Number and Area Size Distributions for Periods with Max Electric Field
Decay Times

Jim Dye

March 18, 2003

The cases shown below are examples to illustrate differences in the
number concentration and area size distributions for periods with both
short and long decay times for individual anvil cases.

June 13, 2000

A complex attached anvil that was investigated for \~3 hours

**Early period** -- the Citation was flying E-W back and forth across
the anvil which was streaming to the NE. In the CAPPI and MER plot below
the A/C flew from E to W from region with only anvil to region with
cells below and precip reaching the ground.

CAPPI 2104-2109

<http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_NEXRAD/hc/000613/hc_2104_2109_000613.gif>

MER 2100-2110

<http://box.mmm.ucar.edu/abfm/webpage/june2000/Mer/000613_NEXRAD/mer_2100_2110_000613.gif>

In the above MER plot note the large increase in particle concentrations
as the A/C flew from edge of the anvil towards higher reflectivities. A
more complete time series of the particle concentrations in different
size intervals is show below. Note that the number of particles in the
intervals 100 to 200 and 200 to 1000 microns increase more rapidly than
those \>1000 microns. \[These are plots are for 30 sec averages and the
size intervals are a little different than the time series plots using
10 sec averages. These use 100 to 200 microns rather than 100 to 400
microns used in the 10 sec average plots.\]

ts_NU_jun_13_2000_2100_2115.gif

By using the actual number of pixels occulted by individual particles in
the 2D and HVPS images we have calculated the area of particles in these
same size intervals.

ts_AR_jun_13_2000_2100_2115.gif

In this plot there is an increase in area of 2 orders of magnitude
(equivalent to variation in ETimeScale in John Willett's decay time
calculations) as the A/C flies from the edge of the anvil towards higher
reflectivities. Most of the area and also most of the increase in area
is in the size interval 200 to 1000 microns. The particles \>1 mm size
contribute some to the area, but proportionally not as much as those 200
to 1000 microns.

The individual number size distributions from 2100 to 2108 also show
gradual increases over the entire size range

NU_jun_13_2000_2100_2108.gif

while the individual area distributions show increases predominantly in
the 200 to 1000 micron size interval.

AR_jun_13_2000_2100_2108.gif

The corresponding calculated decay times using the 30 sec average
measured size distributions are:

2104:00 -- 332 secs

2104:30 -- 692

2105:00 -- 1226

2105:30 -- 1388

2106:00 -- 1989

2106:30 -- 2571

2107:00 -- 3899

2107:30 -- 5094

2108:00 -- 5737

2108:30 -- 4321

2109:00 \-- 3169

Clearly in this case the largest contribution and change in particle
concentrations and area is in the size interval 200 to 1000 microns, and
therefore is the dominant variation responsible for large changes in
Electric Field decay time as the aircraft flies from the edge of the
anvil towards the higher reflectivities.

**Later in the flight** as the A/C is flying along the anvil axis in the
decaying anvil the decay times are \<300 secs until 2244 and all less
than 1400 secs during both passes in towards the storm core and then
back from 2235 to 2305. \[CAUTION: No 2D data from \~2252:20 to
2253:55\].

CAPPI 2243-2248

<http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_NEXRAD/hc/000613/hc_2243_2248_000613.gif>

CAPPI 2248-2253

<http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_NEXRAD/hc/000613/hc_2248_2253_000613.gif>

MER plot 2240-2250

http://box.mmm.ucar.edu/abfm/webpage/june2000/Mer/000613_NEXRAD/mer_2240_2250_000613.gif

The time series for number concentration and also for area for the
period 2240 to 2255 shows a big change in 200 to 1000 um particles for
first 4 min after the A/C first enters the anvil and no \>1 mm
particles. At \~2144:30 \>1mm particles begin to appear and then
increase gradually in concentration and area.

ts_NU_jun_13_2000_2245_2300.gif

ts_AR_jun_13_2000_2245_2300.gif

Even though Emag was as much as 30 kV/m the calculated E field decay
times do not exceed 1600 secs (27 min) and the particle area is almost a
factor of ten less than at 2108 during the Early part of this study (See
above).

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

June 14, 2000

Case 1 \-- A detached anvil in advanced stages of decay

CAPPI 2143-2145
http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_WSR74C/hc_lightning/000614/light_2143_2145_000614.gif

MER 2140 -- 2150

http://box.mmm.ucar.edu/abfm/webpage/june2000/Mer/000614_WSR74C/mer_2140_2150_000614.gif

The No. Size Distribution (PSD) shows a relatively flat distribution
from 0.2 to 0.5 mm (200 to 500 microns) with a max conc. per size bin of
approx 10\*\*-2.

AR_000614_2136_2145.gif

The Area Size Distribution (ASD) shows a mode around a few hundred
microns.

NU_000614_2136_2145.gif

Case 2 -- An anvil(s) attached to active convection containing LDAR
sources.

CAPPI w. lightning 2302-2304

http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_WSR74C/hc_lightning/000614/light_2302_2304_000614.gif

CAPPI w. lightning 2304-2307

http://box.mmm.ucar.edu/abfm/webpage/june2000/CAPPI_WSR74C/hc_lightning/000614/light_2304_2307_000614.gif

MER 2300-2310

http://box.mmm.ucar.edu/abfm/webpage/june2000/Mer/000614_WSR74C/mer_2300_2310_000614.gif

The PSD for the period 2300 to 2303 when A/C was in the farthest
downwind part of the anvil (2300:00 to 2300:30) is quite flat from 100
to 1000 microns with increasing concentrations in size range 100 to
\~300 um as the A/C flies closer toward the core. The ASD for 2300:00 to
2300:30 has a negative slope from 100 to 1000 um. As the A/C approaches
the core the main region of increased area is from 200 to 400 um.

The calculated Etime Scale for 2300:00 to 2300:30 was 965 secs, at
2302:00 -- 2302:30 was 2082 secs.

NU_000614_2300_2308.gif

AR_000614_2300_2308.gif

But note in the above figures that when the A/C was flying near the
storm core at \~2306-2307 the no. concentration of the 100 to 300 micron
particles is a factor 10 or more larger.

Area Distributions for Times of Max EtimeScale or Max Particle
Concentrations

June 7, 2000

AR_00607_1845_1853.gif

June 13, 2000

AR_jun_13_2000_2100_2108.gif

June 14, 2000

AR_000614_2300_2308.gif

June 2, 2001

AR_010602_1930_1938.gif

June 4, 2001

N-S pass close to core

AR_010604_2015_2023.gif

Long pass along anvil axis where E field \~25-30 kV/m continuously

AR_010604_2130_2138.gif

June 5, 2001

Large storm \~150 km offshore

AR_010605_2115_2123.gif

near core of debris in anvil-like storm

AR_010605_2115_2123.gif

June 15, 2001

\~2130???

June 24, 2001

Nearest core

AR_010624_1838_1845.gif

NU_010624_1838_1845.gif

Another time nearest core

AR_010624_1853_1900.gif

NU_010624_1853_1900.gif

June 25, 2001

In decaying, detached anvil debris with max Emag of 3 kV/m at 2006

AR_010625_2000_2008.gif