Scattering from Hydrometeors: Clouds, Snow, Rain

1. Scattering from Hydrometeors:Clouds, Snow, Rain Microwave Remote Sensing INEL 6069 Sandra Cruz Pol Professor, Dept. of Electrical & Computer Engineering, UPRM, Mayagüez, PR

2. Outline: Clouds & Rain • Single sphere (Mie vs. Rayleigh) • Sphere of rain, snow, & ice (Hydrometeors) Find their ec, nc, sb • Many spheres together : Clouds, Rain, Snow a. Drop size distribution b. Volume Extinction= Scattering+ Absorption c. Volume Backscattering • Radar Equation for Meteorology • TB Brightness by Clouds & Rain

3. Clouds Types on our Atmosphere

4. Cirrus Clouds Composition %

5. EM interaction with Single Spherical Particles Si • Absorption • Cross-Section, Qa =Pa /Si • Efficiency, xa=Qa /pr2 • Scattered • Power, Ps • 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

6. Mie Scattering: general solution to EM scattered, absorbed by dielectric sphere. • Uses 2 parameters (Mie parameters) • Size wrt. l : • Speed ratio on both media:

7. Mie Solution • Mie solution • Where am & bm are the Mie coefficients given by eqs 5.62 to 5.70 in the textbook.

8. Mie coefficients

9. Non-absorbing sphere or drop(n”=0 for a perfect dielectric, which is anon-absorbing sphere) c =.06 Rayleigh region |nc|<<1

10. Conducting (absorbing) sphere c =2.4

11. Plots of Mie xe versus c Four Cases of sphere in air : n=1.29 (lossless non-absorbing sphere) n=1.29-j0.47 (low loss sphere) n=1.28-j1.37 (lossy dielectric sphere) n= perfectly conducting metal sphere • As n’’ increases, so does the absorption (xa), and less is the oscillatory behavior. • Optical limit (r >>l) is xe =2. • Crossover for • Hi conducting sphere at c=2.4 • Weakly conducting sphere is at c=.06

12. Rayleigh Approximation |nc|<<1 • Scattering efficiency • Extinction efficiency • where K is the dielectric factor

13. Absorption efficiency in Rayleigh region i.e. scattering can be neglected in Rayleigh region (small particles with respect to wavelength) |nc|<<1

14. Scattering from Hydrometeors  >> particle size Rayleigh Scattering Mie Scattering • comparable to particle size --when rain or ice crystals are present.

15. Single Particle Cross-sections vs.c For small drops, almost no scattering, i.e. no bouncing from drop since it’s so small. • 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

17. Rayleigh-Mie-GeometricOptics • Along with absorption, scattering is a major cause of the attenuation of radiation by the atmosphere for visible. • Scattering varies as a function of the ratio of the particle diameter to the wavelength (d/l) of the radiation. • When this ratio is less than about one-tenth (d/l<1/10), Rayleigh scattering occurs in which the scattering coefficient varies inversely as the fourth power of the wavelength. • At larger values of the ratio of particle diameter to wavelength, the scattering varies in a complex fashion described by the Mie theory; • at a ratio of the order of 10 (d/l>10), the laws of geometric optics begin to apply.

18. Mie Scattering (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.

19. Backscattering Cross-section • From Mie solution, the backscattered field by a spherical particle is Observe that • perfect dielectric (nonabsorbent) sphere exhibits large oscillations for c>1. • Hi absorbing and perfect conducting spheres show regularly damped oscillations.

20. Backscattering from metal sphere • Rayleigh Region defined as • For conducting sphere (|n|= ) where,

21. Scattering by Hydrometeors Hydrometeors (water particles) • In the case of water, the index of refraction is a function of T & f. (fig 5.16) • @T=20C • For ice. • For snow, it’s a mixture of both above.

22. Liquid water refractivity, n’

23. Sphere pol signature Co-pol Cross-pol

24. Sizes for cloud and rain drops

25. Snowflakes • Snow is mixture of ice crystals and air • The relative permittivity of dry snow • The Kds factor for dry snow

26. 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]

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

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

29. For Rayleigh approximation • Substitute eqs. 71, 74 and 79 into definitions of the cross sectional areas of a scatterer. D=2r =diameter

30. Noise in Stratus cloud image-scanning Ka-band radar

31. Volume extinction from clouds • Total attenuation is due to gases,cloud, and rain • cloud volume extinction is(eq.5.98) • Liquid Water Content LWC or mv ) • water density = 106 g/m3

32. Relation with Cloud water content • This means extinction increases with cloud water content. where and wavelength is in cm.

33. Raindrops symmetry

34. Volume backscattering from Clouds • Many applications require the modeling of the radar return. • For a single drop • For many drops (cloud)

35. Reflectivity Factor, Z • Is defined as so that • and sometimes expressed in dBZ to cover a wider dynamic range of weather conditions. • Z is also used for rain and ice measurements.

36. Reflectivity in other references…

37. Reflectivity & Reflectivity Factor h Z (in dB) Reflectivity, h [cm-1] dBZ for 1g/m3 Reflectivity and reflectivity factor produced by 1g/m3 liquid water Divided into drops of same diameter. (from Lhermitte, 2002).

38. Cloud detection vs. frequency

39. Rain drops

40. Precipitation (Rain) • Volume extinction • where Rr is rain rate in mm/hr • [dB/km] and b are given in Table 5.7 • can depend on polarization since large drops are not spherical but ~oblong. [dB/km] Mie coefficients

41. W-band UMass CPRS radar

42. Rain Rate [mm/hr] • If know the rain drop size distribution, each drop has a liquid water mass of • total mass per unit area and time • rainfall rate is depth of water per unit time • a useful formula

43. Volume Backscattering for Rain • For many drops in a volume, if we use Rayleigh approximation • Marshall and Palmer developed • but need Mie for f>10GHz.

44. Rain retrieval Algorithms Several types of algorithms used to retrieve rainfall rate with polarimetric radars; mainly • R(Zh), • R(Zh, Zdr) • R(Kdp) • R(Kdp, Zdr) where R is rain rate, Zh is the horizontal co-polar radar reflectivity factor, Zdr is the differential reflectivity Kdp is the differential specific phase shift a.k.a. differential propagation phase, defined as

45. Snow extinction coefficient • Both scattering and absorption ( for f < 20GHz --Rayleigh) • for snowfall rates in the range of a few mm/hr, the scattering is negligible. • At higher frequencies,the Mie formulation should be used. • The is smaller that rain for the same R, but is higher for melting snow.

46. Snow Volume Backscattering • Similar to rain

47. Radar equation for Meteorology • For weather applications • for a volume

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