1. No category

5. Ice crystal and aggregate properties
(Pruppacher and Klett 1997 Secs. 2.2.1 and 2.2.2 plus various journal articles)
According to the AMS Glossary of Meteorology,
• Ice Crystal = “Any one of a number of macroscopic, crystalline forms in
which ice appears, including hexagonal columns, hexagonal platelets,
dendritic crystals, ice needles and combinations of these forms”
• Snow = “Precipitation composed of white or translucent ice crystals,
chiefly in complex branch hexagonal form and often agglomerated into
snowflakes”
• Snow Crystal = “Any of several types of ice crystal found in snow”
– “A snow crystal is a single crystal, in contrast to a snowflake, which is usually an
aggregate of many single snow crystals.”
• Aggregation = “2. The process of clumping together of snow crystals
following collision as they fall to form snowflakes”
• Snowflake = “Colloquially an ice crystal, or more commonly an
aggregation of many crystals that falls from a cloud”
• In this class
– Snow crystal = single ice crystal
– Snowflake = aggregation of ice crystals = ice aggregate
1
• Ice particles grow by diffusion of water vapor = deposition
•
Called ice crystals or snow crystals
• Snow crystals can grow by collision with other snow crystals = aggregation
•
Aggregates of snow crystals = snowflakes
• Snow crystals (snowflakes) can also grow by collection of supercooled drops that
freeze = riming
•
•
•
Eventually become graupel when crystal habit is lost
Based on observations,
supercooled (liquid
water) clouds are
common occurrence,
especially if cloud top
temperature is > -10°C
With decreasing
temperature, likelihood
of ice increases such
that at -20°C only about
10% of clouds consist
entirely of supercooled
drops (i.e., 90% have
ice) (see below from
PK97)
Pruppacher and Klett (1997) (PK97)
2
5.1 Ice crystal shape (habit)
•
•
Casual observations suggest that
snow crystals appear in a large
variety of shapes (or habits) –
more later
But detailed crystallographic
studies reveal that snow crystals
have one common basic shape –
six-fold symmetric (hexagonal)
prism with two basal planes (of
type 0001) and six prism planes
(of type 1010) (see top)
–
Other crystal faces are more rare
(metastable), grow quickly and
usually form edges (bottom)
Basal face (plane) = c-axis growth
Prism face
(plane) = aaxis growth
Pruppacher and Klett (1997)
• Laboratory experiments reveal that ice crystal habit [or the rate of propagation of
the basal faces (growth along c-axis) relative to that of prism faces (i.e., growth
along a-axis)]varies in a characteristic manner with
• Temperature and
• Supersaturation
3
•
At large vapor density excess (or
supersaturation) with respect to
ice, the snow crystal shape changes
with decreasing temperature from
a plate to a needle, to a column, to
a sector plate, to a dendrite, back
to a sector plate and finally back to
a column
Variation of ice crystal habit with temperature and
supersaturation (top) or vapor density excess (bottom)
– Cyclic plate-column-plate-column
change in habit is due to a cyclic
change of the preferential growth
direction along the a-axis and caxis
– Transition temperatures at -4°C, 9°C, -22°C
– First two transitions are sharp; last
at -22°C diffuse change (several °)
•
•
At very low vapor density excess,
the crystal shape changes between
short column and a thick plate near
-9°C, -22°C
Close to or at ice saturation, ice
crystal shape ceases to vary with
temperature and assumes equilibrium
shape, which is a thick hexagonal
plate with a height-to-diameter ratio
of 0.8
Pruppacher and Klett (1997)
4
•
Although temperature is principal factor, humidity conditions in the environment also
control important growth features of snow
–
–
E.g., prior page, near -15°C, snow crystal habit varies with increasing vapor density excess from thick plate
to thin plate to sector plate and finally to dendrite
E.g., near -5°C, habit varies with increasing vapor density excess from short solid column, to hollow
column to a needle with pronounced growth in c-axis direction
• “Magono-Lee” diagram
(right) summarizes
observations of snow
crystal habits
•
•
“Magono-Lee Diagram”
from observations of natural snow crystals
Observations show
similar temperature and
humidity control of ice
habit
More recent
observations tend to
confirm
• Good agreement between
observations and lab
studies
• Comprehensive “MagonoLee classification” of
natural ice habits next page
Pruppacher and Klett (1997)
5
Magono-Lee Classification of Natural Snow Crystals (for reference)
6
Example of more recent ice
crystal habit observations
from the SPEC CPI
SPEC
Cloud Particle Imager (CPI)
Source:
http://www.specinc.com/cloud-particle-imager
7
Example CPI observations from deep tropical stratiform
precipitation during TRMM Field Campaigns (FCs)
Many of us study convection. What do
ice crystals look like in stratiform regions
associated with convection?
Numerous vapor-grown crystals observed
intermediate (400-600 µm) and large (> 800
µm) size range, including columns, capped
columns, hexagonal plates and branched
crystals.
Initial formation of columns (-20°C to -25°C)
(at echo top above CPI) and then capped
columns as particles fell through planarcrystal growth regime (-12°C to -18°C)
Aggregates with some minimal riming in
larger sizes observed around melting level.
Deposition dominates aggregation/riming in
weak stratiform updrafts
Heymsfield et al. (2002)
8
Example CPI observations from deep tropical stratiform
precipitation during TRMM Field Campaigns (FCs)
Many of us study convection. What do
ice crystals look like on periphery of
convection?
In contrast to last example, particles in
this example were rimed in intermediate
and large sizes with aggregates evident
Inferred updrafts above a few meters/sec
were assessed, indicating deep updrafts,
which led to extensive riming and
complex crystal shapes often associated
with freezing of cloud droplets at low
temperatures
Heymsfield et al. (2002)
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Last one. What do ice crystals look
like in deep anvil generated by
nearby deep and extensive
convection?
Complex rimed crystals and
aggregates of rimed crystals
No supercooled liquid water
measured in anvil so riming must
have been acquired in convection
and then advected to anvil
Complex shapes fairly common for
convective anvil…
Heymsfield et al. (2002)
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•
For more specific and quantitative information on snow crystal shape, it is usually
sufficient to characterize the relative size in two dimensions
– The crystal diameter (d) and the crystal thickness (h) in the case of plate-like crystals
– The crystal length (L) and the crystal width (d) for columnar type crystals
•
From observations, the length of columnar and the diameter of plate crystals
(i.e., major dimension) range between 20 µm and 2 mm.
– Maximum dimensions reach several mm
•
•
Similarly, the thickness of plate-like crystals range from 10 to 60 µm, the width of
warm temperature columns from 10 to 200 µm, and width of needles range from
10 to 150 µm (minor dimension)
For simplicity in radar scatter models, often assume that ice crystals can be
modeled as oblate or prolate spheroids with major and minor dimensions.
– Only appropriate for lower frequency precipitation radar (S-band to X-band) and not
necessarily higher frequency cloud radar (like W-band)
•
Observations further show that thickness and diameter of plate-like crystals and
length and width of columnar crystals are characteristically related to each other
– Power-law relationships between major and minor dimensions for each crystal type
– if d↑, then h↑ for plates; If L↑, then d↑ for columns
– See next page for details
•
Shape for aggregates (snowflakes) difficult to parameterize. As shown in
images, bulk shape can vary from near spherical (major:minor ≈ 1) to highly
asymmetric (very small minor:major << 1)
– Bulk density is very low too so perhaps shape is not as important (i.e., effective sphere)
11
Dimensional
relationships for
snow crystals:
Shape
P1a = hexagonal plate
P1b = sector plate
P1c-r = simple ‘daisytype’ dendrite
P1c-s = dendrite with
sector branches
C1g = thick solid plate
C1e = solid column
C1f = hollow column
Pruppacher and Klett (1997)
P1e,P1f,P2c,P2g,P3c,P4b
= Dendrite (various)
N1a = elementary needle
N1e = Long solid column
C1c, C1d = solid bullet
12
5.2 Snow crystal and snowflake size distributions
•
Similar to MP48, Gunn and Marshall (1958) proposed an
exponential size distribution for aggregates of snow
crystals based on observations (right)
N (D ) = N 0 exp( − ΛD ), [1a ]
where Λ = 25.5R −0.48 cm −1 , N 0 = 3.8 × 103 R −0.87m −3mm −1 , [1b]
and D is the equivalent diameter of the water drop to which the ice
crystal aggregate melts (i.e., equivalent melted drop diameter) and R is
the rate of precipitation in mm h-1 of liquid water
– Variety of snow and snowflake types, including aggregates of plate,
columns and dendrites
– Note typo error in units of Λ in Pruppacher and Klett (1997)
•
Sekhon and Srivastava (1970) found similar form as [1a]
in snow except different equations for Λ, N0 in [1b]
–
–
•
Λ = 22.9 R-0.45 cm-1
N0 = 2.50 × 103 R-0.94 mm-1 m-3
SS70 also derive several useful relationships for snow
–
–
–
Median volume diameter: D0 = 0.14R0.45 (cm)
Liquid water content
W = 0.250R0.86 (g m-3)
Reflectivity:
Z= 1780R2.21 (mm6 m-3)
Gunn and Marshall (1958)
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•
•
Using a very large in-situ aircraft
database from TRMM FC’s, Heymsfield
et al. (2002) parameterized ice particle
size distributions (PSDs) in deep tropical
cirrus and stratiform precipitating clouds
Heymsfield et al. (2002) found that ice
PSD’s were well represented by gamma
distributions of the form
Exponential (exp)
Gamma
N (D ) = N 0 D µ exp(− λD ) [2]
–
•
Also explored exponential distribution by
forcing µ = 0 in [2]
The slope parameter (λ) of both gamma
and exponential distribution varied
systematically with temperature during
spirals (right)
–
–
–
–
What is the trend of size (D0) with height?
Values of exp (N0, λ) similar to past studies
mid-latitude frontal and cirrus clouds
Temperature is not only controlling factor
but is a primary one
Considerable variability of PSD during
spirals manifested in rapid changes in N0
while µ and λ tended to be more stable
Heymsfield et al. (2002)
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5.3 Snow crystal and snowflake density
• Most ice crystals, and all aggregates of ice crystals, have a bulk density less than
that of solid ice (0.916 g cm-3)
–
–
–
Small amounts of air in capillary spaces of single crystals (e.g. hollow columns)
tendency of single snow crystals to grow in skeletal fashion (e.g., dendrites)
obvious air gaps when multiple snow crystals aggregate
For most snow
crystal types,
increasing size
implies decreasing
bulk ice density
Pruppacher and Klett (1997)
From Heymsfield (1972)
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Integrated bulk density and size/aspect ratio information for various snow crystal types
For plates and dendrites
For columns, needles, and bullets
ρ = a1D c [3a ]
ρ = a1Lc [4a ]
h = a2 D f
d = a2 L f
[3b]
ρ: bulk ice density (g cm-3)
D: crystal diameter (cm) (major dimension)
h: crystal thickness (cm) (minor dimension)
[ 4b ]
Coefficients in table below
(Matrosov et al. 1996)
ρ: bulk ice density (g cm-3)
D: crystal length (cm) (major dimension)
d: crystal thickness (cm) (minor dimension)
Matrosov et al. (1996) from various sources in caption.
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•
Bulk density of snow aggregate (ρ, g cm-3) as function of aggregate diameter (D,
cm) (or major dimension) was provided by Passarelli and Srivastava (1979) based
on Magono and Nakamura (1965) data
ρ = 0.015D −0.6 [ g cm −3 ] [5]
•
Illingworth (1994), Matrosov et al. (1996) and Ryzhkov et al. (1998) recommend
relationship for bulk density of snow aggregates (ρ, g cm-3) in terms of the ice
particle major dimension S (mm) (note units!)
if ( S < 0.097 mm ) then
ρ = 0.916 g cm
−3
else
ρ = 0.07 S −1.1 g cm −3
endif
[ 6]
Aggregate bulk ice density (g cm-3)
1
0.9
0.8
0.7
aggregate density Illingworth (1994)
0.6
aggregate density Passarelli and Srivastava (1979)
0.5
0.4
0.3
0.2
0.1
0
0.01
0.1
1
10
Aggregate Major Dimension (cm)
•
Equations [5] and [6] are in OK agreement for major dimension > 1 mm. Likely
large variability in bulk ice density of aggregates under differing conditions
17
5.4 Snow crystal and snowflake orientation and refractive index
•
K
ρ
M=
Ki
ρi
Mi +
Ka
ρa
Refractive index of bulk ice, m=n+ik
Ma
[7 ]
m2 − 1
[8]
K= 2
m +2
•
•
•
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.003
0.0025
0.002
0.0015
n
0.001
k
0.0005
0
0
0.2
0.4
0.6
0.8
1
Imaginary component of refractive
index (k)
•
In radar studies, usually assume major dimension of ice crystal or aggregate is in the
horizontal unless there is a strong electric field, in which case ice particle is aligned with
electric field, which is usually assumed strongest in vertical (Weinheimer and Few 1987)
For dry ice particles (i.e., not in wet growth or melting), the refractive index is calculated with
Debye theory using the bulk density of ice from earlier section. Recall…
Use Debye mixing theory, Debye (1929), for ice and air mixtures (e.g., Battan 1973)
Real component of refractive index (n)
•
Ice density (ρi, g cm-3)
Where M:mass, ρ: density, m: refractive index; subscript i=ice (solid) and a=air (no
subscript=mixture or bulk ice density)
Can simplify [7] by noting that ma in [8] is ≈ 1 so Ka ≈ 0 and M ≈ Mi ∴→ K/ρ is constant.
Hence, K for mixture is
K 
K =  i  ρ [9]
 ρi 
Combine [4] and [5] to solve for refractive index of mixture (m)
m2 =
2χ + 1
where
1− χ
K 
χ =  i  ρ [10]
 ρi 
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