Observations of Lightning NO_x Production From GOES-R Post Launch Test Field Campaign Flights

Abstract

A primary goal of the Geostationary Operational Environmental Satellite R-series Post Launch Test (GOES-R PLT) Field Campaign during spring 2017 was the performance evaluation of the Geostationary Lightning Mapper (GLM) aboard the GOES-16 satellite. The NASA Goddard Geo-CAPE Airborne Simulator (GCAS), an ultra-violet visible spectrometer, piggybacked on the aircraft mission to allow continuous hyper-spectral measurements at high spectral and spatial resolutions simultaneously with optical lightning detection by the Fly’s Eye GLM Simulator while overflying convective systems. NO₂ columns retrieved from GCAS were used to estimate the moles of NO_x produced per flash, referred to as lightning NO_x production efficiency (LNO_x PE) for convective systems over the United States and western Atlantic. The mean PE was determined to be 360 ± 180 mol per flash for optically detected GLM flashes and 230 ± 115 mol per flash for radio-wave detected Earth Networks Total Lightning Network flashes. These values span the commonly cited range of 100–500 mol per flash for midlatitude flashes. LNO_x PE was found to be positively correlated with GLM flash multiplicity and flash optical energy but negatively correlated with flash density. The positive correlations provide encouragement for PE parameterizations in terms of flash energy or multiplicity. Observations during the GOES-R PLT field campaign provide a preview of the analysis that will be possible when continuous lightning detection is coupled with hourly NO₂ columns from a geostationary instrument such as Tropospheric Emissions: Monitoring of Pollution.

Key Points

• NO₂ columns from Goddard Geo-CAPE Airborne Simulator are used to estimate NO_x production per flash

• NO_x production by lightning detected by the Geostationary Lightning Mapper over the United States is found to equal 360 mol per flash

• NO_x production per flash is positively correlated with flash multiplicity and optical energy but negatively correlated with flash density

Plain Language Summary

A goal of the Geostationary Operational Environmental Satellite R-series Post Launch Test (GOES-R PLT) Field Campaign during spring 2017 was evaluation of the Geostationary Lightning Mapper (GLM) aboard the GOES-16 satellite. The NASA Goddard Geo-CAPE Airborne Simulator (GCAS) piggybacked on the aircraft allowing for continuous column measurements of NO₂, a member of the nitrogen oxide family (NO_x) that is also an ozone precursor. NO₂ columns from GCAS were used to estimate the moles of NO_x produced per lightning flash for 10 convective systems over the United States and western Atlantic. The moles of NO_x produced per flash was determined to be approximately 360 mol per flash for optically detected GLM flashes and 230 mol per flash for radio-wave detected Earth Networks Total Lightning Network flashes. These values span the commonly cited range of 100–500 mol per flash for midlatitude flashes. Observations during the GOES-R PLT field campaign provide a preview of the analysis that will be possible when continuous lightning detection is coupled with NO₂ columns from a geostationary instrument such as Tropospheric Emissions: Monitoring of Pollution.

1 Introduction

Lightning produces nitrogen monoxide (NO) as the extreme temperatures (>20,000 K) in lightning channels dissociate molecular oxygen (O₂) and molecular nitrogen (N₂) forming NO, which quickly reacts with ozone (O₃) to form nitrogen dioxide (NO₂) (Zel’dovich et al., 1947). The nitrogen oxides (NO_x; NO + NO₂) produced by lightning (LNO_x) play an important role in determining mid- and upper-tropospheric concentrations of the hydroxyl radical (OH, the atmosphere’s cleanser), methane (CH₄, an especially potent greenhouse gas), and ozone (O₃, a greenhouse gas and pollutant) (DeCaria et al., 2005, 2000; Fiore et al., 2006; Hauglustaine et al., 2001; Labrador et al., 2004, 2005; Liaskos et al., 2015; Pickering et al., 1993, 1996). Therefore, the contribution of lightning to the NO_x budget is of great interest. However, at present, there is a factor of four uncertainty in the amount of NO_x produced globally by lightning (Schumann & Huntrieser, 2007).

A critical quantity needed to infer the global production is the mean number of moles of NO_x produced per lightning flash. Recent estimates for this quantity vary by an order of magnitude with values between 50 and 700 mol per flash (Allen et al., 2019; Bucsela et al., 2019; Davis et al., 2019; Lapierre et al., 2020; Marais et al., 2018; Pickering et al., 2016; Pollack et al., 2016; Zhang et al., 2020). Of course, Lightning NO_x production efficiency (LNO_x PE) may also vary with the flash type (cloud-to-ground versus intracloud) and altitude adding additional uncertainty to the mix (Cummings et al., 2013; DeCaria et al., 2005; Fehr et al., 2004; Fuchs & Rutledge, 2018; Koshak et al., 2014; Mecikalski & Carey, 2018; Ott et al, 2010, 2007; Price et al., 1997).

The Geostationary Operational Environmental Satellite R-series Post Launch Test (GOES-R PLT) Field Campaign was conducted during March-May 2017 to perform validation of the Advanced Baseline Imager and Geostationary Lightning Mapper (GLM) instruments aboard GOES-16. A suite of instruments was carried on the NASA ER-2 high-altitude aircraft with flights based out of Palmdale, CA, and Warner-Robins, GA to observe both clear sky and thunderstorm targets. The NASA Goddard Geo-CAPE Airborne Simulator (GCAS) ultraviolet-visible spectrometer piggybacked on the aircraft mission to enable continuous observations of NO₂ columns simultaneously with optical lightning detection by the NASA Marshall Fly’s Eye GLM Simulator (FEGS) over convective systems. In this study, NO_x production per lightning flash, that is, LNO_x PE is estimated using NO₂ columns from GCAS and flash rates from FEGS, GLM, and the ground-based Earth Networks Total Lightning Network (ENTLN). This collection of observations demonstrates the potential synergy between the continuous GLM lightning detection and the high spatial and temporal NO₂ observations from the Tropospheric Emissions: Monitoring of Pollution (TEMPO, Chance et al., 2019) instrument slated for launch in 2022.

2 GOES-R Validation Campaign

The GOES-R PLT field campaign included flights during both day and night (Padula et al., 2017); however, NO₂ columns from GCAS are only obtainable during daylight storm overpasses. Daytime flights included March 21 over California, April 20 in the vicinity of Lake Erie, April 22 over Alabama, May 8 over Colorado, May 12 over Louisiana, Mississippi, Alabama, and the northern Gulf of Mexico, and May 14 over the western Atlantic east of Kennedy Space Flight Center. These flights were designated as GLM Validation flights. The analysis of LNO_x PE was limited to time periods when cloud top heights from the GOES-R PLT Cloud Physics Lidar (CPL) (McGill et al., 2019), which provides multi-wavelength measurements of cloud- and aerosol-properties with high temporal and spatial resolution, indicated that the ER-2 was over deep convection. Unfortunately, CPL cloud heights were unavailable for the March 21 flight so data from that flight were not examined. Thus, NO_x production by lightning is examined for flights on April 20, April 22, May 8, May 12, and May 14. For analysis purposes, flights were divided into one to three convective systems with minimal or no spatial overlap in the sampling region. Table 1 provides information on the 10 convective systems analyzed here including when GCAS began sampling and the start of the flash accumulation period, which is defined as the time at which flashes were first observed by either ENTLN or GLM within each storm’s sampling region. The areas of flash counting regions were determined by examining the spatial distribution of ENTLN and GLM flashes relative to the ER-2 flight tracks for numerous 10-min periods before aircraft sampling began.

Table 1. Sampling Details for Convective Systems Observed During GOES-R PLT Campaign

System name	Date	GCAS sampling region (°N)	GCAS sampling region (°W)	GCAS sampling time window (UTC)	10-min periods over region	Start of flash accumulation period (UTC)^1
Lake Erie	Apr 20	41–43.5	83–77	2312–2342	4	1900
AL_Ncell	Apr 22	34.6–35.7	88.0^2–85.5	2031–2316	17	1830
AL_Scell	Apr 22	34.0–34.6^3	89–86	2020–2435	12	1830
CO_South	May 08	39.00–40.15	105.5–104.5	2146–2300	6	1900
CO_North	May 08	40.15–41	105.5–104	2146–2345	11	1900
CO_East	May 08	40–41.2	104.8^4–102.6	2353–2459	7	1900
LA_MS_AL Line	May 12	29–32.5	92–86	1410–2013	32	0930
Gulf Line	May 12	28–29.25	93.5–90.5	1510–1640	10	0930
Atl_E system	May 14	29–31	75.5–72	1240–1720	18	0700
Atl_Wsystem	May 14	26.5–28.5	79–77	1420–1534	8	1100

• GCAS, Geo-CAPE Airborne Simulator; GOES-R PLT, Geostationary Operational Environmental Satellite R-series Post Launch Test.
• ¹ Flashes are accumulated from the beginning of the flash accumulation period until the midpoint of the current 10-min sampling period.
• ^2,3 In general, flashes are accumulated over GCAS sampling regions. However, due to movement of the storm systems, the AL_Ncell flash counting region is extended westward to 88.2°W prior to 2000 UTC and the AL_Scell flash counting region is extended northward to 34.9°N prior to 2100 UTC.
• ⁴ The GCAS Sampling Regions of the CO_East and CO_North systems overlap. To avoid including the same flashes in two storm totals, the CO_East flash counting region is restricted to 104.0°W prior to 2300 UTC.

2.1 Determination of the Vertical Column Density of NO₂

GCAS measures solar radiation backscattered from the surface and atmosphere (Kowalewski & Janz, 2014). NO₂ slant column densities (SCDs) are obtained from GCAS-measured spectra using Differential Optical Absorption Spectroscopy (Platt & Stutz, 2006) and the QDOAS spectral fitting package (http://uv-vis.aeronomie.be/software/). GCAS data are retrieved in the form of 250 × 250 m² pixels (31 pixels cross track with averaging along track). The spectral fitting procedure yields differential SCDs with respect to a relatively unpolluted reference location not affected by LNO_x rather than absolute SCDs. The reference time used during the GOES-R PLT campaign was a 2.5-min period centered at 2213 UTC on May 8 when the ER-2 was sampling a cloudy region over the Pawnee National Grassland (∼40.8°N, 104.5°W) to the northeast of Fort Collins, CO. Columns over this region were relatively low and devoid of features.

The differential SCDs are converted to NO₂ vertical column densities (V_NO2) below the aircraft using air mass factors (AMFs) from the vector linearized discrete ordinate radiative transfer code (VLIDORT) (Spurr, 2008). VLIDORT accounts for altitude-dependent differences in the sensitivity of GCAS to NO₂ and variations in observational geometry and atmospheric and surface properties over the course of the flight. Reflectivity data are needed for the AMF calculations. Over cloudy regions, the albedo is assumed to equal 0.8 following Stammes et al. (2008). For clear-sky scenes, collection 5 Moderate Resolution Imaging Spectroradiometer Bidirectional Reflectance Distribution Function data (Schaaf et al., 2002) are used. See Section 3 of Lamsal et al. (2017) for details. The AMFs include shape factors derived from vertical profiles of NO_x and NO₂. These profiles were obtained from moderate resolution (∼0.625° × 0.5°) atmospheric composition simulations of the field campaign period with the NASA Global Modeling Initiative (GMI) model (Allen et al., 2010) run within the GEOS-5 system (Liaskos et al., 2015) driven by meteorological fields from the MERRA-2 reanalysis (Gelaro et al., 2017; Lucchesi, 2017). Profiles of NO₂ and NO_x with a lightning source were obtained by subtraction of fields from a simulation that did not include LNO_x emissions from a simulation that did include LNO_x emissions. Tropopause pressures needed to determine the tropospheric portion of the model column are obtained from MERRA-2. Uncertainty exists as to how far into the storm cloud GCAS is able to detect NO₂. The pressure at the lowest height within a cloud that an instrument such as GCAS can observe is referred to as the optical centroid pressure (OCP). However, OCP has not been computed from the GCAS observations to date. Therefore, when integrating the column to determine V_NO2, a depth of 250 hPa is assumed, which is approximately the mean difference between the CPL cloud top pressure (CTP) and the OCP (Joiner et al., 2012) from the Ozone Monitoring Instrument (OMI) during the May 12 flight, which occurred early enough in the day to span the overpass time of OMI.

2.2 NO_x Production Per Flash

For each of the 10 systems shown in Table 1, LNO_x PE was estimated for each 10-min period that GCAS made at least one valid V_NO2 retrieval over the sampling region. See Equation 1.

(1)

where V_LNO2 (petamolec cm⁻²) is the portion of V_NO2 attributable to recent lightning-NO_x, A is the area (cm²) of the LNO_x “cloud” (see Section 2.4), rNO_x/NO₂ is the ratio of NO_x to NO₂ in the vertical layer visible to GCAS (see Section 2.4), N_A is Avogadro’s constant (6.022 × 10²³ molec mol⁻¹), and F is the number of flashes contributing to the retrieved NO₂ column (see Section 2.3). Here, the tropospheric background, that is, the contribution of non-recent LNO_x and other sources to V_NO2, is assumed to be given by the fifth percentile of V_NO2 within each of the sampling regions. Thus,

(2)

The high spatial resolution of GCAS makes it possible to identify columns minimally affected by lightning-NO_x. The fifth percentile was chosen based on analysis of the LA_MS_AL system, whose flight track included several overpasses of an LNO_x-influenced air mass (see Section 4.1).

Mean values of V_NO2 for each 10-min period during the sampling windows were determined as follows: First, a time series consisting of cross-track averages of V_NO2 was created for each sampling region using the portion of the 31 cross-track pixels with CPL pressures of less than 300 hPa. This threshold is used to ensure that the mean values are obtained using columns over deep convection. These values were then sorted by magnitude. Next, columns with values less than V_NO2 (5%) were discarded. Mean values for the remaining cross-track averages were then determined for 10-min sampling windows. During one 10-min period with few samples, all values of V_NO2 were less than V_NO2 (5%); V_NO2 for that 10-min period was set to V_NO2 (5%) resulting in a value of 0 petamolec cm⁻² for V_LNO2 for that time period. The 10-min periods begin at 0, 10, 20, 30, 40, and 50 min after the hour or at the beginning of the sampling window. For example, the Lake Erie sampling periods are 2312–2319 UTC, 2320–2329 UTC, 2330–2339 UTC, and 2340–2342 UTC, where 2342 UTC is the end of the fourth and last sampling period. The mean value of PE for each system was obtained by weighting the PE values for each 10-min period by the number of valid GCAS V_NO2 retrievals during the period with CPL CTPs of less than 300 hPa. Thus, periods with limited sampling and often high standard errors have a limited impact on the storm-averaged PE.

2.3 Estimation of F, the Number of Flashes Contributing to the VCD of NO₂

The number of flashes contributing to V_LNO2 is estimated using data from the GLM aboard GOES-16 and the ground-based ENTLN (Liu & Heckman, 2011).

2.3.1 GLM Flash Rates

The GOES-16 GLM, which was launched on November 19, 2016, is a near-infrared optical transient detector with a resolution of 8 km at nadir and 14 km at edge that images the Earth at 777 nm every 2 ms allowing the distribution of lightning flashes to be mapped (Goodman et al., 2013; Rudlosky et al., 2019). A GLM event is recorded when transient changes in pixel brightness exceed a dynamic threshold. After removing non-lightning artifacts, events are clustered into groups and flashes using a Lightning Cluster and Filtering Algorithm that gathers adjacent events into groups (Bitzer, 2017; Goodman et al., 2012; Mach, 2020).

The GOES-R PLT field campaign occurred during the satellite post-launch validation period. Thus, both onboard and ground system processing parameters were being adjusted that may affect flash detection and false event rates. To facilitate analysis, reprocessed GLM data sets were created containing flash locations, flash optical energy, and flash multiplicity (groups per flash) as well as other quantities. These re-processed data sets are not affected by operational constraints that limit the total number of events per group and groups per flash to 101 and the flash length to 3 s (Peterson, 2019). The data sets have complete temporal coverage from a few hours before GCAS-sampling began to after it ended; however, most of the re-processed data sets begin too late to capture all of the flashes contributing to the observed columns. Therefore, GLM flash counts during periods that were not included in the reprocessed GLM data set are assumed to be equal to the ENTLN flash total divided by the mean ratio of ENTLN to GLM flashes during periods with reprocessed GLM data. Missing time periods, if any, associated with each storm are discussed in the Appendix.

2.3.2 ENTLN Flash Rates

The ENTLN is a lightning locating system that detects low-frequency sferics (pulses) from CG and IC flashes in the 1-Hz–12-MHz range. Pulses are grouped into flashes using 10-km and 0.7-s thresholds (Liu & Heckman, 2011; Marchand et al., 2019). ENTLN metrics for individual flashes include time, location, type (CG or IC), peak current, and multiplicity (i.e., the number of strokes that compose each flash). Zhu et al. (2017) assessed the quality of ENTLN data through an examination of how well the ENTLN captured rocket-triggered CG flashes at Camp Blanding near Gainesville, FL. They found that the network captured all of the flashes indicating a CG detection efficiency (DE) of 100%. They obtained a mean location error of 215 m and a mean current error of 15%. Of course, IC flashes with smaller peak currents have larger errors. Marchand et al. (2019) examined the DE of GLM relative to ENTLN and vice versa over the contiguous United States during the April 2017 to May 2018 time period. They found GLM DEs relative to ENTLN exceeded 80% over the southcentral and southeastern United States and were 60%–80% for the rest of the United States (see Figure 2a of Marchand et al., 2019). ENTLN DEs relative to GLM were similarly equaling 80% east of the Mississippi river where ENTLN sensors are common, 70%–80% across much of the rest of the United States with values falling off over Mexico and the Atlantic Ocean (see Figure 7a of Marchand et al., 2019). Lapierre et al. (2020) estimated the IC DE of ENTLN for 2014–2015 using TRMM-LIS measurements of total flashes and the assumption that the CG DE of ENTLN is 100%. Using a similar analysis with ISS-LIS data for 2017–2019, an IC DE of 79 ± 18% was found for ENTLN over the region with no clear trend between 2017 and 2019. The 79% value was found by averaging DEs of 1° × 1° cells over the eastern United States after weighting by the number of ENTLN flashes per cell regardless of whether they were matched by ISS-LIS flashes.

2.3.3 Detection-Efficiency Adjusted Flash Rates

The flash DE of GLM and ENTLN during the GOES-R PLT field campaign was estimated via comparison of GLM and ENTLN flash counts with FEGS observations. FEGS (Quick et al., 2017, 2020) is an airborne array of multi-spectral radiometers designed to measure lightning optical emission through the cloud top. It was carried on the ER-2 to provide a one-to-one comparison with GLM. FEGS uses a 5 × 5 array of radiometers sensitive to 777 nm and measures radiance continuously within a ∼10 × 10 km² field of view with a 2-km nominal resolution. Transient light pulses are clustered into flashes using a 330 ms time window mimicking the GLM clustering criterion. The version 2 FEGS data set (Quick et al., 2019) contains both raw and quality-controlled flashes. Only quality-controlled flashes were used in determining the GLM and ENTLN DEs.

Flash rates from FEGS are used as truth in this report to estimate the time variant GLM and ENTLN DEs. For each FEGS flash, a temporal and spatial matching analysis was performed to identify flashes that were simultaneously detected by GLM or ENTLN. The DE for a given period was estimated as the ratio of FEGS flashes with a GLM or ENTLN match over the total number of FEGS flashes. The DE was calculated for each 10-min sampling period for periods when 10 or more FEGS flashes were detected. For sample periods when fewer than 10 FEGS flashes were recorded, a mean DE for the day-of-interest was assigned to the sampling period. FEGS is unable to distinguish between IC and CG flashes, thus the ENTLN DE with respect to FEGS, DE_ENTLN, includes both CG and IC flashes. Here, we assume the ENTLN CG DE = 1 and obtain the ENTLN IC DE (DE_IC) using Equation 3 where F_IC (F_CG) is the number of ENTLN IC (CG) flashes detected during each 10-min period.

(3)

For example, the Gulf Line system had only one 10-min period with 10 or more FEGS flashes. DE_ENTLN with respect to FEGS for that period was found to equal 0.92. The number of detected ENTLN IC (CG) flashes during that period was 35 (18). Thus, DE_IC for that period was 0.88. Table 2 shows DE statistics for each of the storms. Figures 1a and 1b show time series with 10-min temporal resolution of GLM and ENTLN IC DE with respect to FEGS for each of the storms. The GLM DEs are smallest for the CO_North and CO_South systems (45%–55%) likely because the DE of GLM is known to degrade over anomalous polarity structured storms, which are common over the Great Plains (Fuchs & Rutledge, 2018; Rust et al., 2004). Recently, Rutledge et al. (2020) compared GLM flash rates during the CO_N cell with LMA-derived flash rates and obtained DE values of 10%–35% relative to the LMA for this anomalous polarity storm. The GLM DEs are the largest for the southern Alabama cell (92%). The ENTLN DEs are relatively low for the Atlantic systems possibly because the ENTLN DE decreases with distance from the coast. The daytime DE of GLM relative to FEGS during the GOES-R campaign was 75 ± 16% after weighting the means of individual storms by the number of 10-min periods with 10 or more FEGS flashes. Similarly, the mean daytime DE of ENTLN with respect to FEGS was 92 ± 6%. The mean daytime IC DE of ENTLN with respect to FEGS was 90 ± 7%.

Table 2. Statistics for Storms During GOES-R PLT Field Campaign

Storm	GLM DE (%)	ENTLN DE (%)	ENTLN IC DE (%)	Periods ≥ 10 FEGS flashes	FEGS flashes	IC/CG ENTLN	Mean CTP (hPa)	rNOx/NO2 (GEOS-5)
Lake Erie	75 ± 11	93 ± 7	91 ± 9	3/4	57	3.3	194	1.99
AL_Ncell	66 ± 10	97 ± 3	96 ± 3	12/17	1,612	8.6	170	4.04
AL_Scell	92 ± 4	98 ± 4	98 ± 4	10/12	676	6.3	175	3.62
CO_South	45 ± 16	84 ± 18	81 ± 20	5/5	346	3.1	163	3.25
CO_North	55 ± 15	87 ± 8	84 ± 9	10/11	1,358	2.8	162	3.23
CO_East	67	97	97	1/7	39	3.4	165	1.99
LA_MS_AL	89 ± 9	96 ± 5	95 ± 6	20/32	1,222	3.6	177	3.55
Gulf Line	77	91	89	1/10	34	2.7	208	3.69
Atl_Esystem	77 ± 11	83 ± 14	79 ± 16	12/18	378	3.4	224	2.93
Atl_Wsystem	65 ± 20	84 ± 14	82 ± 15	4/8	92	3.1	227	2.91
Mean	75 ± 16	92 ± 6	90 ± 7	–	–	–	186 ± 24	3.32 ± 0.57

• Note. Column 2 (3) shows the mean GLM (ENTLN) DE for each storm and the standard deviation of the means of 10-min periods with 10 or more FEGS flashes. The number of these periods is shown in column 4. Column 5 shows the number of quality-controlled FEGS flashes during the sampling period. Column 6 shows the ENTLN IC/CG. Column 7 shows the mean CPL CTP, and column 8 shows the mean NOx/NO2 ratio from GEOS-5.
• CPL, Cloud Physics Lidar; CTP, cloud top pressure; ELTLN, Earth Networks Total Lightning Network; FEGS, Fly’s Eye GLM Simulator; GLM, Geostationary Lightning Mapper; GOES-R PLT, Geostationary Operational Environmental Satellite R-series Post Launch Test.

Figure 1

Timeseries showing GLM (top) and ENTLN IC (bottom) DEs with respect to FEGS as a function of UTC for 10-min sampling periods during the GOES-R PLT Field Campaign when at least 10 FEGS flashes were recorded. Colors are used to separate flight days with symbols used to identify systems within a flight day. The mean GLM DE with respect to FEGS for each system is shown in Table 2. ENTLN, Earth Networks Total Lightning Network; FEGS, Fly’s Eye GLM Simulator; GLM, Geostationary Lightning Mapper; GLM, Geostationary Lightning Mapper; GOES-R PLT, Geostationary Operational Environmental Satellite R-series Post Launch Test.

GLM and ENTLN (both IC and CG) flash counts were aggregated onto a 0.1 × 0.1 grid, summed over 10-min periods and divided by DE. The gridded GLM data sets also contain the mean optical energy and flash multiplicity, while the IC and CG ENTLN data sets also contain mean values for the absolute value of peak amplitude and multiplicity (pulses per flash). During most time periods, ENTLN flash densities exceeded GLM flash densities. Marchand et al. (2019) obtained similar results and attributed the biases between GLM and ENTLN to differences in what is measured, flash clustering algorithms, and DE. Specifically, ENTLN measures sferics due to lightning pulses within the cloud while GLM measures optical signals of events near the cloud top. When clustering flashes, ENTLN considers pulses to be part of the same flash if they are within 10-km and 0.7-s while GLM requires events to be within 16.5 km and 330 ms and the weighted Euclidean distance (WED) (Hartigan, 1975) to be less than 1. See Mach (2020) for details on how the WED is determined. Clearly, differences in clustering are substantial and may cause a single GLM flash to be clustered into multiple ENTLN flashes or vice versa. With respect to DE, the DE of GLM is known to degrade over inverted polarity storms, severe storms, and storms with deep liquid water content. In addition, false alarms were relatively common during the GOES-R PLT field campaign and could comprise a substantial amount of the total flashes, especially over water due to glint false alarms (see GLM-16 Beta ReadMe file at https://www.ncdc.noaa.gov/data-access/satellite-data/goes-r-series-satellites).

2.3.4 Determination of the Total Number of Flashes in Flash Counting Region

When estimating LNO_x PE for each of the 10-min periods, the number of GLM or ENTLN flashes within the flash-counting region during the flash accumulation period is summed. All of these flashes are assumed to contribute to the mean value of V_NO2 observed by GCAS within the GCAS sampling region during the 10-min period; however, the contribution of any one flash to the column is assumed to decrease with time due to the relatively short lifetime of NO_x in the near field of convection (Nault et al., 2016). Therefore, F used in Equation 1 is given by

(4)

where N is the total number of detected GLM or ENTLN flashes in the flash counting region from the beginning of the flash accumulation period (see Table 1) to the midpoint of the current sampling period, F_i is the flash total assigned to an individual flash after adjusting for DE, t_s is the time GCAS sampled the region (hours), t_i is the time flash i occurred (hours), and τ is the assumed chemical lifetime of NO_x in the near field of convection (hours). Therefore, F_i would equal 1.25 flashes for a flash that occurred during a period when the DE was 0.8. When estimating t_s and t_i, times at the center of the appropriate 10-min sampling periods are used. The value of τ, 2 h, is taken from Nault et al. (2016, 2017) who found that the lifetime of lightning-generated NO_x in the near field of convection is 2–12 h depending on the proximity to convection. The choice of τ is critical because it determines the rate at which the assumed contribution of flashes to the observed column is attenuated with time to account for the fact that the observed NO₂ column attenuates with time. Thus, for a fixed storm area, decreasing τ will lead to an increase in PE. The low-end of the range is used here because GCAS was sampling over active thunderstorms. However, sensitivity simulations were run for τ = 1.5–3 h.

The choice to begin the flash accumulation period as soon as the earliest flashes were detected for a particular storm provides an upper bound on the total number of flashes contributing to the observed NO₂ columns. However, a portion of the NO_x cloud associated with flashes within the flash counting region will be advected out of the sampling region decreasing the NO_x cloud sampled by GCAS while additional LNO_x from flashes not in the flash counting region could increase the NO_x cloud sampled by GCAS. Overall, the impact is most likely an overestimate of the flashes contributing to the column because flash counting regions were chosen to encompass entire systems. The impact of advection on V_LNO2 is likely to be relatively small when large-scale upper-tropospheric winds are aligned with the movement of the convective system. In this case, the NO_x cloud moves with the system and will be well sampled by GCAS. However, a substantial portion of the column may be advected out of the region of interest when upper-tropospheric winds do not align with the system’s movement. The possible significance of the advective loss of LNO_x on PE was estimated qualitatively using trajectories initialized 10-km above mean sea level (see Sections 3.1–3.5, 3.1–3.5, 3.1–3.5) and quantitatively through an examination of the mismatch between upper tropospheric winds and the storm movement (see Section 4.2.2 and Table 4).

2.4 Estimation of NO₂ to NO_x Conversion Factor Needed to Estimate Moles of NO_x

The moles of NO₂ produced by lightning is converted to moles of NO_x by multiplying by a ratio (rNO_x/NO₂) that converts molecules per cm² of NO₂ to molecules per cm² of NO_x. The ratio is obtained from an atmospheric composition replay simulation of the GOES-R PLT time period with the GEOS-5 model driven by meteorological fields constrained by the MERRA-2 reanalysis. Average fields of 3 h from this 0.625° × 0.50° × 72-layer simulation were extracted for the period of the PLT campaign. Upper tropospheric columns of NO_x and NO₂ were then obtained by integrating the model output in a layer that extends from 250 hPa below the CPL CTP to the CPL CTP (see Section 2.1). For each 3-h period, NO_x to NO₂ ratios from GEOS-5 were determined for each grid box within the sampling region with the 90th percentile of the ratios being used as an estimate of rNO_x/NO₂. A percentile greater than the 50th was chosen because the photolysis of NO₂ and hence the NO_x to NO₂ ratio is enhanced in the anvils associated with deep convective systems. The mean is not appropriate because the location of deep convection in GEOS-5 is likely to differ from the actual location. The 90th percentile was used to be consistent with Pickering et al. (2016) and follow-up papers that calculated NO_x to NO₂ ratios using GMI profiles from the day of the month with the third largest LNO_x column amount. Table 2 shows the mean CPL cloud-top and rNO_x/NO₂ for the 10 systems. In general, at the same local time, rNO_x/NO₂ increases with decreasing pressure in the upper troposphere. Thus, rNO_x/NO₂ is largest for the Alabama and Colorado cases that have low CTPs and smallest for the Lake Erie and Atlantic cases. Figure 2 shows the time series of the NO_x to NO₂ ratios used to convert V_NO2 to V_NOx when estimating LNO_x PE for each of these 10 systems. The most noticeable feature of these plots is the strong diurnal variability with moderate values in the morning, high values mid-day, and low values in the evening. For example, the ratio for the AL_Scell decreases from 4.9 to 2.5 between 2020 UTC and 2420 UTC while the ratio for Atl_E system increases from 2.3 to 3.3 between 1240 and 1720 UTC. Geographical variations, while smaller, are also evidently adding an additional challenge to the estimation of NO_x columns from NO₂ columns. Clearly, diurnal constraints from TEMPO (Zoogman et al., 2017) or other geostationary satellites will be useful for reducing temporal uncertainties in the ratio.

Figure 2

Timeseries showing the NO_x to NO₂ ratios used to convert NO₂ VCDs from GCAS to NO_x VCDs when estimating LNO_x PE. The columns were obtained from GEOS-5 by integrating from 250 hPa below the CPL CTP to the CPL CTP. Values are shown every 10 min but were obtained by interpolating between 3-h average values. The minimum and maximum ratios during the sampling periods are shown below the system names. Note local time = UTC–4 h for Lake Erie and Atlantic storms, UTC–6 h for Colorado storms, and UTC–5 h for others. CPL, Cloud Physics Lidar; CTP, cloud top pressure; ELTLN, Earth Networks Total Lightning Network; FEGS, Fly’s Eye GLM Simulator; GCAS, Goddard Geo-CAPE Airborne Simulator; GOES-R PLT, Geostationary Operational Environmental Satellite R-series Post Launch Test; LNO_x PE, lightning NO_x production efficiency.

2.5 Estimation of Storm Area

The area (A) of the NO_x cloud used in estimating LNO_x PE is calculated using the 10-min temporal resolution 0.1° × 0.1° ENTLN and GLM data sets. The area of the cloud, a measure of the area within the flash-counting region influenced by recent ENTLN or GLM lightning, is calculated for each 10-min period within the flash accumulation period. The area for the first 10-min period is determined by summing the area of grid boxes with flashes during this period plus the area of grid boxes that are adjacent in the east-west and north-south directions to the flashing grid boxes. The rationale for including adjacent grid boxes is that the spatial footprint of lightning may extend outside of the grid box where the centroid is located. Similarly, the area for the second 10-minute period is determined by summing the area of grid boxes with flashes during the second time period plus the area of grid boxes that are adjacent in the east-west and north-south directions to the flashing grid boxes. Of course, when determining the LNO_x-influenced region for the second time period, it is also necessary to include the contribution of grid boxes with lightning flashes during the first time period but not the second. The area of these grid boxes is adjusted for chemical decay and added in. For example, for a chemical lifetime of 2 h, the area of these grid boxes is multiplied by exp (−i/12) before adding in where i is the number of 10-min time steps since these grid boxes had lightning or were adjacent to grid boxes with lightning, and 1/12 is the fraction that 10 minutes is of the 2-h lifetime. For time step 2, i = 1 and the multiplication factor is 0.92. For time step 3, i may be 1 or 2 and so forth.

The rationale for including chemical decay when determining the area is straightforward. Flash totals are adjusted to include the effect of chemical decay. Therefore, for consistency purposes, it is appropriate to adjust the area. The area (A) of the LNO_x cloud, which is in the numerator of Equation 1 depends to some degree on the flash total (F), which is in the denominator of Equation 1, thus buffering changes in PE due to changes in flash total. This buffering lessens the dependence of PE on flash total or data set. For example, the ENTLN methodology results in more flashes and thus lower PE than the GLM methodology. However, differences in PE are not directly proportional because the additional flashes are partially balanced by additional area. In order to assess the uncertainty in LNO_x PE associated with the area methodology, the area was also determined using only flashing boxes and using two adjacent grid boxes in the east-west and north-south. The results of those sensitivity simulations are discussed in Section 4.2.3.

2.5.1 Adjustments to Storm Area to Account for Storm Movement

The area of the flash counting regions for the Alabama_N and Alabama_S systems were adjusted prior to 2000 and 2100 UTC, respectively (see footnotes 2 and 3 in Table 1). The adjustments were necessary to ensure that flashes were attributed to the correct systems because the flash counting regions were adjacent in space and the systems were drifting to the south and east. For example, the latitude range of the Alabama_S system was deceased from 34°N−34.9°N to 34°N–34.6°N because the southern cell was drifting southward and flashes that occurred prior to 2100 UTC between 34.6°N and 34.9°N ultimately contributed to V_NO2 for the southern cell despite being within the GCAS sampling region of the northern cell. The abrupt decrease in the area of the flash counting region does not lead to an abrupt decrease in the area of the NO_x cloud because the decayed-area of the NO_x cloud in the shaved-off region (89°W–86°W, 34.6°N–34.9°N) was added in even after 2100 UTC. An analogous approach was followed to ensure that the NO_x cloud area of the Alabama_N system was continuous before and after 2000 UTC.

2.5.2 Adjustments to Storm Area to Account for Missing GLM Flashes

The approach used to estimate the area of the NO_x cloud (A) associated with GLM flashes must also be modified because the standard approach results in an underestimation of A for systems with missing GLM flashes, especially during the first few hours for which GLM data are available. The area-adjustment is not performed for the Alabama, Colorado, and Atlantic_W systems, which have few or no missing GLM flashes; however, it is performed for the Lake Erie, Gulf of Mexico, and Atlantic_E system for which 52%, 32%, and 41% of flashes occur before GLM data are available. For these three systems, A is assumed to be equal to the ENTLN area divided by the ratio of the ENTLN to GLM areas during the last 10-min period GCAS sampled the system. The value from the last 10-min period is used because the ratio during this period is the least sensitive to missing GLM flashes early in the flash accumulation period. Going forward in the text, GLM PE values adjusted for missing GLM flashes are identified as GLMa.

3 LNO_x PE for Each of the Flight Days

LNO_x PE was determined for 10 convective systems on 5 flight days. Sections 3.1–3.5, 3.1–3.5, 3.1–3.5 describe the meteorological conditions on these days and show maps of the flash rate distribution, ER-2 flight tracks, and GCAS V_NO2. In addition, time series are presented of V_NO2, LNO_x PE, LNO_x area, and NO_x-effective flashes (i.e., flashes adjusted for chemical decay) for each of the 10 systems on these days. Finally, Table 3 shows LNO_x PE statistics for the systems including the variation in PE with a flash type (ENTLN, GLM, or GLMa) and the sample-weighted coefficient of variation (c_v). Table 3 also shows system-specific values of V_NO2 (5%). V_NO2 (5%) values ranged from 1.02 petamolec cm⁻² for the Gulf of Mexico system to 1.49 petamolec cm^-2 for the Lake Erie system.

Table 3. LNO_x PE Statistics for the 10 Storm Systems

Storm	VNO2 ^1	VNO2(5%)^1	LNOx PE GLM^2	LNOx PE GLMa^2		Norm σ (cv)^3	LNOx PE ENTLN^2	Norm σ (cv)^3
Lake Erie	2.58	1.49	546 ± 110	381 ± 74		0.19	252 ± 48	0.19
AL_Ncell	2.59	1.48	445 ± 197	442 ± 196		0.44	333 ± 145	0.43
AL_Scell	2.39	1.34	233 ± 56	219 ± 50		0.23	155 ± 37	0.24
CO_South	2.02	1.22	103 ± 59	103 ± 59		0.57	79 ± 43	0.55
CO_North	2.19	1.44	106 ± 39	106 ± 39		0.37	82 ± 25	0.31
CO_East	2.44	1.33	90 ± 42	90 ± 42		0.47	56 ± 25	0.44
LA_MS_AL	2.14	1.17	598 ± 316	536 ± 274		0.51	339 ± 180	0.53
Gulf Line	1.40	1.02	466 ± 146	444 ± 114		0.26	236 ± 61	0.26
Atl_Ecell	1.93	1.19	306 ± 122	271 ± 107		0.40	161 ± 66	0.42
Atl_Wcell	1.46	1.19	174 ± 37	174 ± 38		0.22	111 ± 25	0.23
Overall^4	2.10	1.25	388 ± 274	356 ± 241		0.68	229 ± 158	0.70
Overall^5	GLM: 360 ± 240 (360 ± 180)				ENTLN: 230 ± 160 (230 ± 115)

• ENTLN, Earth Networks Total Lightning Network; GCAS, Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper; LNO_x PE, lightning NO_x production efficiency.
• ¹ Values for V_NO2 and V_NO2 (5%) are given in units of petamolec cm⁻².
• ² The means and standard deviations (mol per flash) are obtained by weighting the values from individual 10-min periods by the number of GCAS retrievals in each period.
• ³ The coefficient of variation or normalized standard deviation (Norm σ) is obtained by dividing the standard deviation by the mean after weighting individual values by the number of observations.
• ⁴ The overall values are obtained by weighting the values from individual 10-min periods by the number of GCAS retrievals in each period. Thus, storms with more GCAS retrievals contribute more to the mean.
• ⁵ Mean values for GLM and ENTLN shown after rounding. The first uncertainties are based on the standard deviation of the 10-min values, while the uncertainties in parentheses are obtained by summing individual uncertainties in quadrature (Section 4.2).

3.1 April 20, 2017

On April 20, scattered thunderstorms developed over Lake Erie to the north of Cleveland at ∼ 1900 UTC. By 2000 UTC, a prefrontal line of storms was forming over southeastern Michigan and beginning to track across Lake Erie (Figure 3a). This line of storms moved slowly eastward intersecting the future ER-2 flight track at approximately 2230 UTC along the southeast shore of Lake Erie (Figure 3b). The ER-2 approached this line of thunderstorms from the south and reached the line by ∼2312 UTC (Figure 3c). The ER-2 flew north and then northeast sampling this line of storms until ∼2342 UTC (Figure 3d) when increasing solar zenith angle caused cessation of valid GCAS retrievals. Back trajectories initialized at 2300 UTC indicated that the large-scale flow pattern in the upper troposphere was from west to east, which is consistent with the direction of the line of storms. Thus, the NO₂ column sampled by GCAS is believed to be consistent with the flash count.

Figure 3

(a–d) Lightning flash density (ENTLN for Figure 3a; GLM for Figures 3b–3d) at current time (gray scale), upcoming ER-2 flight track (black line segments in upper left panel), and GCAS V_NO2 at current time (colored line segments) on April 20 near Lake Erie for 1950–2000 UTC (a), 2220–2230 UTC (b), 2310–2320 UTC (c), and 2330–2340 UTC (d). For 10-min periods with GCAS measurements within the sampling region, the captions also show the mean value of V_NO2 (petamolec cm⁻²) and the LNO_x PE (mol per flash). ENTLN, Earth Networks Total Lightning Network; GCAS, Goddard Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper; LNO_x PE, lightning NO_x production efficiency.

The GLMa-based PE for the system of 381 ± 74 mol per flash exceeded the ENTLN-based PE of 252 ± 48 mol per flash by a factor of 1.5 (Figure 4). The system was only sampled for 32 min. V_NO2 decreased with time leading to a decrease in PE with time although much of the decrease occurred during the last 2 min of sampling and is given less weight when estimating the PE and c_v. After weighting by sample size, the variability of PE with time was relatively small with c_v equaling 0.19 for both GLM and ENTLN.

Figure 4

Time series for the April 20 Lake Erie system showing LNO_x PE (*) from Equation 1 in units of mols per flash (left axis), V_NO2 (¤) from Equation 2 in units of petamolec cm⁻² (right axis), F(Δ) from Equation 4 in units of flashes divided by scaling factor of 5,466 (right axis), and A (+) from Equation 1 in units of km² divided by scaling factor of 51,145 (right axis). The title shows the GCAS-sample weighted mean PE and standard deviation as determined using ENTLN and GLM flashes. Note F is a summation of decay-adjusted flashes (τ = 2 h). Its slope is large during periods with high flash rates and small possibly even negative during periods with low flash rates. LNO_x PE, lightning NO_x production efficiency.

3.2 April 22, 2017

On April 22, the ER-2 sampled northern (Alabama_Ncell) and southern (Alabama_Scell) Alabama (AL) cells within an eastward-moving line of thunderstorms associated with a cold front. By 1840 UTC, a ragged southwest-to-northeast line of thunderstorms was evident over northern Mississippi and southwestern Tennessee. The ER-2 approached this line of thunderstorms from the southeast, entering the sampling region for the southern cell at ∼2020 UTC and encountering the NO_x cloud associated with this cell at ∼2025 UTC. The ER-2 then spent the next few hours sampling both the southern and northern cells. Specifically, it sampled the northern cell from ∼2031 to 2051 UTC (Figure 5a shows 2030–2040 UTC), the southern cell from 2051 to 2100 UTC, the northern cell from 2100 to 2123 UTC, the southern cell from 2124 to 2138 UTC, and finally the northern cell from 2138 to 2147 UTC. From ∼2150 to 2310 UTC, the focus shifted to the northern storm with east-west flights across the system (Figures 5b and 5c show 2150–2200 UTC and 2230–2240 UTC). After the northern storm weakened, the focus shifted to the southern storm, now south of Huntsville, which was overflown from 2320 to 0030 UTC (Figure 5d shows 2330–2340 UTC). Back trajectories initialized at 2300 UTC indicated that large-scale winds in the upper troposphere were strong and from the west-southwest blowing to the east-northeast. However, the storms moved east-southeast. Thus, a substantial portion of the LNO_x cloud associated with these systems could have blown off to the east of the sampling region causing a low bias in PE estimates, especially later in the day.

Figure 5

(a–d) GLM lightning density, ER-2 flight track, and GCAS V_NO2 on April 22 over Alabama for 2030–2040 UTC (a), 2150–2200 UTC (b), 2230–2240 UTC (c), and 2330–2340 UTC (d). The dashed boxes show the sampling regions for the northern Alabama (Figures 5a–5c) and southern Alabama (Figure 5d) systems. See Figure 3 for additional information. GCAS, Goddard Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper.

The mean PE for the northern cell was a robust 442 ± 196 mol per flash for GLMa and 333 ± 145 mol per flash for ENTLN (Figure 6a). The PE was stable for the first hour (2030–2130 UTC), a period with copious flashes and increasing V_NO2. However, the PE then decreased with time between 2130 and 2320 UTC. The first half of this period (2130–2230 UTC) featured high flash rates, which should have contributed to increasing V_NO2 columns; however, V_NO2 columns while noisy did not increase during this period possibly because the angle between upper tropospheric winds and the storm direction approached 40° allowing for up to a third of the LNO_x to be advected out of the sampling region assuming the direction the storm outflow moves is governed by the large scale flow, which is only approximately true because horizontal momentum that has been lofted from the PBL also affects the outflow direction (see Section 4.2 and Table 4). The PE continued to decrease during the latter portion of this period (2230–2320 UTC) due to decreases in V_NO2 with time during a period with decreasing flash rates and decreases in the area of the NO_x cloud. As during the earlier period, advected loss of NO_x may have been substantial. The temporal offset between the earlier peak in NO_x cloud area and later peak in NO_x-effective flashes indicates that the flash density was lower during the early portion of the flash accumulation period, which may also contribute to the higher PE early in the sampling period.

Figure 6

(a–b) Same as Figure 4 but for the April 22 Alabama North (a) and Alabama South (b) systems. The scaling factors for F are 1,904 for the northern cell and 2,319 for the southern cell. The scaling factors for A are 8,170 for the northern cell and 6,711 for the southern cell.

Table 4. Parameters Used in Estimating the Fractional Loss of V_NO2 due to Mismatch Between Upper Tropospheric Winds and Storm outflow

Storm	Hypotenuse (km)	V200 (m/s)	200 hPa wind direction (◦)	ENTLN-based outflow direction (◦)	GLM-based outflow direction (◦)	Mean difference “theta” (◦)	F_loss
Lake Erie	567	36.6	271	277	279	7.7	0.03
AL_Ncell	258	39.3	253	290	292	37.9	0.34
AL_Scell	284	34.1	256	282	283	25.8	0.19
CO_South	154	21.9	204	210	236	19.0	0.16
CO_North	158	21.8	207	236	236	28.5	0.24
CO_East	178	20.5	217	233	237	18.2	0.13
LA_MS_AL	694	44.3	257	282	269	18.0	0.07
Gulf Line	324	50.0	258	286	284	26.8	0.25
Atl_Ecell	404	53.1	263	304	302	40.7	0.31
Atl_Wcell	298	51.9	261	285	284	23.9	0.25
Mean	332	37.4	245	268	271	24.6	0.20

• Note. Meteorological wind directions are shown.
• ENTLN, Earth Networks Total Lightning Network; GLM, Geostationary Lightning Mapper.

The southern system (Figure 6b) was sampled intermittently between 2020 and 2400 UTC. The PE was fairly stable between four disconnected sampling periods. The PE for this system is approximately half that of its northern counterpart equaling 219 ± 50 mol per flash for GLMa and 155 ± 37 mol per flash for ENTLN. According to GLM, the mean flash density of the southern cell (0.033 flashes per km²) is 22% higher than the mean density of the northern cell (0.027 flashes per km⁻²), while the mean optical energy per flash of the southern cell (694 fJ) is 12% lower than that of the northern cell (792 fJ). The higher flash densities and lower optical energies per flash likely contribute a small amount to the lower PE of the southern cell.

3.3 May 8, 2017

On May 8, the upslope flow behind a cold front draped across northern Colorado aided in initiating strong convection in a very unstable air mass. Isolated thunderstorms with low flash rates were evident on the western edge of the Colorado_South sampling region beginning at ∼1900 UTC. At approximately 1940 UTC, a stronger cell developed in the southeast portion of this domain. This cell moved slowly east outward of the domain. By 2020 UTC, supercells that became the focus of the ER-2 developed over Greeley, CO (Colorado_North) and Denver, CO (Colorado_South). The area encompassed by these and other cells increased with time and by 2140 UTC, widespread convection was occurring over northern Colorado (Figure 7a; 2130–2140 UTC). The ER-2 flew a roughly north/south pattern over these two compact high flash rate supercells beginning at ∼2150 and continuing until the southern storm dissipated at 2300 UTC after which the ER-2 focused exclusively on the northern cell until 2345 UTC. Figure 7b shows 2200–2210 UTC when the ER-2 was sampling the southern cell. Figure 7c shows the ER-2 as it sampled the northern cell between 2240 and 2250 UTC. At 2345 UTC, the ER-2 headed east and targeted a third storm that had developed to the east of the northern cell (CO_East) no later than 2200 UTC. This cell was sampled between 2353 and 2459 UTC. Figure 7d shows the region sampled between 2410 and 2420 UTC.

Figure 7

(a–d). GLM lightning density, ER-2 flight track, and GCAS V_NO2 on May 8 over Colorado for 2130–2140 UTC (a), 2200–2210 UTC (b), 2240–2250 UTC (c), and 2410–2420 UTC (d). The dashed boxes show the sampling regions for the southern Colorado (Figures 7a and 7b), northern Colorado (Figure 7c), and eastern Colorado (Figure 7d) systems. See Figure 3 for additional information. GCAS, Goddard Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper.

Trajectories revealed that the large-scale flow pattern was from the south-southwest blowing to the north-northeast. The CO_South and CO_East systems also moved to the north-northeast suggesting little loss of LNOx; however, up to 25% of the LNOx associated with the CO_North system may have blown off as the CO_North system moved at a 28° angle to the upper-tropospheric winds (see Section 4.2.2 and Table 4).

The Colorado_south cell (Figure 8a) was sampled between 2150 and 2210 UTC and then again between 2220 and 2300 UTC. The ER-2 approached the cell from the southeast and initially sampled mostly background air with low values of V_NO2 to the south of the lightning activity. V_NO2 increased dramatically as the ER-2 moved north and sampled the center of the southern cell (2200–2210 UTC). The ER-2 continued flying north sampling the northern cell before returning to the southern cell after 2220 UTC. Overall, PE was a bit lower during the second sampling period (2220–2300 UTC) with variations driven by changes in V_NO2 with time. The vast majority of flashes associated with this system occurred early during the flash accumulation period as can be seen by the slow decrease in the flash area with time and the small temporal changes in NO_x effective flashes. Mean PE values over the cell were low equaling 103 ± 59 mol per flash for GLMa and 78 ± 43 mol per flash for ENTLN.

Figure 8

(a–c) Same as Figure 4 but for the May 8 Colorado South (a), Colorado North (b), and Colorado East systems. The scaling factors are 2225, 2262, and 2641 for F and 3677, 4907, and 4986 for (a).

The Colorado_north cell (Figure 8b) was sampled for portions of 11 consecutive 10-min time periods. Unlike the southern cell, flashes were plentiful for the first 80 min of the sampling period (note the increase in NO_x effective flashes with time between 2200 and 2320 UTC). Mean PE values for the northern cell were approximately the same as those of the southern cell equaling 106 ± 39 mol per flash for GLMa and 82 ± 25 mol per flash for ENTLN. The 30% difference in mean PE between GLMa and ENTLN for the southern and northern Colorado cells were the smallest observed during the campaign. Variability in PE with time was relatively low; c_v equaled 0.37 for GLMa and 0.31 for ENTLN. LNO_x PE decreased slowly with time as slow increases in V_NO2 and cloud area with time nearly balanced larger increases in flash totals with time.

The Colorado_east cell (Figure 8c) was sampled late in the day (2353–2459 UT) when ratios of NO_x to NO₂ were small (see Figure 2). These low ratios were a contributing factor to PE values of 90 ± 42 mol per flash for GLMa and 56 ± 25 mol per flash for ENTLN. Changes in PE with time were driven by changes in V_NO2 as the number of flashes and the NO_x-cloud area increased with time throughout the sampling period. The PE decreased slightly with time; however, the decrease with time was relatively small compared to period-to-period variations in V_NO2. The primary cause of the low PE for the May 8 Colorado cells is discussed in Section 4.3.

3.4 May 12, 2017

On May 12, the ER-2 sampled a quasi-linear convective system as it moved slowly from northwest to southeast across Louisiana, Mississippi, Alabama, and the northern Gulf of Mexico. From 0930 to 1100 UTC, widely scattered storms were present in a line extending from southwestern to northeastern Louisiana. By 1100 UTC, the eastern edge of the line was crossing into Mississippi impacting the northwestern edge of the LA_MS_AL sampling region. From 1100 to 1400 UTC the line continued to move slowly to the southeast. The ER-2 approached the line from the northeast first intercepting it at 1410 UTC. From 1410 to 1509 UTC, the ER-2 sampled the line as it extended southwest to northeast across southeastern Louisiana from the Gulf Coast to the Louisiana/Mississippi border. Figure 9a highlights the flight track between 1420 and 1430 UTC. Then the ER-2 headed southwest sampling convection over the Gulf of Mexico (Gulf_Line) from 1520 to 1645 UTC. Figure 9b shows 1530–1540 UTC. When the cell over the Gulf dissipated, the ER-2 headed to the northeast and re-sampled the LA_MS_AL system which was slowing to a crawl near the coast of far southeastern Louisiana and coastal Mississippi. This line was sampled multiple times over the next 3 h as it approached the western panhandle of Florida including 1650–1700 UTC (Figure 9c) and 1920–1930 UTC (Figure 9d) until the ER-2 headed to base at 2013 UTC. Trajectories revealed that the large-scale upper tropospheric flow pattern was blowing from the west-southwest to east-northeast with individual cells moving to the east-southeast for the Gulf system and to the east for the LA_MS_AL system. This relatively small mismatch may have led to the loss of up to ∼7% of the LNOx associated with the large LA_MS_AL system and up to ∼ 25% of the LNOx associated with the smaller Gulf of Mexico system (see Section 4.2 and Table 4).

Figure 9

(a–d) ER-2 flight track, GLM lightning flashes, and GCAS V_NO2 on May 12 for 1420–1430 UTC (a), 1530–1540 UTC (b), 1650–1700 UTC (c), and 1920–1930 UTC (d). The dashed boxes show the sampling regions for the LA_MS_AL (Figures 6a–6d) and Gulf of Mexico (Figure 6b) systems. See Figure 3 for additional information. GCAS, Goddard Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper.

The LA_MS_AL coastal line system (Figure 10a) was sampled between 1410–1520 UTC and 1650–2020 UTC on May 12, although a few additional samples were taken just before and after 1540 UTC when the ER-2 “strayed” into the coastal line domain while sampling the Gulf of Mexico cell. LNO_x PE was large early in the sampling period (1410–1500 UTC) when large columns were observed at a time when flashes were still relatively few in number. Overall, the PE was a robust 536 ± 274 mol per flash for GLMa and 339 ± 180 mol per flash for ENTLN. The LNO_x PE time series was noisy throughout the sampling period (c_v equaled 0.51 for GLMa and 0.53 for ENTLN) with no clear temporal trend. Ironically, the largest flash rates occurred between 1540 and 1710 UTC (note the change in slope of the “NO_x Flash#” lines indicating an increase in flash rate) when the ER-2 was mostly sampling the Gulf of Mexico cell.

Figure 10

(a–b). Same as Figure 4 but for the May 12 LA_MS_AL (a) and Gulf of Mexico (b) systems. The scaling factors are 5,246 and 945 for F and 69,228 and 22,904 for (a).

The Gulf of Mexico cell (Figure 10b) was sampled for 10 consecutive 10-min periods between 1510 and 1640 UTC on May 12. Flashes were not plentiful during the sampling period with NO_x-effective flashes decreasing slightly over time over the sampling period. Overall, the PE was 444 ± 114 mol per flash for GLMa and 236 ± 61 mol per flash for ENTLN. Variations in PE with time were relatively small with c_v equaling 0.26 for both GLM and ENTLN. The GLM PE increased with time as increases in the NO_x cloud area with time more than compensated for smaller decreases in V_NO2 and NO_x-flashes with time.

3.5 May 14, 2017

On May 14, the ER-2 headed east sampling two separate convective systems off the eastern coast of Florida that were within range of the Kennedy Space Flight Center LMA. An isolated thunderstorm associated with a cold front was present in the far western edge of the flash-sampling region of the eastern system (Atl_E system) by 0700 UTC, ∼400 km east of Daytona Beach, FL. More widespread deep convection was present by 0930 UTC just to the north of the future flight track. Over the next 3 h, an area of increasingly widespread lightning moved slowly to the south covering the western half of the future flight track. The ER-2 arrived in the region at ∼1240 UTC and began sampling. Initially, it encountered fairly clean air to the south of the air mass impacted by LNOx but by 1330 UTC it was sampling the heart of the system (Figure 11a; 1320–1330 UT). It disengaged from the cell at 1359 UTC after 79 min of sampling, exited the sampling region at 1404 UTC, and headed west toward a second convective system (Atl_W system) just north of the Bahamas over the Gulf Stream that began forming to the south of the future flight track around 1315 UTC and was well-developed by 1350 UTC. The flash accumulation period for this system was chosen to begin at 1100 UTC in order to include the contribution from earlier flashes from a relatively weak storm that was present by 1230 UTC. The ER-2 intercepted the western system (Figure 11b) at ∼1425 UTC when it was beginning to weaken and sampled it until ∼1535 UTC when the plane headed northeast to re-engage the eastern system. Figures 11c shows the ER-2 flight track and GCAS NO₂ columns during the 1530–1540 UTC portion of the western system sampling. The weakening eastern system was re-engaged at ∼1555 UTC and sampled until 1713 UTC. Figure 11d shows 1610–1620 UTC. Trajectories initialized from the corners of the Atl_E and Atl_W system domains revealed that the large-scale 300 hPa flow pattern was from west to east. The Atl_E cell moved to the southeast at a 40° angle to the upper-tropospheric winds allowing for a loss of up to ∼ 30% of LNOx, while the Atl_W cell moved to the east-southeast at a 24° angle to the flow allowing for the loss of up to ∼25% of the LNO_x.

Figure 11

(a–d) ER-2 flight track, GLM lightning flashes, and GCAS V_NO2 on May 14 for 1320–1330 UTC (a), 1440–1450 UTC (b), 1530–1540 UTC (c), and 1610–1620 UTC (d). The dashed boxes show the sampling regions for the eastern Atlantic (Figures 11a and 11d) and western Atlantic (Figures 11b and 11c) systems. See Figure 3 for additional information. GCAS, Goddard Geo-CAPE Airborne Simulator; GLM, Geostationary Lightning Mapper.

The Atlantic eastern system was sampled between 1240 and 1410 UTC and then again between 1550 and 1710 UTC (Figure 12a). When sampling this system there was one 10-min period, 1250–1300 UTC, when all values of V_NO2 were less than V_NO2 (5%). This period was unusual because it only had 5 retrievals satisfying the 300 hPa CTP threshold due to breaks in the cloud cover. LNO_x PE for this 10-min period is 0 mol per flash as V_NO2 = V_NO2 (5%). Overall, the PE equaled 271 ± 107 mol per flash for GLMa and 161 ± 66 mol per flash for ENTLN. LNO_x PE increased between the early- and late-morning periods although the increase is minimal if one chooses to ignore the first 30 min when values of V_NO2 are low and indicative of background air. LNO_x PE varied considerably between 10-min sampling periods with c_v equaling ∼0.4 for both GLMa and ENTLN. This variation is also indicative of a mix of background and NO_x-influenced air. Lightning associated with the eastern system began at ∼0700 UTC, over 5 h before the ER-2 began sampling. Thus, many of the flashes responsible for the NO₂ observed by GCAS were aged and both NO_x-effective flashes and storm cloud area decreased with time during the late morning portion of the sampling period.

Figure 12

(a–b) Same as Figure 4 but for the May 14 Atlantic Eastern (a), and Atlantic Western (b) systems. The scaling factors are 5,573 and 3,486 for F and 28,134 and 29,705 for (a).

The Atlantic western system was sampled between 1420 and 1540 UTC with mean PE values of 174 ± 38 mol per flash for GLMa and 111 ± 25 mol per flash for ENTLN (Figure 12b). In general, PE decreased with time as relatively large increases in flashes were only partially offset by increases in the NO_x cloud area. Variations in V_NO2 over the sampling period were small with c_v equaling ∼0.2 for GLMa and ENTLN.

3.6 Synthesis

LNO_x PE time series were obtained for 10 convective systems observed by GCAS and the CPL on 5 flight days during the GOES-R PLT field campaign. Sampling locations included the northeastern United States (April 20), southeastern United States (April 22), front range of Colorado (May 8), south-central United States and northern Gulf of Mexico (May 12), and western Atlantic east of Florida (May 14). Individual systems were sampled at local standard times (LSTs) ranging from 0740 LST over the western Atlantic to 1842 LST near Lake Erie making it necessary to consider diurnal variations in NO_x/NO₂ ratios when using NO₂ columns to estimate LNO_x PE. PE values were estimated for 10-min periods for time spans averaging 112 min and ranging from 40 min (Lake Erie) to 320 min (LA_MS_AL system).

The overall PE for the GOES-R PLT field campaign before adjusting for biases was determined to be 360 ± 240 mol per flash for GLMa and 230 ± 160 mol per flash for ENTLN (see Table 3). The means and standard deviations assume a NO_x lifetime of 2 h and were obtained by weighting the PE values from the 124 10-min time periods with GCAS samples by the number of along-track GCAS retrievals within respective sampling regions. The GLMa-based PE is 57% more than the ENTLN PE due to differences in the flash clustering algorithm and also because GLM is unable to detect some smaller/weaker flashes detected by ENTLN due to differences in lightning-observing techniques. ENTLN detects low-frequency sferics, while GLM detects optical emissions of lightning from near the cloud top. As a result, ENTLN has both more flashes and greater LNO_x area, both of which affect the calculated PE.

The primary factors responsible for intra-system temporal variations in PE were examined by comparing values of the c_v for V_LNO2, NO_x-effective flashes per unit area, and rNO_x/NO₂ for the various systems. Variations in V_LNO2 were the largest contributor to variations in PE for 9 out of the 10 systems; values of V_LNO2 were nearly constant with time for the western Atlantic cell. Variations in flash density were the most important factor for the western Atlantic cell and at least 50% as important as variations in V_LNO2 for northern Alabama, northern Colorado, and Gulf of Mexico systems. Variations in rNO_x/NO₂ were less important for most systems but were important for the southern Alabama cell, which was sampled extensively in the late afternoon when the ratio was decreasing rapidly with time.

The primary factors responsible for inter-system variations in PE were also examined. Variations in flash density were most important (c_v = 0.63), followed by variations in V_LNO2 (c_v = 0.40), and rNO_x/NO₂ (c_v = 0.24). The large variability in flash density and the possible dependence of PE on flash density suggests that a wide range of flash densities should be included in storm ensembles if the goal is to scale up the PE values from individual systems to a larger scale.

4 Discussion

4.1 An Alternate Approach of Estimating LNO_x PE

For most of the GOES-R PLT field campaign convective systems, variations in LNO_x PE with time are substantial primarily due to large spatial variations in V_NO2 within the sampling region. This adds uncertainty to the estimation of LNO_x PE; however, differences in V_NO2 between periods with low and high V_NO2 can also be used to develop an alternative approach to estimating V_LNO2. PE values from this alternate approach can then be compared to the standard values and used to determine if V_NO2 (5%) is a reasonable choice for the tropospheric background.

On May 12, from 1650 to 1950 UTC, that is, for 18 10-min periods, the ER-2 repeatedly crossed the LA_MS_AL coastal line alternately sampling locations with near-background and LNO_x-influenced columns. In the alternate approach, V_LNO2 is assumed to be given by the difference in V_NO2 between periods when V_NO2 is high and GCAS is assumed to sample the LNO_x cloud and periods when V_NO2 is low and GCAS is assumed to sample background air. Mathematically, Equation 2 is replaced by Equation 5.

(5)

where values for V_NO2 (LNO_x-influenced) and V_NO2 (background) are obtained by taking sample-weighted means of V_NO2 for 10-min periods with high- and low-columns. A caveat with this approach is that samples from most if not all 10-min periods include both background and LNO_x-influenced air thus it is unclear what portion of this time period should be used to estimate values of V_NO2 (LNO_x-influenced) and V_NO2 (background). A lower bound on the PE is obtained when all 18 periods are used with the 9 highest classified as NO_x-influenced and the 9 lowest classified as background-influenced. When all 18 10-min periods are used, the PE using Equations 1 and 5 is 443 mol per flash for GLMa and 265 mol per flash for ENTLN where values for A, rNO_x/NO₂, and F are the sample-weighed means over LNO_x-influenced and background time periods. These values are ∼ 13% lower than values from the standard approach (Equation 1 and 2) for this 3-h period, which are 510 mol per flash for GLMa and 303 mol per flash for ENTLN. The alternate PE increases if time periods with moderate levels of V_NO2 are removed from the data set before estimating the PE. For example, the GLMa (ENTLN) PE increases to 541 (322) mol per flash if only the highest 7 and lowest 7 10-min periods during the 1650–1950 UTC time period are used. This is an increase of 18%–22% from the value for all 18 time periods and an increase of ∼6% from the value for the standard approach. Of course, even higher PEs could be obtained if fewer 10-min periods were used in the determination. However, the use of 14 out of the 18 periods seems like a reasonable compromise as it uses data from most of the 3-h time period while eliminating the four periods with the most mixing between background and LNO_x-influenced air. The relatively small biases support the use of V_NO2 (5%) as the tropospheric background with the standard approach and indicate that the standard approach for estimating V_LNO2 given by Equation 2 is sound, but with a methodology uncertainty of ∼10%.

4.2 Analysis of Biases and Uncertainty

The coefficient of variation-based uncertainty of 67%–70% (see Table 3) is within the formally determined range obtained by Allen et al. (2019) (see Section 4) for a study using OMI NO₂ columns and World Wide Lightning Location Network (WWLLN) (Virts et al., 2013) flashes. They obtained an uncertainty of 58%–73% after summing in quadrature uncertainties in WWLLN DE (±25%–50% depending on DE value), tropospheric background (±30%), A_LNOx* (20% ± 30%), NO_x lifetime (±25%) and several other less important error sources

4.2.1 PE Biases due to Biases in AMF

Allen et al. (2019) included a positive PE bias of 20% due to biases in AMF arising from positive biases in modeled NO/NO₂ ratios in the upper troposphere (Allen et al., 2019; Bucsela et al., 2019; Lapierre et al., 2020; Laughner & Cohen, 2017; Silvern et al., 2018). This study also assume a 20% high bias in PE due to biases in AMF.

4.2.2 PE Biases due to Advective Loss of LNO_x

Advection will move LNO_x into and out of the sampling region (see Section 2.3) with the net effect likely a loss of LNO_x because the bounds of flash counting regions are chosen to include most if not all flashes associated with each system. The fractional loss of LNO_x (F_loss) can be estimated using Equation 6:

(6)

where dt is the time period over which the loss is calculated (s), V₂₀₀ is the mean 200 hPa wind speed from MERRA-2 within the sampling region (m/s), theta (radians) is the difference in direction between the upper-tropospheric winds and the movement of the storm, and Hypotenuse (m) is the square root of x² + y² where x and y are the east-west and north-south lengths (dimensions) of the sampling region from Table 1. The value of dt is set to 3600 s. A value of 1 h was chosen because advective loss is most important during the first hour after flash occurrence due to the assumed 2-h lifetime of NO₂ in the near field of convection. The direction of the storm is the angle whose tangent is equal to -dy over -dx where dx and dy are the east-west and north-section distance the storm traveled during a time period beginning 3 h before the ER-2 arrived in the sampling region and ending when the ER-2 left the sampling region. The initial storm location used in the calculation of dx and dy is given by the centroid of ENTLN (GLM) flashes during the 60 min following the first 10-min period that at least 100 (50) ENTLN (GLM) flashes were recorded within the sampling region. The final storm location is given by the centroid of ENTLN (GLM) flashes during the last hour GCAS sampled the storm. The direction of the upper-tropospheric winds is the angle whose tangent is equal to -vwind over -uwind where uwind and vwind are the mean u and v components of the wind during this time period. Table 4 shows the direction of the storm as determined using ENTLN and GLM flashes. Overall, the two directions are a quite similar lending credence to the method used to determine the storm direction and fractional loss. The potential fractional loss of LNO_x due to advection ranges from ∼5% for the Lake Erie and LA_MS_AL systems to 30%–35% for the northern Alabama and Atlantic_E systems. However, individual values for loss should not be given too much weight because the outflow direction is determined by more factors than the large-scale flow. Therefore, the PE values for individual systems are not adjusted for fractional loss. However, the mean fractional loss (20%) is likely to be more robust and approximately cancels the 20% high-bias due to biases in the AMF. Thus, the PE derived from the GOES-R PLT field campaign data is assumed to be unbiased. However, keep in mind that this cancellation assumes that dt is on the O(1 h), that is, it assumes that most of the flashes occurred recently.

4.2.3 Uncertainties

From Equation 1, the PE is proportional to A/F, V_LNO2, and rNO_xNO₂ where A/F is combined because the NO_x cloud area depends on the spatial and temporal distribution of flashes. The uncertainty in PE associated with uncertainties in A/F can be estimated by analyzing the sensitivity of PE to DE, chemical lifetime, and method used to estimate the area of the NO_x cloud. Table 2 shows the mean GLM and ENTLN DE for each of the storms. The uncertainty in PE due to uncertainties in DE are assumed to be given by the normalized standard deviation of the GLM DE, which is 21% or 0.16/0.75. The normalized standard deviation of the ENTLN DE is smaller and not used here. In order to estimate the uncertainty due to chemical lifetime, the PE was also estimated for NO_x lifetimes of 1.5 and 3 h (see Table 5). These lifetimes were chosen to bracket the 2-h NO_x lifetime assumed here. Decreasing τ from 2 to 1.5 h increased the PE by 17%–20% per flash while increasing τ from 2 to 3 h reduced the PE by 15%–19%. Thus, the uncertainty associated with chemical lifetime is ∼±18%. To assess the uncertainty associated with cloud area, the PE was re-calculated using smaller and larger estimates of the LNO_x cloud area (Table 5). When only flashing grid boxes were used the LNO_x PE decreased by 46% for GLMa and 33% for ENTLN. When flashing boxes plus two adjacent boxes were used, the LNO_x PE increased by 25% for GLMa and 15% for ENTLN. The percent change is not symmetric as a larger change is observed going from the standard approach to only flashing boxes. However, this does not imply that the standard approach has a high-bias as the change in the area associated with going from the standard approach to non-flashing boxes is larger than the change in the area resulting from including an additional box. Therefore, no bias adjustment is made and the uncertainty is assumed to be equal to ±30%, which is the average of the absolute values of these four numbers. Summing these four terms in quadrature, the uncertainty in PE due to uncertainties in A/F equals 41%, which is the square root of 0.21² + 0.18² + 0.30².

Table 5. Sensitivity of LNO_x PE to Assumed Chemical Lifetime (τ) and Method of Determining the Flash Area (Flashing Plus 1 Adjacent Box Versus Flashing-Only or Flashing Plus 2 Adjacent Boxes)

Method of determining A	NOx τ (h)	GLMa (mol per flash)	ENTLN (mol per flash)
Flashing + adjacent	2	356 ± 241	227 ± 158
Flashing + adjacent	1.5	427 ± 290 (20% ↑)	265 ± 182 (17% ↑)
Flashing + adjacent	3	290 ± 196 (19% ↓)	192 ± 137 (15% ↓)
Flashing	2	191 ± 131 (46% ↓)	151 ± 111 (33% ↓)
Flashing + 2 adjacent	2	446 ± 326 (25% ↑)	260 ± 181 (15% ↑)

• ENTLN, Earth Networks Total Lightning Network; GLM, Geostationary Lightning Mapper.

Allen et al. (2019) use a value of 30% for the uncertainty in PE due to uncertainties in rNO_xNO₂. Here, the uncertainty in PE due to uncertainties in rNO_xNO₂ was calculated using two different approaches. In the first approach, the sensitivity of PE to the rNO_xNO₂ percentile was examined. The standard approach uses the 90th percentile. If the 50th percentile was used instead, the PE decreases by ∼10%. In the second approach, the c_v of rNO_xNO₂, 21%, was used as an estimate of the uncertainty. Both of these estimates are lower than 30%. The larger of these two values will be used as an estimate of the uncertainty here. The larger is used because the variability in rNO_xNO₂ is likely underestimated because the ratios were obtained from a 0.625° × 0.50° model simulation that may not capture inter-storm variations in the ratio.

The uncertainty in V_LNO2 is dominated by uncertainties in the tropospheric background, that is, to the difference in V_NO2 between LNO_x-influenced and background locations. Here, LNO_x PE was calculated using two different methods of determining V_LNO2 causing ∼10% changes in PE. This may be used as a lower limit on the uncertainty because it is based on only one of the 10 storm cases. Allen et al. (2019) assumed an uncertainty of ±30% for this term. This value seems high because the spatial resolution of the GCAS measurements is much higher than the spatial resolution of the OMI retrievals allowing for much more accurate separation of LNO_x-influenced and background air masses. Therefore, we split the difference between the two estimates and assume an uncertainty of ±20%. Going forward, uncertainties associated with the tropospheric background could be reduced if future field campaigns with high-resolution measurements of NO₂ column include flight patterns similar to the one used on July 12. On that date, the ER-2 repeatedly crossed the system alternately making measurements of NO₂ over sampling locations with near-background and LNO_x-influenced columns.

Here, the main measurement gap is the lack of a direct measurement of the OCP from GCAS. The location of the OCP is the pressure at the lowest altitude in the cloud that GCAS can observe NO₂. Here, an observing depth of 250 hPa below the CPL cloud top is estimated using data from one GCAS flight that overlapped temporally with OMI (see Section 2.1). The use of a constant depth adds uncertainty to the result. However, sensitivity calculations for the May 12 flight indicate that local variations in observing depth obtained from differences between paired OMI OCP and CPL CTPs caused less than a 10% change in PE when averaged over the flight. Thus, the uncertainty associated with this term is assumed to be minor and grouped with uncertainties due to systematic errors in slant column, stratospheric vertical column, and LNO_x below the OCP. The total uncertainty of these terms is assumed to be minor (±10% in aggregate) because these errors mostly cancel when V_LNO2 is calculated using Equation 2 or 5. Summing in quadrature, the overall uncertainty is determined to be the square root of the total of 0.41² + 0.21² + 0.20² + 0.10² or 51.5%. Therefore, the best estimate of PE for the GOES-R PLT field campaign is 360 ± 180 mol per flash for GLM and 230 ± 115 mol per flash for ENTLN.

4.3 Relation Between PE and Other Flash Metrics

Figures 13a–13d show the correlation between flash density and LNO_x PE (a), flash optical energy and PE (b), flash multiplicity and flash optical energy (c), and flash multiplicity and PE (d) for GLMa flashes. The storm-averaged values for each quantity were obtained by weighting the values for individual 10-min periods by the number of GCAS observations. The 10-min averages for flash multiplicity and optical energy were obtained by averaging values for the sampling region from a 0.1°× 0.1 gridded data set derived from the reprocessed GLM data set. The flash density is defined as the number of flashes divided by the NO_x cloud area (A) (see Section 2.4), where the number of flashes is not adjusted for chemical decay. LNO_x PE is well correlated with flash optical energy (r = 0.83) and flash multiplicity (r = 0.77), and negatively correlated with flash density (r = −0.73), while flash multiplicity and optical energy are highly correlated (r = 0.97). The positive correlation of PE with flash multiplicity and flash optical energy is driven by flashes from the three Colorado systems, which have very low multiplicities, energies, and production efficiencies. The mean GLMa PE for the non-Colorado systems is 409 mol per flash while the mean PE for the Colorado systems is 103 mol per flash. Thus, the mean PE for the Colorado systems is only ∼1/4 that of the non-Colorado systems. The causes of this result include the low multiplicities, low optical flash energies, and high flash densities of the Colorado storms. Several studies indicate that on average flash energy is larger at marine locations than continental locations (Beirle et al., 2014; Hutchins et al., 2013; Mach et al., 2011). However, this result is only marginally supported here. The lowest optical flash energies (95–213 fJ) are found over Colorado; however, the highest flash energy (882 fJ) is found for the LA_MS_AL system, whose sampling domain includes continental and marine locations over southern Louisiana, Mississippi, Alabama, and the northern Gulf of Mexico (see Figure 9a). The optical flash energies associated with the Atlantic systems are unremarkable although the energy of the western cell (261 fJ) that is over the Gulf Stream and closer to the continental United States is less than half that of the eastern cell (594 fJ). PE being negatively correlated with flash density is consistent with the finding that storms with high flash densities have smaller individual flash channel lengths (Bruning & MacGorman, 2013; Davis et al., 2019; Mecikalski et al., 2015; Zhang & Cummins, 2020) and therefore likely produce less NO_x per flash. However, here, this result cannot be given too much weight because a portion of the negative correlation is due to the fact that the area of the NO_x cloud is in the numerator of Equation 1 while the flash total is in the denominator. The high correlation between flash optical energy and PE and the very high correlation between flash multiplicity and flash optical energy supports efforts to parameterize PE in terms of GLM flash optical energy or GLM groups. In addition, much of the scatter in flash rate versus PE plots is caused by inter-flash differences in flash optical energy, which are in turn related to inter-flash differences in multiplicity.

Figure 13

Scatterplots showing the GLMa-derived relationship between (a) LNO_x PE (mol per flash) and flash density (flashes km⁻²), (b) LNO_x PE and flash energy (fJ), (c) flash energy and flash multiplicity, and (d) LNO_xPE and flash multiplicity. Colors are used to separate flight days while symbols are used to separate system within each flight day. Correlations are shown in the upper right. GCAS, Goddard Geo-CAPE Airborne Simulator.

Figures 14a–14d show the correlation between flash density and LNO_x PE (a), peak amplitude and PE (b), flash multiplicity and peak amplitude (c), and the IC/CG ratio and PE (d) for ENTLN flashes. The values for multiplicity and peak amplitude are weighted storm averages over the sampling region derived from the 0.1° × 0.1° gridded CG ENTLN data sets. As with GLM, the storm-averaged values for each quantity were obtained by weighting values for individual 10-min periods by the number of GCAS observations. Similar to GLM, LNO_x PE is moderately negatively correlated with flash density (r = −0.63); however, positive correlations between ENTLN PE and peak amplitude (r = 0.47) and flash multiplicity (r = 0.19) (not shown) are weaker. The weaker positive correlations could be caused by only using CG flashes when determining the relationship. Lapierre et al. (2020) found a robust correlation between stroke (as opposed to flashes used here) amplitude and PE. The correlation between flash multiplicity and peak amplitude is only 0.35 possibly because of an anomalously high peak amplitude of ∼50 Kamps for the Gulf of Mexico system. The correlation increases to 0.63 when this storm is excluded.

Figure 14

(a–d) Scatterplots showing the ENTLN-derived relationship between (a) LNO_x PE (mol per flash) and flash density (flashes km⁻²), (b) LNO_x PE and peak amplitude (Kamps), (c) peak amplitude and flash multiplicity, and (d) LNO_x PE and the ratio of IC to CG flashes. Colors are used to separate flight days while symbols are used to separate system within each flight day. Correlations are shown in the upper right. ELTLN, Earth Networks Total Lightning Network; LNO_x PE, lightning NO_x production efficiency.

The IC/CG ratio from ENTLN is uncorrelated (r = 0.03) with LNO_x PE, which is surprising as the mean amplitude of ENTLN IC flashes here is only 15%–35% the peak current of CG flashes depending on the system and a positive relationship was found between peak amplitude and LNO_x PE. Lapierre et al. (2020) did a much more detailed study of CG/IC differences in LNO_x PE using ENTLN data over the United States and OMI NO₂ columns. They found that the PE of CG flashes (strokes) was 3 (10) times greater than that of IC flashes (strokes) with differences in peak current being the main cause of the differences with contributions from flash length (Huntrieser et al., 2008) and duration differences. In addition, differences in flash altitude between IC and CG flashes and between normal and anomalous polarity storms may also affect PE (Fuchs & Rutledge, 2018) due to the dependence of PE on pressure (Wang et al., 1998). While these results do indicate a positive correlation between peak current and LNO_x PE, this provides little insight into the relationship between flash type and PE. A moderate to strong negative correlation would be expected if on average an IC flash produced substantially less NO_x than a CG flash.

4.4 Relationship of These Findings to Recent Studies

Recent studies have used a variety of approaches to estimate LNO_x PE over the mid-latitudes of the Northern Hemisphere. Pollack et al. (2016) used in situ measurements of storm inflow and outflow to estimate the PE for eight isolated storms sampled over Oklahoma and Colorado during the Deep Convective Clouds and Chemistry (DC3) field experiment. Assuming the enhanced LNO_x was distributed over the volume of the observed cloud and adjusting for uncertainties, they obtained a PE of 117–332 mol NO_x flash⁻¹. Davis et al. (2019) examined the PE for three anomalous and two normal polarity DC3 storms that occurred within the range of Lightning Mapping Arrays (LMAs). After assuming LNO_x production was proportional to channel length and pressure, they obtained a PE of 61–158 mol per LMA flash. They noted that their slightly low range could be due to shorter than normal channel lengths (the flash rates were high) and/or the high DE of LMAs. Marais et al. (2018) obtained 280 ± 80 mol per flash through comparison of upper tropospheric NO₂ from an OMI-based cloud-slicing technique (Choi et al., 2014; Ziemke et al., 2001) with GEOS-Chem output.

Recent satellite-based estimates of PE over the United States include studies by Bucsela et al. (2019), Lapierre et al. (2020), Pickering et al. (1996, 2016), and Zhang et al. (2020). Pickering et al. examined LNO_x PE over the Gulf of Mexico in a study that used OMI NO₂ columns and WWLLN flashes. They obtained a relatively low PE of 80 ± 45 mol per flash mostly because they did not adjust for the short-lifetime of NO₂ in the near field of convection. Bucsela et al. obtained a mean PE of 180 ± 100 moles LNO_x per flash using OMI NO₂ columns and WWLLN flashes for a midlatitude study region focused over continents. They noted that the PE decreased with flash rate. Lapierre et al. used Berkeley High-Resolution (BEHR) NO₂ columns (Laughner et al., 2018) from OMI and stroke counts from ENTLN and National Lightning Detection Network to examine differences in lightning-NO₂ (LNO₂) PE between IC and CG strokes over three US regions. For relatively high flashing storms, they found that the PE varied with current and was approximately 10× larger for CG strokes than IC strokes. Zhang et al. obtained a PE of 90 ± 50 mol LNO_x per flash in an eastern United States study using BEHR NO₂ columns and ENTLN strokes/flashes that highlighted the sensitivity of LNO_x PE to AMF. Thus the PEs found here for 10 spring storms over the United States and western Atlantic agree best with Marais et al. and are near the upper edge of the ranges found by Allen et al., Bucsela et al., and Davis et al.

5 Conclusions

The Warner-Robins, GA deployment of the GOES-R PLT Field Campaign was conducted during April-May 2017 using the NASA ER-2 aircraft. One of the primary goals of the deployment was validation of the GLM satellite instrument aboard GOES-R. GCAS piggybacked on the aircraft mission to allow continuous observations of NO₂ slant columns simultaneously with lightning detection by FEGS while overflying convective systems. The Warner-Robins deployment included 5 days with daylight storm overpasses and CPL cloud top heights. NO_x production per lightning flash, that is, LNO_x PE, was examined for 10 convective systems that occurred on those days over Lake Erie (April 20), Alabama (April 22), Colorado (May 8), the south-central United States and the Gulf of Mexico (May 12), and the western Atlantic east of Kennedy Space Flight Center (May 14).

GCAS measures solar radiation backscattered from the surface and atmosphere. Differential NO₂ SCDs were obtained from GCAS-measured spectra and used with AMFs to estimate vertical columns of NO₂ (V_NO2) over deep convective scenes. The spatial variability in V_NO2 was then used to estimate the portion of the column (V_LNO2) due to recent lightning. LNO_x PE is estimated by dividing the moles of NO_x associated with V_LNO2 by the flashes contributing to the observed NO₂ column. The former term is obtained by multiplying V_LNO2 by the area of the lightning-NO_x cloud (A) and by the upper-tropospheric ratio of NO_x to NO₂ from GEOS-5. The PE is obtained for each 10-min period of GCAS sampling with values being averaged to obtain an estimate of PE for the entire system. The area and flash total are obtained using data from GLM and ENTLN, a ground-based lightning network. The area of the NO_x cloud is assumed to equal the area within the flash-counting region with recent ENTLN or GLM lightning. Thus, a grid box with current lightning contributes its entire area to the NO_x cloud area, while a grid box with past lightning contributes an amount that decays with time. Flash totals are adjusted for DE, summed over the flash counting region from the beginning of the flash accumulation period to the sampling time, and decayed exponentially to account for the short NO_x lifetime in the vicinity of deep convection.

For an assumed LNO_x lifetime of 2 h, the mean PE for the 10 convective systems analyzed during the GOES-R PLT campaign was determined to be 360 ± 180 mol per flash when GLM was used as the source of lightning data and 230 ± 115 mol per flash when ENTLN was used as the source. The PE values differ by 57% because ENTLN and GLM use different lightning-observing techniques and different methods for clustering flashes. ENTLN detects low-frequency sferics, while GLM detects optical emissions of lightning from near the cloud top and may miss flashes that are smaller or weaker or occur beneath deep convection. The cause of differences in PE between optically and radio-detected storms are varied but include the fact the GLM preferentially detects flashes with longer channel lengths. Future studies investigating differences in DE between optical detection systems and radio-wave systems for normal and anomalous polarity storms are needed and will be useful in determining if the contribution of undetected (by GLM) short-lived short-length flashes to NO_x production is relatively small.

LNO_x PE is positively correlated with flash multiplicity and flash energy but negatively correlated with flash density, while GLM flash multiplicity and flash optical energy are found to be highly correlated. The negative correlation of PE with flash density is consistent with the belief that storms with higher flash densities have smaller individual flash channel lengths and produce less NO_x per flash. The high correlation (r = 0.83) between flash optical energy and PE is driven by three Colorado systems whose flashes had low multiplicities, low energies, and consequently low PEs. The high correlation between flash optical energy and PE and the very high correlation between flash multiplicity and flash energy argue for PE parameterizations in terms of flash energy or multiplicity. These studies are already beginning as flash multiplicity is an intermediate product obtained during the clustering of flashes, flash energy can be inferred from optical flash energy, and the flash channel length is related to the flash area and can also be estimated using data from LMAs.

The configuration of observations during the GOES-R PLT field campaign allowed for a demonstration of the future synergy between continuous lightning detection from GLM and the high spatial and temporal NO₂ observations from the TEMPO instrument slated for launch in 2022.

Acknowledgments

Funding awarded to S. Janz, GSFC PI, under the GEO-CAPE project (Project Lead, J. Al-Saadi), with sub-award (NASA Grant NNX17AE21 G) to D. Allen, UMD PI. The authors thank to Luke Oman for assistance in setting up the GMI replay simulations. The authors also thank Heidi Huntrieser of the German Aerospace Center (DLR) who provided comments on a draft version of this manuscript.

Appendix

On April 20, the GLM data set begins at 2139 UTC and is first used at 2140 UTC, which is ∼2 h before the ER-2 began sampling the storms but well after the line developed. According to the ENTLN, 52% of the flashes associated with the Lake Erie system occurred before 2140 UTC. On April 22, the GLM data set begins at 1930 UTC, 2 h before the ER-2 began sampling the storms, near the time when the line began to strengthen, but an hour after the flash accumulation period began. According to the ENTLN, 0.5% of flashes associated with the northern system occurred before 1930 UTC while 7.4% of the flashes associated with the southern system occurred before 1930 UTC. Thus, missing GLM data should have minimal impact on LNO_x PE calculations for these systems. On May 8, the GLM data set begins before the flash accumulation period starts. On May 12, the GLM data set begins at 1310 UTC, which is 60 min before the ER-2 began sampling the LA_MS_AL Line and 130 min before it began sampling the Gulf Line. According to the ENTLN, 32% of the flashes associated with the Gulf Line occurred before 1310 UTC, while 16% of flashes associated with the LA_MS_AL line occurred before the same time. On May 14, the GLM data set begins at 1120 UTC, which is 80 min before the ER-2 began sampling the eastern cell but several hours after flashes began. According to the ENTLN, 41% of the flashes associated with the eastern system occurred before GLM data are available. GLM data were available by the time the first flashes associated with the western storm occurred.

Open Research

Data Availability Statement

During the field program, co-author Douglas Mach of NASA Marshall obtained filtered L1b data from GLM contractor, Lockheed Martin, and clustered the fields into the L2 data sets that are used here. GCAS NO₂ slant and vertical columns for the GOES-R PLT field campaign are accessible on the Aura validation data center website at "https://avdc.gsfc.nasa.gov/pub/data/aircraft/GCAS_GOESR/" \o "https://avdc.gsfc.nasa.gov/pub/data/aircraft/GCAS_GOESR/" \t “_blank”https://avdc.gsfc.nasa.gov/pub/data/aircraft/GCAS_GOESR/. GLM flashes during the time period of the GOES-R PLT field campaign are accessible at http://dx.doi.org/10.5067/GOESRPLT/GLM/DATA101. ENTLN data were obtained freely by request from Earth Networks (https://www.earthnetworks.com).