Koshak, William

NASA Technical Reports Server

Lightning Flash Energetics
William Koshak
NASA Marshall Space Flight Center (MSFC), Huntsville, AL
Bolide Meeting, 6 February 2019
Lockheed Martin Advanced Technology Center (LMATC)
Palo Alto, California
https://ntrs.nasa.gov/search.jsp?R=20190000679 2019-08-30T10:12:08+00:00Z
Koshak, NASA/MSFC
Increased 
Convection
Increased 
Lightning
Increased 
LNOx
Increased 
O3 and 
other GG
Warming 
Climate
Impacts:
death/injury
wildfires
power outages
crop damage
property damage
delays (airport, launch)
.
.
.
higher albedo 
(cooling)
Multiple
Effects
Other 
Drivers
Flash Energy is Important 
Lightning/Climate Interaction
Lightning Increase Over Land
17%/oC (dry bulb)
40%/ oC (wet bulb)
56% /oC (wet, N. Hem)
Flash Energy
Koshak, NASA/MSFC
LNOx Production P in moles:
P =

Y
NA
 
E =

Y
 NA
 
Q , Q in Joules
Y ⇠ 1017 molecules J 1 (Thermochemical Yield)
NA = 6.022⇥ 1023 molecules mol 1 (Avogadro’s Number)
  ⇠ 1.35997⇥ 10 22 ) ave P = 250 moles/flash over 1st 10 mo of 2018 reference year
Flash Energy E when P = 250 moles is:
E =
NAP
Y
= 1, 505, 500, 000 J ⇠ 1.5 GJ
Koshak, NASA/MSFC
⇠¯ ijaj
isotropy assumed
sum upward flux
from each event
Q =
mX
i=1
nX
j=1
Aj  j !j ⇠¯ ij (in fJ) [GLM ]
   =
mX
i=1
nX
j=1
⇡⇠¯ ijaj (in mJ nm
 1) [LIS]
Two Optical Energy Metrics
Sensor-Intercepted Energy
Total Upward Energy (from cloud-top surface) 
Koshak, NASA/MSFC
⇠¯ ij
aj
isotropy assumed
to sensor
(pixel footprint)
J ij =
Z
2⇡
cos ✓0⇠¯ ijd⌦0 = ⇠¯ ij
Z 2⇡
0
Z ⇡/2
0
cos ✓0 sin✓0d✓0d'0
) J ij = ⇡⇠¯ ij (µJ m 2nm 1)
)    =
mX
i=1
nX
j=1
J ijaj =
mX
i=1
nX
j=1
⇡⇠¯ ijaj
[Upward time-integrated spectral flux density 
from jth pixel footprint for ith frame]
✓0
'0
LIS
Koshak, NASA/MSFC
Front Lens Incident solid - angle - averaged spectral energy density (in µJ m 2sr 1µm 1) :D
⇠ (⌦ˆ)
E
=
1
 ⌦
Z
 ⌦
Z tm
to
I (⌦ˆ, t)dtd⌦
LIS
Koshak, NASA/MSFC
D
⇠ (⌦ˆ)
E
=
1
 ⌦
Z
 ⌦
Z tm
to
I (⌦ˆ, t)dt
 
d⌦ =
1
 ⌦
Z
 ⌦
"
mX
i=1
Z ti
ti 1
I (⌦ˆ, t)dt
#
d⌦ =
1
 ⌦
Z
 ⌦
"
mX
i=1
⇠ i(⌦ˆ)
#
d⌦
=
1
 ⌦
mX
i=1
Z
 ⌦
⇠ i(⌦ˆ)d⌦
 
=
1
 ⌦
mX
i=1
24 nX
j=1
Z
 !j
⇠ i(⌦ˆ)d⌦
35 = 1
 ⌦
mX
i=1
nX
j=1
 !j ⇠¯ ij '  !
 ⌦
mX
i=1
nX
j=1
⇠¯ ij
Hence: D
⇠ (⌦ˆ)
E
' 1
n
mX
i=1
nX
j=1
⇠¯ ij
where:
i = 1, ...,m (m = # frames covered by the flash)
j = 1, ..., n (n = # pixels illuminated by the flash 6= # of EVENTS!, in general)
⇠ i(⌦ˆ) ⌘
Z ti
ti 1
I (⌦ˆ, t)dt = spectral energy density function in i
th frame
⇠¯ ij ⌘ 1
 !j
Z
 !j
⇠ i(⌦ˆ)d⌦ = mean spectral energy density heading toward j
th pixel in ith frame
 ⌦ =
nX
j=1
 !j = n ! = flash solid angle;  ! ⌘ 1
n
nX
j=1
 !j = mean pixel solid angle in the flash
Solid Angle Averaged Spectral Energy Density
(in µJ m 2sr 1µm 1)
LIS
Koshak, NASA/MSFC
By correcting the HDF data product ⇣ ij(cL), one can estimate the true incidence:
⇠¯ ij ⇠= 0.985⇣ ij(cL)
Fj
So put all the pieces together:D
⇠ (⌦ˆ)
E
' 1
n
mX
i=1
nX
j=1
⇠¯ ij ' 1
n
mX
i=1
nX
j=1
0.985⇣ ij(cL)
Fj
   ⌘
mX
i=1
nX
j=1
⇣ ij(c)
But, a flash is fairly localized to one boresight region so that Fj ' F¯ :D
⇠ (⌦ˆ)
E
' 0.985
nF¯
mX
i=1
nX
j=1
⇣ ij(cL) =
0.985
nF¯
  
Hence:
   ' nF¯
0.985
D
⇠ (⌦ˆ)
E So data product generally overestimates true incidence by about a factor of n.
At max boresight the correction is n(0.82)/0.985 = 0.832n
LIS
Koshak, NASA/MSFC
Heritage Flash Amplitude Baseline Computed by Koshak
Using Raw Data Results from Various Investigators
• OTD: poor sensitivity, only CONUS stats done, Z estimate … not best to use.
• More data in LIS Post-Boost than in Pre-boost … so Post-Boost better sample size
• Buechler & Christian study has 1 more year of data than the Beirle et al. study, and more specific mean 
event footprints (since Beirle didn’t separate out Pre-boost from Post-boost).
• So best estimate currently is 6th column above (bolded).D
⇠ (⌦ˆ)
E
⇠ 60 µJ
m2sr nm
 
 
 
 
Raw  
Data  
Source 
Koshak  
OTD 
CONUS  
1999-2000 
Z = 3 weighting 
Resolution Model 
Koshak  
OTD  
CONUS 
1999-2000 
data weighting 
Resolution Model 
Buechler & 
Christian  
LIS  
GLOBAL 
1998-Jul 2001 
Pre-boost 
Resolution Model 
Buechler & 
Christian  
LIS  
GLOBAL 
Sep 2001-2013 
Post-boost 
Resolution Model 
Buechler & 
Christian  
LIS 
GLOBAL 
1998-Jul 2001 
Pre-boost 
Res: data 22.6 
km2 
Buechler & 
Christian  
LIS 
GLOBAL 
Sep 2001-2013 
Post-boost 
Res: data 25.3 
km2 
Beirle et al.  
LIS 
GLOBAL 
1998-2012 
both Pre- & 
Post- 
Res: BC data 24.7 
km2 
Koshak  
Computation 
79.8 72.8 55.7 57.9 67.9 59.9 60.3 
 
 
Summary (from OTD/LIS)
Koshak, NASA/MSFC
Koshak, W. J, Lightning NOx estimates from space-based lightning imagers, 16th Annual CMAS Conference, 
Chapel Hill, NC, October 23-25, 2017 
" =
1
No
NoX
k=1
  k  
Trends down to 2011, then trends up.
Oscillates!  ... with peak in Winter.
Long-Term Trend of TRMM/LIS Mean CONUS Upward Flash Optical Energy ℇ
LIS
Koshak, NASA/MSFC
G16 Flash Optical Energy Q  
9.5 mo (2018: Jan 1 – Oct 15);  ~ 300 M flashes
Size = 298,386,767
Mean = 254.3 fJ
Std. Dev. = 557.7 fJ
Max = 100,004.4 fJ
Median = 87.0 fJ
Min = 1.5 fJ
Flash Energy
Freq. Dist.
Mean Daily Flash Energy TREND  (fJ)
0   
100
200
300
400
Time (days since start)
0   300200100
G17 Flash Optical Energy Q  
G16 Count
G17 Q larger than G16’s 
because of:
• Boresight Effect  (most G17 
flashes at large boresight)
• Ocean Effect  (most G17 
flashes over ocean)
• Statistical Effect (G17 sample 
of natural lightning not as 
large relative to noise: glint, 
radiation dots)
• Seasonal Effect (flash energies 
peak in January per LIS study 
in Koshak, 2017)
G16 Energy Q
Koshak, NASA/MSFC
10 mo Trend (Jan-Oct, 2018) CONUS Flash Density 
GLM-16
Koshak, NASA/MSFC
10 mo Trend (Jan-Oct, 2018) of GLM-16 CONUS Incident Flash Optical Energy Q 
Mean Q per flash 
in grid cell Total Q from all flashes
in grid cell
Q =
mX
i=1
nX
j=1
qij =
mX
i=1
nX
j=1
Aj  j !j ⇠¯ ij (in fJ)
Q¯
Monthly Variation
Koshak, NASA/MSFC
10 mo Trend (Jan-Oct, 2018) of GLM-16 CONUS LNOx Production P Estimate 
Mean P per flash 
in grid cell Total P from all flashes
in grid cell
P¯
P =

Y
 NA
 
Q (in moles)
Monthly Variation
Koshak, NASA/MSFC
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Lightning Flash Energetics

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