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

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1000000

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ary

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ary

Mar

chApr

ilM

ayJu

ne July

Augus

t

Septe

mbe

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Octobe

r

Novem

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Decem

ber

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ikes

Percent Positive

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January February March April May June July August September October November December

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Percent Positive

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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

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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

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10

20

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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?