3. Hail and graupel properties According to the AMS Glossary of Meteorology, • Hail (hailstone)= “precipitation in the form

of balls or irregular lumps of ice, always produced by convective clouds, nearly always cumulonimbus. By convention, hail has a diameter of 5 mm or more.”

– Spheroidal, conical, or irregular in shape – Large hail can have lobes – Grow via accretion/riming of supercooled water – Spheroidal often exhibit layered internal structure

with layers of ice containing many air bubbles (dry growth) alternatively with layers of relatively clear ice (wet growth)

– Large hail may contain liquid water and be spongy (ice/water mixture) but usually solid ice with density > 0.8 g cm-3

– Density of small hail typically < 0.8 g cm-3, sometimes much less

– Small hail may be indistinguishable from larger graupel except for the convention that hail must be larger than 5 mm in diameter

1

Cross-polarized Ordinary

Hubbert et al. (1998)

Knight and Knight (1970)

According to the AMS Glossary of Meteorology, • Graupel=“heavily rimed snow particles;

often indistinguishable from very small soft hail except for the size convention that hail diameter > 5 mm”

– Conical, hexagonal or lump (irregular) shaped

– Blurry microphysical boundary between graupel and small hail

• In polarimetric radar remote sensing, there may be no discernible difference between small hail and graupel (Straka et al. 2000).

– Modeled property differences are context specific

– Many hydrometeor identification methods treat small hail and graupel as one category because polarimetric observables are usually not sufficiently different

2

Straka et al. (2000)

Pruppacher and Klett (1997)

3.1 Particle Size distributions (PSDs) • Most studies show PSD for graupel and hailstones

are fitted best by an exponential distribution (Douglas 1964; Federer and Waldvogel 1975; Smith et al. 1976; Cheng and English 1983; Xu 1983; Ziegler et al. 1983; Cheng et al. 1985)

• For hailstorms over Alberta, Cheng and English (1983) found that

– Where A=115, b=3.63, N0: m-3 mm-1, Λ: mm-1

– With [2], exponential PSD [1] is convenient form that reduces to 1 parameter distribution

– Note A and b likely varies by region/storm. CE83 sample had maximum D of 13 mm (1.3 cm)!

• Federer and Waldvogel (1975) found exponential PSD, [1], parameters that varied between

– 1.5 ≤ N0 ≤ 52 m-3 mm-1

– 0.33 ≤ Λ ≤ 0.64 mm-1

– Mean spectrum: N(D) = 12 exp(-0.42D)

N(D)=115exp(-0.125D) D ≥ 6 mm

Xu (1983)

Federer and Waldvogel (1975)

]2[

]1[)exp()(

0

0bAN

DNDNΛ=

Λ−=

3

• Some investigators have found that a gamma function better fits some hailstone size PSD’s (Ziegler et al. 1983; Xu 1983; Straka et al. 2000)

• A few studies have found that PSD of graupel and hailstones can be described by power law of form N(D)=ADB where D: diameter (Auer et al. 1970, Auer 1972)

• Choice of hail PSD important for relative contribution of small and large hydrometeors

– Effects realism of modeled polarimetric radar observables. How?

4

Ziegler et al. (1983)

Gamma Hailstone PSD’s

3.2 Hailstone and graupel shape • 3.2.1 Hailstone shapes vary –

conical, oblate spheroidal, irregularly shaped, and sometimes with spikes and lobes

• Oblate spheroidal common (Barge and Issac 1973; Matson and Huggins 1980; Knight 1986)

– Most have axis ratio (min:max dimension) of ≈ 0.8

• Hailstone shapes are less spherical or more oblate with increasing size

– Tendency for axis ratio to vary with size from 0.95 for small hail (max=5 mm ) to 0.6 to 0.7 for large hail (max: 50-60 mm)

– Different for different areas – Embryo type(CO: conical graupel;

OK: frozen drops), growth mode + rate (dry/wet) and fall mode affect shape and vary regionally

– Bump in axis ratio caused by onset tumbling?

5

Knight (1986)

Embryo: frozen drop – more spherical initially

Embryo: conical graupel– less spherical initially

Bump: Onset of tumbling?

Conical to Oblate spheroidal

Hubbert et al. (1998)

Hailstone shapes Irregular with icicle lobes

Pruppacher and Klett (1997)

Hailstone shape vs. size: More uncertainty than raindrops!

3.2.2 Lobe structures can be found on hailstones, altering their shape either subtly or drastically

– Can make modeling shape complicated – uncertainty

• Two kinds of lobe structures on hailstones (Knight and Knight 1970a, JAS, 667-671)

– Cusped lobes – Icicle lobes

• Cusped lobes: – form in dry growth (freeze in place) – result from a collection efficiency effect

where lobes grow faster than their surroundings

– Mostly when hailstone is tumbling

• Icicle lobes: – Wet or spongy growth – Form more as icicles form – by flow of liquid water over hailstone

surfaces and preferential freezing at tips of projections due to enhanced ventilation, heat exchange with environment 6

Cusped Lobes

Icicle lobes

Wet growth icicle lobes

Spongy growth – hyperfine growth layers with wavy icicle lobes

Knight and Knight (1970a)

3.2.3 Hailstone embryos • Impact on shape during hail

growth • Distinct early growth mode of

large hail suggests that embryo formation is followed by hailstone accretional growth

• Three identifiable types: 1) conical (60%), 2) spherical, clear (25%), 3) spherical, bubbly (10%) and 4) “other” (5%) (Knight and Knight 1970b, JAS, 749-774)

– Conical = graupel – Spherical clear = likely frozen

raindrop – Spherical bubbly = partially

melted and then refrozen lightly rimed aggregate (?)

• Regional differences % frozen drop embryo: Colorado(6-27%); Oklahoma (70%), Switzerland (63%); South Africa Lowveld (62-83%), Highveld (35-54%) (Knight 1981)

7

Hubbert et al. (1998) (Colorado hailstorm)

1. Conical embryo=graupel

2. Spherical clear=frozen drop

Frozen drop: single large crystal, spherical clear with internal crack

3. Spherical bubbly

All other figs: Knight and Knight (1970b)

3.2.4 Graupel shape • Conical graupel, lump graupel most

common shapes • Axial ratio (Dmin/Dmax,

Height/Dmax, Dmiddle/Dmax) – Consider scatter but some trends

noted (right)

• Heymsfield et al. (1978)

8 Pruppacher and Klett (1997) Heymsfield et al. (1978)

Conical: • D < 1 mm, graupel

break-up on probe • For D > 1 mm, mean

Dmin/Dmax axial ratio =0.75 – 0.90

• Cone angle=30°-80° with mean 60°

Lump: • For D < 1 mm,

mean axial ratio (Dmin/Dmax) =0.53

• For D > 1 mm, mean axial ratio (Dmin/Dmax) =0.7

Bringi et al. (1986) Graupel shape model for radar scattering study

Cone angle: α

Heymsfield et al. (1978)

3.3 Hailstone and Graupel Fall Mode (Orientation) • Conical graupel falls with apex up most often (Pflaum et al.

1978) – Secondary motions: helical/spiral fall, axial rotation, bell-swing motion

about apex (i.e., canting) • Uncertainty exists in modeling hailstone fall mode

– Contradictions in literature exist, due to difficulties of measurement, theory and likely also because real behavior is complex and varied

– Summary Pruppacher and Klett (1997) below • List (1959) lab study suggests hailstone oblate spheroids fall

with minor axis vertical – List et al. (1973) theory study finds tumbling about minor axis vertical

• In later theoretical and experimental studies, List and colleagues (Kry and List 1974a,b; Stewart and List 1983; Lesins and List 1986; List 1990) found that hailstones gyrate while freely falling, spins about minor axis, which remains approximately horizontal but wobbles causing precession and nutation of spin

• Knight and Knight (1969; 1970c, JAS, 672-681) conclude from hailstone internal structure that hailstones tumble as they fall

– “very exaggerated wobble about the short axis, such that the short axis is not far from horizontal, could explain all growth features of oblate hailstones”

– “like the motion of a coin some time after it has been spun rapidly on edge on a flat surface”

9 Knight and Knight (1970c)

3.4 Graupel and Hailstone Density • Bulk density of large rimed ice particles varies greatly, depending on

denseness of packing of cloud drops frozen on the ice crystal, growth mode (dry vs. wet), surface (dry vs. wet), and internal state (solid ice, air/ice mixture, ice/water mixture)

• Density of graupel particles range from 0.05 g m-3 to as high as 0.89 (g cm-3). See Table 2.8 Pruppacher and Klett (1997) – Depends on air in ice/air mixture (i.e., tightness of packing of cloud drops

frozen on surface vs. trapped air). • Density of hailstones usually approaches solid ice (0.917 g cm-3),

especially if in wet growth – Growth mode and history (and melting/freezing) matters – External wet surface during wet growth or melting can slightly increase

bulk density of particle – Earlier dry growth can reduce overall bulk density – But water can soak into ice/air matrix and dramatically increase bulk

density of particle

10

3.5 Graupel and hail dielectric (or Refractive index) • Use Debye mixing theory (Debye (1929) for ice and air mixtures (e.g., Battan

1973)

• Where M:mass, ρ: density, m: refractive index; subscript i=ice and a=air (no subscript=mixture)

• Can simplify [3] by noting that ma in [4] is ≈ 1 so Ka ≈ 0 and M ≈ Mi ∴→ K/ρ is constant. Hence, K for mixture is

• Combine [4] and [5] to solve for refractive index of mixture (m)

11

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• For melting hail, you can model it as 1) concentric oblate spheroids with ice inside and liquid melt water outside or 2) spongy ice

• For 2) spongy hail, Deybe mixing theory does NOT apply. Cannot be strongly absorbing.

• For 2) spongy hail, must use different theory like Maxwell Garnett (1904) mixing theory to calculate dielectric (e.g., Bohren and Battan 1980; Longtin et al. 1987 JTECH)

– Dielectric of spongy ice εsi is a function of dielectric constant of solid ice εi, liquid water εw and volume of water fraction (f) in ice-water mixture

– Where assumed ice inclusions in water matrix best simulates spongy ice where f is high

12 Longtin et al. (1987)

[7]

Bohren and Battan (1980)

“MG ice in water” = spongy ice Where ƒ is high

C-band