The intense heating of air by a lightning channel, and subsequent rapid cooling, leads to the production of lightning nitrogen oxides (NOx = NO + NO2) as discussed in Chameides [1979]. In turn, the lightning nitrogen oxides (or "LNOx" for brevity) indirectly influences the Earth's climate because the LNOx molecules are important in controlling the concentration of ozone (O3) and hydroxyl radicals (OH) in the atmosphere. Climate is most sensitive to O3 in the upper troposphere, and LNOx is the most important source of NOx in the upper troposphere at tropical and subtropical latitudes; hence, lightning is a useful parameter to monitor for climate assessments. The National Climate Assessment (NCA) program was created in response to the Congressionally-mandated Global Change Research Act (GCRA) of 1990. Thirteen US government organizations participate in the NCA program which examines the effects of global change on the natural environment, human health and welfare, energy production and use, land and water resources, human social systems, transportation, agriculture, and biological diversity. The NCA focuses on natural and human-induced trends in global change, and projects major trends 25 to 100 years out. In support of the NCA, the NASA Marshall Space Flight Center (MSFC) continues to assess lightning-climate inter-relationships. This activity applies a variety of NASA assets to monitor in detail the changes in both the characteristics of ground- and space- based lightning observations as they pertain to changes in climate. In particular, changes in lightning characteristics over the conterminous US (CONUS) continue to be examined by this author using data from the Tropical Rainfall Measuring Mission Lightning Imaging Sensor. In this study, preliminary estimates of LNOx trends derived from TRMM/LIS lightning optical energy observations in the 17 yr period 1998-2014 are provided. This represents an important first step in testing the ability to make remote retrievals of LNOx from a satellite-based lightning sensor. As is shown, the methodology can also be directly applied to more recently launched lightning mappers, such as the Geostationary Lightning Mapper, and the International Space Station LIS

Koshak, William J.

Koshak, William

NASA Technical Reports Server

Koshak, NASA/MSFC
Lightning NOx Estimates from 
Space-Based Lightning Imagers
Dr. William Koshak (NASA/MSFC)
16th Annual CMAS Conference, Chapel Hill, NC
25 October 2017
https://ntrs.nasa.gov/search.jsp?R=20170010353 2019-08-31T01:33:36+00:00Z
Koshak, NASA/MSFC
Basic idea:
Use observed 
optical energy to infer 
total flash energy E 
… then multiply by 
thermo-chemical yield 
to get LNOx.
Koshak, NASA/MSFC
What to use for Flash Optical Energy?
Koshak, NASA/MSFC
isotropy assumed
to sensor
(pixel footprint)
Upward flux density from pixel footprint for ith frame
Koshak, NASA/MSFC
OPTICAL		ENERGY		INTERCEPTED
LIS
CLOUD		TOP
Lightning	Optical
Emission
(	( )	)
Joule	Heating:	Pressure	Wave	(Thunder),
Dissociation,	Ionization,	Rotation,	Vibration
Direction	Loss
Near	IR
Radiation
Detected
(if	above	
threshold)
Transport		Losses: Acoustical,
Radiative,	Conductive,
Convective	Mixing
E Q L= +
E Q L= +
Q = Flash (optical) energy detected by LIS
U = Flash energy undetected by LIS 
E = Q + U = Total Flash Energy
β = Q/E = fraction of total energy detected  by LIS
tiny	absorbed
Koshak, NASA/MSFC
Boccippio, D. J., W. J. Koshak, R. J. Blakeslee, Performance assessment of
the Optical Transient Detector and Lightning Imaging Sensor. Part I:
predicted diurnal variability, J. Atmos. Oceanic Technol., 19, 1318-1332,
2002.
Correcting for LIS 
sensitivity roll-off
In dataset
Koshak, NASA/MSFC
LIS
GLM
[μJ m-2 sr-1 nm-1]
[ μJ ]
What do you do for GLM ?
Koshak, NASA/MSFC
LNOx production from kth flash
Koshak, NASA/MSFC
LNOx Production for a region/period
this estimative term not needed 
for GLM since GLM continuously monitors
(observed + unobserved)
(f
J/
fl
as
h
)
(f
J/
fl
as
h
)
Annual		Mean
Monthly Mean
Koshak, NASA/MSFC
TRMM/LIS  Mean Q per flash (fJ/flash)
• 2014  added to the record
• 2015 partial year + issues, so not used
• Generally a downward trend (drop in 2001 
mostly due to orbit boost)
• Upward trend starting in 2011
• Strong increase in 2012 drought (these are 
per flash results)
drought year
drop mostly from orbit boost
Koshak, NASA/MSFC
TRMM/LIS  Mean 𝛤𝜆𝛥𝜆 per flash  ≡  ℇ (mJ/flash)
• Monthly Plots: Maxima occurs in January but 
this is all normalized (i.e. per flash values)
• Jan max possibly indicative of large current 
+CGs and/or small vertical optical depth, 
common in winter thunderstorms.
drought year
orbit boost 
bias removed
Koshak, NASA/MSFC
TRMM/LIS Mean LNOx Production per flash  ≡  𝜦 (moles/flash)
drought year
Koshak, NASA/MSFC
TRMM/LIS  LNOx Production P (megamoles)
drought year
• Since this is total LNOx production, time-
series trends are now modulated by the flash 
count … so peaks are in the summer months 
(see monthly plot). 
• Previous plots were normalized wrt flash 
count.
Koshak, NASA/MSFC
Thank   You


Lightning NOx Estimates from Space-Based Lightning Imagers

Presented at the 16th Annual CMAS Conference, Chapel Hill, NC, October 23-25, 2017 
1 
LIGHTNING NOX ESTIMATES FROM SPACE-BASED LIGHTNING IMAGERS 
 
William J. Koshak* 
Earth Science Branch, NASA Marshall Space Flight Center, Huntsville, AL, USA 
 
 
 
 
 
1. INTRODUCTION 
 
     The intense heating of air by a lightning 
channel, and subsequent rapid cooling, leads to 
the production of lightning nitrogen oxides (NOx = 
NO + NO2) as discussed in Chameides [1979]. In 
turn, the lightning nitrogen oxides (or "LNOx" for 
brevity) indirectly influences the Earth's climate 
because the LNOx molecules are important in 
controlling the concentration of ozone (O3) and 
hydroxyl radicals (OH) in the atmosphere 
[Huntrieser et al., 1998]. Climate is most sensitive 
to O3 in the upper troposphere, and LNOx is the 
most important source of NOx in the upper 
troposphere at tropical and subtropical latitudes; 
hence, lightning is a useful parameter to monitor 
for climate assessments [Schumann and 
Huntrieser, 2007]. 
     The National Climate Assessment (NCA) 
program was created in response to the 
Congressionally-mandated Global Change 
Research Act (GCRA) of 1990. Thirteen US 
government organizations participate in the NCA 
program which examines the effects of global 
change on the natural environment, human health 
and welfare, energy production and use, land and 
water resources, human social systems, 
transportation, agriculture, and biological diversity. 
The NCA focuses on natural and human-induced 
trends in global change, and projects major trends 
25 to 100 years out. 
     In support of the NCA, the NASA Marshall 
Space Flight Center (MSFC) continues to assess 
lightning-climate inter-relationships [Koshak et al., 
2015]. This activity applies a variety of NASA 
assets to monitor in detail the changes in both the 
characteristics of ground- and space- based 
lightning observations as they pertain to changes 
in climate.  In particular, changes in lightning 
characteristics over the conterminous US 
(CONUS) continue to be examined by this author 
using data from the Tropical Rainfall Measuring 
                                                      
*Corresponding author: William J. Koshak, Earth 
Science Branch, NASA-MSFC, Mail Stop ST11, Bud 
Cramer Research Hall, 320 Sparkman Dr., Huntsville, 
AL 35805; e-mail: william.koshak@nasa.gov 
Mission Lightning Imaging Sensor (TRMM/LIS; 
Christian et al. [1999]; Cecil et al. [2014]).  
     In this study, preliminary estimates of LNOx 
trends derived from TRMM/LIS lightning optical 
energy observations in the 17 yr period 1998-2014 
are provided. This represents an important first 
step in testing the ability to make remote retrievals 
of LNOx from a satellite-based lightning sensor. 
As is shown, the methodology can also be directly 
applied to more recently launched lightning 
mappers, such as the Geostationary Lightning 
Mapper (GLM; Goodman et al., [2013]), and the 
International Space Station LIS (ISS/LIS; 
Blakeslee and Koshak [2016]).  
 
2. METHODOLOGY 
      
     The approach taken is to estimate the total 
production P of LNOx from (the low Earth orbiting) 
LIS as         
 
 
 
Here, Pk is the LNOx production from the kth flash 
observed by LIS, and No is the total number of 
flashes observed by LIS in a particular 
geographical region and period of interest. 
Because of the low Earth orbit, LIS will have a 
limited view-time of the geographical region during 
the period of interest, and LIS also has a flash 
detection efficiency below 100% that varies 
diurnally. Hence, these instrument characteristics 
can be used to infer the total flash count N for the 
region during the period (see Cecil et al. [2014] for 
additional details). The number of flashes 
undetected by LIS is then Nu = N-No. The second 
term in (1) is simply Nu times the LIS estimate of 
the mean production per flash.  
     A distinct advantage of GLM over TRMM/LIS 
and ISS/LIS is that it continuously monitors a 
region. Hence, the second term in (1), which is 
estimative, is not required for GLM. 
     Next, the LNOx production Pk from the kth flash 
can be estimated from the detected optical energy. 
https://ntrs.nasa.gov/search.jsp?R=20170010354 2019-08-31T01:33:40+00:00Z
Presented at the 16th Annual CMAS Conference, Chapel Hill, NC, October 23-25, 2017 
2 
One could consider using the optical energy 
incident on the sensor as was done in Koshak et 
al. (2014), but this quantity depends on three 
sensor parameters (i.e., orbit altitude, entrance 
pupil area, and bandwidth). To facilitate the inter-
comparison of results derived from different 
sensors, it is beneficial to introduce a quantity  
that is invariant to these three sensor parameters, 
and is given by  
 
 
 
This is the entire cloud-top upward optical 
emission from a particular flash (the k subscript is 
dropped here for brevity). The flash illuminates a 
total of n pixels and spans a duration of m frames. 
So,  is the sum of each upward emission 
associated with the jth pixel footprint in each ith 
frame. The pixel cloud-top footprint aj emits a 
"spectral energy density" ij (in units of 
J/m2/sr/nm) that represents the radiant intensity 
integrated over one LIS charge coupled device 
(CCD) frame period (~ 2 ms); the overbar above 
this quantity in (2) refers to averaging over the 
pixel solid angle. The factor of  in (2) comes from 
the upper hemispherical solid angle integration 
shown and the assumption that the observed 
spectral energy density is emitted isotropically 
from each cloud-top footprint.   
     The estimate of LNOx Pk (in moles) from the kth 
flash can then be written as  
  
 
 
where Y ~ 1017 molecules per Joule is the NOx 
thermochemical yield (Borucki and Chameides, 
1984), NA = 6.0221023 molecules per mole is 
Avogadro's number,  is the known sensor 
bandwidth (in nanometers), and  ~ 3.9410-11 is a 
dimensionless calibration scaling factor whose 
magnitude is chosen such that the mean LNOx 
per flash in the (arbitrarily selected) reference year 
1998 is 250 moles/flash (i.e. a production value 
per flash commonly cited in the literature). The 
units of k used in (3) are Joules per nanometer.  
  
 
 
3. COMPUTATION USING LIS DATA 
 
     An estimate of the mean spectral energy 
density incident on the LIS instrument is provided 
in the LIS event "radiance" data product, but the 
magnitude of this product has not been corrected 
to account for the angle-of-incidence to the lens. In 
other words, the amount of optical energy actually 
ingested by a pixel depends on several factors 
that change with incident boresight angle (i.e., lens 
system transmission, pixel quantum efficiency, 
entrance pupil diameter, bandwidth, and pixel solid 
angle). The net effect of the boresight dependence 
(i.e., roll-off of LIS sensitivity with increasing angle 
of incidence) has been quantified in the correction 
plot shown in Fig. 1 of Boccippio et al. (2002), but 
has not previously been applied. In order to 
improve the accuracy of results provided here, the 
correction has been implemented as follows 
 
 
 
where Fj is the correction factor ("roll-off" curve) 
associated with the jth pixel of a given incidence 
angle, and was extracted from the Boccippio et al. 
(2002) study. For mid-range boresight angles, the 
value of Fj ~ 0.985; i.e., midrange incidence has 
no net correction. The variable ij is the spectral 
energy density value in the LIS event "radiance" 
data product.  
     Hence, for LIS, (4) is used to obtain the 
spectral energy densities required in the definition 
of    so that the flash LNOx production in (3) can 
be estimated by LIS. The LIS data also provides 
the optical event footprint aj needed in the  
calculation. 
 
4. COMPUTATION USING GLM DATA 
 
The GLM transient (lightning) optical 
amplitude calibration relates sensor digital count 
output to incident radiant optical energy (in 
Joules), rather than to a spectral energy density as 
done with LIS. Hence, the GLM digital count 
output that provides incident lightning optical 
energy qij values must be used to infer the 
associated incident spectral energy density. This 
is accomplished via the expression 
 
 
 
Presented at the 16th Annual CMAS Conference, Chapel Hill, NC, October 23-25, 2017 
3 
where A is the GLM entrance aperture area,  j is 
the GLM pixel solid angle, and  again 
represents the sensor bandwidth (for GLM in this 
case). Hence, (5) easily gives the values of the 
spectral energy densities that are needed in the  
calculation, and no correction is required for 
sensitivity roll-off with increasing boresight angle; 
i.e., the GLM design did not employ a wide-angle 
lens system as did the design of LIS. 
     The GLM and ISS/LIS are presently still under 
Post Launch Testing (PLT) validation with ongoing 
upgrades being made to the data products. 
Hence, the methodology presented here for 
making estimates of lightning optical energies and 
LNOx from these instruments will be applied at a 
later date.  
 
  5. RESULTS FOR TRMM/LIS 
 
     In support of the NCA program discussed in 
section 1, the above methodology for LIS was 
applied to analyze a 17 yr period (1998-2014) of 
TRMM/LIS data. The analysis region examined 
was the portion of the conterminous US (CONUS) 
covered by TRMM/LIS; i.e., up to about 38oN 
latitude.  
 
Fig. 1. The value of  (mJ/flash) derived from TRMM/LIS 
across the 17 yr period 1998-2014. Top plot is average 
optical energy per flash over a year, and bottom plot the 
average over a month. These "raw" results are only for 
flashes actually observed by TRMM/LIS. 
      
     The trend in the mean optical energy per flash 
 (in units of milliJoules per flash) was obtained by 
summing up the flash optical energy k for all k 
= 1, . . . , No flashes observed across the analysis 
region and then dividing by No to get the mean 
value for that period. Two analysis periods were 
considered: annual, and monthly. The long-term 
trends of these quantities are provided in Fig. 1. 
Even though these plots implicitly assume 
isotropic emission in the calculation of the k 
values for each kth flash, this is a minor point since 
each k value is still based on direct observations 
of the spectral energy density as shown in (2).  
     The associated trend in average LNOx 
production per flash  (in moles per flash) is 
estimated by using (1) and then dividing by N; i.e.,  
 = P/N. The results are provided in Fig. 2. Again, 
both annual and monthly averaging periods are 
used. Whereas Fig. 1 shows results based only on 
direct observations of the No observed flashes in a 
period, the results in Fig. 2 attempt to account for 
the effects of all flashes N, where N = No + Nu as 
discussed in section 2.    
 
 
Fig. 2. The value of  (in moles/flash). These plots are 
based on the boosting of the "raw" (i.e. directly 
observed) flash count by the finite view-time and 
detection efficiency of the TRMM/LIS (see section 2 for 
details). 
 
     The total LNOx production obtained using (1) is 
provided in Fig. 3. Because the lightning flash 
count varies from year-to-year and from month-to-
month, the LNOx production trends obviously 
depend on lightning frequency. Hence, whereas 
the plots in Figs. 1 and 2 are normalized with 
respect to flash count, the results in Fig. 3 are not. 
Normalizing with respect to flash count has the 
advantage of revealing how the typical LNOx 
production per flash varies over a long-term basis, 
and therefore is a more specific indicator of how 
the physics of individual flashes might be changing 
over time. By contrast, Fig. 3 shows net changes 
in LNOx production due to all flashes; i.e., the 
trend in total LNOx production depends not only 
Presented at the 16th Annual CMAS Conference, Chapel Hill, NC, October 23-25, 2017 
4 
on the production per flash, but also on the flash 
count. 
 
Fig. 3. The TRMM/LIS trend in total LNOx production P 
(in megamoles) as computed using (1). These plots 
depend not only on the variation of LNOx production per 
flash, but also on the flash count. 
    
6. DISCUSSION 
 
     The first thing to note from the Annual Mean 
plots in Figs. 1 and 2 is that there is not a sharp 
(artificial) drop in energy and LNOx in going from 
year 2000 to 2001 due to the TRMM/LIS orbit 
altitude boost in August of 2001. That is, the 
higher the orbit altitude, the less energy will be 
incident on the sensor. Specifically, the incident 
lightning optical energy on TRMM/LIS changes 
from 909.1 fJ/flash (the average in 2000) down to 
793.1 fJ/flash (the average in 2001), or a drop of 
12.8%. The unit fJ here is femtojoules. Since the 
orbit altitude invariant quantity  has been 
employed in this study instead of incident optical 
energy, the artificial drop (bias) due to increased 
orbit altitude has been avoided in the results of 
Figs. 1 and 2. Overall, there is a downward trend 
in optical energy and LNOx followed by an upward 
trend that starts in 2011. 
     Secondly, note the interesting cyclic pattern in 
the monthly trends of Figs. 1 and 2. The optical 
energy per flash peaks typically in January of each 
year, which might be indicative of a higher fraction 
of large current positive polarity cloud-to-ground 
lightning and/or smaller vertical cloud optical 
depths, as commonly associated with wintertime 
thunderstorms. In the monthly trends of Fig. 3, the 
maxima occur in the summer months because of 
high flash counts in the summer. 
     Finally, all the trend patterns provided in 
section 5 must be interpreted carefully. The 
similarity in the trend patterns between Fig. 1 and 
Fig. 2 is because of the constant factor Y/(NA) that 
was assumed in the relationship between flash 
optical energy and flash LNOx production given in 
(3). In addition, as described above, the value of  
= 250 moles/flash in 1998 is a direct (intentional) 
consequence of the specific value chosen for  in 
order to reference or "calibrate" the overall plot 
trend to the widely-cited value of 250 moles/flash. 
For example, the value of  could be changed 
such that it forces the mean in 1998 to be some 
other value, say 500 moles/flash ... but the overall 
pattern of the trend (relative shape) would not be 
affected by this change. These nuances must 
always be kept in mind when interpreting the 
LNOx results provided here. In general, the value 
of  is not constant as assumed here, but rather 
depends on specific properties of the lightning 
channel, cloud optical scattering properties, and 
the instrument. So, the value of  technically 
changes from flash to flash. The accuracy of the 
method provided here clearly depends on how 
much the complicating fluctuations in  get 
"washed out" from statistical averaging over many 
flashes and cloud morphologies. In this respect, 
the annual trends shown here are likely more 
accurate than the monthly trends. 
 
7. SUMMARY 
 
     A straight-forward methodology was provided 
that shows how one can attempt to estimate LNOx 
from an arbitrary satellite-based lightning imager 
(e.g., TRMM/LIS, ISS/LIS, or GLM). Flash LNOx 
production is estimated by first estimating the total 
flash energy from the observed flash optical 
energy emission. Multiplying the total flash energy 
by a NOx thermochemical yield and dividing by 
Avogadro's number converts the total flash energy 
into LNOx production in units of moles.  
     The observed cloud-top lightning optical energy 
is a tiny fraction of the total flash energy, and this 
tiny fraction varies from flash to flash. However, on 
a statistical basis (i.e., over many flashes and 
many cloud morphologies) one can infer the value 
of this tiny fraction that is needed in order to 
produce a reasonable average LNOx production 
per flash, such as 250 moles/flash. This is the 
basic approach taken in this writing. Therefore, the 
trends in LNOx per flash found in this study should 
be interpreted carefully, and represent relative 
trends only.  
     There are several improvements provided in 
this study over that provided in Koshak et al. 
(2014). First, an upward spectral energy  was 
Presented at the 16th Annual CMAS Conference, Chapel Hill, NC, October 23-25, 2017 
5 
employed to describe the flash optical emission, 
and this approach removes sensor biases (such 
as the effects of sensor orbit altitude, or sensor 
entrance pupil area). Second, TRMM/LIS lightning 
optical energy amplitudes were corrected for 
sensor sensitivity roll-off with boresight angle. 
Third, in addition to the standard annual mean 
trends, long term trends of monthly mean LNOx 
per flash were provided here. These trends show 
interesting cycles across each year, with maxima 
in mean LNOx/flash occurring in January. Fourth, 
the trending of TRMM/LIS LNOx production in this 
study was extended to one additional year, 
resulting in a total analysis period of 17 yrs (1998-
2014).  
     In the future, the method provided here will also 
be used to estimate LNOx production from ISS/LIS 
and GLM datasets after post-launch testing of 
these instruments is completed.   
 
Acknowledgments. This work was supported by 
NASA Headquarters program announcement 
number NNH14ZDA001N-INCA under Dr. Jack 
Kaye and Dr. Lucia Tsaoussi in support of the 
National Climate Assessment program.  
 
8. REFERENCES 
 
Blakeslee, R. J., and W. J. Koshak, 2016: LIS on ISS: 
expanded global coverage and enhanced applications, 
The Earth Observer, Volume 28, Issue 3, May-June. 
 
Boccippio, D. J., W. J. Koshak, R. J. Blakeslee, 2002: 
Performance assessment of the Optical Transient 
Detector and Lightning Imaging Sensor. Part I: predicted 
diurnal variability, J. Atmos. Oceanic Technol., 19, 
1318-1332. 
 
Borucki, W. J., and W. L. Chameides, 1984: Lightning: 
estimates of the rates of energy dissipation and nitrogen 
fixation, Rev. Geophys. Space Phys., 22, 363–372. 
 
Cecil, D. J., D. E. Buechler, and R. J. Blakeslee, 2014: 
Gridded lightning climatology from TRMM-LIS and OTD: 
dataset description, Atmos. Res., 135 -136, 404 – 414. 
 
Chameides,W. L., 1979: Effect of variable energy input  
on nitrogen fixation in instantaneous linear discharges, 
Nature, 277, 123–125. 
 
Christian, H. J., et al., 1999: The Lightning Imaging 
Sensor, in 11th Int. Conf. on Atmospheric Electricity, pp. 
746–749, ICAE, Guntersville, AL. 
 
Goodman, S. J., et al., 2013: The GOES-R 
Geostationary Lightning Mapper (GLM), Atmos. Res., 
125-126, 34–49. 
 
Huntrieser, H., H. Schlager, C. Feigl, and H. Holler, 
1998: Transport and production of NOx in electrified 
thunderstorms: Survey of previous studies and new 
observations at midlatitudes, J. Geophys. Res. , 103 , 
28,247–28,264. 
 
Koshak, W. J., B. Vant-Hull, E. W. McCaul, and H. S. 
Peterson, 2014: Variation of a lightning NOx indicator for 
National Climate Assessment, XV International 
Conference on Atmospheric Electricity, Norman, 
Oklahoma, June 15-20. 
 
Koshak, W. J., K. L. Cummins, D. E. Buechler, B. Vant-
Hull, R. J. Blakeslee, E. R. Williams, H. S. Peterson, 
2015: Variability of CONUS Lightning in 2003-12 and 
Associated Impacts, J. Appl. Meteorol. Climatology, 54, 
No. 1, 15-41. 
 
Schumann, U., and H. Huntrieser, 2007: The global 
lightning-induced nitrogen oxides source, Atmos. Chem. 
Phys., 7, 3823–3907. 
 
 
 


Lightning NOx Estimates from Space-Based Lightning Imagers

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