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

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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

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Basic premise is that large andsmall ice particles along withsupercooled droplets, collide andrebound in a cloud, with chargeof opposite sign being retained on the graupel and small iceparticles, respectively.

Graupel charges negatively under certain conditions andpositively under otherconditions.

Williams, Scientific American 422-

Looked at surface state of graupel, between deposition and sublimation. From lots of earlier papers on NIC, it was concluded that “the fastest growing iceparticle takes on positive charge”. Growth condition of the particle’s surface statedetermines the sign of charge on the particle. Williams et al. examined the surfacestate 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 ev(surface)=ev(enviornment). At liquid water contents greater than the critical value, the particle actually falls into a sublimational state. What is WL, the critical liquid water content at which point deposition ceases?

Heat balance is: specific heat of water

HEAT CONDUCTION

TERM

s oT T T Ts= particle surface temp

To= temp of accreted water

s oT T

s aT T T

Ta= ambient temperature

o aT T

A good approximation

Some of the latent heatreleased heats the surfaceof the particle

721-

Let

, ,) 4deposition v v V V r

dmCf D

dt

)accretion c L L

dmAE VW GW

dt ST T

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,

,v v hf f

, ,V V r

,

4 v aL crit

f

f CK TW

G L c T

Where is the temperature increment above ambient at which T

,V

ST

, ,V V r

is assumed to be (saturated with respect to water)

is slightly greater than

,V s

aT ~ 2T C or less 821-

Critical liquid water contents

(Houghton 1985)

Characteristic ofconvective cloudsonly

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.

921-

Takahashi used a fixed 1.5 mm radius probeto 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;

2) ( )dry l c

dmr V r W E

dt

1121-

WET GROWTH

Heat to be dissipated to environment

1) )wg f w o

dq dmL c T T

dt dt oT surface temperature 273°K

T ambient temperature

Rate that heat is dissipated, (to environment)

2 , ,) 4 o h e v V r V v

dqr K T T F L D F

dt

1 2) ) )wgdq dq dm

yieldsdt dt dt

, ,4)

( )

o h e v V r V v

wgf w o

r K T T F L D Fdm

dt L c T T

) )wg dry

dm dm

dt dt

Heat conduction

Evaporative cooling

Then

With Yields critical liquid water content.

2L c

dmr Vw E

dt 1221-

Therefore,

, ,

( ) / 4o h e v V r V v

c l

f f w o

K T T F L D FE W

rV r L c T T

Conduction Evaporation

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(Young 1993)

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‘Rough Hailstones’

More efficient heat conduction to environment(Pruppacher & Klett 1978)

1521-

(Young 1993)

Schumann-LudlamLimit

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Spongy ice ice-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.

1721-

LOW HIGH

Electrical Double or Faraday layerThermoelectric 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, positivecharge points into vaporand negative charge pointsinto the solid; orientation ofwater dipole moment

- - - - - - - - - - - - - - - - - - - - -

Screening layer; Baker andDash (1989)

The key to this theory is that twoparticles, with different QLL thicknesses collide, and during the contact time (micro to milliseconds) mass is transferredfrom the particle with the thicker QLL to theparticle with the thinner QLL. Mass is transferredto attempt to equilibrate the Gibbs free energiesof the contacting QLL’s. (μQLLNQLL)

So what processes contribute to QLL thickness?

Particles growing by deposition will have a thicker QLL compared to particlesundergoing sublimation.

Recall for deposition

Consider two particles, both growing by deposition. The larger particle will begrowing faster and therefore have a thicker QLL. This particle may also be growing byriming, 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 higherliquid water content environment compared to the example above, will now be in astate 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 chargeflows to the larger particle with the rebounding smaller particle carrying net positivecharge. So charge transfer is driven by mass transfer, owing to equalize the chemicalpotentials between the contacting QLL’s.