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)
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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
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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
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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?
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
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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)
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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