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

Ed ElorantaUniversity of Wisconsin-Madison http://lidar.ssec.wisc.edu

HSRL-Radar particle size measurement

For droplets which are small compared to the radar wavelengthbut large compared to the lidar wavelength:

Radar scattering cross section = βradar ~ <V2> ~ <D6> ------- Rayleigh scatteringLidar 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

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:

The lidar extinction cross section = 2 * Number density * < Area >

< Mass >Deff = --------------- < Area>

/2

The radar weighted fall velocity, <Vrf>:

Where the fall velocity, Vf , is computed from:

And the mass weighted fall velocity, <Vmf>:

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

a = 0.5

a= 4.0

a = 0.5

a = 4.0

Gamma = 1, 2, 3, 4

g = 1

g = 4

a = 1, g = 4.0

g=1

g=4

a= 0.5a = 4

N(D) = Daexp(-(D/Dm)3)

g=1

g=4

P180/4p0.02

0.03

0.05

be = bb * 4p /P(180)

Extinction derived from backscatter cross sectionusing assumed value of backscatter phase function

Diffraction peak q = l/D ~ 0.5 micron/500 micron = 1 mr

Molecular return

Altit

ude

Extinction is derived from the slope of the molecular returnMultiple scattering reduces apparent extinction

Total molecular return

Single scatter

Extinction derived from p(180)/4p vs direct extinction measurment

Ext

P(180)/4 = 0.03p

 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

Diameterl =532nm

Backscatter phase function for water drops averaged over sizeparameter intervals of 0.14. (Shipley 1978)

P(180)/4p

0.5 mm532 nmLidar ratio = 18.6P180/4p =0.0536

1 mm532 nm

Lidar ratio = 4p/P(180)

P(180)/4p = 0.20.5 mm at 532 nmLidar ratio = 4.0

O’Connor et. al. (2004)

Lidar ratio = 4p/P(180)

P(180)/4p = 0.20.5 mm at 532 nmLidar ratio = 4.0

O’Connor et. al. (2004)

Deff_prime computed from directly measured extinction cross section