Robin Hogan, Chris WestbrookRobin Hogan, Chris WestbrookUniversity of ReadingUniversity of Reading

Lin TianLin TianNASA Goddard Space Flight CenterNASA Goddard Space Flight Center

Phil BrownPhil BrownMet OfficeMet Office

Why it is important that ice Why it is important that ice particles are Smarties not particles are Smarties not

Gobstoppers to a radarGobstoppers to a radar

Introduction and overviewIntroduction 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 Dual-wavelength ratio comparisoncomparison

• 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 sizeCharacterizing 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 Error 1: Rayleigh Z overestimateoverestimate

• 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

Particle shapeParticle shape• We propose ice is modelled as

Smarties rather than Gobstoppers!– Korolev and Isaac (2003) found

typical aspect ratio =Dshort/Dlong of 0.6-0.65

– 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 Error 2: Non-Rayleigh overestimate overestimate

SpheroidSphere

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: Independent verification: Z Z drdr

• A scanning polarized radar measures differential reflectivity, defined as: Zdr = 10log10(Zh/Zv)

Solid-ice sphere

Solid-ice oblate spheroid

Sphere: 30% ice, 70% air

Dshort/Dlong:

Dependent on both aspect ratio and density (or ice fraction)

If ice particles were spherical, Zdr would be zero!

• Reflectivity agrees well, provided Brown & Francis mass used with Dmean

• Differential reflectivity agrees reasonably well for oblate spheroids

Chilbolton 10-cm radar + UK Chilbolton 10-cm radar + UK aircraftaircraft

CWVC IV: 21 Nov 2000

The CIRRAD flight, 8 Oct 1997The CIRRAD flight, 8 Oct 1997

CWVC IV: 21 Nov 2000CWVC IV: 21 Nov 2000

CWVC III: 20 Oct 2000CWVC III: 20 Oct 2000

CWVC IV: 21 Nov 2000CWVC IV: 21 Nov 2000

POL-45• 35-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 Z drdr statistics statistics• 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)

Consequences for IWC Consequences for IWC retrievalsretrievals

• Empirical formulas derived from aircraft will be affected, as well as any algorithm using radar:

Raw aircraft data Empirical IWC(Z,T) fit

Spheres with D =Dmax

Hogan et al. (2006) fitNew spheroids

Radar reflectivity ~5 dB higher with spheroids

Retrieved IWC can be out by a factor of 5 using

spheres with diameter Dmax

Note: the mass of the particles in these three examples are the same