on non-inductive charging, Williams et al. (1991) and Baker and Dash

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Precipitation Based
Air Motion Based (Convective Charging)
Williams, Scientific American
22-
1
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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2
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
22-
3
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.
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4
Williams, Scientific American
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 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?
specific heat of water
Heat balance is:
HEAT
CONDUCTION
dm
dm
TERM
Ls
dt
) deposition + (L f - cDT ¢ )
dt
)accretion = 4p cf v,h ka DT
T   Ts  To
T  Ts  Ta
Ts= particle surface temp
Some of the latent heat
released heats the surface
of the particle
To= temp of accreted water
Ts  To
Ta= ambient temperature
To  Ta
A good approximation
21-
7
Let
dm
) deposition  4 Cf v Dv  V ,  V ,r 
dt
dm
) accretion  AEcVWL  GWL
dt
Particle x-sec area
Combining above equations,
fv ventilation term for vapor
deposition
T  TS
Density of vapor at surface
of particle
é DT ¢
ù
4p Cfu Dv ê K a
- Ls rV ,¥ - rV ,r ú
D
ë
V
û
WL =
G L f - cDT ¢
(
)
(
The value of WL at which point deposition ceases is,
WL ,crit
Where
V ,
 V ,r 
f v  f v ,h
T  is the temperature increment above ambient at which V ,  V ,r
V ,
TS
4 f vCK a T 

G  L f  cT  

)
is assumed to be
V , s
is slightly greater than
Ta
(saturated with respect to water)
21-
T ~ 2 C or less
8
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
21-
9
Wet growth
Williams et al. (1991)
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;
dm
) dry   r 2V (r )Wl Ec
dt
21-
11
WET GROWTH
Heat to be dissipated to environment
dq
dm
)1 
) wg  L f  cw To  T  
dt
dt
To  surface temperature 273°K
T  ambient temperature
Rate that heat is dissipated, (to environment)
Evaporative cooling
dq
) 2  4 r  K To  T  Fh  Le Dv  V ,r  V ,  Fv 
dt
Heat conduction
Then
dq
dq
dm
)1  ) 2  yields
) wg
dt
dt
dt
4 r  K To  T  Fh  Le Dv  V ,r  V ,  Fv 
dm
) wg 
dt
L f  cw (To  T )
With
dm
dm
) wg 
) dry
dt
dt
Yields critical liquid water content.
dm
  r 2VwL Ec
dt
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12
Conduction
Therefore,
EcWl 
Evaporation
K To  T  Fh  Le Dv  V ,r  V ,  Fv
rV f ( r )  L f  cw To  T   / 4
21-
13
(Young 1993)
21-
14
‘Rough Hailstones’
More efficient heat
conduction to environment
(Pruppacher & Klett 1978)
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15
(Young 1993)
Schumann-Ludlam
Limit
21-
16
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 SchumannLudlam 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.
21-
17
Thermoelectric effect
Electrical Double or Faraday layer
LOW
HIGH
How do we explain sign of charge transfer for the cases of deposition
and sublimation for the rimer?
Baker and Dash (1994)
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.
G = ms Ns + mQLL NQLL + mv Nv + As sv (h)
m __ represents __ chemical __ potential
N __ represents __ number __ concentration
A __ is __ the __ area __ of __ the __ ice __ vapor __int erface
s __ is __ the __int erfacial __ energy
s sv (h) = s lv + s ls ___ as __ h ® ¥
s sv (h) = s sv ___ as __ h ® 0
N QLL = ?????
Screening layer; Baker and
Dash (1989)
Vapor
--------------------++++++++++++++++++++++
----------------------
QLL
Solid
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. (μQLLNQLL)
Faraday layer, positive
charge points into vapor
and negative charge points
into the solid; orientation of
water dipole moment
So what processes contribute to QLL thickness?
Particles growing by deposition will have a thicker QLL compared to particles
undergoing sublimation.
Recall for deposition
dm / dt = 4p R2 Dv d rv / dr
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.
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