drizzle measurements with the hsrl and the kazr: sensitivity to assumptions ed eloranta university...
Post on 17-Jan-2016
214 Views
Preview:
TRANSCRIPT
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
top related