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

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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


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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:


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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

< Mass >

Deff= ---------------

< Area>

/2


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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:


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

a = 0.5

a= 4.0


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

a = 0.5

a = 4.0


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

Gamma = 1, 2, 3, 4

g = 1

g = 4


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

a = 1, g = 4.0


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

g=1

g=4


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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

a= 0.5

a = 4


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

g=4

g=1


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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

P(180)/4p = 0.03

Ext


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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)


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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)


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

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)


Drizzle measurements with the hsrl and the kazr sensitivity to assumptions

Deff_prime computed from directly measured extinction cross section


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