Drizzle measurements with the HSRL and the KAZR:
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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

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

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


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>:

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:


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


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

a= 0.5

a = 4


g=4

g=1


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


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


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

P(180)/4p = 0.03

Ext


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)


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)


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)


Deff_prime computed from directly measured extinction cross section


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