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Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions

Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions. Ed Eloranta University of Wisconsin-Madison http:// lidar.ssec.wisc.edu. HSRL-Radar particle size measurement. For droplets which are small compared to the radar wavelength

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Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions

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  1. Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions Ed Eloranta University of Wisconsin-Madison http://lidar.ssec.wisc.edu

  2. HSRL-Radar particle size measurement For droplets which are small compared to the radar wavelength but large compared to the lidar wavelength: Radar scattering cross section = βradar ~ <V2> ~ <D6> ------- Rayleigh scattering Lidar extinction cross section = βlidar ~ <A> ~ <D2> ------- Geometric optics Where: <V2> = average volume squared of the particles <A> = average projected area of the particles We can define: Where: λradar= radar wavelength kw = dielectric constant of water

  3. Assuming a gamma distribution of particle diameters: Where: N = number of particles D = particlle Diameter Dm= mode diameter The effective diameter prime can be written as: Solving for the mode diameter, Dm:

  4. The lidar extinction cross section = 2 * Number density * < Area > < Mass > Deff= --------------- < Area> /2

  5. The radar weighted fall velocity, <Vrf>: And the mass weighted fall velocity, <Vmf>: Where the fall velocity, Vf , is computed from: Khovostyanov and Curry, JAS May 2005, Vol 62 And the Beard Number, X expressed in terms of particle area, volume and density along with the acceleration of gravity, air density, particle diameter and the dynamic viscosity:

  6. a = 0.5 a= 4.0

  7. a = 0.5 a = 4.0

  8. Gamma = 1, 2, 3, 4 g = 1 g = 4

  9. a = 1, g = 4.0

  10. g=1 g=4

  11. N(D) = Daexp(-(D/Dm)3) a= 0.5 a = 4

  12. g=4 g=1

  13. Extinction derived from backscatter cross section using assumed value of backscatter phase function be = bb * 4p /P(180) P180/4p 0.02 0.03 0.05

  14. Extinction is derived from the slope of the molecular return Multiple scattering reduces apparent extinction Total molecular return Altitude Single scatter Molecular return Diffraction peak q = l/D ~ 0.5 micron/500 micron = 1 mr

  15. Extinction derived from p(180)/4p vs direct extinction measurment P(180)/4p = 0.03 Ext

  16. 0.170 0.366 0.788 1.70 mm Diameter l =532nm 0.017 0.036 0.078 0.079  0.5 mm 532 nm Lidar ratio = 18.6 P180/4p =0.0536 0.072 0.064 1 mm 532 nm 0.056 0.048 P(180)/4p Backscatter phase function for water drops averaged over size parameter intervals of 0.14. (Shipley 1978)

  17. Lidar ratio = 4p/P(180) P(180)/4p = 0.2 0.5 mm at 532 nm Lidar ratio = 4.0 O’Connor et. al. (2004)

  18. Lidar ratio = 4p/P(180) P(180)/4p = 0.2 0.5 mm at 532 nm Lidar ratio = 4.0 O’Connor et. al. (2004)

  19. Deff_prime computed from directly measured extinction cross section

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