Observing U.S. Regional Variability in Lightning NO₂ Production Rates

Abstract

Lightning is a large and variable source of nitrogen oxides (NO_x ≡ NO + NO₂) to the upper troposphere. Precise estimates of lightning NO_x (LNO_x) production rates are needed to constrain tropospheric oxidation chemistry; however, controls over LNO_x variability are poorly understood. Here, we describe an observational analysis of variability in LNO₂ with lightning type by exploiting U.S. regional differences in lightning characteristics in the Southeast, South Central, and North Central United States. We use satellite NO₂ measurements from the Ozone Monitoring Instrument with Berkeley High Resolution vertical column densities, a combined lightning data set derived from the Earth Networks Total Lightning Network and National Lightning Detection Network^TM measurements, and hourly winds from the European Centre for Medium-Range Weather Forecasts climate reanalysis data set (ERA5) over May–August 2014–2015. We find evidence that cloud-to-ground (CG) strokes produce a factor of 9–11 more NO₂ than intracloud (IC) strokes for storms with stroke rates of at least 2,800 strokes·cell⁻¹·hr⁻¹. We show that regional differences in LNO₂ production rates are generally consistent with regional patterns CG and IC stroke frequency and stroke current density. A comparison of stroke-based and flash-based CG/IC LNO₂ estimates suggests that CG LNO₂ is potentially underestimated when derived with flash data due to the operational definition of CG lightning. We find that differences in peak current explain a large portion of CG/IC LNO₂ variability, but that other factors must also be important, including minimum stroke rate. Because IC and CG strokes produce NO_x in distinct areas of the atmosphere, we test the sensitivity of our results against the atmospheric NO₂ vertical distribution assumed in the a priori profiles; we show that the relative CG to IC LNO₂ was generally insensitive to the assumed NO₂ vertical distribution.

Key Points

• Lightning NO₂ production rates in the United States vary with regional differences in average current per stroke
• Cloud-to-ground (CG) strokes produce more LNO₂ than intracloud (IC) strokes in the United States
• LNO₂ derived from flash rather than stroke data may obscure CG and IC NO₂ production per stroke differences

1 Introduction

In the upper troposphere (UT), nitrogen oxides (NO_x ≡ NO + NO₂) largely control the atmospheric oxidation capacity and the chemical production of ozone (O₃), a short-lived greenhouse gas and air pollutant (Labrador et al., 2004; Liaskos et al., 2015; Murray et al., 2013; Murray et al., 2014; Tost, 2017). Lightning is the dominant source of NO_x to the UT at 2- to 8-Tg N·year⁻¹ (Schumann & Huntrieser, 2007), contributing as much as 70% of UT NO_x in the tropics, subtropics, and summertime midlatitudes (Allen et al., 2010; Jourdain & Hauglustaine, 2001; Lawrence et al., 1995; Sauvage et al., 2007; Zhang et al., 2003). The mechanism by which lightning produces NO is generally known; however, it has proven difficult to precisely derive lightning NO_x production rates (LNO_x) by correlating measurements of lightning frequency with space-based NO₂ observations in the vicinity of storms (Beirle et al., 2010; Pickering et al., 2016; Schumann & Huntrieser, 2007). Reported LNO_x production per flash spans three orders of magnitude (Beirle et al., 2010; Bucsela et al., 2010; Cooray et al., 2009; Cummings et al., 2013; Finney et al., 2016; Huntrieser et al., 2008; Huntrieser et al., 2009; Huntrieser et al., 2011; Jourdain et al., 2010; Koshak, 2014; Koshak et al., 2014; Laughner & Cohen, 2017; Liaskos et al., 2015; Martini et al., 2011; Miyazaki et al., 2014; Murray, 2016; Murray et al., 2013; Nault et al., 2017; Ott et al., 2010; Pollack et al., 2016) and, averaged over the globe, is subject to a factor of 4 uncertainty (Schumann & Huntrieser, 2007). The wide range in LNO_x estimates is thought to be caused by multiple factors such as challenges associated with correlating measured NO₂ and/or NO with lightning frequency in the dynamic atmosphere; NO_x and lightning measurement uncertainties and variable detection efficiencies; differences in employed instrumentation and lack of standardized LNO_x metrics; influences of nonlightning UT NO_x sources, such as aircraft or the convection of surface emissions; and the natural variability in many lightning physical properties that affect LNO_x production, including lightning type, peak current, and flash length (Wang et al., 1998; Huntrieser et al., 2007; Ripoll et al., 2014a; Ripoll et al., 2014b; Bruning & Thomas, 2015; Koshak, Solakiewicz, et al., 2015).

Lightning nomenclature consists of two fundamental definitions: strokes and flashes. A stroke (sometimes referred to as return stroke in the case of lightning connecting to the ground or K-change for an intracloud stroke) is defined as an impulsive surge of current occurring during a lightning discharge, with this surge thought to cause NO production. A flash consists of one or more strokes connected through a complex structure of hot channels and (cold) streamer coronas. Lightning monitoring networks measure both strokes and flashes and define flashes as one or more strokes sufficiently close in time and space as determined by the specific spatial and temporal parameters of the stroke clustering. LNO_x studies have been conducted using a variety of approaches, including with satellite observations, theoretical models, laboratory experimentation, and aircraft sampling, and a challenge in the literature is that results are reported in units of per flash or per stroke and as LNO, LNO₂, or LNO_x depending on what nitrogen oxide measurements are available. To our knowledge, LNO_x analyses utilizing Lightning Location System (LLS) measurements have to date based LNO_x estimates on flash data, rather than strokes.

Lightning strokes are categorized as cloud to ground (CG) or intracloud (IC). By definition, CG flashes are stroke clusters with one or more CG strokes that may also include one or more IC strokes; IC flashes are stroke clusters with no CG strokes. CG strokes discharge between the lower-cloud charge region (~3–5 km above ground level [agl]) and the ground. IC strokes discharge between intracloud charge regions, typically consisting of a midlevel negative charge region (~5 km agl) and an upper-level positive charge region (~10 km agl) (Stolzenburg et al., 1998). Total and relative CG and IC stroke frequency is a direct function of the charge structure of thunderstorms, with higher-altitude charge regions favoring IC strokes and producing few to no CG strokes (Mansell et al., 2002; Mansell et al., 2010; Rust et al., 2005). The altitudes of the charge regions are related to cloud liquid water depletion, with slower liquid depletion rates leading to higher-altitude in-cloud charge regions (Bruning et al., 2014). Because of this, the ratio of CG to IC strokes varies regionally with climate and geography (Koshak, Cummins, et al., 2015;  Medici et al., 2017; references therein). While IC strokes are more common, accounting for ~70% of all lightning, CG strokes tend to exhibit higher peak currents and typically have longer channel lengths and greater cloud-top optical area extent than IC strokes (Koshak, 2010; Koshak, 2014; Rakov & Uman, 2003). As a result, individual CG strokes are theorized to produce 10 times more NO_x per stroke than individual IC strokes (Price et al., 1997).

Variability in lighting type, that is, CG versus IC stroke prevalence, could contribute a portion of the estimated LNO_x uncertainty (Huntrieser et al., 2008; Schumann & Huntrieser, 2007), but observational evidence is inconclusive. Some studies indicate greater LNO_x for CG strokes and flashes, but others suggest comparable CG and IC LNO_x production rates. For example, Koshak et al. (2014) found that CG flashes produced approximately 10 times more LNO_x than IC flashes (mean values of 484- and 35-mol NO_x·flash⁻¹, respectively) in Northern Alabama August thunderstorms (2005–2009). These estimates were obtained using the NASA Lightning Nitrogen Oxides Model (LNOM), which ingested three-dimensional lightning channel mapping data from the North Alabama Lightning Mapping Array (LMA), peak current information from the National Lightning Detection Network^TM (NLDN), and laboratory-derived LNO_x production parameterizations and theoretical considerations. In an expanded analysis over 9 years (2004–2012) in the same region, Koshak (2014) computed CG and IC production rates of 604- and 38-mol NO_x·flash⁻¹, respectively. Carey et al. (2016) widened the application of the LNOM to include a suite of radar measurements of storm environment, such as storm updraft volume and graupel mass and volume, to calculate CG/IC LNO_x of ~8 (919/116-mol NO_x·flash⁻¹).

By contrast, there are reports that CG and IC strokes/flashes produce similar amounts of NO_x. From a purely electrostatic analysis of the charge neutralized by a lightning flash, Gallardo and Cooray (1996) concluded that CG and IC flashes dissipate similar amounts of energy, which, assuming LNO_x scales linearly with energy per flash, produced comparable LNO_x. Cooray et al. (2009) predicted that CG and IC flashes both produced 3.3-mol NO per coulomb of charge neutralized in a theoretical analysis. Barthe and Barth (2008) found low LNO_x sensitivity to CG/IC flash variability, in this case using vertical winds in convective cells to parameterize LNO_x in a cloud-resolving model (~125-mol NO·flash⁻¹). DeCaria et al. (2005) and Ott et al. (2010) also found comparable CG and IC LNO_x production (500-mol NO·flash⁻¹), determined using cloud-resolved model simulations of several thunderstorms using various CG and IC LNO_x parameterizations, constraining them with in-cloud NO_x distributions measured by aircraft. The NASA Global Modeling Initiative chemical transport model assumed equivalent per flash CG and IC LNO_x but implemented geographic differences between midlatitude (500-mol NO·flash⁻¹) and tropical (250-mol NO·flash⁻¹) lightning, in agreement with empirical studies of midlatitude (480-mol NO·flash⁻¹) (Allen et al., 2010; Jourdain et al., 2010) and tropical (250-mol NO·flash⁻¹) lightning (Bucsela et al., 2010). At the same time, Marais et al. (2018) did not observe differences between midlatitude and tropical LNO_x, deriving LNO_x of 280 ± 80-mol NO_x per total (CG + IC) flash using satellite-based lightning measurements that do not distinguish between CG and IC.

In light of uncertainties in CG versus IC LNO_x production rates, here we exploit regional differences in relative CG and IC stroke frequency across the United States to investigate variability in the ratio of mean LNO₂ produced by CG strokes to that produced by IC strokes (CG/IC LNO₂). We combine observations of NO₂ from the satellite-based Ozone Monitoring Instrument (OMI) Berkeley High Resolution (BEHR) retrieval and lightning data from a combined data product using the Earth Networks Total Lightning Network (ENTLN) and NLDN across the contiguous United States (CONUS) and in three geographic areas, the Southeast, South Central, and North Central United States, where there are pronounced differences in CG/IC strokes (Figure 1, Table 1). We focus on storms with short spatial and temporal delays between stroke occurrence and NO₂ observation and NO₂ measurements with high cloud radiative fraction (CRF) conditions, using a methodology developed by Pickering et al. (2016). Second, we compare CG and IC LNO_x estimates when derived from stroke versus flash frequency data and describe LNO_x variability as a function of stroke peak current data, as opposed to total or type-speciated stroke number. Finally, we discuss uncertainties and test the sensitivity of our results against different OMI BEHR a priori NO₂ profiles.

Figure 1

Total (CG + IC) stroke density, CG/IC, and CG stroke density in the Southeast (red), South Central (blue), and North Central (green) United States according to a combined ENTLN and NLDN data set. Regions are demarcated following CG/IC and CG parameter definitions in Medici et al. (2017) and Koshak, Cummins, et al. (2015). Note that Medici et al. (2017) reported results as IC/CG rather than CG/IC; these have been converted. Bounding box corners (lower left; upper right) for each region are Southeast (25°N, 84°W; 35°N, 79°W); South Central (28.5°N, 103°W; 39°N, 88°W); and North Central (40°N, 103°W; 49°N, 82°W).

Table 1. Mean Daily Stroke Number (Strokes), Daily Current Density (A·Stroke⁻¹), and Daily Current (A) According to a Combined ENTLN and NLDN Data Set Over May–August 2014–2015 for Total (CG + IC), CG, IC, and CG/IC for Lightning 0–2.4 hr Before the OMI Overpass Time (1:50 p.m. LT) in CONUS and Southeast, South Central, and North Central Regions

U.S. region	CONUS	Southeast	South Central	North Central
Mean daily stroke number (x 10^3 strokes)
Total	179	85.4	116	86.8
CG	11.0	5.9	7.7	3.4
IC	168	79.5	108	83.5
CG/IC (unitless)	0.065	0.074	0.071	0.041
Mean daily current density (x 10^3 A·stroke^−1)
Total	5.7 ± 1.9	5.0 ± 2.0	5.7 ± 1.6	5.2 ± 1.8
CG	21.0 ± 4.5	20.9 ± 4.1	20.5 ± 4.0	17.9 ± 4.8
IC	4.5 ± 1.3	3.6 ± 1.2	4.6 ± 1.1	4.6 ± 1.4
CG/IC (unitless)	4.7	5.8	4.5	3.9
Mean daily current (x 10^6 A)
Total	990	403	686	484
CG	231	125	152	60.5
IC	759	279	534	423
CG/IC (unitless)	0.30	0.45	0.28	0.14

• Note. Daily current density uncertainties are 95% confidence intervals.

2 Observations

The OMI onboard the Aura satellite observes the total atmospheric NO₂ column density with global coverage obtained every 2 days since 2008 (due to the OMI row anomaly), passing over the United States at ~1:50 p.m. local time (LT). OMI detects NO₂ by differential optical absorption spectroscopy and is a nadir-viewing imaging spectrometer that measures backscattered solar radiation over the wavelength range 270–500 nm with a spectral resolution of approximately 0.5 nm. We use tropospheric vertical column densities from the BEHR product Version 3-0A, which is a regional retrieval focused on North America that incorporates a number of high-resolution a priori inputs (Laughner et al., 2018; Russell et al., 2011). The BEHR V3-0A air mass factor (AMF) is based on high spatial resolution albedo measurements (0.05° × 0.05°) from the Moderate Resolution Imaging Spectroradiometer 6 MODIS BRF product and monthly NO₂ and temperature profiles simulated by WRF-Chem at 12-km spatial resolution. Modeled NO₂ profiles include a source for lightning NO₂ and boundary layer pollution lofted to the UT by convection, and the profiles were updated to year 2012 emissions (Laughner et al., 2018). We used the “visible-only” product, defined as vertical columns in which the below-cloud NO₂ contributions have not been inferred, regridded to 0.05° × 0.05°.

To limit the impact of anthropogenic pollution on lightning production estimates, we first removed NO₂ columns greater than 3 × 10¹⁵ molecules·cm⁻², which have been shown to be typical of urban NO₂ concentrations (Beirle et al., 2010). A factor of 2 increase or decrease in this cutoff did not alter our conclusions. Second, we only considered NO₂ columns with a CRF greater than 0.9. Pickering et al. (2016) demonstrated that this CRF threshold effectively filtered out most below-cloud NO₂. While these two selection criteria increased the sensitivity of our analysis by reducing noise from below-cloud surface NO_x sources, they potentially biased the results low because a portion of lightning-generated NO₂ should be located beneath the upper portion of clouds. OMI provides cloud optical centroid pressures, which are the atmospheric pressures to which NO₂ is detected, and these pressures are often deeper than the tops of most thunderstorm clouds at 400–600 hPa (Vasilkov et al., 2008).

We created a combined stroke data product using observations from the ENTLN and NLDN. The networks continuously measure lightning stroke occurrence times, geographic locations, type (CG versus IC), polarity, and peak currents. Both networks detect radio frequency radiation emitted by lightning using magnetic direction finding (NLDN) and time of arrival (NLDN and ENTLN) (Rakov, 2013). For the joint product, we merged the ENTLN and NLDN data sets following a methodology similar to Bitzer and Burchfield (2016), ultimately keeping a set of unique strokes and flashes. In brief, we first included all events detected by either network, then tested for duplicates (i.e., events recorded by both networks) determined as any match within the specified time and distance constraints of 1 ms and 25 km. The time constraint was limited by the NLDN 1-ms time resolution. In the case of a match, the duplicate event was counted as a single unique event, and data from ENTLN were incorporated into the final merge. If either network reported a stroke as CG, then that unique stroke was categorized as CG.

ENTLN and NLDN CG stroke detection efficiencies are generally considered to be >90% within the CONUS. High detection efficiencies result from CG strokes being easier to detect at low sensor density (Liu & Heckman, 2011) because they are on average more powerful, larger, and longer in duration. A localized study in Florida reported 97% CG detection by ENTLN using high-speed video confirmation that channels connected to ground indicate (Zhu et al., 2017). Due to high CG detection efficiencies across both networks, we use CG stroke counts as is (no detection efficiency correction applied). Zhu et al. (2017) empirically determined peak current estimation errors of ±15% by comparing ENTLN measurements to observations of triggered—CG strokes, which we included as an additional source of uncertainty in current-based results.

IC stroke detection efficiencies are lower and more variable with network sensor density than CG detection efficiencies. Therefore, to evaluate regional variability in CG/IC LNO_x, we first needed to consider the impacts of spatially variable IC detection efficiencies. To do this, we compared the ENTLN and NLDN combined product (ENTLN + NLDN) with observations from the Lightning Imaging Sensor (LIS) onboard the Tropical Rainfall Measuring Mission (TRMM) satellite. TRMM-LIS has a detection efficiency for total lightning flashes (TRMM-LIS does not distinguish between CG and IC) in North America of ~80% (Bitzer et al., 2016; Boccippio et al., 2002). Because most lightning flashes and strokes are IC (e.g., 94% of strokes in CONUS in May–August 2014; Table 1), LIS group number (similar to stroke number) approximately equals IC stroke number. To determine stroke/group matches between ENTLN + NLDN and TRMM-LIS data sets, we employed the same selection criteria as Bitzer et al. (2016): ±10 ms and 20 km. The resulting total stroke detection efficiency map is shown in Figure 2. Average IC stroke detection efficiencies in the CONUS (up to 38° latitude), Southeast, and South Central United States regions were 45%, 63%, and 44%, respectively, and in general agreement with past estimates for North America (Rudlosky, 2015; Thompson et al., 2014). The average IC flash detection efficiency in CONUS was 88%. The North Central United States was out of view of TRMM-LIS; therefore, we compared IC stroke observations from ENTLN (not the combined product) for each region to those from the International Space Station (ISS) LIS over the time period March–December 2017. ISS-LIS is the same lightning sensor as TRMM-LIS but onboard the ISS, which has an orbit that extends up to ~55° latitude and covers the globe in ~1.5 hr. Detection efficiencies in the North Central region were approximately equal to the South Central United States using ISS-LIS; therefore, we use the detection efficiency value of 44% derived using TRMM-LIS for the North Central United States in this study.

Figure 2

Total stroke detection efficiency of the ENTLN + NLDN data product relative to the space-based TRMM-LIS in areas where TRMM-LIS observations exist over May–August 2014.

ENTLN flash criteria were 0.7 s and 10 km (Liu & Heckman, 2011), and NLDN flash criteria were 1 s and 10 km (Cummins et al., 1998). In May–August 2014, across CONUS, the average number of strokes per flash, known as the multiplicity, was 6.3 for CG + IC, 8.7 for CG flashes, and 5.9 for IC (with IC strokes corrected for detection efficiency). In the case that multiplicity is high and the relative number of CG strokes in the cluster is low, a CG flash, as operationally defined for LLS data sets, would appear to produce a similar amount of NO_x as an IC flash, assuming a similar number of strokes. Multiplicity varied geographically across CONUS, with higher strokes per flash in the U.S. Mid-Atlantic and Florida (Figure 3). High multiplicity areas were better sampled by the LLS. Regional detection efficiency-corrected multiplicities (May–August 2014) were as follows: Southeast, 7.3 (CG + IC), 10.7 (CG), and 6.8 (IC); South Central, 8.1 (CG + IC), 12.2 (CG), and 7.7 (IC); and North Central, 5.9 (CG + IC), 9.5 (CG), and 5.6 (IC).

Figure 3

(a–c) Average number of ENTLN total, CG, and IC strokes per flash (multiplicity) for May–August 2014 uncorrected for detection efficiency. (d–f) ENTLN multiplicity for total, CG, and IC strokes after applying a detection efficiency correction derived from the comparison of the combined ENTLN + NLDN product and TRMM-LIS.

To account for displacement of LNO_x downwind of lightning before OMI sampling, we used hourly winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) climate reanalysis data set (ERA5) (Dee et al., 2011). ERA5 has 37 pressure levels and a horizontal resolution of 31 km².

3 Deriving LNO₂

LNO_x is produced in the form of NO, while OMI detects NO₂. NO is converted to NO₂ through reactions with O₃ and peroxy radicals, and in the presence of sunlight, NO₂ is photolyzed back to NO, regenerating O₃. This chemistry reaches steady state within minutes during the daytime and NO_x partitions to an NO-to-NO₂ ratio as a function of the atmospheric oxidant concentration, temperature, and solar radiation (Leighton, 1961). While O₃ abundance in the UT near storms usually ranges from 60–100 ppb, O₃ mixing ratios at storm cloud edges have been reported as high as 150–400 ppb, with elevated O₃ filaments extending approximately a hundred kilometers downwind of storms (Pan et al., 2014). Enhanced UT O₃ is caused in part by the overshooting of thunderclouds into the stratosphere, which pull high concentrations of O₃ into the troposphere (Pan et al., 2014), new O₃ chemical production from precursors lifted to the UT in convective updrafts (Brunner et al., 1998; Huntrieser et al., 2016b; Pickering et al., 1990), and potentially direct O₃ formation from cold ionization (electrical corona discharge) around the hot plasma channel (Bozem et al., 2014; Kotsakis et al., 2017; Minschwaner et al., 2008). Using aircraft observations from the Deep Convection Clouds and Chemistry (DC3) experiment, Pan et al. (2014) found evidence of stratospherically influenced elevated O₃ concentrations at cloud edges on more than half of the flight segments that sampled of tropopause-reaching storms. All else being equal, a change in O₃ from 80 to 160 ppb would alter NO/NO₂ by more than 40%, adding uncertainty to LNO_x (or LNO) estimates derived from NO₂ observations. This estimate was computed at 10 km agl following data presented for the Southeast U.S. region during the SEAC⁴RS mission (Silvern et al., 2018): j_NO2 = 0.014 s⁻¹ (NO₂ photolysis rate), k_{NO + O3} = 3 × 10⁻¹²exp(−1,500/T) (NO + O₃ rate expression; Burkholder et al., 2015), T = 240 K, and with 75% of the NO to NO₂ conversion occurring via reaction with O₃. Because of the temperature dependence of k_{NO + O3}, modeled NO/NO₂ ratios increase sharply with altitude (Burkholder et al., 2015); however, aircraft observations indicate that NO/NO₂ ratios are lower than predicted in the UT. On average, over the Southeast United States during SEAC⁴RS, NO/NO₂ ratios above 8 km equaled 1.4 mol·mol⁻¹, which were less than half those modeled by the GEOS-Chem chemical transport modeled and sampled along the flight track (Travis et al., 2016). The cause of this discrepancy is uncertain, with Silvern et al. (2018) suggesting a combination of positive interferences in aircraft NO₂ measurements from known and unknown thermally unstable organic nitrates (Nault et al., 2015; Silvern et al., 2018) and errors in j_NO2 and k_{NO + O3} at low temperatures. As a result, we opted not to assume an NO/NO₂ ratio but instead reported our results as LNO₂ rather than LNO_x. To facilitate comparison with previously published LNO_x estimates, when required, we use the observed NO/NO₂ ratio 1.4 mol·mol⁻¹ or NO_x/NO₂ ratio 2.4 mol·mol⁻¹ (Silvern et al., 2018).

NO₂ is chemically lost on timescales of hours, and oxidation of lightning NO_x prior to the OMI overpass time will artificially lower LNO₂ estimates. The NO₂ lifetime against chemical conversion to organic nitrates and nitric acid in the near field of thunderstorms has recently been revised to ~3 hr from multiple days (Nault et al., 2017). We accounted for NO₂ chemical loss using equation 1 (Nault et al., 2017). We solved for the initial NO₂ concentration, NO₂(0) or NO₂ at t = 0, where NO₂(t) was the NO₂ column density measured by OMI and t was the travel time across a 1° × 1° grid cell. The factor 0.5 represented the assumption that, given a uniform distribution of lightning throughout the grid cell, the average time between NO₂ production and detection, if both are within the same grid cell, will be half the maximum travel time. We used the value of τ equal to 3 hr from Nault et al. (2017). We calculated the cross-cell travel time to be 2.4 ± 1.4 hr, determined using the ECMWF mean wind speed of 16 ± 9 m·s⁻¹, computed over CONUS during the study period at pressure levels 500–100 hPa, and the average grid cell diagonal distance of 136 km.

(1)

To compute LNO₂, we adapted the method described in Pickering et al. (2016), which is outlined here as follows. First, stroke measurements from the combined ENTLN + NLDN data set were summed over a 1° × 1° grid for the local time period of 11:26 a.m. LT (2.4 hr before the OMI overpass) to 1:50 p.m. LT (OMI overpass time), and the NO₂(0) data were averaged to this same grid. Correlations between NO₂(0) and strokes were limited to those co-occurring in the same grid cell in order to reduce LNO₂ variability caused by atmospheric mixing and chemistry on longer timescales. To distinguish the LNO_x signal from UT background NO₂ (NO_2,background) “noise,” Pickering et al. (2016) used a flash frequency threshold of 1,000 flashes·cell⁻¹·hr⁻¹. However, Bucsela et al. (2019) recently demonstrated that LNO_x production efficiency varied with storm flash rate such that lower flash rates yielded higher LNO_x, suggesting that LNO_x estimates were highly sensitive to the application of a minimum flash number. That said, without a flash frequency threshold, there was no guarantee that grids used in the analysis were even electrically active, and, under this condition, the R² of the NO₂(0) and strokes correlation across CONUS was ~0. Here, we opted to apply a minimum hourly flash rate of 1,000 following Pickering et al. (2016), thereby only including grids with lighting in the calculation. Because the average cell residence time was 2.4 hr, our flash frequency threshold was therefore 2,400 flashes·cell⁻¹. During our study period, flashes produced 2.8 times more LNO₂ than strokes (calculated without a minimum flash or stroke threshold), so the equivalent minimum stroke number per cell was 6,720. To test the sensitivity of our results to this stroke rate threshold, we repeated our full analysis at minimum stroke rates spanning 1–10,000 strokes·cell⁻¹·hr⁻¹ (Figure 4a). In agreement with Bucsela et al. (2019), we observed a decreasing trend in LNO₂ with increasing stroke frequency that was accompanied by an increasing trend in R². For example, increasing the minimum stroke rate to 5,000 strokes·cell⁻¹·hr⁻¹ decreased total LNO₂ by 13% and increased R² to 0.6 (from 0.54). At a higher minimum stroke rate of 10,000 strokes·cell⁻¹·hr⁻¹, total LNO₂ decreased by 31%, and R² increased to 0.66. As a consequence of focusing on higher stroke rate storms, our absolute LNO₂ production efficiencies yielded lower LNO₂ per flash compared to those that would be derived using a lower threshold and should be interpreted in the context of the LNO_x dependence on stroke frequency (Bucsela et al., 2019). Critical to this work, we also observed a dependence on minimum stroke rate for the CG/IC LNO₂, which was largely caused by variability in CG LNO₂ (Figure 4), which we report in section 4.1 and discuss in section 4.3.

Figure 4

Stroke threshold sensitivity analysis. (a) Total LNO₂ (solid black circles) and CG/IC LNO₂ (open green circles). (b) IC LNO₂ (brown squares) and CG LNO₂ (orange diamonds). (c) Number of cells per hour (N).

We calculated LNO₂ in units mol NO₂(0)·stroke⁻¹ as the unweighted least squares linear regression slope of the correlation of NO₂(0) versus stroke number after the detection efficiency correction. To simultaneously derive separate estimates for CG and IC LNO₂, we solved the polynomial model with two independent variables in equation 2 (D'Errico, 2019), also as an unweighted least squares linear regression. An example of daily stroke count, NO₂(0), and CRF is shown in Figure 5. The grid boxes marked with Xs denote cells meeting the stroke and CRF criteria that would be included for that day. Equation 2 outputs were the production efficiency for IC and CG strokes (IC_LNO2 and CG_LNO2), the correlation slope, and NO_2,background, a constant representing NO₂ contribution from nonlightning sources analogous to the y-intercept. Equation 2 was also solved for LNO₂ in units mol NO₂(0)·flash⁻¹ using IC and CG flash data. Regressions treated uncertainty in the y-direction only, as NO₂ measurement errors were much larger than stroke frequency errors (discussed in section 4.3). We calculated LNO₂ separately for CONUS (174 days with one or more cells meeting the selection criteria) and the Southeast (58 days), South Central (78 days), and North Central (44 days) U.S. regions.

(2)

Figure 5

Sample day (25 June 2014) showing stroke count, NO₂(0), and CRF. The grid boxes marked with an X meet analysis criteria, stroke number ≥ 6,720, and CRF ≥ 0.9. Note that the white strips in the NO₂(0) and CRF plots are due to the known row anomaly.

4 Results and Discussion

4.1 Total (CG + IC), CG, and IC LNO₂ by Region

Correlations between NO₂(0) and stroke number for CONUS and the three U.S. regions are shown in Figure 6. The resulting LNO₂ (mol NO₂·stroke⁻¹) is given in Table 2 for all strokes (CG + IC) and for CG and IC separately. The highest total (CG + IC) LNO₂ production rates were observed in the South Central United States, the region with the most frequent lightning strokes and where strokes have the largest mean stroke current density (Table 1). The Southeast United States experienced similar average LNO₂ compared to CONUS but experienced the lowest stroke frequency and stroke current density. The North Central region had the lowest total LNO₂ production rate, but stroke number and daily stroke current densities were comparable to the Southeast United States. The significance and statistical characteristics of LNO₂ correlations are presented in Tables 3 and 4, respectively. Regional LNO₂ (CG + IC) differences were significant at the 5% level, with the exception of the Southeast and South Central United States, where differences were statistically significant at the 10% level (Table 3). Total LNO₂ in the Southeast United States was statistically indistinguishable from CONUS, while the South Central and North Central United States were significantly different at the 10% level. The linear fits resulted in y-intercepts of ~10% or less of the LNO₂ estimates (Table 4), indicating small contributions from nonlightning sources in all regions. Correlation coefficients for CONUS and in the South Central and Southeast United States were R² 0.5–0.6. The poorest correlation was observed in the North Central United States (R² = 0.39), which was potentially caused in part by the smaller number of data points in the fitting (N) and uncertainty in the detection efficiency correction because of the lack TRMM-LIS overlap.

Figure 6

Daily NO₂(0) versus total (CG + IC) strokes using ENTLN + NLDN for (a) CONUS, (b) Southeast, (c) South Central, and (d) North Central United States. The solid line is the linear fit, and the dashed lines represent 95% slope confidence intervals.

Table 2. LNO₂ (Mol NO₂·Stroke⁻¹) in CONUS, Southeast, South Central, and North Central United States Determined Using Stroke Frequency Data for Total (CG + IC), IC, and CG Lightning

	LNO2 (mol NO2·stroke^−1)
U.S. region	CONUS	Southeast	South Central	North Central
Total	1.6 ± 0.1	1.6 ± 0.2	1.9 ± 0.2	1.2 ± 0.2
CG	10.7 ± 2.5	9.7 ± 2.9	10.9 ± 4.4	8.7 ± 11.5
IC	1.1 ± 0.1	0.9 ± 0.3	1.2 ± 0.4	0.9 ± 0.5
CG/IC (unitless)	9.7	10.8	9.1	9.7

• Note. LNO₂ was calculated for grids with a minimum stroke rate of 2,800 strokes·cell⁻¹·hr⁻¹. Uncertainties are 95% confidence intervals.

Table 3. p Values Describing Significance of CONUS and Regional LNO₂ (Mol NO₂·Stroke⁻¹) Differences for Results in Table 2

	p values for slope differences
U.S. region	CONUS	Southeast	South Central	North Central
CONUS	-	0.93	0.004	<0.001
Southeast	0.95	-	0.088	0.008
South Central	0.09	0.040	-	<0.001
North Central	0.006	0.030	<0.001	-

Table 4. Statistical Characteristics of Linear Correlations in Figure 6: y-Intercept (Mol NO₂), Number of Data Points (N), R², and R² Values for the CG-IC Model (Equation 2) in CONUS, Southeast, South Central, and North Central United States

U.S. region	y-intercept (x 10^6)	N	R^2 (CG + IC)	R^2 (equation 2)
CONUS	0.17 ± 0.03	174	0.54	0.57
Southeast	0.07 ± 0.02	58	0.63	0.67
South Central	0.15 ± 0.03	78	0.50	0.55
North Central	0.14 ± 0.03	44	0.39	0.39

• Note. Results include grids with a minimum stroke rate of 2,800 strokes·cell⁻¹·hr⁻¹.

Solving equation 2, we calculated greater CG than IC LNO₂ production rates (mol NO₂·stroke⁻¹) (Table 2). For CONUS, we found ~9.7 times higher LNO₂ by CG compared to IC strokes. By region, we computed over 11 times greater CG than IC LNO₂ in the Southeast, ~9 times greater in the South Central, and ~10 times greater than IC LNO₂ in the North Central United States. R² values only slightly improved by conducting the linear fit with equation 2, except in the North Central United States where there was no change, suggesting that factors other than stroke type influenced the variance. Regional variability in CG versus IC LNO₂ corresponded to CG to IC differences in mean daily current densities (Table 1), with the highest ratio of CG to IC current densities in the Southeast and the lowest in the North Central United States (CG/IC rather than absolute CG current densities). In most regions, small ratios of CG to IC LNO₂ were accompanied by smaller ratios of CG to IC daily current densities, and vice versa, so differences in CG/IC LNO₂ were compensated for by relative current density differences; however, the North Central region was an outlier. Regional CG/IC differences were not explained by regional variability in IC detection efficiencies. Uncounted IC strokes, or undercorrected detection efficiencies, would have led to false enhancements in CG/IC LNO₂; instead, we observed both the largest CG/IC and highest IC detection efficiencies in the Southeast United States. Absolute values of CG/IC LNO₂ were comparable to ratios reported by other researchers. Koshak et al. (2014) and Carey et al. (2016) used the LNOM and data from the LMA to estimate CG/IC LNO_x of 7.9–13.8 flashes over Alabama, located between the South Central and Southeast United States. While their studies were performed using a small number of thunderstorms, as opposed to the several months of storms in this study, the LMA has a near perfect detection efficiency within its field of view of ~200-km radius (Thomas et al., 2000; Thomas et al., 2004), providing flash extent information to account for differences in flash length. Wang et al. (1998) also found a positive correlation between NO production and current in laboratory sparks, although the correlation was nonlinear.

While the results above were calculated with a minimum stroke rate of 2,800 strokes·cell⁻¹·hr⁻¹, we also tested the sensitivity of CG/IC LNO₂ to this threshold (Figure 4). We observe a decreasing trend in CG/IC LNO₂ from 23 when the threshold is 1 stroke·cell⁻¹ down to 1.6 when it is 10,000 strokes·cell⁻¹·hr⁻¹. That said, even at minimum stroke rate as high as 10,000 strokes·cell⁻¹·hr⁻¹, which only included 386 grids over the study window compared to 2,246 for a minimum stroke rate of 1 stroke·cell⁻¹, CG LNO₂ was still at least 50% greater than IC LNO₂ (CG/IC LNO₂ = 1.6). The trend in CG/IC was driven by decreasing CG LNO₂ with increasing stroke rates, with IC LNO₂ comparatively steady over the minimum stroke rate range. This suggests that observations of the total LNO₂ dependence on storm stroke rate were caused in large part by changes CG LNO_x production efficiency. This variability with stroke rate may also provide at least a partial explanation for differences in CG/IC determined in past observations studies, as past studies have used inconsistent filtering for storm flash frequency.

4.2 Influence of Lightning Data: Stroke, Flash, and Current

To investigate how stroke-based LNO₂ production rates differed from results derived using flash data, we compared stroke-based results to flash-based absolute and CG/IC LNO₂ across CONUS (Figure 7, Table 5). On average, there were 6.3 strokes per flash; however, the total (CG + IC) LNO₂ per flash was only 2.8 times larger than when calculated per stroke. This implies that the use of flash data may underestimate per-flash total LNO₂ by ~55% and per-flash CG LNO₂ by ~70%. We computed that CG/IC LNO₂ equaled 3.4 using flash data (at a minimum flash rate of 1,000 flashes·cell⁻¹·hr⁻¹), which was considerably lower than the ratio of 9.7 determined using stroke data and consistent with our hypothesized biases based on the CG flash operational definition.

Figure 7

CONUS daily NO₂(0) versus total (CG + IC) peak stroke current (a) and total flash number (b). The solid line is the linear fit, and the dashed lines are the 95% slope confidence intervals.

Table 5. CONUS LNO₂ (Mol NO₂·Stroke⁻¹) Estimated Using Stroke Frequency, Flash Frequency, and Peak Stroke Current Data for Total (CG + IC), IC, and CG Lightning

	CONUS LNO2
Lightning data	Stroke (mol NO2·stroke^−1)	Flash (mol NO2·flash^−1)	Peak current (mol NO2·stroke^−1)
Total	1.6 ± 0.1	6.6 ± 4	1.6 ± 0.1
CG	10.7 ± 2.5	18.5 ± 7.9	4.7 ± 2.7
IC	1.1 ± 0.2	5.4 ± 0.9	1.3 ± 0.2
CG/IC (unitless)	9.7	3.4	3.6

• Note. Current has been converted to units mol NO₂·stroke⁻¹ by dividing by the average current per stroke. Uncertainties are slope 95% confidence intervals.

Because NO is presumably produced by current along a lightning channel, comparison of OMI NO₂ with measured lightning current should provide a more direct correlation and may reveal errors inherent in quantifying LNO₂ from stroke or flash frequency observations. We calculated LNO₂ using ENTLN peak current (mol NO₂·A⁻¹) for CONUS by least squares linear regression and equation 2 (Figure 7). To facilitate comparison with stroke-based LNO₂ and literature flash-based estimates, we multiplied the current-based LNO₂ by the mean current per stroke for each lightning type: 5.6 kA (CG + IC), 20.9 kA (CG), and 4.5 kA (IC). Current-based total and IC LNO₂ were within 10% of stroke-based estimates but lower than flash-based LNO₂ results. Current-based CG LNO₂ was 56% lower than calculated using stroke data LNO₂ but as much as 76% lower than flash-based LNO₂.

If LNO₂ production rates for CG versus IC lightning were only a function of peak current, we would expect CG/IC ≈ 1 in units mol NO₂·A⁻¹/NO₂·A⁻¹; however, current-derived CG/IC equaled 3.6. The difference in stroke-based CG/IC and current-based CG/IC (Table 5) indicates that peak current may account for up to ~60% of CG/IC LNO₂ differences but that other factors, to which CG strokes are more sensitive than IC strokes, are also important. In addition to higher peak currents, CG strokes tend to be larger and longer (Koshak, 2014), which may contribute to differences not explained by peak current alone. Huntrieser et al. (2008) found that flash size played a key role in LNO_x production, while peak current was minor, even though the analysis used a model predicting a positive correlation between spark current and NO_x production (Wang et al., 1998). To reduce detection efficiency effects, Huntrieser et al. (2008) only included lightning strokes larger than 10 kA in both subtropical and tropical storms. However, tropical storms tend to have smaller flashes and by extension lower peak current flashes. It is therefore possible that selecting flashes with currents larger than 10 kA introduced a selection bias toward tropical results over subtropical results and obscured the effect of peak current on LNO_x production.

4.3 Comparisons and Uncertainties

To compare our results to previous work, we converted the stroke-based LNO₂ (units mol NO₂·stroke⁻¹) to LNO_x (mol NO_x·flash⁻¹) by assuming NO_x/NO₂ ratio 2.4 mol·mol⁻¹ and 6.3 strokes·flash⁻¹. For CONUS, total (CG + IC) LNO_x was 24.2-mol NO_x·flash⁻¹, which was lower than previous midlatitude results that range 33- to 500-mol NO_x·flash⁻¹ (e.g., Beirle et al., 2010; Ott et al., 2010; Schumann & Huntrieser, 2007). Recently, Nault et al. (2017) proposed that CONUS LNO_x should be increased to 665-mol NO·flash⁻¹, contrary to the low production rate inferred here. There were three key differences between Nault et al. (2017) and this study: the NO₂ measurement timing and source (satellite-based versus aircraft observations); lightning discharge data type (strokes versus flashes); and inference method of lightning production rates (direct calculation versus model-observation comparison). While the focus of our study was not to improve LNO_x accuracy but instead on identifying differences in CG/IC NO_x emissions, we attributed the lower estimates derived here at least in part to inherent differences between different LLS detection sensitivities (discussed below), coarse OMI spatiotemporal resolution compared to aircraft data, statistical rather than case study-based analysis, and the decision to limit NO₂ data to high CRF pixels. In addition, Allen et al. (2019) used the North Alabama LMA to correct the World Wide Lightning Location Network (WWLLN) detection efficiency and TRMM-LIS for a second-order, region-specific correction for a study in the tropics, finding tropical flashes produced 170 ± 100-mol NO_x·flash⁻¹. Because recent work has demonstrated that LNO_x production rates vary with flash rate, such that LNO_x decreases with increasing storm flash frequency (Bucsela et al., 2019), LNO_x comparisons between studies are complicated as results often do not report storm flash rates. With no flash frequency threshold, Bucsela et al. (2019) found an LNO_x rate of 180 ± 100-mol NO_x·flash⁻¹. Under the same conditions (minimum flash rate = 1), we computed LNO_x equal to 36-mol NO_x·flash⁻¹. The higher observed LNO_x in Allen et al. (2019) and Bucsela et al. (2019) may be a combined result of differences in WWLLN detection efficiency correction, which is larger than for ENTLN, as well as the stroke versus flash biases discussed earlier in this paper. Finally, Gordillo-Vázquez et al. (2019) performed a global modeling study using various parameterizations for lightning to determine that LNO_x was on average between 310–441 mol·flash⁻¹; however, oceanic lightning is known to have larger peak currents than continental lightning (Nag & Cummins, 2017), which should result in higher LNO_x.

Because LLS systems, such as ENTLN, NLDN, and WWLLN, are more sensitive to CG than IC strokes (Murphy et al., 2014; Rudlosky & Shea, 2013; Zhu et al., 2016), the measured current per stroke (or flash) is biased high even after correcting for detection efficiency. The ENTLN detects both CG and IC lightning with varying detection efficiencies across CONUS (Liu & Heckman, 2011; Rudlosky, 2015; this study). While past analyses using NLDN and WWLLN have applied corrections for CG and IC detection efficiencies, these corrections do not account for the temporal and spatial variability in detection efficiency inherent in all lightning data sets. This is especially true for IC strokes and flashes, as the detection efficiency corrections are large and therefore highly uncertain. Bucsela et al. (2010) used TRMM-LIS measurements to upscale CG/IC observations from the Costa Rica Lightning Detection Network, a system with similar sensors to the NLDN. Bucsela et al. (2010) ultimately estimated LNO_x of 100–250 mol·flash⁻¹, greater than both our stroke-based (77% greater) and flash-based (84% greater) results. While our method is otherwise similar, Pickering et al. (2016) estimated total LNO_x over the Gulf of Mexico using WWLLN data, with total (CG + IC) corrected using LIS, to be 80 ± 45-mol NO_x·flash⁻¹, which is ~70% larger than our stroke-based results and 80% greater than our flash-based results.

LNO₂ uncertainties were added in quadrature, treating individual errors as uncorrelated (Table 6): NO₂ slant column measurements, ±15%; unobserved NO₂ below the OMI optical centroid pressure, ±15%; stratospheric vertical column subtraction, ±40% (Pickering et al., 2016); and wind-related variability in the stroke counting window (t), ±15%. We estimated ENTLN detection efficiency errors as ±16% for total and IC strokes, which was the standard deviation of detection efficiency estimates over CONUS relative to TRMM-LIS. Due to high detection efficiencies for CG strokes, we estimated uncertainties of ±5%. The y-intercepts (~10⁵ mol) implied small contributions from nonlightning sources. Intercept values were larger than in Pickering et al. (2016), which were stated to be near 0; however, their region of study was the Gulf of Mexico, where surface NO₂ emissions were minimal. Cloud-resolving models and aircraft studies over rural areas found that 83–90% of NO_x within the anvil of a storm was produced by lightning (DeCaria et al., 2000; DeCaria et al., 2005); as a result, we considered errors in the tropospheric background NO₂ column to be ±20% (Bucsela et al., 2019). We used ENTLN current errors of ±15% (Zhu et al., 2017), determined for negative polarity CG strokes. We know of no estimates of IC current error and therefore applied ±15% to all current measurements. Combined uncertainties were ±50% (CG) and ±52% (IC) LNO₂ using stroke frequency data and ±52% (CG) and ±54% (IC) LNO₂ using current data. Since most strokes were IC, we used IC uncertainty estimates for total (CG + IC) LNO₂.

Table 6. Estimated Errors for Stroke, Flash, and Current-Based LNO₂ Analyses

Errors	CG	IC
Strokes and Flashes
Slant column measurementd	5%	5%
Optical centroid pressurea^,d	15%	15%
Stratospheric NO2 removalb	40%	40%
Stroke/flash counting due to wind	15%	15%
Detection efficiency	5%	16%
Tropospheric backgroundd	20%	20%
Total	50%	52%
Current
Current estimatesc	15%	15%
Total	52%	54%

• ^a Pickering et al. (2016).
• ^b Krotkov et al. (2017).
• ^c Zhu et al. (2017).
• ^d Bucsela et al. (2019).

Restricting the analysis to high CRF pixels may have also contributed to LNO₂ estimates that were biased low and influenced the relative CG to IC results, as approximately 30% of LNO_x is expected below the cloud (Pickering et al., 2016). To investigate this, we performed four sensitivity tests varying the a priori NO₂ profile and combining these custom profiles with BEHR scattering weights to derive AMFs using equation (3) in Laughner et al. (2018). New AMFs were applied to OMI slant columns to compute vertical column densities, which were then used to recalculate LNO₂. Because of slight differences in how the AMF was applied here from the BEHR retrieval, we included a baseline run with BEHR a priori NO₂ profiles. Lightning NO₂ profiles were represented by a vertical Gaussian distribution for which we varied altitude of the peak (hPa), peak magnitude (ppb), and peak width (hPa) inferred from the NO and NO_x aircraft measurements in thunderstorm outflows during the DC3 campaign reported in Huntrieser et al. (2016a). The sensitivity test parameters were as follows: peak altitude, 200 and 500 hPa; magnitude, 0.1 and 0.9 ppb NO₂; and width, 60 and 120 hPa. We found that the relative CG to IC LNO₂ was generally insensitive to the NO₂ vertical distribution, with case study results varying by less than 5% (Table 7). The largest effects on CG/IC were observed by increasing the width of the NO₂ distribution, effectively adding more LNO₂ throughout the cloud. The greatest total LNO₂ was determined when the majority of NO₂ was narrowly distributed (0.1 ppb and 60 hPa) high in the atmosphere (200 hPa) or the original magnitude (0.9 ppb and 60 hPa) low in the atmosphere (500 hPa). Changing the NO₂ distribution peak height had a stronger effect (15%) on CG LNO₂ than changing the peak magnitude (8%). Overall, this analysis implied that the NO₂ profile did not have a major impact in the total LNO₂, with less than 15% difference between all test cases. Increasing the source height from 500 to 200 hPa produced a 13% difference, less than our 30% estimated errors due to our use of high CRF data. Furthermore, these results suggested that relative CG to IC LNO₂ was not a result of the NO₂ profile used by BEHR. Because the DC3 campaign focused on anvil sampling, not on sampling entire clouds, the vertical extent of LNO_x in active storm clouds could be greater than used here (60 and 120 hPa); however, the effect of widening the distribution would likely be too small to alter our conclusions.

Table 7. CONUS LNO₂ (Mol NO₂·Stroke⁻¹) Estimated With Stroke Frequency Data for Total, GC, and IC Lightning Using BEHR NO₂ Profiles in Four Profile Sensitivity Studies, in Which the Gaussian Distribution Parameters of Peak Altitude, Magnitude, and Width Were Varied

	LNO2 (mol NO2·stroke^−1)
Parameters	Test 1	Test 2	Test 3	Test 4	BEHR a priori
Altitude (hPa)	200	200	500	200
Magnitude (ppb)	0.1	0.9	0.9	0.9
Width (hPa)	60	60	60	120
Total	1.5 ± 0.1	1.3 ± 0.1	1.5 ± 0.1	1.3 ± 0.1	1.5 ± 0.1
CG	9.8 ± 2.2	9.0 ± 1.9	10.4 ± 2.1	8.5 ± 1.8	10.2 ± 2.4
IC	1.0 ± 0.2	0.9 ± 0.1	1.0 ± 0.1	0.9 ± 0.1	1.1 ± 0.2
CG/IC (unitless)	9.8	10	10.4	9.4	9.3

• Note. Uncertainties are 95% confidence intervals.

The theoretical advantage of the BEHR profiles was that the high spatial resolution of the profiles is theoretically better able to capture the vertical distribution of NO₂ resulting from lightning than retrievals that use coarser profiles (the subproduct with daily profiles would theoretically better capture the temporal variation in vertical distribution due to lightning but did not cover the time period of interest for this study). However, the profile sensitivity results suggested that the variability in profile shape unique to lightning had smaller effect on LNO₂ estimates than did errors from other sources. Here, we used the “visible-only” AMFs, which did not estimate the below-cloud NO₂. Given that the error due to obscured below-cloud NO₂ is 30%, a hybrid approach using daily BEHR profiles to estimate the below-cloud component could be a significant improvement. To date, validation of the BEHR a priori profiles has focused on the day-to-day variability in urban areas (Laughner et al., 2019) or the average performance in rural areas with significant lightning influence (Laughner et al., 2019; Laughner & Cohen, 2017). Recent work by Zhu et al. (2019) has improved the average accuracy of the simulation from which BEHR a priori profiles are derived, but validating the ability of those profiles to reproduce the day-to-day variability of lightning NO₂ in the profiles remains to be done.

5 Conclusions

We conducted an observational analysis using OMI BEHR NO₂ columns and a combined ENTLN + NLDN lightning data product to investigate variability in per-stroke LNO₂ as a function of lightning type. For CONUS, we found that total (CG + IC) LNO₂ equaled 1.6 ± 0.1-mol NO₂·stroke⁻¹, which was lower than typically reported in the literature. We computed LNO₂ production rates for three U.S. geographical regions, the Southeast, South Central, and North Central United States, with distinct lightning characteristics, relative prevalence of CG and IC lightning strokes, and stroke current densities. We showed that regional LNO₂ differences were generally explained by variability in these lightning properties, with average current per stroke being an especially strong predictor of LNO₂ variability. We separately estimated the CG and IC LNO₂, finding a factor of 9–11 difference in CG/IC for all regions. We also find that this factor is significantly dependent on the storm stroke rate, with CG/IC LNO₂ decreasing with increasing stroke frequency, which may provide partial explanation as to why some past observational studies have found similar CG and IC NO₂ production efficiencies. Because of how CG and IC flashes are operationally defined, we demonstrated that LNO₂ estimates derived from flash data underestimated CG/IC compared to stroke-based results. Due to the larger uncertainties in current measurements, it was unclear whether the stroke or current data were more accurate. Finally, we studied the sensitivity of our results to various BEHR NO₂ a priori profile shapes, finding that CG/IC was generally insensitive to changes in the magnitude, height, and width of a Gaussian NO₂ distribution derived from empirical aircraft measurements.

Acknowledgments

The authors thank Dr. Scott Rudlosky for his helpful comments and insight. BEHR NO₂ V3 vertical columns are available for download at https://behr.cchem.berkeley.edu/download-behr-data/. ENTLN measurements were obtained freely by request from Earth Networks (https://www.earthnetworks.com). The authors acknowledge Vaisala, Inc., for providing the NLDN data set. The ERA5 is provided by ECMWF (http://apps.ecmwf.int/data-catalogues/era5/). ECMWF data contain modified Copernicus Climate Change Service Information 2014–2015.