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Radar Range Equation for Weather Radar
Weather radar systems use many equivalent principles to primary radar. The discussion in this module assumes some knowledge of the principles of primary radar. The considerably difference between the echoing area σ of an aircraft or other flying „machine” is, weather is normally much larger and more fluid.
In the case of rain, the size of a rain drop is wery much smaller than the radar wavelength and therefore the Rayleigh backscatter equation gives the echoing area of a raindrop |
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where D is the drop diameter and |
| where ε is the | ||||
For radar bands L to X water has |K |2= 0.93 and for ice |K |2= 0.2 | ||||||
If we sum all the echoing areas contained in 1 m3 we get |
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where Z is the radar reflectivity and η is the radar reflectivity per unit volume. |
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  (5)When the rain fills the beam,
than the volume sample in one range cell is | ||||||
The basic weather radar equation (see module „radar fundamentals”) can be written:
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 (6) (6) | |||||
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The effects of the reflectivity can be seen when looking at a weather pattern with a radar. At high altitudes the reflectivity from snow is low. At lower levels, when the snow starts to melt, the snow flakes become coated with water and dramatically increase the radar returns. Finally the snow flakes melt completely and coalesce into raindrops which are smaller than the snowflakes and fall faster, giving a reduced radar echo. This effect causes the "bright band" on the radar display. | ||||||
This difference in the principle of the Radar Range Equation when it is applied to Weather Radar systems is identified.
This form is still completely unsuitable for meteorological radar applications. It isn't looked at here
from the view of a meteorologist, special from the view of a radar unit mechanic either.
If this equation is rearranged again that it can be used to the computing of the range,
one then recognizes that the familiar fourth root will be replaced by a square root.
But why?
Figure: relationship of volume and reflectivity
The raindrop-filled volume blows up proportionally of the square of the distance!
Very much more reflective raindrops fit in the volume at same density.
And so very much more energy is reflected
as if it is filled with a single aircraft only.
