The volume backscatter coefficient represents the portion of light reflected back towards the ceilometer from a distance (for example, from water droplets). A dense cloud gives a stronger reflection. This can be expressed as follows:
| Variable | Description | |
|---|---|---|
| ß(z) | Backscatter coefficient | |
| z | Distance | |
| k | Proportionality constant [1/srad] | |
| σ (z) | Extinction coefficient (the attenuation factor in forward direction) [1/m] | |
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), the extinction coefficient is:
| Variable | Description | |
|---|---|---|
| V | MOR visibility (5 % contrast) [m] | |
The proportionality constant, k, also called the lidar ratio, has been subjected to a lot of research. Although the lidar equation can be solved without knowing the ratio, 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 (down to 0.02) in high humidity, and higher (up to 0.05) in low humidity conditions. However, in precipitation conditions, k can have a wider range of values.
Assuming k value of 0.03 sr-1, visibility in clouds in the range of 15 to 150 m (50 to 500 ft), gives the following range for β:
β = 0.0006 ... 0.006 m-1sr-1 = 0.6 ... 6 km-1sr-1