Formation and Growth of Ice Crystals by dxizRr


									                       Ideas for Term Paper

   • Biosphere-Atmosphere interactions: N fixers in
     Leaf-cutter ants
   • Oceans unsaturated wrt CaCO3, plankton
     skeletons may dissolve.
   • Paleoatmospheres – S isotopes and ore deposits
   All found in Science 20 Nov. 2009.
1. What are the adverse impacts on the environ or what is the benefit to forecasting
weather or climate.

2. What is the chemistry or physics behind the impact. For example sources and sinks
of a trace species or parameterization of a weather process such as graupel or
convective clouds. Is there a quantitative relationship that is useful for future studies?

3. Is the paper well written? good or bad? right or wrong? consistent or not? Are there
mistakes or steps left out?

4. Summary of what you learned from the paper,
      Some more paper on clouds and ice.

•   Herman J. R., G. Labow, N. C. Hsu, D. Larko (2009), Changes in cloud and
    aerosol cover (1980–2006) from reflectivity time series using SeaWiFS, N7-TOMS,
    EP-TOMS, SBUV-2, and OMI radiance data, J. Geophys. Res., 114, D01201,

•   Weigelt A., M. Hermann, P. F. J. van Velthoven, C. A. M. Brenninkmeijer, G.
    Schlaf, A. Zahn, A. Wiedensohler (2009), Influence of clouds on aerosol particle
    number concentrations in the upper troposphere, J. Geophys. Res., 114, D01204,
    doi:10.1029/2008JD009805. Waliser D., et al. (2009),
•   Cloud ice: A climate model challenge with signs and expectations of progress, J.
    Geophys. Res., 114, D00A21, doi:10.1029/2008JD010015.
•   20 July 2009 | Nature | doi:10.1038/news.2009.705, How raindrops fall
•   Exploding drops produce miniature showers. By Fiona Tomkinson concerning
    Villermaux, E. & Bossa, B. Nature Phys. doi:10.1038/NPHYS1340 (2009).

             AOSC 620
Formation and Growth of Snow and Ice
             (Cold Cloud Microphysics)
   (Rogers and Yau Chapt. 9; Wallace and Hobbs, Chapt. 6)
                Russell Dickerson, 2009




                            Millions of km2
                                              Arctic Ice Extent, Summer


















  AOSC 620 Formation and Growth of Ice Crysta
                  Lecture 23
     •Direct observations show that supercooled liquid
     cloud water is common at temperatures well below
     0°C (i.e., -20°C)
     •Small droplets of pure H2O freeze only below
     temperatures of -40°C, the spontaneous freezing level.
     •At higher temperatures, pure water droplets freeze
     only if injected with tiny foreign particles called ice
     •The equilibrium vapor pressure over ice is lower
     than that over liquid water.

March 2, 2009
Getty Images / Win McNamee
Water favors ice.

       Common Ice Crystal Shapes

Hexagonal Plates       Hexagonal Prisms

Stellar Crystal/           Ice needles
Goal: To shed light on the origin of the myriad of
sizes and shapes of ice and snow.                    7

          Molecular 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.
                     O H O

              O               O

                  O   H   O
Ice in the hexagonal
crystalline structure.   10
                  Ice Formation

       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.

   Qualitative Description of Freezing
• Consider a volume of air with T < 0°C in which
  water droplets are suspended.
• The H2O molecules in a drop at a given instant
  may come into temporary alignment similar to that
  of an ice crystal. This lower entropy increases the
  free energy of the transition.
• Such molecular aggregates may grow but they may
  also be destroyed by random molecular motions.
• If an aggregate happens to grow to such a size that
  it is no longer affected by these thermal agitations,
  the entire droplet quickly freezes. The probability
  of growth of an aggregate to this critical size
  increases as T decreases. (Fleagle and Bussinger)
                   H 2 Ol ↔ H 2 Os
            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.
   Qualitative Description of Freezing

• Add a foreign particle to droplet
• The particle makes the initial growth more
  probable by attracting a surface layer of H 2O
  molecules on which the ice crystal lattice can form
  more readily than in the interior of the liquid.
• Freezing of a droplet requires that only one
  aggregate reach critical size.

          Ice Nucleation Mechanisms

• Heterogeneous Deposition - vapor is
  transformed to ice on a nucleus.
• Condensation Followed by Freezing - droplet
  forms on a nuclei which then freezes.
• Contact - nuclei makes contact with a droplet
  which then freezes (airplane wing).
• Immersion- nuclei becomes immersed in a droplet
  which then freezes about the nuclei.

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.
Ice Forming

    Important Features of Ice Nuclei

• Temperature
• Lattice structure - many of the most active
  natural nuclei have crystal structures similar to
• Molecular binding -
• Low interfacial energy
  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
Ice in the hexagonal     hexagonal crystalline
crystalline structure.   structure.
                         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]
 Kaolinite (Al2Si2O5(OH)4) Clay Particles

                           Ca2+ Mg2+ K+

                       Acids can replace nutrient
                       cations with H+ for
Electron micrograph.   efficient nucleation, but in
                       soils, acids reduce fertility.
           Ice Nuclei Concentration

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
                      ln(N) = a(T1 – T)
Where N is then umber of ice nuclei, 0.3 < a <0.8, and T 1 is
the temp for one active ice nucleus per liter.

Number of active ice nuclei as a
 function of supersaturation.

  N (m-3)

             S (or –DT)

      If Nuclei Are So Rare, Why Are There
                So Many Crystals?

  Once freezing of supercooled droplets starts, it
  progresses rapidly through a cloud.

Drop + nucleus             Thin film of transparent
                           ice on outside
                                           The entire shell
As interior freezes and expands            may explode to
the outer shell may rupture through        produce hundreds of
which a jet of water emerges and           splinters, each of
freezes to form a spike                    which can act as a
                                           freezing nucleus
   Also,   collisions between crystals                           22
     Diffusional Growth of Ice Crystals

Basic Assumptions
• The surface of the crystal has uniform temperature;
  therefore, it has uniform vapor pressure.
• The vapor pressure at an infinite distance is
  assumed uniform as is the temperature.
• The vapor pressure and vapor density in the
  neighborhood of the crystal may be represented by
  surfaces that follow the contour of the crystal.
• Beyond a certain neighborhood of the crystal these
  surfaces approach a spherical shape.

                   Vapor Diffusion

                                             Contours of
                                             vapor density

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.
       Ice Crystal Growth Equations
            (similar to eq’s for liquid water)

                    = 4CD(  v   vc )  DiffusionEq.
           Ls       = 4CK (Tc  T )  Conduction Eq.
                                    Ls  1 1  
                esi = esi (T ) exp      CC Eq.
                                   R T T 
                                    v       c 

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.
                                Shape Factor
                                Skip for 2009 instead read:
Tao, W.-K., et al., 2009: Multi-scale modeling system: Development, applications and
critical issues, Bull. Amer. Meteor. Soc. 90, 515-534.

This one might be good too: Zeng, X., et al., 2009: The indirect effect of ice
nuclei on atmospheric radiation. J. Atmos. Sci., 66, 41-61.

    The shape factor is nothing but the capacitance of a subject. It depends upon
    the geometrical shape of the crystal. It has units of length. Examples:

            Sphere C = r               Circular disk           C=

 Prolate spheroid of major                                                a 2  b2
                                                    C =
                                                              ln  a      a 2  b 2  b
 and minor semi-axes a and b
                                                                                      
              Crystal Growth Rate Estimate
                       e     e
        Let       Si =      =
                       esi   ei
                  Si denotes saturation ratio
          Following the procedure used for a water
          droplet (S is the saturation w.r.t. liquid
          water) we obtain:
                    dM            ( Si  1)         
                        =                     2
                                                  = M 'ice
                     dt       RvT        L
                                             s
                            4DCesi RvT 4KC

                          e   es        es 
     Note that      Si =              = S      
                          es   esi      esi 
Supersaturation wrt ice (S i) grows linearly as cloud temps drop below 273 K.
Comparison of Droplet and Crystal Growth

 For a liquid water droplet of radius r

     dM      4r ( S  1)
         =              2
                          = M 'w
      dt   RvT       Lv
           Des RvT KC2
                                          At T = -15°C and
                                          for S = 1.001

 For an ice crystal                          M 'ice
                                                     120
                                             M 'w         r
   dM      4C ( Si  1)
       =              2
                         = M 'ice
    dt   RvT       Ls
                                         R&Y Figure 9.4
         Desi RvT2 K
                     Saturation Vapor Pressure Relative
                          to Ice and Liquid Water

             7                                                                               0.3
             6      Saturation Vapor Pressures
                     at Different Temperatures

                                                                      e (T) - e si(T) (mb)
e (T) (mb)

                                e (T)
             3                   s
                                e si (T)

             2                                                                                                         e s (T) - e si (T)

             0                                                                                0
              -40   -35   -30        -25   -20   -15   -10   -5   0                            -40   -35   -30   -25     -20   -15    -10   -5    0
                            Temperature (°C)                                                                 Temperature (°C)

                    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?

                                            Growth of
                                            shapes is

A molecular kinetic approach is required to explain
different habits/shapes.                                  31
              Growth by Accretion
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
Aggregation is the clumping together of ice crystals to
form snowflakes
           Growth 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.

Accretional growth     = Ew l R 2 V (Rogers and Yau, eq. 9.8)
Aggregational growth      = Ew i R 2 (V  v) (eq. 9.9)

   E – collection Efficiency; M condensed water mass
   (R&Y use m); R – radius; V – fall speed.
Crystal Fall Speeds

              Fig. 9.7 from Rogers and Yau, 1989

      Snowflake Growth - Qualitative

• Must have an appropriate number of ice nuclei to
  initiate freezing - 0.1 to 1 per liter at -20°C.
• Crystals form around nuclei and grow by diffusion.
• A few crystals grow faster and larger than their
  neighbors by either enhanced diffusion or by
  chance collisions with other crystals or droplets.
• These crystals fall faster than their neighbors and
  grow by diffusion and by collisions with other
  crystals or cloud droplets until they reach a size
  where they can fall against an updraft and reach
  the ground. A snowflake of 1 cm diameter requires
  a cloud depth of about 1500 m.

Both coalescence and aggregation can happen in a Cb.
       Times Required for Growth is different.

        Droplet collision - coalescence

               crystal - diffusional

     Precipitation Growth - Summary

•Condensation-diffusion is more effective for ice clouds
than for water clouds.
•In warm clouds, coalescence is the major scheme for
precipitation to occur.
•In cold clouds, both diffusion and aggregation are
•Ice nuclei remain mysterious.
•Loss is glaciers and sea ice is a major environmental

Stopping By Woods On A Snowy Evening
                                 Robert Frost
Whose woods these are I think I know.   He gives his harness bells a shake
His house is in the village though;     To ask if there is some mistake.
He will not see me stopping here        The only other sound's the sweep
To watch his woods fill up with snow.   Of easy wind and downy flake.

My little horse must think it queer     The woods are lovely, dark and deep.
To stop without a farmhouse near        But I have promises to keep,
Between the woods and frozen lake       And miles to go before I sleep,
The darkest evening of the year.        And miles to go before I sleep.


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