**Subject :**Radar and sonar engineering

## Meteorological Echoes

**Introduction: **

In general, radars at the lower frequencies are not bothered by meteorological or weather effects, but at the higher frequencies, weather echoes may be quite strong and mask the desired target signals just as any other unwanted clutter signal.

**Radar Equation for Meteorological Echoes:**

· The simple radar equation is:

………………………… (1)

**·** If it is assumed that the scatterers are distributed over the volume of the beam, the received power from meteorological echoes averaged over many

independent radar sweeps may be written

…………………………… (2)

Where A_{e} = effective antenna aperture ≈ Gλ^{2}/4≈λ^{2}/Θ_{B}ɸ_{B}.

**·** Taking the average of P_{r} corresponds to smoothing the signal fluctuations which result from the random motion of the particles with time.

**·** The above equation shows that the average received power is inversely proportional to the square of the range rather than the fourth power.

**·** This assumes that the beam is completely filled with scatterers; if not, a correction must be made.

**·** The beam of most weather radars is small relative to the regions occupied by the scatterers, except perhaps at long ranges or where the "**bright-band**"

phenomenon (to be described later) is present.

**·** It can be shown that if the wavelength is long compared with the circumference of a scattering particle of diameter D (Rayleigh scattering region), the radar

cross section is

............................................ (3)

**·** Where |K|^{2} depends upon the dielectric constant of the scatterer and varies slowly with wavelength.

**·** In particular, K = (m^{2} — l)/ (m^{2} 2), where m is the complex index of refraction and is equal to m = n —ik, n is the refractive index, and k is the absorption

coefficient of the material involved.

**·** The value for ice at all temperatures is about 0.197 and is independent of frequency in the centimeter-wavelength region.

**·** Substituting Eq. (3) into (2) yields

…………………………………….. (4)

· Equation (4) is the echo signal power from meteorological particles averaged over many independent sweeps. It does not include the attenuating effects of the precipitation itself. The two-way attenuation of the radar signal in traversing the range R and back is an exponential function of the distance ; that is,

Attenuation = exp (—2αR)

- Where α is the one-way attenuation coefficient. The average received power is therefore.

……………………………………… (5)

- · If a is not a constant over the path R, attenuation may be expressed as