Page 105 - Fundamentals of Radar Signal Processing

ratio of the sphere radius a to the radar wavelength λ is small, specifically

2πa/λ 1, the radar cross section associated with the ith scatterer can be
expressed as

(2.40)

where D is the drop diameter, usually given in millimeters, and
i

(2.41)

with m the complex index of refraction. The index of refraction is a function of
both the temperature and wavelength. However, for wavelengths between 3 and

10 cm [radar frequencies between X band (10 GHz) and C band (3 GHz)] and
2
temperatures between 0 and 20°C, the value of |K| is approximately a relatively
constant 0.93 for scatterers composed of water and 0.197 for ice. Substituting
Eq. (2.40) in Eq. (2.39) gives

(2.42)

Now define the quantity

(2.43)

Z is called the reflectivity factor and is usually expressed in units of mm /m .
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Due to the large range of values observed for Z, it is commonly expressed on a
decibel scale and denoted as dBZ. Using this definition in Eq. (2.42) gives the
following expression for the observed RCS

(2.44)

Thus, given a measured echo power, the radar range equation can be used to
estimate η, and then Eq. (2.44) can be used to convert η to Z.

Because it is related only to the volume density and size of scatterers,
meteorologists prefer to express radar echo strength in terms of the reflectivity Z