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

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

Radar equation for Meteorology For weather applications for a volume

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

Rain drops

Clouds Types in our Atmosphere

Sizes for hydrometeors cloud drops & rain drops

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

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 1 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.

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

Mie coefficients

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

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.

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

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]

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

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]