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
–
–
–
–
Hubbert et al. (1998)
Cross-polarized
Ordinary
Knight and Knight (1970)
1
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
Pruppacher and Klett (1997)
Straka et al. (2000)
2
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)
•
N(D)=115exp(-0.125D)
D ≥ 6 mm
For hailstorms over Alberta, Cheng and English
(1983) found that
Xu (1983)
N ( D ) = N 0 exp( − ΛD ) [1]
N 0 = AΛb [2]
– 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)
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)
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
Gamma Hailstone PSD’s
Ziegler et
al. (1983)
– Effects realism of
modeled polarimetric
radar observables. How?
4
3.2 Hailstone and graupel shape
•
•
3.2.1 Hailstone shapes vary –
Conical to Oblate spheroidal
Irregular with icicle lobes
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
Hubbert et al. (1998)
Pruppacher and Klett (1997)
Embryo: frozen drop – more spherical initially
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?
Knight (1986)
Bump: Onset of tumbling?
Embryo: conical graupel–
less spherical initially
Hailstone shape vs. size: More uncertainty than raindrops!
5
3.2.2 Lobe structures can be found on
hailstones, altering their shape either subtly
or drastically
Cusped Lobes
– 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
•
Knight and
Knight
(1970a)
Wet growth icicle lobes
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
Icicle lobes
Spongy growth – hyperfine
growth layers with wavy
icicle lobes
6
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,
1. Conical embryo=graupel
2. Spherical clear=frozen drop
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(627%); Oklahoma (70%),
Switzerland (63%); South Africa
Lowveld (62-83%), Highveld
(35-54%) (Knight 1981)
Frozen drop:
single large
crystal,
spherical
clear with
internal crack
3. Spherical bubbly
Hubbert et al. (1998)
(Colorado hailstorm)
All other figs: Knight and Knight (1970b)
7
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)
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°
•
•
•
Heymsfield et al. (1978)
Lump:
• For D < 1 mm,
mean axial ratio
(Dmin/Dmax)
=0.53
• For D > 1 mm,
mean axial ratio
(Dmin/Dmax) =0.7
Cone angle: α
Bringi et al. (1986)
Graupel shape
model for radar
scattering study
Pruppacher and Klett (1997)
Heymsfield et al. (1978)
8
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”
Knight and Knight (1970c)
9
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)
ρ
M=
Ki
ρi
Mi +
Ka
ρa
Ma
m −1
[4]
K= 2
m +2
2
•
•
0.0025
0.002
0.0015
n
0.001
k
0.0005
0
0
0.2
0.4
0.6
0.8
1
Ice density (ρi, g cm-3)
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
K 
K =  i  ρ
 ρi 
•
[3]
0.003
Imaginary component of refractive
index (k)
K
Real component of refractive index (n)
Refractive index of bulk ice, m=n+ik
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
[5]
Combine [4] and [5] to solve for refractive index of mixture (m)
2χ + 1
m =
where
1− χ
2
 Ki 
χ =   ρ
 ρi 
[ 6]
11
•
•
•
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 icewater mixture
C-band
[7]
– Where assumed ice inclusions in water matrix
best simulates spongy ice where f is high
Longtin et al. (1987)
Bohren and Battan (1980)
“MG ice in water” = spongy ice
Where ƒ is high
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