1. Rain Detection & Attenuation for Remote sensing; & auxiliary sensors
Dr. Sandra Cruz-Pol
INEL 5995
DCAS –network weather radars

2. Outline Radar Equation for Meteorology Raindrops Volume scattering
Mie scattering
Rayleigh approximation
Radar reflectivity & reflectivity
Dielectric factor, K
Ancillary Sensors
Rain gauges
disdrometers

3. Radar equation for Meteorology
For weather applications
for a volume

4. Radar Equation
For power distribution in the main lobe assumed to be Gaussian function.

5. Rain drops

6. Clouds Types in our Atmosphere

7. Sizes for hydrometeors
cloud drops
&
rain drops

8. EM interaction with Single drop
Absorption
Cross-Section, Qa =Pa /Si
Efficiency, xa= Qa /pr2
Scattered
Cross-section , Qs =Ps /Si
Efficiency, xs= Qs /pr2
Total power removed by sphere from the incident EM wave, xe = xs+ xa
Backscatter, Ss(p) = Sisb/4pR2
Efficiency, xb= sb /pr2

9. Mie Scattering (necessary if d/l1),
Mie theory : A complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in 1908.
In contrast to Rayleigh scattering, the Mie theory embraces all possible ratios of diameter to wavelength. The Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and cloud scattering.
When d/l neither Rayleigh or Geometric Optics Theory applies. Need to use Mie.
Scattering of radar energy by raindrops constitutes another significant application of the Mie theory.

10. Mie Solution
Mie solution
where am & bm are the Mie coefficients

11. Mie coefficients

12. Backscattering from metal sphere
Rayleigh Region defined as
For conducting sphere (|n|= )
Where,

13. Single Particle Cross-sections vs.c for Rayleigh region
Scattering cross section
Absorption cross section
In the Rayleigh region (nc<<1) =>Qa is larger, so much more of the signal is absorbed than scattered. Therefore
For small drops, almost no scattering, i.e. no bouncing from drop since it’s so small.

14. Scattering from Hydrometeors
Rayleigh Scattering
Mie Scattering
 >> particle size
comparable to particle size
--when rain or ice crystals are present.
95GHz (3mm)
33GHz (9mm)

15. Volume Scattering Two assumptions:
particles randomly distributed in volume-- incoherent scattering theory.
Concentration is small-- ignore shadowing.
Volume Scattering coefficient is the total scattering cross section per unit volume.
[Np/m]

17. Total number of drops per unit volume
in units of mm-3

18. Volume backscattering
Using...
It’s also expressed as
or in dB/km units,
[Np/m]
[s,e,b stand for scattering, extinction and backscattering.]
[dB/km]