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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 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 Dual-wavelength ratio comparison 10 GHz, 3 cm Error 1: constant 5-dB overestimate of Rayleigh10 GHz, 3 cm scattering reflectivity 94 GHz, 3.2 mm 94 GHz, 3.2 mm Difference • NASA ER-2 aircraft in tropical cirrus 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: Dmax Dlong Dmean=(Dlong+Dshort)/2 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 Randomly oriented in aircraft probe: Particle shape • 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: Error 2: Non-Rayleigh overestimate Transmitted wave Sphere 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: Zdr = 10log10(Zh/Zv) Dshort/Dlong: Dependent on both aspect ratio and density (or ice fraction) Solid-ice oblate spheroid If ice particles were spherical, Zdr would be zero! Sphere: 30% ice, 70% air Solid-ice sphere Chilbolton 10-cm radar + UK aircraft • Reflectivity agrees • Differential well, provided Brown reflectivity agrees & Francis mass used reasonably well for CWVC IV: 21 Nov 2000 with Dmean oblate spheroids The CIRRAD flight, 8 Oct 1997 CWVC IV: 21 Nov 2000 CWVC III: 20 Oct 2000 CWVC IV: 21 Nov 2000 POL-45 • 35-GHz radar reflectivity at 45 degrees Cirrus: aggregates Mixed-phase: plates & dendrites Rain: differential attenuation • 35-GHz differential reflectivity at 45 degrees • 905-nm lidar backscatter at vertical Z dr statistics • One month of data from a 35GHz (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) Consequences for IWC retrievals • Empirical formulas derived from aircraft will be affected, as well as any algorithm using radar: Radar reflectivity ~5 dB higher with spheroids Raw aircraft data Retrieved IWC can be out by a factor of 5 using spheres with diameter Dmax 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