be expressed as follows:
ß(z) = k·
σ
(z)
where
k
= A constant of proportionality.
σ
(z) = The extinction coefficient (the attenuation factor in a
forward direction).
The extinction coefficient relates to
visibility
in a straightforward
manner. If visibility is defined according to a 5 % contrast threshold
(World Meteorological Organization definition for Meteorological
Optical Range MOR, equals daylight
horizontal
visibility), then
σ
= 3 / V
where
σ
=
The extinction coefficient
V =
MOR visibility (5 % contrast)
The constant of proportionality, k, also called the Lidar Ratio, has
been subjected to a lot of research. Although the Lidar Equation can
be solved without knowing its value, it must remain constant with the
height if accurate estimates of the extinction (or visibility) profile are
to be made.
It has been discovered that in many cases, k can be assumed to equal
0.03, tending to be lower in high humidity (to 0.02), and higher in low
humidity (to 0.05). However, in precipitation of various kinds, for
example, k will have a wider range of values.
Assuming a value of 0.03 (srad
-1
) for k, visibility in clouds being in
the range of 15 to 150 m (50 to 500 ft), gives the following range of
value for
β
:
β
= 0.0006 ... 0.006 m
-1
srad
-1
= 0.6 ... 6 km
-1
srad
-1
