Midlatitude Lightning NOx Production Efficiency Inferred From OMI and WWLLN Data

Oxides of nitrogen are critical trace gases in the troposphere and are precursors for nitrate aerosol and ozone, which is an important pollutant and greenhouse gas. Lightning is the major source of NOx (NO + NO2) in the middle to upper troposphere. We estimate the production efficiency (PE) of lightning NOx (LNOx) using satellite data from the Ozone Monitoring Instrument and the ground‐based World Wide Lightning Location Network in three northern midlatitudes, primarily continental regions that include much of North America, Europe, and East Asia. Data were obtained over five boreal summers, 2007–2011, and comprise the largest number of midlatitude convective events to date for estimating the LNOx PE with satellite NO2 and ground‐based lightning measurements. In contrast to some previous studies, the algorithm assumes no minimum flash‐rate threshold and estimates freshly produced LNOx by subtracting a background of aged NOx estimated from the Ozone Monitoring Instrument data set itself. We infer an average value of 180 ± 100 moles LNOx produced per lightning flash. We also show evidence of a dependence of PE on lightning flash rate and find an approximate empirical power function relating moles LNOx to flashes. PE decreases by an order of magnitude for a 2 orders of magnitude increase in flash rate. This phenomenon has not been reported in previous satellite LNOx studies but is consistent with ground‐based observations suggesting an inverse relationship between flash rate and size.


Introduction
Trace gases individually represent less than 1% of all components of the Earth's atmosphere but play significant roles in atmospheric chemistry. In particular, nitric oxide (NO) and nitrogen dioxide (NO 2 ), collectively NO x , are critical in regulating concentrations of other trace gases. In pollution-free regions, the total NO x column is dominated by the stratospheric component. There, NO x occurs naturally as a by-product of photodissociation of N 2 O transported across the tropopause and plays a major role in the catalytic destruction of stratospheric ozone (Finlayson-Pitts & Pitts, 1999;Seinfeld & Pandis, 1998). Significant amounts of NO x also exist in the troposphere with global production estimates of~48 Tg N/year (Miyazaki et al., 2016). Tropospheric NO x is generated by high-temperature reactions involving N 2 and O 2 . These are mainly anthropogenic and include combustion of fossil fuels and biomass burning. On average, some 90% of tropospheric NO x resides in the boundary layer, where it is a precursor to lower tropospheric ozone.
The major natural sources of tropospheric NO x are soil emissions and lightning (Finlayson-Pitts & Pitts, 1999;Seinfeld & Pandis, 1998;Vinken et al., 2014). In the upper troposphere, the lightning source dominates. It is estimated that lightning NO x (LNO x ) accounts for 60-70% of free-tropospheric NO x . In the mid-upper troposphere, lightning dissociates N 2 and O 2 , into free N and O within the extremely hot flash channel. These in turn react with ambient N 2 and O 2 to produce NO, which remains after the lightning channel cools. During the conversion between NO and NO 2 , ozone is generated in the presence of HO 2 and organic peroxy radicals, collectively called RO 2 . Ozone is a significant greenhouse gas in the upper troposphere (e.g., Rap et al., 2015). It is sensitive to LNO x amounts, which are believed to be responsible for 35-45% of global free-tropospheric ozone Dahlmann et al., 2011;Liaskos et al., 2015). Pickering et al. (1993Pickering et al. ( , 1996 have shown persistent ozone enhancements downwind of convection. These long-range enhancements are consistent with NO x lifetimes of at least two to three days in the upper troposphere (Jaeglé et al., 1998;Martin et al., 2007;, although initial lifetimes near the lightning source have been shown to be as short as 2-12 hr (Nault et al., 2017). In addition to its direct effect on radiative forcing, ozone can photodissociate and react with water vapor to create hydroxyl (OH), a strong oxidant. Among other roles, OH plays a large role in the destruction of methane (CH 4 ), another major greenhouse gas (DeCaria et al., 2000(DeCaria et al., , 2005Finlayson-Pitts & Pitts, 1999;Fiore et al., 2006;Labrador et al., 2004;Liaskos et al., 2015;Seinfeld & Pandis, 1998). Although its largest chemical impact is on the free troposphere, LNO x plays a small but nonnegligible role in boundary layer air quality (Allen et al., 2012;Murray, 2016).
Production rates of LNO x depend, in part, on lightning flash rates, and knowledge of these rates is critical in developing chemical transport models (CTMs). On the mesoscale, flash rates have been shown to vary as a power function of cloud top height (Price & Rind, 1992;Williams, 1985). Modeling studies have employed CTM flash parameterizations based on cloud top height, convective precipitation rate, anvil-level ice amounts, and vertical mass transport in updrafts Tost et al., 2007). Murray et al. (2012) showed that flash rates in CTMs may be constrained with satellite measurements of lightning. Globally, mean annual flash rates are estimated to be approximately 46 fl/s (e.g., Cecil et al., 2014).
Lightning NO x production estimates also require knowledge of the moles of NO x produced per flash, known as the production efficiency (PE). This quantity is considerably less well known than the global flash rate and has been estimated in theoretical, laboratory, aircraft, and satellite investigations. The review studies of Schumann and Huntrieser (2007) and Murray (2016) cite PE estimates spanning 2-3 orders of magnitude, with values ranging from~5 to >1,000 mol/fl. Schumann and Huntrieser (2007) suggest a global average PE of 250 mol/fl, which when coupled with the mean annual flash rate yields a global production of 5 ± 3 Tg N/year when uncertainties are included. Studies, including Price et al. (1997) (theory) and Koshak (2014) (measurement and theory), have indicated PEs of cloud-to-ground flashes (CG) to be an order of magnitude higher than those of intracloud (IC) flashes. However, aircraft observations in conjunction with cloud-scale models have found that IC and CG flashes are approximately equally productive (Cummings et al., 2013;DeCaria et al., 2005;Huntrieser et al., 2011;Ott et al., 2007Ott et al., , 2010, with mean PE values ranging from~70 to 700 mol/fl. Regional differences have also been noted. There is some evidence that midlatitude flashes are more productive than those in tropical regions (Hudman et al., 2007;Huntrieser et al., 2006Huntrieser et al., , 2008, and several CTMs including the Goddard Earth Observing System Chemistry (GEOS-Chem) (van Donkelaar et al., 2008) and Global Modeling Initiative (GMI) CTMs ) assume a higher PE in the midlatitudes (~500 mol/fl) than tropics (~250 mol/fl). Other investigations indicate differences in continental and marine flashes. Boersma et al. (2005) found that continental flashes were~1.6 times more productive than those over water, while Allen et al. (2019) estimated marine flashes to be twice as productive than continental flashes, consistent with earlier findings of more energetic flashes over oceans (Beirle et al., 2014;Chronis et al., 2016).
Satellite observations of LNO x combined with ground-or satellite-based lightning flash counts have become increasingly valuable in PE investigations. Satellites directly measure NO 2 , which must be converted to NO x . Methods to estimate PE from satellite measurements generally fall into two categories: those using longterm trace-gas measurements of species like O 3 and HNO 3 to constrain NO x PEs in CTM simulations and those that constrain PE using retrievals of freshly produced NO x and concurrent lightning data. Examples of the former include the model assimilations of Boersma et al. (2005), Martin et al. (2007), and Miyazaki et al. (2014), which yielded NO x production rates equivalent to mean global PEs of 55 ± 320, 300 ± 100, and 320 ± 70 mol/fl, respectively. More recently, Marais et al. (2018) combined three years of NO 2 data obtained from the Ozone Monitoring Instrument (OMI) retrieved by cloud slicing (Choi et al., 2014;Ziemke et al., 2001) with lightning measurements from Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) and the GEOS-Chem model to obtain a mean PE of 280 ± 80 mol/fl. Investigations based on freshly produced LNO x face a number of observational hurdles. Some of these are instrument-related, such as the low spatial resolutions of satellite instruments, which can complicate comparisons with lightning in small-scale convective systems, as well as saturation of instrument pixels over bright convective clouds (L. Lamsal, H. Eskes, private communications). As in assimilation studies, the dominant stratospheric part of the satellite-measured total NO 2 column must be removed from the smaller LNO 2 component. A variety of schemes are used to do this, each yielding different results on subsynoptic scales (Beirle et al., 2016;Boersma et al., 2011;Bucsela et al., 2013;Richter & Burrows, 2002;Wenig et al., 2003;Yang et al., 2014). Ambient tropospheric NO x must also be distinguished from the fresh LNO x signal. The use of cloudy scenes limits contamination of the lightning signal by NO x in the lower troposphere with a likely anthropogenic source (Allen et al., 2019;Beirle et al., 2010;Marais et al., 2018;Pickering et al., 2016). High flash-rate restrictions have also been imposed to ensure that lightning NO x is the predominant component of the satellite signal and that the background contribution is minor (Beirle et al., 2010;Pickering et al., 2016). Approaches for estimating the background have been described by Bucsela et al. (2010), Pickering et al. (2016), and Allen et al. (2019). An additional challenge is synchronization of NO 2 data with concurrent lightning measurements. To date, all satellite LNO x studies have been based on low Earth orbit instruments, which make, at best, only one NO 2 measurement per day of a given region. Their local time (LT) for overpass is also before the late-afternoon convective peak, as with the Global Ozone Monitoring Experiment (LT = 10:30), the Scanning Imaging Absorption Cartography instrument (LT = 10:00), OMI (LT = 13:45), and the Tropospheric Monitoring Instrument (LT = 13:30).
The PEs derived from fresh LNO x measurements have generally yielded smaller PEs than assimilations. Using tropical data from the Tropical Composition, Cloud and Climate Coupling Experiment, Bucsela et al. (2010) found a mean PE of 174 ± 219 mol/fl based on OMI NO 2 measurements and lightning data from World Wide Lightning Location Network (WWLLN) and the Costa Rica Lightning Detection Network. Pickering et al. (2016) estimated a mean PE of 80 ± 45 mol/fl over the Gulf of Mexico, using data sets from OMI and the WWLLN. Over the same region, using Global Ozone Monitoring Experiment data, Beirle et al. (2006) derived a similar value of 90 (range of 32 to 240) mol/fl. However, Beirle et al. (2010) obtained a nearly null result in their Scanning Imaging Absorption Cartography-based study of 287 convective events, with no detectable LNO x enhancement over most storms and overall negligible correlation with flash counts. Allen et al. (2019) used updated versions of the Pickering et al. (2016) data sets, similar to those of the present study to estimate a PE value of 170 ± 100 mol/fl in the tropics. They also noted a decrease in PE with increasing lightning flash rate, as well as the higher values over water relative to land.
The present study examines three midlatitude regions (eastern North America, Europe, and East Asia and adjacent waters), using 15 months of data from the five boreal summers (June-July-August) of 2007-2011 to investigate the LNO x PE. NO 2 observations from OMI are compared with lightning flashes detected by the WWLLN and converted to NO x using air mass factors based on LNO x and LNO 2 profiles from a chemical-transport model. NO x retrieved in regions of deep convection without lightning flashes are subtracted as the tropospheric NO x background. This investigation and the tropical study of Allen et al. (2019) are the largest-scale satellite studies to date (in terms of observed convective events) of the amount of NO x production from observed flash data.

OMI
The Dutch-Finnish OMI spectrometer is one of four instruments on NASA's Aura satellite, launched 15 July 2004 Schoeberl et al., 2006). The satellite is in a Sun-synchronous orbit with equator and midlatitude crossing times of 13:45 and~13:30 LT, respectively. OMI operates in push-broom configuration with a swath spanning 2,600 km. In normal mode there are 60 pixels across the swath, and the field of view of nadir pixels is 13 × 24 km 2 . There are~1,600 swaths per orbit and~15 orbits per day. Midlatitude LTs across a swath can differ from nadir by as much as ±1 hr, and there is significant overlap between adjacent orbits. However, averaging of data in the present study minimizes the effects of LT variation. Beginning in 2007, OMI pixels were affected by the row anomaly (RA), first described by Dobber et al. (2008). The RA reduced valid data across each swath by~3 to~30 pixels between 2009 and 2011, and doubled the time required for global coverage from one to two days. Bad-pixel flagging and CCD dark current also grew by a factor of~2 during the 2007-2011 period, and signal-to-noise ratio decreased (Schenkeveld et al., 2017). NO 2 slant columns densities (SCDs) used in this study are obtained from the v3.0 NASA OMI NO 2 standard data product (Krotkov et al., 2017;Marchenko et al., 2015). Relative to SCDs in the previous v2.1 product (Boersma et al., 2011;Bucsela et al., 2013), the v3.0 SCDs are 10-40% smaller. The v3.0 algorithm employs an iterative spectral fitting routine in the 402-464-nm range that corrects errors in wavelength registration and separately fits the Ring spectrum due to rotational Raman scattering and absorption cross sections for NO 2 , H 2 O, and C 2 H 2 O 2 (glyoxal). Data quality at these wavelengths has been relatively stable over the instrument's lifetime. Radiometric degradation, stray light interference, and wavelength calibration errors have remained below 3%, 0.5%, and 0.002 nm, respectively Marchenko & DeLand, 2014;Schenkeveld et al., 2017). However, NO 2 SCD measurements between 2005 and 2015 over the central Pacific showed an increase in standard deviation from 0.8 × 10 15 to 1.0 × 10 15 cm 2 (Krotkov et al., 2017).
NO 2 SCDs are combined with level-2 NO 2 stratospheric vertical column densities (VCDs) and stratospheric air mass factors (AMFs), also from the v3.0 product. AMFs are based on a priori cloud and terrain inputs as well as chemical-transport and radiative-transfer model output. Cloud optical centroid pressure (OCP) and cloud radiance fraction (CRF) are obtained from the OMI O 2 -O 2 algorithm, where OCP is the effective cloud top pressure visible from OMI (Acarreta et al., 2004;Sneep et al., 2008;Stammes et al., 2008;Vasilkov et al., 2009). Terrain pressures and reflectivities are obtained, respectively, from a digital elevation model and OMI clear-sky measurements . The GMI chemistry-transport model (section 2.3) computes monthly NO 2 profile shapes and tropopause pressures for the AMFs. Atmospheric scattering weights are calculated by TOMRAD (Davé, 1965). The AMFs are also used in the stratosphere-troposphere separation (STS) algorithm (Bucsela et al., 2013) to derive the stratospheric VCDs from the total SCDs.

WWLLN
The World Wide Lightning Location Network is a continuously operating ground-based global array of very low frequency radio wave sensors that detect sferics from lightning (Dowden et al., 2002;Lay et al., 2005;Virts et al., 2013). The number of active sensors grew from 11 at initial global deployment in 2003 to~30 in 2007, to~60 in early 2012 (Hutchins et al., 2012). The increase between 2003 and 2007, alone, led to a growth in the number of lightning detections by~165%. Relative to LIS, detection efficiencies (DEs) in 2011 were estimated to be on the order 6-15% in the Western Hemisphere tropics by Rudlosky and Shea (2013) and~20% and~30% by Pickering et al. (2016) in the ±60°latitude band and Gulf of Mexico regions, respectively. Detection range is~10,000 km, allowing reasonable coverage with a sparse array (Lay et al., 2005;Rodger et al., 2006Rodger et al., , 2009. Spatial and temporal accuracies are~5 km and <10 μs, respectively (Abarca et al., 2010). Sensitivities are higher for CG than IC flashes (Rodger et al., 2009;Rudlosky & Shea, 2013), although we do not distinguish between the two in the present study.
The WWLLN detections used in this study are calibrated against satellite climatologies to estimate WWLLN DEs. Similar approaches were used by Pickering et al. (2016) and Allen et al. (2019). In the present study, adjustment factors were applied to the observed WWLLN strokes to ensure that the mean WWLLN flash rate over the 2007 to 2014 time period at each grid box matches that of the v2.3 OTD/LIS climatology (Cecil et al., 2014). The climatology is derived from measurements by the Optical Transient Detector (Boccippio et al., 2000(Boccippio et al., , 2002, operational from 1995 to 2000, and the Lightning Imaging Sensor, with useful full-year data during the years 1997 to 2013. Comparisons were limited to the latitude ranges of the instruments, which are ±35°for LIS and ±70°for OTD. Details of the methodology are given in Appendix A. WWLLN flashes are summed over the 1-hr period before 13:30 LT, the approximate OMI overpass time. Figure 1 shows WWLLN sensor locations and Northern Hemisphere detection efficiencies. In the geographical domain of this study, area-weighted DEs in 2007 (2011) were 3.6% (10.6%), 2.3% (4.5%), and 2.7% (8.0%), respectively. These values correspond to an average~3-8% increase over five years in the probability that WWLLN detects a given flash. Thus, the chance of detecting a flash more than doubles. The impact of interannual variability is likely small, since it is only approximately ±10% during the period. Since most flashes occur over land, where DEs are smaller (see Figure 1), the actual fraction of flashes detected by WWLLN is 10-50% less than the area-weighted DE. The small magnitude and high spatial and temporal variability of the DE make the WWLLN flash counts a major source of uncertainty in the present results.

GMI
NASA's Global Modeling Initiative model Duncan et al., 2007;Strahan et al., 2007Strahan et al., , 2013Ziemke et al., 2006) is the CTM used in both the OMI standard NO 2 product and here to estimate shapes of LNO 2 and LNO x vertical profiles for AMF calculations. The GMI simulations for this study were driven by meteorological fields from GEOS-5 Modern Era Retrospective analysis for Research and Applications (MERRA) (Rienecker et al., 2011). Year-specific monthly mean GMI output was computed for 2007-2011 using Emission Database for Global Atmospheric Research 2000 fossil fuel data and biomass burning emission inventories (van der Werf et al., 2010) with annual scaling factors from the Goddard Earth Observing System-Chemical Transport Model (GEOS-Chem) (van Donkelaar et al., 2008). In this study, we compute LNO 2 and LNO x profiles as the difference between model output with and without a lightning source. The lightning contribution is based on Allen et al. (2010) and assumes a PE of 500 mol/fl poleward of ±26°and 250 mol/fl equatorward of ±26°. This stepwise change in PE affects modeled amounts of LNO 2 and LNO x but has relatively little impact on their on their profile shapes. Between latitudes 20°and 40°, latitudinal variation of AMF is nonsystematic with a range of~0.3 to~0.7. Any AMF discontinuity near the 26°l atitude line is <0.05.

Data Domain
The domain for this study was selected based on the quality of available OMI and WWLLN data. Increases in noise and the effects of the row anomaly significantly compromised OMI data from 2009 onward. However, increasing WWLLN DEs reduced uncertainties in the WWLLN flash counts during the same period. The five summers of 2007-2011 were chosen as a compromise between the years of highest OMI and WWLLN data quality. Measurements during this period were taken in three midlatitude regions having high climatological lightning frequency. The regions are (1) the eastern and Central United States and southern Canada along with adjacent parts of the western Atlantic, Gulf of Mexico, and Caribbean between longitudes −115°and −55°and latitudes 20°to 60°; (2) Europe and the Mediterranean, between longitudes −10°and 60°and latitudes 30°to 60°; and (3) East Asia and the western Pacific between longitudes 90°and 150°a nd latitudes 20°to 60°. Further data selection criteria are given in section 3.

Method
Here we describe retrieval of LNO x amounts from the level-2 OMI NO 2 data. Vertical-column tropospheric NO x over deep convective grid boxes (V LNOx *) is derived from OMI pixel data: Here S is the total SCD from the OMI NO 2 spectral fit v3.0 algorithm (Marchenko et al., 2015). A strat is the stratospheric air mass factor, which depends on viewing geometry. A LNOx is the air mass factor that converts the tropospheric NO 2 slant column to the NO x vertical column, denoted here as V LNOx * (see Allen et al., 2019;Pickering et al., 2016). The asterisk indicates that the vertical column includes contributions from nonlightning NO x sources and nonrecent lightning; that is, a background correction has not been made. V stratZonal is the zonally averaged v3.0 stratospheric VCD (V strat ; Bucsela et al., 2013;Krotkov et al., 2017). It is obtained by smoothing V strat in pixels with CRF > 0.97 and OCP < 500 hPa, using a ±180°longitude and ±3°latitude running boxcar. Zonal smoothing eliminates longitudinal variations in stratospheric NO 2 concentration, tropopause height, and the a priori troposphere used in the STS algorithm. The smoothing is needed because the STS algorithm can erroneously assign small amounts of tropospheric NO 2 to the stratosphere (Allen et al., 2019;Beirle et al., 2016;Bucsela et al., 2013). We multiply the smoothed stratospheric VCD by the stratospheric AMF and subtract from the total SCD to obtain the tropospheric NO 2 SCD, that is, the term in parentheses in equation (1).
The tropospheric SCD is divided by an air mass factor, A LNOx , computed from model GMI NO 2 and NO x profiles and TOMRAD (Davé, 1965) scattering weights. The profiles were created using the difference between model runs with and without a lightning source of NO. Following Pickering et al. (2016), the profile at a given location is chosen from the day with the third largest LNO x column during a given month and year and is considered representative of moderate-to-active convective environments. Midlatitude profile examples for June 2007 are shown in Figure 2. Conceptually, A LNOx is the ratio of the modeled tropospheric LNO 2 SCD to the modeled LNO x * VCD from tropopause to ground. Retrieved V LNOx * therefore includes LNO x * below the OCP that cannot be directly observed by OMI. For the domain of this study, the mean OMI OCP is 483 hPa with a standard deviation of~100 hPa. The corresponding GMI fraction of the LNO x column below the OCP is~10-30%. This range is consistent with profiles from the cloud-resolved simulations of Ott et al. (2010) from the CRYSTAL-FACE campaign.
Only pixels with CRF > 0.97 and OCP < 500 hPa are used in the analysis. These restrictions favor data from the bright, opaque clouds associated with deep convection (Pickering et al., 2016), and minimize contamination by low-and middle-level NO 2 , especially over low-level stratus clouds, which enhance visibility of ambient NO 2 immediately above them (Martin et al., 2002a). LNO x * vertical columns are binned in the 1°longitude × 1°latitude grid boxes used for the WWLLN flashes, with a minimum of 3 OMI pixels per box. The number of LNO x * molecules in each box is obtained by multiplying the average of the vertical columns from the pixels by grid box area. This scheme was chosen over pixel-area weighting (e.g., Nault et al., 2017), which imparts too much weight to pixels at swath edges, where adjacent orbits overlap, and local times can differ from local time at nadir (13:30 LT) by as much as 1 hr. We count WWLLN flashes in a 1-hr window prior to the 13:30 LT OMI overpass. This window minimizes advection of fresh lightning NO x out of boxes before the OMI measurement. The choice of 1 hr is based on mean midlatitude GEOS-5 MERRA upper tropospheric (UT) wind speeds, which are estimated in the range 11 to 21 m/s. It is shorter than the 3-hr window used by Pickering et al. (2016) in their Gulf of Mexico study, where summertime UT wind speeds are 6 to 11 m/s. A tropospheric NO x background is subtracted from the LNO x * in each grid box to remove ambient NO x not generated within the 1-hr flash window. The background is a weighted temporal average of boxes at each geographic location having zero to one flash during the window. Background boxes are subject to the same OCP and CRF restrictions as boxes with lightning and are weighted according to the number of OMI pixels contributing to each. The gridded background is smoothed with a 5°× 5°boxcar to lessen noise and fill in gaps. Subtraction of the two-dimensional background array from the three-dimensional array (longitude, latitude, day) of LNO x * yields an array of LNO x values, defined as LNO x * corrected for background. Grid boxes containing both valid LNO x and nonzero flashes will be referred to as "flashing boxes." LNO x was also corrected for convectively lofted pollution and chemical decay. The amount of lofted pollution is assumed to be proportional to LNO x , as both are assumed to scale with convective updraft strength. Therefore, pollution is considered a fraction of the LNO x signal, rather than an absolute component of the mean background, which consists of boxes without active lightning. The magnitude is derived from DeCaria et al. (2000DeCaria et al. ( , 2005, who examined a midlatitude storm NNE of Denver near the Wyoming border on a day with boundary layer flow from the east. They estimated pollution to comprise <~20% of total anvil-level NO x . We choose a slightly lower 15% pollution correction to account for the mix of rural and urban regions in the data domain. The estimate of chemical decay is based on the 3-hr LNO x lifetime of Nault et al. (2017), which was obtained from measurements in near-field convective outflow. With this value, the average decay over a 1-hr period is~15%, and we adjust measured LNO x upward accordingly. This adjustment approximately cancels the lofted-boundary layer NO x correction; however, both corrections are included in the algorithm.

Geographic Distribution
Maps of OMI and WWLLN data are shown in Figure 3. The red boxes outline the three areas of study -eastern North America, Europe, and East Asia. The fields shown are temporal means of V init -V StratZonal (ΔV NO2 ), LNO x *, LNO x , and lightning in flashing boxes for the five summer (June-July-August) periods. V init is the "initial" vertical column retrieved from OMI, defined as S/A strat , or the ratio of the total OMI NO 2 slant column to the (approximately geometrical) stratospheric AMF. As such, it depends only on the OMI spectral fit with no further geophysical assumptions. In the figure, the fields have been smoothed with a 3°longitude × 3°latitude boxcar for clarity. Qualitatively, Figure 3 shows that the three regions of study contain higher ΔV NO2 , LNO x *, LNO x , and lightning relative to other northern midlatitude areas. Spatial correlations of LNO x * with lightning are highest in China and the southeastern United States. These regions also have relatively high flash rates. Pearson's correlation coefficients, r, between LNO x * and lightning are 0.22, 0.12, 0.25, and 0.22 for North America, Europe, East Asia, and the combined region, respectively. Correlations between LNO x and lightning are weaker, in part due to noise in the subtracted background, but can be seen qualitatively on scales of~2,000 km.
The r values for LNO x are 0.16, 0.15, 0.21, and 0.18 for North America, Europe, East Asia, and their sum, respectively. The significance of these small r values will be examined in section 4.3. Regions with low WWLLN detection efficiencies may be misclassified as background, lessening the contrast between flashing and nonflashing boxes and reducing the LNO x signal. For example, the LNO x * enhancement over NW India and Pakistan is weak in the LNO x field. Lightning climatologies from OTD/LIS do show enhanced lightning in this region (Cecil et al., 2014), but detected flashes are few during the time immediately preceding OMI overflights. The disparity may indicate poor WWLLN coverage with incorrect DE estimates, an inaccurate diurnal distribution of flashes, or lingering ambient LNO x * from earlier convection. Differences in the LNO x * and LNO x fields in the southeastern United States that are less prominent in the LNO x field may also result from lightning before the 1-hr flash window, including recirculation around the Bermuda High (Cooper et al., 2006(Cooper et al., , 2007.

Mean Production Efficiency
The 15-month LNO x and 1-hr flashes were summed over all grid boxes in the data domain to estimate an average PE. This approach is comparable to the summation method of Pickering et al. (2016). Mean LNO x is 130 kmol per flashing box, which is 45% of mean LNO x *. On average, the same flashing boxes contain 740 WWLLN flashes. We compute the ratio of total LNO x to total flashes and obtain an average PE of 180 ± 100 moles LNO x per flash. Bias and error estimates are discussed in section 5. We define the average PE as described to facilitate comparisons with previous studies. If this PE value is representative of all flashes globally, combining it with the estimated mean global flash rate (Cecil et al., 2014) would yield an annual global LNO x budget of 3.5 ± 2.0 Tg N/year. The possibility of regional differences in PE is examined in sections 4.4 and 5.2.

Data Correlations
In Figure 4, ΔV NO2 and LNO x from individual flashing boxes are plotted against DE-adjusted WWLLN flash rates. The points represent the~32,000 flashing boxes in the data set. Approximately 39% of these have negative LNO x values due, in part, to overestimation of the tropospheric background at those locations. ΔV NO2 also contains negative values, indicating some overestimation of stratospheric NO 2 . Data at higher flash rates are relatively sparse, with less than 10% of flashing boxes containing over 2 kfl/hr and~1% having rates exceeding 6 kfl/hr (see also Figure 11). Because of these issues, any relationship between the OMI data and lightning is difficult to discern in the figures. Correlations with adjusted flash rates are r = 0.20 for ΔV NO2 and 0.18 for LNO x .
Although the correlations are not large, they are significant. The p value corresponding to Figure 4b is p < 0.0005. The significance can be further demonstrated by comparing correlations between WWLLN flashes in a given box with OMI-derived LNO x in other boxes. The plots in Figure 5 show r values  Figure 5b, r = 0.18 in the central box represents the value for the LNO x correlation with lightning in the same boxes on the same days. The correlations in surrounding boxes are lower and may be due to advection and/or lightning occurring before the 1-hr integration period. The slight enhancement northeast (to the upper right) of the central box is consistent with the typical southwesterly flow environment for northern midlatitude convection (e.g., Markowski & Richardson, 2011). Figures 5a and 5c also illustrate spatial correlations but compare LNO x on a given day with 1-hr flashes from the preceding and following days, respectively. In the central boxes, LNO x shows minimal correlation with lightning from the previous day (maximum value of r = 0.08 in the central box) and approximately none with lightning on the next day (r = 0.04 in the central box). Together these results are strong evidence that a sizable portion of the LNO x in each grid box is produced by lightning flashes in the same box during the hour before OMI overpass.
A relationship between the OMI and WWLLN data becomes clearer when the lightning-NO x metrics V init , ΔV NO2 , LNO x *, and LNO x are binned by flash rate, as shown in Figures 6a-6d, respectively, using three OCP thresholds. The fields from Figures 6a-6d represent successively greater amounts of processing applied to the OMI data. Specifically, V init depends only on OMI slant columns (and a geometrical AMF), ΔV NO2 assumes a stratospheric estimate, LNO x * adds the assumption of a model-based AMF, and LNO x includes the additional tropospheric background estimate. All fields exhibit qualitatively similar behavior, showing  a nonlinear dependence on flash rate, with the slopes of the curves implying a decrease in production efficiency as flash rate increases. The curves in Figures 6a-6d are also somewhat more linear for OCP < 400 hPa than for larger OCP thresholds, resulting in higher LNO x * and LNO x (Figures 6c and 6d) at the highest flash rates (see section 4.5). However, V init and ΔV NO2 (Figures 6a and 6b) are both uniformly lower at all flash rates for OCP < 400 hPa due to neglect of LNO 2 in those fields below the OCP altitude. We quantify these effects below and discuss geophysical bases for the nonlinearity in section 5.

Quantitative Dependence of PE on Flash Rate
In Figure 7, LNO x values are averaged in 500-fl/hr bins between 0 and 10,000 fl/hr, with each bin containing at least three flashing boxes. The linear correlation coefficient for the binned data is r = 0.87. Two weighted fits were performed: an ordinary least squares linear fit (blue) and a power function fit (red) given by respectively, where x is kfl/hr and y is kmol LNO x . Weights are inverse standard errors of the mean, shown as error bars. The LNO x PEs are the derivatives of equations (2) and (3). For the linear fit we find a = 79 ± 29 kmol and b = 64 ± 10 mol/fl, where b is the regression-based PE, assuming a linear relationship between flashes and LNO x . The power law coefficient is α = 8.0 ± 0.8 kmol, with exponent β = 0.45 ± 0.01. Fits to the unbinned LNO x data yield a = 94 kmol, b = 45 mol/fl, α = 10.3 kmol, and β = 0.42, with negligible standard errors. While binning clarifies the relationship between LNO x and flashes, the comparable fitted values suggest that results do not depend strongly on binning scheme (see also section 4.5). Reduced chi squares (χ 2 r ) for the linear and power-function fits to the binned data are 10.1 and 1.5, respectively. The comparison shows the power function to be a much better fit than a straight line. In Figure 7a, the data are plotted with   Table 1.

Dependence on OCP
Vertical profiles of mean flash rate and mean LNO x as a function of OCP are shown in Figure 9. Flash and LNO x values for flashing boxes have been averaged in 30-hPa-wide bins. The average flash rate increases with decreasing OCP (Figure 9a), indicating more frequent flashes in deeper convection. This result is in qualitative agreement with the findings of Williams (1985) and Price and Rind (1992), who describe a power   Table 1.

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Journal of Geophysical Research: Atmospheres law dependence on altitude, with exponents of~5 and 1.7 for continental and marine regions, respectively. Sparse high-flash rate marine data in the present study preclude a comparison of the two regions. However, using WWLLN flash rates from all boxes, we find an overall weaker altitude dependence, corresponding to an exponent of 0.87 ± 0.04, as indicated by the dashed line. The fifth power dependence for continental regions is theoretical and based on IR cloud top heights rather than OCP-derived altitudes as used here. Significant averaging is used in the flash-count processing, which could also obscure the apparent altitude dependence. Figure 9b shows average LNO x as a function of OCP. LNO x increases with altitude at large OCPs but decreases and becomes more variable above the 450-hPa level. The cause of the decrease could be related to a bias in the model profiles below the OCP, although a somewhat weaker altitude dependence of LNO x is plausible at higher altitudes, where increases in LNO x due to more flashes may be countered by decreases in PE. This behavior contrasts with the finding of Boersma et al. (2005) that LNO 2 increases with the fifth power of altitude, a result similar to the continental flash-rate dependence of Price and Rind (1992).
As noted in section 4.3, Figure 6 shows that the flash-rate dependence varies with OCP range. The dependences of the fields V init , ΔV NO2 , LNO x *, and LNO x on flash rate become slightly less linear at larger OCPs (lower cloud tops). Exponents, β, for a power law fit to LNO x versus flash, binned as in Figures 7  and 8, are 0.55, 0.45, and 0.40 at OCP thresholds of 400, 500, and 600 hPa, respectively, indicating a progressive decrease in linearity. The β values for the three geographic regions in Table 1 reflect a similar dependence on OCP. Mean OCPs are largest over the convectively active regions of Europe and smallest over convection in SE Asia. These two regions also have the smallest and largest β values, respectively.
Fitting statistics are shown in Figure 10 as a function of the number of bins in the 0 to 10,000 flash-per-hour range. The correlation coefficient, r, decreases from roughly 0.9 to 0.5 at all OCPs (with a small overall decrease toward smaller OCPs) as the number of bins increases from 20 to 200 due to increased scatter. With OCP thresholds of 500 and 600 hPa, reduced chi-squares for the linear fits decrease from approximately 12 to 3.5 and >12 to 4.5, respectively, while those for the power-function fits are relatively constant at~1.5. For an OCP threshold of 400 hPa, the respective reduced chi-squares for the linear and power-function fits have~constant values of 3.5 and 2.5. At that threshold, the smaller disparities between linear and power function fits as well as the weaker dependence of the linear fit on number of bins result from both poorer statistics (due to sparser data above the 400-hPa level) and β values closer to unity than for larger OCP thresholds. Qualitatively, it was found that this OCP dependence does not depend significantly on the form of the OCP restrictions (e.g., whether OCP thresholds or narrow ranges of OCP values are specified), the model-estimated fraction of LNO x below OCP (implicit in A LNOx ), or whether a background is subtracted. Furthermore, there is no known dependence of WWLLN DE on cloud top height. The effects could conceivably result from variations in flash properties, including duration, extent, and radiance, for high-and lowtopped convection, but further exploration is needed to draw any conclusions regarding geophysical causes. The role of flash extent is examined in section 5. Note. Statistics are computed with flashes averaged in 20 bins of 0.5 kfl/ hr.

Flash-Rate Dependent Production
The present results are the first satellite-based study to suggest that LNO x production follows a power function with exponent 0 < β < 1. This relationship appears robust at rates above~100 fl/hr in each grid box but must be modified near a zero-flash rate to avoid an infinite PE. The mean PE is a weighted average of PEs at specific flash rates with weights proportional to the number of flashes at each rate. For a unit flash integration period, let N be the total number of flashing boxes. Also, let x be the flash rate per box, f(x) be the PE, and p(x) dx be the probability of a flash rate between x and x + dx. Integrating over flash rate, the total number of flashes is The corresponding number of moles LNO x produced is and the weighted mean production efficiency is PE = μ/ϕ. Figures 11a-11c are histograms of p(x), x p(x), and f(x). Figure 11a is effectively a density histogram of the scatterplots in Figure 4. All three quantities decrease with flash rate, and Figure 11b indicates that total flash count is dominated by storms with the lowest flash rates. Flash rates in the 32,000 flashing boxes range from 1 to 45,000 fl/hr. Approximately 90% of boxes have rates less than 2,000 fl/hr and these account for 50% of all flashes.
The smaller PE at high flash rates may explain difficulties in detecting significant LNO x in some studies. Pickering et al. (2016) imposed a minimum threshold of 1,000 fl/hr in 1°× 1°grid boxes and obtained a relatively low PE of 80 mol/fl. The 287 cases examined by Beirle et al. (2010) were restricted to rates equivalent to a threshold of 9,000 fl/hr. They found an LNO x -flash correlation coefficient of only 0.04 and PEs less than 15 mol/fl in approximately half of their examined cases. These values are consistent with the present study at comparably high flash rates.

Geophysical Implications
Studies have suggested that PE may be directly related to flash size, with larger flashes producing more LNO x (Carey et al., 2014;Huntrieser et al., 2008;Marais et al., 2018). During the TROCCINOX campaign, Huntrieser et al. (2008) attributed lower tropical PE values to shorter stroke lengths relative to those of midlatitude storms. The effect of flash extent and LNO x production was quantified by Carey et al. (2014). They applied the NASA Lightning Nitrogen Oxides Model (Koshak, 2014) to observations made during the Deep Convective Cloud and Chemistry campaign and computed LNO x production per meter of channel length from a Lightning Mapping Array, based on laboratory measurements and theoretical assumptions.

Journal of Geophysical Research: Atmospheres
They found LNO x production to be highly correlated with flash extent (correlation coefficient of r = 0.99), indicating that the PE is controlled almost entirely by the flash size.
Evidence from field campaigns have also shown a relationship between flash rate, flash size, and updraft strength. In a study of two 2004 supercells, Bruning and MacGorman (2013) reported that increasing updraft strength is associated with smaller flash extents and higher average flash rates. Similar associations were noted by Carey et al. (2005), Kuhlman et al. (2006), and Weiss et al. (2012), as well as studies from the Deep Convective Cloud and Chemistry campaign (Barth et al., 2015;Bruning & Thomas, 2015;Carey et al., 2014;Mecikalski et al., 2015). Bruning and Thomas (2015) demonstrated that the anticorrelation between flash rate and size is strongest during the decay phase of the storm as the updraft weakens and flash rates drop, while the total energy from lightning diminishes. Marais et al. (2018) noted a stronger correlation of LNO x with flash extent than with flash duration or radiance, implying that the dependence of flash extent on flash rate may be the dominant factor driving the PE dependence on flash rate, consistent with Carey et al. (2014). Together, the above studies provide a possible geophysical basis for the dependence of PE on flash rate found in the present investigation.
Many CTMs parameterize LNO x production with the assumption that midlatitude flashes produce more NO per flash than tropical flashes based on analyses of data from field campaigns Hudman et al., 2007;Murray et al., 2012;Ott et al., 2010). In general, tropical production is constrained by satellite and sonde measurements of O 3 , while upward adjustments in midlatitude production have been applied to match in situ aircraft data (Martin et al., 2002b;Martin et al., 2006). The contention of Huntrieser et al. (2008) that higher midlatitude PEs are related to longer midlatitude strokes was based, in part, on speculation that the stronger wind shear in that region generates longer flashes. However, this hypothesis is contradicted by the association between stronger wind shear and stronger updrafts (e.g., Markowski & Richardson, 2011). These updrafts yield more frequent, but smaller, less productive flashes, as noted above. The midlatitude PE of the present study does not differ significantly from the tropical value of 170 ± 100 mol/fl from Allen et al. (2019), given the large uncertainties in the two results. The two are comparable since both analyses were based on the relationship between V LNOx * and WWLLN flashes, although the method of estimating PE from the relationship differed. Marais et al. (2018) also found no significant difference between middle and tropical latitudes and noted that the higher GEOS-Chem midlatitude PE of 500 mol/fl overestimated observed OMI NO 2 .

Estimate of Uncertainty in the Average PE
In general, PE estimates are strongly dependent on the methods used to process the data (see Appendix B). For this study, the sensitivity of the PE to algorithmic assumptions was used to quantify systematic errors, which are the main components of the error budget. Statistical errors in OMI and WWLLN data were found to be negligible, as in Bucsela et al. (2010). We discuss the error sources individually and combine them to obtain a net uncertainty in the mean PE.

Stratosphere
Stratospheric NO 2 is the largest component of the total NO 2 column, constituting~95% of the NO 2 vertical column for all grid boxes in the data domain and~85% for boxes with >5,000 fl/hr. As such, it is a

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Journal of Geophysical Research: Atmospheres significant, though not the largest, contributor to the total error budget, as described below. Zonal smoothing of the NASA OMI NO 2 stratosphere mitigates aliasing of parts of the tropospheric signal into the stratosphere (Allen et al., 2019;Beirle et al., 2016;Bucsela et al., 2013). Although the smoothing does alias stratospheric features that depart from the zonal mean into the troposphere, these departures have a mean value of~0 and do not bias the average PE. Figure 12 shows mean V init and mean stratospheric NO 2 with and without zonal smoothing as a function of flash rate. V init increases by~0.5 × 10 15 molecules/cm 2 as the flash rate increases from~0 to~12,000 fl/hr. Over the same range, V StratZonal increases slightly by 0.04 × 10 15 . However, V strat shows a larger increase of 0.15 × 10 15 as the flash rate increases due to stratospheric aliasing of LNO 2 . The difference in the mean values of V strat for boxes with a flash rate of zero, which are used for the background estimate, and the values in flashing boxes introduce a low bias in LNO x and PE for the unsmoothed stratosphere. The PE derived from the latter is 120 mol/fl, which is~30% lower than that derived from a zonally smoothed stratosphere.
To test the effects of stratospheric column errors, a uniform bias of ±2 × 10 14 cm 2 was applied to the zonally smoothed stratosphere. The magnitude of this bias is in line with previous stratospheric NO 2 uncertainty estimates (Boersma et al., 2004(Boersma et al., , 2007Bucsela et al., 2006). It is twice the error assumed by Allen et al. (2019) and Bucsela et al. (2010) in the tropics, where stratospheric columns are approximately half those at midlatitude, and the absolute uncertainty is assumed to be smaller. A ±2 × 10 14 -cm 2 error is 5-10% of the total midlatitude NO 2 column,~90% of which is stratospheric. However, its effect on PE is only ±14% since it is uniform and is partially canceled in the background subtraction. Without background subtraction, the stratospheric bias would have a >90% effect on PE. The stratospheric component of the PE error is taken to be ±15% (see also Allen et al., 2019).

Transport and Chemistry Effects
In this study, all LNO x from lightning in the 1-hr integration period before the 13:30 LT OMI overpass is assumed to be accounted for in the retrieval and full correction made for contamination by ambient NO x . The fact that OMI measurements are made well before the late-afternoon convective peak complicates the retrieval by decreasing the component of fresh LNO x in the total NO x signal. Derived LNO x amounts are affected by errors in estimates of lofted pollution, LNO x lifetime, advection, and background. The 3-hr lifetime for LNO x in near-field of convection (Nault et al., 2017) is shorter than previous estimates of approximately two to eight days (Jaeglé et al., 1998;Martin et al., 2007;, which would make chemical loss negligible. B. Nault (private communication) gives an uncertainty range in his lifetime of 2 to 12 hr depending on the proximity to deep convection. In a 1-hr window, this introduces a PE uncertainty of ±10%. For boundary layer contamination, we assume a possible range of 10-20% for lofted pollution (DeCaria et al., 2000(DeCaria et al., , 2005, which brackets our 15% downward adjustment in PE by ±5%. Advection of LNO x from flashing boxes could result in a negative PE bias. If upper tropospheric wind speeds are~16 m/s (a reasonable value for the midlatitudes in summer), a simple calculation shows that approximately 30% of the LNO x would be advected out of the box during the hour before measurement, with a reduction in PE by the same amount. The net loss would be lower if advection into the boxes from upwind sources compensates for some of the loss. The amount of this loss may also be estimated by comparing PEs derived from flashes over 1-and 2-hr intervals. Assuming an accurate NO x , higher flash rates over a longer window should be offset by a smaller background, with minimal net effect on PE. It was found that the PE based on 2-hr flashes is 15% smaller than the PE derived from 1-hr flashes. We attribute this difference mainly to advection. Overall, we estimate advection introduces a potential negative bias in PE of~20% and assume an uncertainty of ±10%. The mean midlatitude background estimated from nonflashing boxes is 55 ± 10% of total LNO x *, where the uncertainty is the standard deviation of interannual variability. This is~3 times the a priori 18 ± 15% background of Pickering et al. (2016) in the Gulf of Mexico. The ±10% background error here propagates as a PE uncertainty of ±15%. Background days not only lack flashes during the 1-hr flash-integration window but also contain relatively few flashes during preceding hours. As such, even though they meet the CRF and OCP criteria used in this study, they may represent a less convectively active environment than that of flashing boxes, which are more likely to have flashes preceding the integration window. This may introduce a bias in the background, and therefore PE, although the effect is difficult to quantify. We assign an uncertainty of ±20%, which is less than the~30% uncertainty obtained by Allen et al. (2019), who based their value on the sensitivity of PE to uncertainties in the y intercept of their regression-based estimate of PE.

NO 2 Profiles
Retrieved LNO x * is inversely proportional to the air mass factor A LNOx in equation (1). Beirle et al. (2009Beirle et al. ( , 2010 estimated AMFs for a variety of storm environments and found that a fixed average AMF of 0.46 was adequate for their LNO x retrievals from Scanning Imaging Absorption Cartography NO 2 data. We find this value reasonable, since substitution of the Beirle et al. AMF decreased the present PE by only 13%. The AMF is computed with GMI a priori NO 2 and NO x profile shapes from days with the third largest LNO x column in a given month but is relatively insensitive to the rank within the month. Using the first or tenth largest columns changed the PE by only~5%. Midlatitude simulations put 10-15% of LNO x at altitudes below 600 hPa,~20% below 500 hPa, and~30% below 400 hPa. Between OCP thresholds of 400 and 600 hPa, the average PE varies by ±12%. We adopt a net PE uncertainty of ±15% due to errors in profile shape and OCP threshold. The partitioning of NO x into NO and NO 2 in GMI/GEOS-Chem, which affects the AMF, has been re-examined recently by Travis et al. (2016) and Silvern et al. (2018). They found GEOS-Chem NO/NO 2 ratios near and above 10 km to be approximately a factor of 2 larger than those of in situ measurements from the SEAC 4 RS campaign. Travis et al. (2016) attribute this to model underestimation of HO 2 and RO 2 , but Silvern et al. (2018) suggest that their required model adjustments of peroxy radicals are inconsistent with observations. Instead, Silvern et al. (2018) posit a combination of model errors in the NO 2 -to-NO photolysis rate and the NO + O 3 reaction rate, k 1 , along with possible bias in the in situ data due to a neglected labile NO x reservoir. They noted that a k 1 increase of a factor of 1.4 and a photolysis rate decrease of 20% reduced the model NO/NO 2 by~40%. The net effect is a~28% reduction in NO x /NO 2 and hence an increase in A LNOx with a corresponding 28% decrease in PE. However, given that their factor of 1.4 represents an~2σ change in k 1 , that there are also possible significant measurement interferences, and that Silvern et al. and Travis et al. are relatively recent studies, we account for the potential error as a 20% high bias with a ±15% uncertainty (see also Allen et al., 2019).

WWLLN DE
The WWLLN flash counts are the largest source of PE uncertainty. Pickering et al. (2016) estimated a ±30% uncertainty in their WWLLN counts for the Gulf of Mexico, based on two independent schemes for estimating the DE, which differed by 25-30%. Their DEs were~10-25% in the years 2007-2011. Citing North Alabama Lightning Mapping Array (Koshak et al., 2004) data, Allen et al. (2019) questioned whether the Pickering et al. ±30% was too low, given the small size of the Gulf region and the temporal variation of their DEs. In their tropical study, Allen et al. assigned uncertainties to the WWLLN data proportional to area-size and WWLLN DE. Adopted uncertainty values were ±25% for the tropics as a whole and approximately twice that value for subregions that included the tropical Americas, Africa, and the Pacific, as well as the Gulf of Mexico. The mean area-weighted DE for the tropics was~13%, and the entire geographic area covered was 2.6 × 10 8 km 2 . In the present study, the mean area-weighted DE is~6% over our total geographic area of 0.6 × 10 8 km 2 . Based on these considerations, we assign a conservative uncertainty of ±45% to our WWLLN flash counts. Journal of Geophysical Research: Atmospheres

Net Uncertainty
The net uncertainty in average PE combines the major sources of systematic error described above and summarized in Table 2. An additional uncertainty of ±5% is included to account for errors in the NO 2 slant columns (Allen et al., 2019;Krotkov et al., 2017;Zara et al., 2017). The biases are defined as the change in PE resulting from neglect of an error source. Net positive and negative biases turned out to be equal in magnitude and so have no net effect on average PE. Following Bucsela et al. (2010), Pickering et al. (2016), and Allen et al. (2019), errors are added in quadrature. The resulting uncertainty is ±58%.

Conclusions
The production efficiency of LNO x and its apparent dependence on flash rate have been explored with OMI NO 2 and WWLLN lightning measurements. We obtain an average summertime northern midlatitude PE of 180 ± 100 mol/fl. The midlatitude data set and algorithm used here are comparable to those of the tropical study of Allen et al. (2019) and the Gulf of Mexico study of Pickering et al. (2016). Both were based on OMI and WWLLN data but employed significantly different approaches. The Allen et al. tropical results do not provide compelling evidence of a systematic difference in PE between the tropics and midlatitudes, since the error bars in theirs and the present study have significant overlap. This conclusion was also reached by Marais et al. (2018), who obtained a relatively large PE of 280 mol/fl. However, their use of climatological NO 2 data from cloud slicing and an OTD/LIS lightning climatology in constraining the GEOS-Chem model differs from the present study and complicates direct comparisons with our results. Pickering et al.'s smaller 80 mol/fl is also attributable to algorithmic differences, particularly involving tropospheric background estimation, flash-rate threshold, and NO x lifetime. Their high flash-rate threshold and that of Beirle et al. (2010) are consistent with the small or difficult-to-measure PEs found in those studies, given the strong inverse relationship between PE and flash rate that we have shown here.
We find an approximate power law relationship between the rates of LNO x production and flashes, corresponding to a PE that decreases by an order of magnitude when flash rate is increased by~2 orders of magnitude. A slightly weaker dependence of PE on flash rate is seen over convective clouds having an OCP < 400 hPa. A possible mechanism for the decrease in PE with flash rate may be inferred from several LMA studies showing that flash size and flash rate are also inversely correlated (e.g., Bruning & Thomas, 2015). The flashrate dependence implies a need for caution when extrapolating PE values from limited data sets to estimate global LNO x production. For such estimates, flash rate and size distributions must be taken into account. However, if northern midlatitude distributions in the boreal summer are representative of those globally, then our average estimate of 180 ± 100 mol/fl is equivalent to 3.5 ± 2.0 Tg N/year LNO x , or roughly 16% of total global NO x production.
Future satellite missions with improved instrumentation and temporal coverage will help verify and refine the present PE. In particular, the Tropospheric Monitoring Instrument is providing NO 2 measurements unaffected by OMI's row anomaly and at higher spatial resolution (3.5 × 7 km 2 ) from low Earth orbit (Veefkind et al., 2012). Geostationary instruments, with their measurements spanning the afternoon diurnal peak of convection, will likely prove revolutionary in answering questions raised in previous LNO x studies. The Tropospheric Emissions: Monitoring of Pollution instrument (Zoogman et al., 2017) and Geostationary Environment Monitoring Spectrometer (Kim, 2012) will be such instruments. Their data can be combined with continuous DE-adjusted flash counts from the GOES-16 and GOES-17 Geostationary Lightning Mapper instruments (Goodman et al., 2013).
1. WWLLN stroke data for individual days are partitioned into 15-min time periods and aggregated onto a 2°latitude × 2.5°longitude grid. 2. The gridded stroke data are smoothed temporally and spatially via the applications of a running 31-day average, a 3-hr average, and a 3-point north-south and east-west boxcar smoother. 3. The smoothed WWLLN strokes are averaged over 85 12-month periods with starting dates between January 2007 and January 2014. The annually averaged flash rates from the resulting 85-member time series are then divided by the v2.3 OTD/LIS climatological annual flash rate to obtain annual adjustment factors for each grid box. 4. Initial monthly adjustment factors are obtained by averaging annual scaling factors from the 12 annual periods that contain the month of interest. For example, the July 2011 scaling factor is obtained by averaging scaling factors from 12 periods beginning with the August 2010 to July 2011 period and ending with the July 2011 to June 2012 period. Effectively, the adjustment factors are weighted averages of a 23month period with flashes from the month of interest having a weighting of 12, flashes from the month before and after the month of interest having a weighting of 11, flashes from months two months away from the month of interest having a weighting of 10, and so forth. 5. The month-specific adjustment factors are smoothed via the 3 times application of a seven-point boxcar average and interpolated onto a 1°× 1°global grid. 6. The month-specific adjustment factors are applied to the raw WWLLN flashes and the total flash rate for 2007-2014 is determined and compared to the v2.3 OTD/LIS climatology at each grid box. The adjustment factors are then adjusted to ensure that the mean monthly average flash rate over the 2007-2014 time period at each grid box matches the OTD/LIS climatological flash rate.
The updated month-specific adjustment factors are applied to the raw WWLLN strokes and the total flash rate for 2007-2014 is determined and compared to the bihourly OTD/LIS Low Resolution Annual Diurnal Climatology (Cecil et al., 2014) after it is interpolated from its original 2.5°× 2.5°UTC grid onto a 1°× 1°h ourly grid as a function of LT. The adjustment factors are then modified to ensure that the mean hourly flash rate over the 2007-2014 period at each grid box matches the diurnal climatology.
potentially compromised the accuracy of their background estimate. Their average tropical PE of 174 mol/fl is similar to the present midlatitude value, but the uncertainty is large, and it is based on a limited number of events.
In their LNO x study, Marais et al. (2018) used climatological NO 2 and lightning data to derive a PE of 280 ± 80 mol/fl. Seasonal mean OMI LNO x columns from the v3.0 NASA OMI standard product were obtained by cloud slicing (Choi et al., 2014;Ziemke et al., 2001), with an OCP range of 280-450 hPa and no explicit adjustment for LNO 2 below OCP. Since climatological data represent ambient NO x , accumulated from multiyear lightning activity, no background subtraction is used. The 2006-2008 OMI data were divided into geographic regions 20°× 32°in longitude and latitude and compared with a lightning climatology from OTD/ LIS, which was also used in the present study to calibrate the WWLLN counts. The PE was estimated by constraining the LNO x source strength in GEOS-Chem to best fit the OMI cloud-sliced NO 2 observations. Unlike the present study, they made no correction for a model discrepancy in the NO/NO 2 ratio relative to aircraft data (see section 5.3.3), which could partially account for their relatively high PE. Because of the above differences, comparison of our mean PE with theirs is more challenging than with Pickering et al. (2016).
The recent study of Allen et al. (2019) in the tropics is also similar to the present one. Allen et al. compared OMI LNO x * amounts measured during five austral and boreal summers with WWLLN flashes counted 1-6 hr before OMI overpass. The flashes and LNO x * were processed with the same methods used here. However, their average PE of 170 ± 100 mol/fl was estimated by linear regression, rather than by the present summation method of dividing total LNO x by total flashes. In their approach, the line slope and intercept are the PE and tropospheric background, respectively. Analysis in separate geographic areas revealed higher PEs where flash rates were lower, as well as a larger mean PE over marine relative to continental regions. Their flashrate dependence is consistent with the present study, and their mean tropical PE is statistically equal to our midlatitude value of 180 ± 100 mol/fl.