Review for Exam 2 Fall 2011 Topics on exam: Class Lectures: Ice phase processes: homogeneous and heterogeneous nucleation, ice particle growth processes Class Lectures: Lecture 19 through Lecture 26

Lecture 24: 1. This problem deals with graupel growth. Write a continuous-collection equation for the time rate of change of the mass of a graupel particle due to riming. Define / explain each term in your equation. Show how to set up the equation to solve for the radius of the particle as a function of time (analytically or numerically). Lecture 24:

(graupel problem, continued) b. For the more general case, the graupel particle could also gain (or lose) mass by other process(es) as it moves through the atmosphere. What other process(es) might be occurring (explain)? Tg Water freezes instantly  vapor pressure over graupel = pice(Tg) Supercooled drops Vapor pressure = pwater(Tamb)

(graupel problem, continued) For the graupel particle in part (b), what terms would exist in the energy budget? (You can write these in words; include signs.) d. Write an equation for part (c); define / explain terms. Water freezes instantly  vapor pressure over graupel = pice(Tg) Tg Supercooled drops Vapor pressure = pwater(Tamb)

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 ev(surface)=ev(environment). At liquid water contents greater than the critical value, the particle actually falls into a state where it begins to sublime. What is WL, the critical liquid water content at which point deposition ceases? Heat balance is: specific heat of water HEAT CONDUCTION TERM Ts= particle surface temp To= temp of accreted water Ta= ambient temperature Some of the latent heat released heats the surface of the particle A good approximation fv.h is a ventilation coefficient (not discussed here)

Let fv ventilation term for vapor deposition Density of vapor at surface of particle Particle x-sec area Combining above equations, The value of WL 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

Lecture 21 Give at least 2 examples of particle types known to serve as ice nuclei. Are they natural or anthropogenically derived? Silver iodide Snomax Certain dusts What requirements must a particle satisfy to serve as an ice nucleus? Give a brief explanation of how / why each requirement arises.

3. Show how to write the change in Gibbs free energy for the homogeneous freezing process (that is, a germ of ice forming in a solution particle). Define / explain each term. (You do not need to solve for the critical energy barrier, but indicate how you would go about that.) Lecture 19

Not asked, but of note:

4. Use the information below (Figure 1, Table 1) to answer the following questions. An ice crystal is in an environment at -20 C and ambient water vapor pressure of 1 mbar. Is it growing or evaporating? Justify your answer with (brief) calculations. Lecture 19

If the ice crystal in (a) were instead a liquid drop of radius 20 micron, would it be growing or evaporating? Calculate the rate of change of its radius (assuming only condensation / evaporation are occurring, and neglecting latent heat effects) and briefly discuss implications. Lecture 22 “C” has units of length. Note C = r for spherical geometry, as expected.

A cloud forms at 5 C and then is lifted and cooled to -20 C A cloud forms at 5 C and then is lifted and cooled to -20 C. What supersaturations with respect to water, and with respect to ice, are expected at this endpoint? Justify your reasoning.

5. The sketch below (Figure 2) shows the collision efficiency for thin oblate spheroid ice crystals (plates) collecting supercooled, spherical liquid droplets. Explain why the curves have the shapes that they do, including discussion of the crystal and drop sizes involved. If a similar plot were constructed for dendritic crystals collecting droplets, explain which plot features might be expected to change, and how. Lecture 24: Observations indicate that there is indeed a minimum size below which riming does not occur (for given crystal type) 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).

6. a) Describe and discuss the conditions when ice nuclei concentrations are not representative of observed ice crystal concentrations. Lecture 22:

b) Critique, describe and discuss a proposed mechanism for ice multiplication.

(continued) Enhanced ice nucleation in regions of spuriously high supersaturations in the presence of high number concentrations of supercooled raindrops or in a turbulent cloud environment It is generally agreed that, in the absence of precipitation, peak supersaturations in convective clouds are below ~1% But if precipitation drops accrete a large proportion of cloud drops, this may overly deplete the sink for generated supersaturation in rapidly rising convective towers  supersaturation rises (up to 5 – 10% ?) This could enhance ice nucleation (if occurring at the right Ts) Similar mechanism may occur in turbulent regions May not be able to explain large enhancements on its own, but could initiate enough ice formation to kick off ice multiplication processes Ice particle generation during evaporation of ice particles Oraltay and Hallett (1989) and Dong et al. (1994) observed as many as 30 pieces per crystal formed when evaporating at RH < 70% Fits with observed enhancements in evaporating cloud regions and in heavily mixed regions Do pieces survive long enough in entrainment regions to serve as embryos for further crystal growth?