Why it is important that ice particles are Smarties not Gobstoppers to a radar

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

2. Introduction 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

3. Dual-wavelength ratio comparison Error 2: large overestimate in the dual-wavelength ratio, or the “Mie effect” • NASA ER-2 aircraft in tropical cirrus 10 GHz, 3 cm Error 1: constant 5-dB overestimate of Rayleigh-scattering reflectivity 10 GHz, 3 cm 94 GHz, 3.2 mm 94 GHz, 3.2 mm Difference

4. 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: Dmax Dlong Dmean=(Dlong+Dshort)/2

5. Error 1: Rayleigh Z overestimate • 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

6. Particle shape Randomly oriented in aircraft probe: • We propose ice is modelled as Smarties rather than Gobstoppers! • Korolev and Isaac (2003) found typical aspect ratio a =Dshort/Dlong of 0.6-0.65 • Aggregate modelling by Westbrook et al. (2004) found a value of 0.65 Horizontally oriented in free fall:

7. Error 2: Non-Rayleigh overestimate Transmitted wave Spheroid Sphere Sphere: returns from opposite sides of particle out of phase: cancellation Spheroid: returns from opposite sides not out of phase: higher Z

8. 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:

9. 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:

10. Independent verification: Z dr • A scanning polarized radar measures differential reflectivity, defined as: Zdr = 10log10(Zh/Zv) Dshort/Dlong: Solid-ice oblate spheroid Dependent on both aspect ratio and density (or ice fraction) If ice particles were spherical, Zdr would be zero! Solid-ice sphere Sphere: 30% ice, 70% air

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

12. The CIRRAD flight, 8 Oct 1997

13. CWVC IV: 21 Nov 2000

14. CWVC III: 20 Oct 2000

15. CWVC IV: 21 Nov 2000

16. POL-45 Rain: differential attenuation Cirrus: aggregates Mixed-phase: plates & dendrites • 35-GHz radar reflectivity at 45 degrees • 35-GHz differential reflectivity at 45 degrees • 905-nm lidar backscatter at vertical

17. 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) Z dr statistics

18. Empirical formulas derived from aircraft will be affected, as well as any algorithm using radar: Consequences for IWC retrievals Retrieved IWC can be out by a factor of 5 using spheres with diameter Dmax Radar reflectivity ~5 dB higher with spheroids Raw aircraft data Empirical IWC(Z,T) fit Spheres with D =Dmax Hogan et al. (2006) fit New spheroids Note: the mass of the particles in these three examples are the same