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 (88-D) then D = 5 mm or less for Rayleigh scattering

If l = 3 cm (X-band) then D = 1.5 mm or less for Rayleigh scattering

So, X-band is more susceptible to Mie scattering, and therefore violating the radar equation than S-band radars (88-D).

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 non-water 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:

1. Rayleigh scatterers
2. water

even though this is often not the case.