1. The ice phase in clouds We began to look at how ice crystals, once formed, grow in the atmosphere Growth from vapor phase Analogies to drop growth, but many characteristics not really governed by the same diffusion-limited process Crystal habits are important and depend on temperature and supersaturation Important to remember how supersaturation with respect to ice varies with temperature Peak is near -12 C Max growth rates are at slightly lower T’s Vapor deposition can be an efficient means of generating precipitation-sized particles Now consider remaining 2 mechanisms, Growth by aggregation Growth by accretion of supercooled water (riming) L&V: Ch 9.2.2; 9.4 -9.6; 12.4; Cotton notes: Ch. 10

2. (Lamb & Verlinde) Progression from nucleated particles to precipitation-sized particles

3. GROWTH BY AGGREGATION Most snowfall situations consist of aggregates of individual ice crystals; aggregates are also found in the upper parts of many summertime convective clouds and cirriform clouds. These aggregates are produced by coalescence, or collision & sticking of individual ice crystals. ICE CRYSTALa pristine, individual ice particle AGGREGATE (snowflake) a collection of many (10’s to 100’s) ice crystals Aggregation is especially effective at relatively high temperatures (within a few degrees of 0 ˚C); dendrites are most common and result in the large sizes between - 15 and -12 ˚C; aggregates of needles form at ~ -5 ˚C

4. This figure indicates the expected trend that the number of component crystals increases with increasing snowflake diameter. Pruppacher & Klett (1978) <1.5mm1.5<D<2.5 >3.5mm average diameter of component crystals # of component crystals Similar to figure from L & V on previous slide: Rapid increase in snowflake diameter with T Most aggregates consist of planar type crystals with dendritic features Aggregates of needles also observed Aggregates of simple plates and short columns are relatively rare

5. Aggregates of dendrites are the most common type of snowfall in mid- latitudes, so there is strong motivation to model this process well (included in all cloud / storm models as part of the cold-cloud microphysics) BUT: The problem of aggregation is complicated by the geometries and orientations of the falling ice crystals (need a spherical equivalent to use the simple equation given; also the mass-radius relationship depends on the densities). These quantities are needed to determine good estimates for the fall velocities and for the efficiencies of collection. We typically model the fall speeds of ice crystals as V(D) = a D b And also, crystals of the same mass can have different fall speeds due to geometry. This is quite different from the case of liquid drops, where there is small probability of drops with the same mass coalescing. Also, once they make contact, ice crystals do not always stick together. - The large sizes near 0 ˚C in the previous figure are thought to be caused by sintering – a surface process that occurs near melting points - The second peak near colder temperatures is likely caused by mechanical interlocking (arms of dendrites)

6. The initial phase of aggregation is stochastic; need equations for the increase in aggregate concentrations and for the decrease in pristine ice concentrations:

7. After the initial phase, when there is a population of aggregates falling through the population of smaller ice crystals, aggregation growth may be modeled using the continuous collection model: Where we have assumed fallspeed of smaller crystals “ice water” content of the cloud collection efficiency Further simplification is to invoke spherical geometry (same approach as for drops),  r 2 = cross-sectional area of aggregate Are collection kernels available, in order to compute E c ?

8. The problems with measuring and applying collection efficiencies are discussed in some detail in Prof. Cotton’s notes (CH. 10). In brief: Because snowflakes of a given mass can have a spectrum of sizes, shapes and fall speeds  particles of the same mass have a finite chance of collision (different from the case for spherical drops) Passarelli and Srivastava (1979) explored two contrasting models: (1) snowflakes of a specified mass were assumed spherical with a unique diameter, but spectrum of fall speeds (2) snowflakes spherical, but each assigned mass had a spectrum of bulk densities  spectrum of fall speeds and diameters Compared to the “standard” treatment, (1) produced an aggregation rate that was much smaller (~10% of standard), whereas (2) resulted in much larger aggregation rates. Wider spectrum  more rapid aggregation Finally, the concentrations of pristine ice crystals are not predicted well (+/- 3 orders of magnitude). This means that there is a 10 6 uncertainty in initial aggregation rates!

9. Collection efficiency increases with T Collection efficiency has secondary maximum near -12°C, dendritic growth. A pseudo-liquid film exists on the surface of ice particles which promotes “sticking” This is pronounced for T>-5° Sintering leads to the formation of an ice neck at temperatures above -20°C Sticking efficiency inhibited for Ice Neck Bridge COLLECTION (Pruppacher & Klett 1978) Some published data ….

10. Sintering Sintering is a process whereby two ice particles adhere to one another, even at temperatures well below freezing Based on premise that the surface of ice consists of liquid-like layer Liquid-like layer is most pronounced at temperatures > -20 C. Consistent with everyday observations: snowballs are hard to form when snow is well below 0 C; snowballs are easy to make when the temperature is closer to 0 C Sintering occurs when the two liquid like layers merge and freeze. Likened to a cold-welding process. The area of contact between the two particles grows rapidly with time. One theory of sintering relies on diffusion of water molecules across the ice surface towards the point of contact, growing a bridge of ice between the two particles

11. Lamb & Verlinde 2011 PLATE SECTOR PLATE DENDRITE STELLAR We see from this figure that crystals with more pronounced dendritic features exhibit smaller fall speeds relative to equal-size (same radius) disks / plates. Since a dendrite or stellar of radius r has less mass than a plate of the same radius, mg is smaller and terminal fall speed is lower. Drag on dendrite also reduces the fall speed. The loss of sensitivity to diameter at large diameters for dendrites is because the increasing drag balances the change in gravitational force. FALL SPEEDS for pristine crystals

12. Fallspeed of hexagonal plate decreases with diameter. Larger area (same mass) implies larger drag force. Columns behave in similar fashion. Fallspeed maximums for plates ~1 m s -1 Fallspeed maximums for columns ~50 cm s -1 Drag force decreases with height, associated with lower air density  Fallspeeds are higher at upper levels in cloud PLATESCOLUMNS

13. BULK DENSITIES for pristine crystals (needed to relate mass and “size”)

14. Snowflake fallspeeds for various aggregate types. (Young 1993) Leads to insensitivity to snowflake diameter AGGREGATES

16. Density of aggregates vs. aggregate diameters (Young 1993)

17. (Lamb & Verlinde) RIMING: Collection of supercooled liquid drops by crystals (also recall it is an important component of secondary ice formation)

18. Rimed plates Rimed column (Pruppacher & Klett 1978) Rimed sector plate

19. ~ several mm (Pruppacher & Klett 1978) CONICAL GRAUPEL LUMP GRAUPEL (“Hail” is larger than 5 mm)

21. GROWTH RATE BY RIMING In mixed phase clouds, ice particles can grow rapidly by riming, the collection of supercooled cloud droplets. Both aggregates and ice crystals can grow via riming. Mass deposited on the surface of the crystals is known as rime. Air bubbles become trapped in the ice mesh and lead to opaque ice. Heavily rimed particles are termed graupel. Consider continuous collection equation, Supercooled liquid water content Acceptable to treat r 1 =constant, so for example, a plate-like ice crystal of radius r 1 grows into a quasi- spherical graupel particle. Note: V 1 can also be expressed as function of m 1, particle mass.

22. 1) Cut-off to zero E for both large and small droplets Small droplets flow around plates Large droplets have similar fallspeeds, so collisions are rare 2) There is a minimum crystal size below which droplets can’t be collected. For hexagonal plates this minimum crystal size is ~150 µm. The ice crystals must grow by vapor deposition to this size before appreciable riming growth can occur! (Lamb & Verlinde) Riming Collision Efficiencies Calculations orient crystals for maximum drag

23. Size at which crystals effectively begin to collide “PLANAR” ICE CRYSTALS unrimed crystals rimed crystals PLATE SECTOR PLATE DENDRITES a)Observations indicate that there is indeed a minimum size below which riming does not occur (for given crystal type) b)Minimum size increases to larger crystal sizes for increasing dendritic features 500 µm dendrite falls more slowly than 500 µm plates So a larger dendrite is required, before dendrite can overtake droplets (fall speed effect). (Pruppacher & Klett 1978)

24. Summary of onset conditions for different crystal habits

25. HEAT BALANCE FOR GRAUPEL PARTICLES Consider a graupel particle growing by riming in a water saturated environment. Hence the possibility exists that the particle will also be growing by vapor deposition. Accreted droplets freeze on graupel particles and therefore release latent heat. This latent heat release effectively slows depositional growth. At some critical LWC, depositional growth will cease. At this point e v (surface)=e v (environment). At liquid water contents greater than the critical value, the particle actually falls into a state where it begins to sublime. What is W L, the critical liquid water content at which point deposition ceases? Heat balance is: specific heat of water HEAT CONDUCTION TERM T s = particle surface temp T o = temp of accreted water T a = ambient temperature A good approximation Some of the latent heat released heats the surface of the particle f v.h is a ventilation coefficient (not discussed here)

26. Let f v ventilation term for vapor deposition Density of vapor at surface of particle Particle x-sec area Combining above equations, The value of W L at which point deposition ceases is, Where is the temperature increment above ambient at which is assumed to be (saturated with respect to water) is slightly greater than or less

27. Critical liquid water contents As we will see later, the surface growth state of a graupel particle, whether it be in a depositional or sublimational state, controls the sign of electrical charge retained by the particle (in a non-inductive charging process) (Houghton 1985) Characteristic of convective clouds only Interestingly: a particle may actually be in a sublimational state with respect to vapor transfer while it is growing by collecting supercooled liquid water. Water freezes instantly when it is collected.

28. Formation of HAIL Associated with convective storm systems. Provides large supercooled liquid water contents to promote hail growth Provides strong updraft velocities, that suspend and carry hail aloft, promoting growth Diameters to >13cm Weight ~1kg! Embryo required to “kick-off” hail growth Growth regimes: Dry growth: low to moderate liquid water contents Wet growth: Alternating dry and wet growth regimes promotes hailstone layered structure Dry growth opaque ice Wet growth clear ice graupel frozen drop

29. (Young 1993)

30. DRY GROWTH WET GROWTH Latent heat is released due to freezing of water; this heat that is liberated warms the surface of the stone. At low to moderate LWC’s, this heat can be effectively dissipated to the surrounding air. Hence the stone remains below 0°C, and its surface is dry. This type of growth results in opaque ice since the rime contains quite a bit of air. At larger riming rates (higher LWC’s and/or larger hail stones) latent heat release will warm the stone to 0°C, hence preventing most of the liquid water from being frozen. In this case the surface of the stone becomes an ice-water mesh, promoting the term ‘spongy ice’. Even higher LWC’s promote a complete liquid surface, called wet growth. Clear ice develops as this liquid layer freezes. This liquid surface may be partially shed in the wake of the hailstone. The shed water produces drops that may then rapidly freeze and become new hail embryo sources.