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

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

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

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

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

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:

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

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:

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:

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!

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

The CIRRAD flight, 8 Oct 1997

CWVC IV: 21 Nov 2000

CWVC III: 20 Oct 2000

CWVC IV: 21 Nov 2000

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

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)

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