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Robin Hogan, Chris Westbrook University of Reading Lin Tian NASA Goddard Space Flight Center Phil Brown Met Office Why it is important that ice particles are Smarties not Gobstoppers to a radar

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Introduction and overview To interpret 94-GHz radar reflectivity in ice clouds we need –Particle mass: Rayleigh scattering up to ~0.5 microns: Z mass 2 –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 comparison 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 size An image measured by aircraft can be approximated by a... Sphere (but which diameter do we use?) Spheroid (oblate or prolate?) Note: D max D long D mean =(D long +D short )/2

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Error 1: Rayleigh Z overestimate Brown and Francis (1995) proposed mass[kg]= D mean [m] 1.9 –Appropriate for aggregates which dominate most ice clouds –Rayleigh reflectivity Z mass 2 –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 D max –This particle has D max = 1.24 D mean –If D max 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 shape We propose ice is modelled as Smarties rather than Gobstoppers! –Korolev and Isaac (2003) found typical aspect ratio =D short /D long of –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 overestimate Spheroid Sphere 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: Z dr A scanning polarized radar measures differential reflectivity, defined as: Z dr = 10log 10 (Z h /Z v ) Solid-ice sphere Solid-ice oblate spheroid Sphere: 30% ice, 70% air D short /D long : Dependent on both aspect ratio and density (or ice fraction) If ice particles were spherical, Z dr would be zero!

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Reflectivity agrees well, provided Brown & Francis mass used with D mean Differential reflectivity agrees reasonably well for oblate spheroids Chilbolton 10-cm radar + UK aircraft CWVC IV: 21 Nov 2000

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The CIRRAD flight, 8 Oct 1997

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CWVC IV: 21 Nov 2000

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CWVC III: 20 Oct 2000

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CWVC IV: 21 Nov 2000

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POL 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 dr statistics One month of data from a 35- GHz (8-mm wavelength) radar at 45° elevation –Around 75% of ice clouds sampled have Z dr < 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 Z dr 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 retrievals Empirical formulas derived from aircraft will be affected, as well as any algorithm using radar: Raw aircraft dataEmpirical IWC(Z,T) fit Spheres with D =D max Hogan et al. (2006) fit New spheroids Radar reflectivity ~5 dB higher with spheroids Retrieved IWC can be out by a factor of 5 using spheres with diameter D max Note: the mass of the particles in these three examples are the same

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