Transcript Mm-wave Scattering Properties of Randomly Oriented Ice

A Simple Model of the Mm-wave Scattering
Parameters of Randomly Oriented Aggregates of
Finite Cylindrical Ice Hydrometeors :
An End-Run Around the Snow Problem?
Jim Weinman
University of Washington
Min-Jeong Kim
NASA GSFC/UMBC GEST
•Terrestrial snowfall may be dry or wet.
The dielectric constant will be affected.
• Land surface and snow accumulation
affect emission from the surface.
Solution:
Utilize absorption by water vapor in the
boundary layer to screen mm-wave
emission from snow-covered surfaces.
March 5-6, ‘01 New England Blizzard
NOAA NWS NEXRAD Data
AMSU-B 89 GHz
• Surface effect
(Ocean/Land)
• Hard to discriminate
snow storm from ocean
surface
AMSU-B 183.3 ± 7 GHz
Surface effect is
screened out.
Model Assumptions
• We
assume that snow is dry and that the refractive index,
m = 1.78.
• We let the mass of the particles M = ζ Lη where
ζ = (.026 + .001) N 0.93+0.02 and η = 1.88 + 0.03, for 1 < N < 4
and L is the length of the constituent cylinders.
•That corresponds to an aspect ratio, α = 0.20 L-0.59 , which
comes from Auer & Veal S = 0.20 L 0.41 for L > 1 mm, and
where S is the diameter of the constituent cylinders.
Aspect ratios, , depend on the habit,
they are not always constant
Sample imagery from the PMS 2D-C probe aboard the UW Convair-580
aircraft on 13–14 Dec 2001. Solid line with arrow heads shows flight track.
The sample particle images were observed at the points indicated by the
blue arrows. The region of ice-phase precipitation is indicated by gray
fallstreaks, and the top of the cloud liquid water region is indicated by the
gray-scalloped cloud outline. Height is indicated on the left axis and
temperature is indicated by the labeled horizontal line segments.
Schematic views of model aggregates
C-1
C-2
C-3
C-4
95 GHz
183 GHz
340 GHz
Asymmetry factor
Extinction cross section
DDA Calculated Single Scattering Parameters
Accurate bench mark, but very time consuming.
Theoretical Considerations
•Equivalent spheres have been used to represent
randomly oriented aggregates of prisms.
•Spheres with large real refractive indices are probably
the worst models to represent irregularly shaped
particles. (Infinitely long cylinders are not much better)
•Because spheres are high Q spherical resonators,
surface waves produce artificial ripples that distort the
results.
•Surface waves can be attenuated by complex refractive
indices, but how to define the imaginary part?
• Use Equivalent Finite Cylinders to
Represent Numerous Aggregates of
Cylinders.
• The trick is to define the equivalent
dimension, Δ
•Anomalous Diffraction Theory smoothes the surface
wave resonances by neglecting reflection at the
surfaces. The scattering efficiency is determined by
the phase delay parameter between the incident and
scattered waves, ρ = 2  (m - 1) Δ ν /c. (van de Hulst)
• The definition of the effective diameter, Δ, is crucial
• Assume that definition is: Δ = 4 V / π A┴ , where V is
the volume and A┴ is the area perpendicular to the
incident radiation.
• For a single randomly oriented cylinder,
Δ = 4 α L / π (1 + α / 2) . Life gets more complicated
for aggregates with N > 1.
Scattering Efficiency , Q, as a Function of
Phase Delay Parameter, 
T-Matrix
DDA
(o) C-1, (x) C-2, () C-3, (
 = 0.24
) C-4, (--) TMM, (- -) TMM
 = 0.4
 = 0.6
Asymmetry Factor as a Function of Phase Delay Parameter, 
(o) C-1, (x) C-2, () C-3, (
 = 0.24
) C-4, (--) TMM, (- -) TMM
 = 0.4
 = 0.6
•Once we have Q(ρ) / ρ, we can compute, Cext / M , the
extinction cross section (mm2) per mass (mg):
Cext / M = {0.008 (m - 1) ν / c δ } Q(ρ)/ ρ
where ν is frequency (GHz), δ is density (gm/cm3), c (300
mm/s) and m = 1.78 for ρ < 3. We can fit
Q(ρ)/ ρ = 0.34 ρ2 / (1 + 0.02 ρ4.12 )
Q(ρ)/ ρ ={ c δ / 8 (m - 1) } Cext / (M . ν)
•Similarly, the asymmetry factor can be fitted by:
g = 0.25 ρ2 / (1 + 0.14 ρ2.5 )
•Computing the scattering parameters for the idealized
aggregates that were displayed is thus greatly simplified.
Asymmetry Factor as a Function of Phase Delay
Parameter, 
Empirical Fit
Scattering Efficiency , Q, as a Function of
Phase Delay Parameter, 
Empirical Fit
Table 1: Extinction cross section (mm2) per mass (mg), Cext / M,
at ν =183 GHz for α = 0.20 L-0.59
L (mm) \ N
1
2
3
4
1
0.98
1.12
1.36
1.66
2
1.33
1.49
1.69
1.91
3
1.56
1.72
1.89
2.04
4
1.73
1.88
2.01
2.10
Table 2: Asymmetry factor, g,
L (mm) \ N
1
1
0.11
2
0.20
3
0.27
4
0.33
2
0.15
0.25
0.32
0.39
3
0.21
0.31
0.39
0.45
4
0.30
0.40
0.46
0.51
Table 3: Irradiance attenuation factor / mass, (1- g) Cext / M
L (mm) \ N
1
2
3
4
1
0.87
0.95
1.07
1.16
2
1.06
1.12
1.17
1.15
3
1.14
1.17
1.15
1.10
4
1.16
1.15
1.11
1.03
Mean value: 1.10 + .05
Conclusions
•Mm-wave scattering properties of randomly oriented ice
cylinders and aggregates can be computed from the
phase delay parameter using the T-Matrix method or a
simple analytic approximation.
•Mm-wave properties of snow need to be measured at the
same time as particle volumes and 2-D projected areas.
• Scattering parameters in optically thick snow clouds
may not be sensitive to particle models, but absorption
may prevent establishment of the diffusion regime where
(1-g) Cext could be effective. This requires radiative
transfer model runs.
• Other shapes may produce different scattering
parameters.