The importance of ice particle shape and orientation for spaceborne radar retrievals

1. The importance of ice particle shape and orientation for spaceborne radar retrievals 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 • 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 Error 2: large overestimate in the dual-wavelength ratio, or the “Mie effect”

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 oblate spheroids ratherthan spheres • 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. 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

9. Chilbolton 10-cm radar + UK aircraft • Reflectivity agrees well, provided Brown & Francis mass used with Dmean • Differential reflectivity agrees reasonably well for oblate spheroids

10. One month of data from a 35-GHz (8-mm wavelength) radar at 45° elevation Around 75% of ice clouds sampled have Zdr< 1 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

11. 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