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Cloud to Ground Lightning Climatology and Hail Prediction in
the Mid-South
Matthew Reagan
Mississippi State University
Objective
• Create model to predict severe hail events using strictly cloud-to-ground lightning
Hypothesis
• Cloud to ground lightning activity will change as a hail core descends to the ground
Charge Structure
• Precipitation Theory– Krehbiel 1986– Lang and Rutledge
2002
• Dipole Structure– Krehbiel 1986– Dotzek et al. 2001– Rakov and Uman 2003
Krehbiel 1986
Cloud-to-Ground Lightning
• Percentage of Positive and Negative Strikes– Reap and MacGorman 1989
• Severe Weather and Positive CG– Reap and MacGorman 1989– MacGorman and Burgess 1994– Liu et al. 2006
Return Strokes
• Krehbiel 1986
• Reap and MacGorman 1989
Scope
Lightning ClimatologyMonth Positive Strikes Total Strikes Percent Positive
January 13,299 99,632 13.34
February 27,246 241,931 11.26
March 44,114 445,583 9.90
April 65,672 898,260 7.31
May 98,938 1,907,591 5.19
June 53,999 1,425,001 3.79
July 84,880 2,252,011 3.77
August 66,082 1,840,011 3.59
September 18,677 381,223 4.90
October 19,779 293,909 6.73
November 27,104 276,274 9.81
December 22,360 144,544 15.47
Total 542,150 10,205,970 5.31
2,795 strikes per day
Lightning Climatology
0
500000
1000000
1500000
2000000
2500000
Janu
ary
Febru
ary
Mar
chApr
ilM
ayJu
ne July
Augus
t
Septe
mbe
r
Octobe
r
Novem
ber
Decem
ber
Str
ikes
Percent Positive
0
2
4
6
8
10
12
14
16
18
January February March April May June July August September October November December
Per
cen
t
Percent Positive
0
2
4
6
8
10
12
14
16
18
January February March April May June July August September October November December
Per
cen
t
Return Strokes
• Reap and MacGorman 1989– Positive: 78%– Negative: 31%
• Reap & MacGorman– NSSL Network
• Mid-South Study– NLDN
Positive Negative
January 75.5 47.3
February 75.1 51.4
March 76.8 50
April 74.4 52.4
May 74.3 53.4
June 72.5 51.3
July 73.1 49.1
August 72.7 49.6
September 72.4 51.1
October 76.2 51.6
November 77.9 51.9
December 76.3 50.5
Total: 74.3 50.9
Diurnal Climatology
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
1000000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour (z)
Str
ikes
Pulse Thunderstorms
Storm Collection
• Hail Storms– Storm reports
• Non hail producing storms– VILD between 2.5 and
3.5 kg/m3
Extraction
Extraction
Storm of Interest
Model Creation• Lightning in 5 minute increments
– Total CG– Total Positive Strikes– Return Strokes Per Strike
• 355 storms– 300 for training– 55 for testing
• Jack knifing– 300 times in training– 55 times in testing
• Test finalists on independent data set
Models Used
• Logistic Regression
• Artificial Intelligence– Polynomial– Linear– Radial– Sigmoid
What is Artificial Intelligence?
What is Artificial Intelligence?
y z
x o x x o x o
o x
x
y
Percent Correct
Probability of Detection
False Alarm Ratio
Probability of False Detection
Bias
Heidke Skill Score
• Eliminated– D2 & D3 Polynomials– Sigmoid– Radial E001 C100
• Remaining– D1 Polynomials– Linear– Radial– Logistic
Model Families
Radial E01 C10 Radial E001 C1
PC Bias FAR POD POFD HSS
Polynomial D1 C10 0.69 1.06 0.29 0.76 0.40 0.36
Linear C100 0.69 1.06 0.28 0.76 0.38 0.38
Radial E001 C10 0.67 1.12 0.32 0.77 0.44 0.34
Logistic Regression 0.69 1 0.28 0.74 0.33 0.38
PC Bias FAR POD POFD HSS
Polynomial D1 C10 0.004 0.029 0.009 0.004 0.014 0.017
Linear C100 0.001 0.025 0.004 0.004 0.007 0.007
Radial E001 C10 0.004 0.018 0.004 0.006 0.012 0.016
Logistic Regression 0.002 0.036 0.006 0.008 0.012 0.010
Median Statistics
Variance
Independent Data Set
• 2002-2008 storms used for training– 355 events
• 2009-2010 storms used for testing– 205 events
Linear C100Logistic
Regression
PC 0.53 0.63
Bias 0.86 0.82
FAR 0.40 0.29
POD 0.51 0.58
POFD 0.44 0.30
HSS 0.07 0.28
2002-2010 Average Total CG
0
5
10
15
20
25
30-25 25-20 20-15 15-10 10-5 5-0
Time Step (minutes prior to event)
Str
ikes
Severe 02-08
Non Severe 02-08
Severe 09-10
Non Severe 09-10
January 20, 2010
0
10
20
30
40
50
60
70
80
90
30-25 25-20 20-15 15-10 10-5 5-0
Minutes Prior to Event
Str
ikes Event b
Event c
Total Strikes Hail SizeEvent a 209 1Event b 15 1Event c 295 1Event d 50 1Event e 360 1.75
0
10
20
30
40
50
60
70
80
90
30-25 25-20 20-15 15-10 10-5 5-0
Minutes Prior to Event
Str
ikes
Event a
Event b
Event c
Event d
Event e
January 20, 2010 Event b
January 20, 2010 Event c
January 20, 2010 Event c
EHI and Average Strikes
ML CAPE 0-3 SRH EHI Average Strikes
Nov. 15, 2005 2121 354 4.69 64.9
Nov. 29, 2010 2491 478 7.44 205.3
May 07, 2010 2251 220 3.10 138.6
May 10, 2006 1797 142 1.59 147.3
March 29, 2002 2575 324 5.21 74.3
2002-2010 Average Positive Strikes
0
0.2
0.4
0.6
0.8
1
1.2
1.4
30-25 25-20 20-15 15-10 10-5 5-0
Time Step (minutes prior to event)
Str
ikes
Severe 02-08
Non Severe 02-08
Severe 09-10
Non Severe 09-10
Center
7.5 Radius
2002-2010 Average Return Strokes
1.7
1.8
1.9
2
2.1
2.2
2.3
30-25 25-20 20-15 15-10 10-5 5-0
Time Step (minutes prior to event)
Ret
urn
Str
oke
s p
er S
trik
e
Severe 02-08
Non Severe 02-08
Severe 09-10
Non Severe 09-10
Limitations
• Hail Report Bias¼” Pea
½” Marble
¾” Penny
7/8” Nickel
1" Quarter
1 ¼” Half Dollar
1 ½” Walnut/Ping Pong Ball
1 ¾” Golf Ball
2" Hen Egg
2 ½” Tennis Ball
2 ¾” Baseball
3" Teacup
4" Grapefruit
4 ½” Softball
Hail Size Frequency
1” 161
1 ¼” 18
1 ½” 13
1 ¾” 101
2” 4
2 ½” 2
2 ¾” 10
4” 3
4.50” 1
Limitations
• Hail Report Bias• Non Severe VILD
Threshold
Limitations
• Hail Report Bias• Non Severe VILD
Threshold• Cloud to ground
lightning only
Summary
• CG lightning peaks in summer months
• Positive CG accounts for 5.31% of CG lightning with a peak in winter months
• Script has proven flexible with storm mode
• Logistic regression model out performed artificial intelligence
• Storm environment factors need to be studied
Questions?