Rayleigh and Mie Scattering
 In deriving the radar equation on the previous page, we've
assumed that the targets scattering radiation back to the radar are Rayleigh
scatterers.
 A target is a Rayleigh
scatterer if D<<l where D is the
diameter of the target.
 If D > l or D < l
or D is approximately equal to l, then the target
is a Mie scatterer.
 If Mie scattering is occurring, you will not
obtain a correct radar reflectivity factor value from the radar equation.

Rayleigh Regime 
Water Spheres: 

Ice Spheres: 

If l = 10 cm (88D) then D =
5 mm or less for Rayleigh scattering
If l = 3 cm (Xband) then D
= 1.5 mm or less for Rayleigh scattering
So, Xband is more susceptible to Mie scattering, and
therefore violating the radar equation than Sband radars (88D).
EQUIVALENT RADAR REFLECTIVITY FACTOR
We have previously derived the radar equation for distributed
targets:
(18)
 Although
not stated, using this radar equation assumes all
scatterers are Rayleigh.
 Thus, if you are targets that are Rayleigh scatterers, the
above radar equation will give you an accurate value of the radar
reflectivity factor (Z). However,
you need to know if the targets are water, ice or otherwise to use the
proper value of the complex dielectic factor.
 It is often the case that you have either nonwater targets
or Mie scatterers present within the pulse volume.
 To account for these types of targets, we define the "equivalent
radar reflectivity factor", Z_{e}.
 Thus the radar equation becomes:
(19)
This
form of the radar equation assumes that all targets are:
 Rayleigh
scatterers
 water
even
though this is often not the case.