Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions Ed Eloranta University...
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![Page 1: Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions Ed Eloranta University of Wisconsin-Madison .](https://reader036.fdocuments.in/reader036/viewer/2022062518/5697bf861a28abf838c87f57/html5/thumbnails/1.jpg)
Drizzle measurements with the HSRL and the KAZR: sensitivity to assumptions
Ed ElorantaUniversity of Wisconsin-Madison http://lidar.ssec.wisc.edu
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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
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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:
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The lidar extinction cross section = 2 * Number density * < Area >
< Mass >Deff = --------------- < Area>
/2
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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
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a = 0.5
a= 4.0
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a = 0.5
a = 4.0
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Gamma = 1, 2, 3, 4
g = 1
g = 4
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a = 1, g = 4.0
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g=1
g=4
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a= 0.5a = 4
N(D) = Daexp(-(D/Dm)3)
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g=1
g=4
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P180/4p0.02
0.03
0.05
be = bb * 4p /P(180)
Extinction derived from backscatter cross sectionusing assumed value of backscatter phase function
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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
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Extinction derived from p(180)/4p vs direct extinction measurment
Ext
P(180)/4 = 0.03p
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 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
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Lidar ratio = 4p/P(180)
P(180)/4p = 0.20.5 mm at 532 nmLidar ratio = 4.0
O’Connor et. al. (2004)
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Lidar ratio = 4p/P(180)
P(180)/4p = 0.20.5 mm at 532 nmLidar ratio = 4.0
O’Connor et. al. (2004)
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Deff_prime computed from directly measured extinction cross section
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