AOSC 620 Formation and Growth of Ice Crystals Lecture 24.
A hailstone found in Vivian, SD by Les Scott July 23, 2010 was the record largest U.S. hailstone by weight and diameter. Previous record 2003. This 8-inch diameter stone, pictured above, weighed in at an incredible 1.94 lbs. Updraft estimated at 75 m/s. BAMS91(10), 2010.
AOSC 620Formation and Growth of Snow and Ice(Cold Cloud Microphysics)(Rogers and Yau Chapt. 9; Wallace and Hobbs, Chapt. 6)Russell Dickerson
“Now, if you haven't heard this, the ice at the North Pole, arctic ice, is at a record amount this early in the post-summer season.”
AOSC 620 Formation and Growth of Ice Crystalshttp://arctic.atmos.uiuc.edu/cryosphere/multiyear.ice.quikscat.mov
March 2, 2009
Getty Images / Win McNamee
Air pollution aerosols inhibit precipitation from relative thin clouds associated with gentle, warm rain but invigorate deep, icy clouds related to heavy rain lightning, and severe weather. ARM site in Oklahoma; Feng Niu (2010)
Impact of aerosols on tropical clouds. Precipitation rate (left) and corresponding cloud top temperature (right) as functions of AI for mixed-phase (blue dots) and liquid clouds (red dots) over ocean. Please note only clouds with the precipitation rate higher that 1 mm/h are included here. The far right axis is oC is for liquid clouds. From Feng Niu, 2010.
Goal: To shed light on the origin of the myriad of sizes and shapes of ice and snow.
OMolecular Structure of Ice
X-Ray and neutron diffraction experiments have shown the basic crystal structure of ice at atmospheric temperatures to consist of six oxygen atoms arranged in a hexagon. Each oxygen atom is bonded to two hydrogen atoms and (if you count H-bonding) each hydrogen is bonded to two oxygen atoms.
Ice in the hexagonal crystalline structure.http://www.its.caltech.edu/~atomic/snowcrystals/class/snowtypes4.jpg
Generally considered to be of two types
1. Deposition - transformation from vapor to solid
(the reverse is sublimation) Note that homogeneous deposition does not occur in the atmosphere.
2. Freezing - transformation from liquid to solid. Includes riming, the freezing of supercooled water droplets.
Hhttp://www.its.caltech.edu/~atomic/snowcrystals/class/snowtypes4.jpg2Ol ↔ H2Os
DG = DH –T Df = 0 at 273 K
DH = – 6008 J/mole (334 J/g)
Df = DH/T = 334/273 = – 1.22 J/gK (22.0 J/moleK)
As the temperature drops, the free energy becomes more negative.
Liquid cloud water at temperatures below –40°C is rare, but supercooled water is common, and a hazard to aviation.
Bottom line: Homogeneous nucleation doesn’t happen in real clouds.
The relative importance of the different modes has not
been established. It is difficult to distinguish between
deposition and freezing mechanisms. Usually refer to
the process as ice nucleation and the nuclei as ice nuclei.
Theory not yet able to explain which is most important but, the most common natural nuclei appear to be surface clays such as kaolinite. However, it has been discovered that bacteria in decaying plant leaf material can be effective nuclei, but its importance has not yet been established. (Russ Schnell & Gabor Vali)
Silver iodide (AgI) in the hexagonal crystalline structure.http://www.its.caltech.edu/~atomic/snowcrystals/class/snowtypes4.jpg
Solubility is low ~3 × 10−7 g/100mL, at 20 °C.
[Bernard Vonnegut, the older brother of the late novelist Kurt, uncovered silver iodide's weather-modifying properties as a researcher for General Electric in 1946. He later taught atmospheric science at the State University of New York at Albany before passing away in 1997. See Cat’s Cradle by K. Vonnegut]
Ice in the hexagonal crystalline structure.
Acids can replace nutrient cations with H+ for efficient nucleation, but in soils, acids reduce fertility.
Typical concentration is one nucleus per liter of air at a temperature of -20°C, increasing by a factor of ten for each additional 4°C of cooling. However, the count on any given day may be greater or less than the typical values by an order of magnitude!
Taking 104 cm-3 as the typical concentration of atmospheric aerosols, one nucleus per liter is only one aerosol particle in 107! That is, ice forming nuclei are a very rare component of atmospheric aerosols.
The concentration of active ice nuclei is a strong function of temperature.
ln(N) = a(T1 – T)
Where N is the number of ice nuclei, 0.3 < a <0.8, and T1 is the temp for one active ice nucleus per liter.
S (or –DT)
Thin film of transparent supersaturation.ice on outside
Drop + nucleusIf Nuclei Are So Rare, Why Are There So Many Crystals?
Once freezing of supercooled droplets starts, it progresses rapidly through a cloud.
The entire shell may explode to produce hundreds of splinters, each of which can act as a freezing nucleus
As interior freezes and expands
the outer shell may rupture through
which a jet of water emerges and
freezes to form a spike
Also, collisions between crystals
The flux of water vapor to the crystal by diffusion occurs in the direction normal to the surfaces of constant vapor density. Therefore, near a sharp point vapor diffuses toward the point from all directions. Ice may accumulate more rapidly there than on flat surfaces.
where Tc and T¥ are the temperatures of the crystal and environment (¥), respectively, K is the thermal conductivity of air, and C is the crystal shape factor.
Sphere C = r supersaturation.
Prolate spheroid of majorand minor semi-axes a and bShape Factor
The shape factor is nothing but the capacitance of an object. It depends on the geometrical shape of the crystal. It has units of length. Examples:
Note that supersaturation.Crystal Growth Rate Estimate
Following the procedure used for a water droplet (S is the saturation w.r.t. liquid water) we obtain:
Supersaturation wrt ice (Si) grows linearly as cloud temps drop below 273 K.
At T = -15°C and supersaturation.for S = 1.001Comparison of Droplet and Crystal Growth
For a liquid water droplet of radius r
For an ice crystal
R&Y Figure 9.4
Absolute value of es – ei peaks ~ – 12oC, but relative difference grows at lowest temps.
From Eq. 9.4 we see that the ice growth rate due to diffusion varies inversely with pressure and reaches a max near – 15oC at tropospheric pressures.
Why so many forms and shapes of ice?
A molecular kinetic approach is required to explain different habits/shapes.
Definitions (following Rogers and Yau, 1989; Glossary of Meteorology, 2000)
Accretion is the capture of supercooled droplets by an ice-phase precipitation particle. If the droplets freeze immediately on contact, this forms a rimed crystal or graupel. Slow freezing creates a denser structure; e.g., hail (dia. hail > 5 mm).
Coalescence is the capture of small cloud droplets by larger cloud drops.
Agglomeration is the collection of smaller ice particles.
Aggregation is the clumping together of ice crystals to form snowflakes
Accretional growth diffusion varies inversely with pressure and reaches a max near – 15
Aggregational growthGrowth by Accretion - cont.,or how do we get rain and snow?
The derivation of an equation for the continuous growth of ice crystals by capture of other crystals or cloud droplets would follow the same procedures as for liquid drops. Complications arise due to difficulties in prescribing the dependence of crystal fall speeds and their collection efficiencies.
Snowflake sizes indicate that significant aggregation occurs only for T > -10°C.
E – collection Efficiency; M condensed water mass (R&Y use m); R – radius; V – fall speed.
Fig. 9.7 from Rogers and Yau, 1989
Droplet collision - coalescence
crystal - diffusional
Stopping By Woods On A Snowy Evening diffusion varies inversely with pressure and reaches a max near – 15
Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.
My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.
He gives his harness bells a shake
To ask if there is some mistake.
The only other sound's the sweep
Of easy wind and downy flake.
The woods are lovely, dark and deep.
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.