robin hogan, chris westbrook university of reading lin tian nasa goddard space flight center phil...
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Robin Hogan, Chris WestbrookRobin Hogan, Chris WestbrookUniversity of ReadingUniversity of Reading
Lin TianLin TianNASA Goddard Space Flight CenterNASA Goddard Space Flight Center
Phil BrownPhil BrownMet OfficeMet Office
Why it is important that ice Why it is important that ice particles are Smarties not particles are Smarties not
Gobstoppers to a radarGobstoppers to a radar
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Introduction and overviewIntroduction and overview• To interpret 94-GHz radar reflectivity in ice clouds we need
– Particle mass: Rayleigh scattering up to ~0.5 microns: Z mass2
– Particle shape: non-Rayleigh scattering above ~0.5 microns, Z also depends on the dimension of the particle in the direction of propagation of the radiation
• Traditional approach:– Ice particles scatter as spheres (use Mie theory)– Diameter equal to the maximum dimension of the true particle– Refractive index of a homogeneous mixture of ice and air
• New observations to test and improve this assumption:– Dual-wavelength radar and simultaneous in-situ measurements– “Differential reflectivity” and simultaneous in-situ measurements
• Consequences:– Up to 5-dB error in interpretted reflectivity– Up to a factor of 5 overestimate in the IWC of the thickest clouds
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Dual-wavelength ratio Dual-wavelength ratio comparisoncomparison
• NASA ER-2 aircraft in tropical cirrus
10 GHz, 3 cm
94 GHz, 3.2 mm
10 GHz, 3 cm
94 GHz, 3.2 mm
Difference
Error 1: constant 5-dB overestimate of Rayleigh-
scattering reflectivity
Error 2: large overestimate in the dual-wavelength
ratio, or the “Mie effect”
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Characterizing particle sizeCharacterizing particle size• An image measured by aircraft can be approximated by a...
Sphere (but which diameter do we use?) Spheroid (oblate or prolate?)
Note:
Dmax Dlong
Dmean=(Dlong+Dshort)/2
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Error 1: Rayleigh Z Error 1: Rayleigh Z overestimateoverestimate
• Brown and Francis (1995) proposed mass[kg]=0.0185 Dmean[m]1.9
– Appropriate for aggregates which dominate most ice clouds
– Rayleigh reflectivity Z mass2
– Good agreement between simultaneous aircraft measurements of Z found by Hogan et al (2006)
• But most aircraft data world-wide characterized by maximum particle dimension Dmax
– This particle has Dmax = 1.24 Dmean
– If Dmax used in Brown and Francis relationship, mass will be 50% too high
– Z will be too high by 126% or 3.6 dB– Explains large part of ER-2
discrepancy
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Particle shapeParticle shape• We propose ice is modelled as
Smarties rather than Gobstoppers!– Korolev and Isaac (2003) found
typical aspect ratio =Dshort/Dlong of 0.6-0.65
– Aggregate modelling by Westbrook et al. (2004) found a value of 0.65
Randomly oriented in aircraft probe:
Horizontally oriented in free fall:
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Error 2: Non-Rayleigh Error 2: Non-Rayleigh overestimate overestimate
SpheroidSphere
Transmitted wave
Sphere: returns from
opposite sides of particle out
of phase: cancellation
Spheroid: returns from
opposite sides not out of
phase: higher Z
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Useful scattering approximations
• Dense particles smaller than the wavelength:– Rayleigh theory: spheres– Gans (1912) theory: ellipsoids
• Rayleigh-Gans theory: arbitrary shapes of low refractive index– Backscatter cross-section given by:
– where:– Function for spheroids is:
– Resulting backscatter cross-section:
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Modified Rayleigh-Gans• But ice particles are only low density (and therefore low
refractive index) when they are large– Merge Rayleigh-Gans theory (large, low density) with Gans (1912)
theory (small, arbitrary density): Gans-Rayleigh-Gans theory?– Result:
– where:
– Integrate over a distribution to get the radar reflectivity factor:
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Independent verification: Independent verification: Z Z drdr
• A scanning polarized radar measures differential reflectivity, defined as: Zdr = 10log10(Zh/Zv)
Solid-ice sphere
Solid-ice oblate spheroid
Sphere: 30% ice, 70% air
Dshort/Dlong:
Dependent on both aspect ratio and density (or ice fraction)
If ice particles were spherical, Zdr would be zero!
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• Reflectivity agrees well, provided Brown & Francis mass used with Dmean
• Differential reflectivity agrees reasonably well for oblate spheroids
Chilbolton 10-cm radar + UK Chilbolton 10-cm radar + UK aircraftaircraft
CWVC IV: 21 Nov 2000
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The CIRRAD flight, 8 Oct 1997The CIRRAD flight, 8 Oct 1997
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CWVC IV: 21 Nov 2000CWVC IV: 21 Nov 2000
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CWVC III: 20 Oct 2000CWVC III: 20 Oct 2000
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CWVC IV: 21 Nov 2000CWVC IV: 21 Nov 2000
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POL-45• 35-GHz radar
reflectivity at 45 degrees
• 35-GHz differential reflectivity at 45 degrees
• 905-nm lidar backscatter at vertical
Cirrus: aggregates
Mixed-phase: plates & dendrites
Rain: differential attenuation
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Z Z drdr statistics statistics• One month of data from a 35-
GHz (8-mm wavelength) radar at 45° elevation– Around 75% of ice clouds
sampled have Zdr< 1.3 dB, and even more for clouds colder than -15°C
– This supports the model of oblate spheroids
• For clouds warmer than -15°C, much higher Zdr is possible– Case studies suggest that this
is due to high-density pristine plates and dendrites in mixed-phase conditions (Hogan et al. 2002, 2003; Field et al. 2004)
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Consequences for IWC Consequences for IWC retrievalsretrievals
• Empirical formulas derived from aircraft will be affected, as well as any algorithm using radar:
Raw aircraft data Empirical IWC(Z,T) fit
Spheres with D =Dmax
Hogan et al. (2006) fitNew spheroids
Radar reflectivity ~5 dB higher with spheroids
Retrieved IWC can be out by a factor of 5 using
spheres with diameter Dmax
Note: the mass of the particles in these three examples are the same