Precipitation Based Air Motion Based (Convective Charging) Williams, Scientific American 122-

Convective Charging Theory - Normal fair-weather E field establishes + charge concentration in lower troposphere (via corona processes), which when carried by updrafts to the top of storms, attracts negative free ions, which are then carried down by downdrafts on cloud edges -Charge is separated by the up- and downdrafts -Found by Chiu and Klett (1976) that this method is unlikely to produce sufficient cloud charging 2 22-

Noninductive charging (Precipitation-based charging Consistent with lots of observational data that suggest strong E fields and lightning only occur in clouds that have developed a robust mixed-phase precipitation process 322-

Basic premise is that large and small ice particles along with supercooled droplets, collide and rebound in a cloud, with charge of opposite sign being retained on the graupel and small ice particles, respectively. Graupel charges negatively under certain conditions and positively under other conditions. Williams, Scientific American 4 22-

Looked at surface state of graupel, between deposition and sublimation. From lots of earlier papers on NIC, it was concluded that “the fastest growing ice particle takes on positive charge”. Growth condition of the particle’s surface state determines the sign of charge on the particle. Williams et al. examined the surface state of graupel in context of Takahashi’s results.

Motivation Reynolds et al. (1957) earliest paper on NIC Takahashi (1978) and others expanded on this early study and quantified amount of charge separation as a function of T and LWC, plus sign of charge on rimer Williams et al. wanted to examine the surface state of the graupel particle in the same parameter space shown by Takahashi Relevant physics are: Sublimation vs. deposition Wet vs. dry growth

HEAT BALANCE OF 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 the particle 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 (enviornment). At liquid water contents greater than the critical value, the particle actually falls into a sublimational state. 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 7 21-

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 8 21-

Critical liquid water contents (Houghton 1985) Characteristic of convective clouds only Hence 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 Takahashi used a fixed 1.5 mm radius probe to simulate graupel

Williams et al. (1991) Wet growth

At large riming rates, latent heat release essentially outpaces heat conduction, and the surface of the ice particle warms to 0°C, preventing the liquid water accreted from freezing. Wet growth can then occur. Schumann-Ludlam Limit conditions that define the growth of an ice particle which freezes all the drops it collects and where surface temperature is 0°C. –Liquid surface exists beyond SL limit. water that cannot be frozen may either be incorporated into a ice/water mix (spongy ice) or it may be shed. -Hailstone growth rate For dry growth;

WET GROWTH Heat to be dissipated to environment surface temperature 273°K ambient temperature Rate that heat is dissipated, (to environment) Heat conduction Evaporative cooling Then With Yields critical liquid water content

Therefore, Conduction Evaporation

(Young 1993)

‘Rough Hailstones’ More efficient heat conduction to environment (Pruppacher & Klett 1978)

(Young 1993) Schumann-Ludlam Limit

Spongy iceice-water mixture on surface of hailstone. Most liquid water is accumulated around equator of particle. Johnson and Rasmussen (1992)- argued that once a hail particle reached Schumann- Ludlam limit, its surface will become smoother, thereby reducing drag and increasing fallspeed. Therefore the hailstone will stay in the wet growth regime at lower LWC’s compared to those required to get it into wet growth to begin with. Lower ventilation rates too----heat is dissipated less effectively

LOWHIGH Electrical Double or Faraday layer Thermoelectric effect

Baker and Dash (1994) How do we explain sign of charge transfer for the cases of deposition and sublimation for the rimer?

NIC studies summarized as follows.. Significant charge transfer (10’s of fC per collision) occurs during rebounding collisions between ice crystals and graupel when supercooled droplets are present in the cloud. Significant charge transfer occurs only when both particles are “growing” from the vapor. The charge transferred to the riming surface tends to be positive at higher temperatures and higher liquid water contents and negative at lower temperatures and moderate liquid water contents.

Gibbs Free Energy Theory of charge separation and sign of charge transfer rests on Gibbs Free energy Consider a system with ice, vapor and a quasi-liquid layer (QLL), a thin layer 10’s of molecules that represents a transition between the vapor and solid phases.

Solid QLL Vapor Faraday layer, positive charge points into vapor and negative charge points into the solid; orientation of water dipole moment Screening layer; Baker and Dash (1989) The key to this theory is that two particles, with different QLL thicknesses collide, and during the contact time (micro to milliseconds) mass is transferred from the particle with the thicker QLL to the particle with the thinner QLL. Mass is transferred to attempt to equilibrate the Gibbs free energies of the contacting QLL’s. (μ QLL N QLL )

So what processes contribute to QLL thickness? Particles growing by deposition will have a thicker QLL compared to particles undergoing sublimation. Recall for deposition Consider two particles, both growing by deposition. The larger particle will be growing faster and therefore have a thicker QLL. This particle may also be growing by riming, at low liquid water contents such that its surface is still in a depositional state. Upon contact, mass will flow from the large particle to the small particle. The mass transfer also carries net negative charge the small particle (ice crystal). Consider again two dissimilar sized particles. The larger particle, growing in a higher liquid water content environment compared to the example above, will now be in a state of sublimation. Hence this particle will have a thinner QLL compared to the smaller particle which is still growing by deposition (its not collecting as much SLW as the bigger particle owing to its smaller size). Therefore upon contact net negative charge flows to the larger particle with the rebounding smaller particle carrying net positive charge. So charge transfer is driven by mass transfer, owing to equalize the chemical potentials between the contacting QLL’s.