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

6. 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 = β radar ~ ~ ------- Rayleigh scattering Lidar extinction cross section = β lidar ~ ~ ------- Geometric optics Where: = average volume squared of the particles = average projected area of the particles We can define: Where: λ radar = radar wavelength k w = dielectric constant of water

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

10. The lidar extinction cross section = 2 * Number density * D eff = --------------- /2

12. The radar weighted fall velocity, : Where the fall velocity, V f, is computed from: And the mass weighted fall velocity, : 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: Khovostyanov and Curry, JAS May 2005, Vol 62

15.  = 0.5  = 4.0

17.  = 0.5  = 4.0

18. Gamma = 1, 2, 3, 4  = 1  = 4

19.  = 1,  = 4.0

20.  =1  =4

21.  = 0.5  = 4 N(D) = D  exp(-(D/D m ) 3 )

22.  =1  =4

24. P180/4  0.02 0.03 0.05  e =  b * 4  /P(180) Extinction derived from backscatter cross section using assumed value of backscatter phase function

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

26. Extinction derived from p(180)/4p vs direct extinction measurment Ext P(180)/4 

27.  0.170 0.366 0.788 1.70 mm 0.017 0.036 0.078 0.079 0.072 0.064 0.056 0.048 Diameter =532nm Backscatter phase function for water drops averaged over size parameter intervals of 0.14. (Shipley 1978) P(180)/4  0.5 mm 532 nm Lidar ratio = 18.6 P180/4  =0.0536 1 mm 532 nm

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

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

30. Deff_prime computed from directly measured extinction cross section