Lightning NO2 simulation over the Contiguous US and its effects on satellite NO2 retrievals

Lightning is an important NOx source representing ~10% of the global source of odd N and a much larger percentage in the upper troposphere. The poor understanding of spatial and temporal patterns of lightning contributes to a large uncertainty in understanding upper tropospheric chemistry. We implement a lightning parameterization using the product of convective available potential energy (CAPE) and convective precipitation rate (PR) into Weather Research and Forecasting-Chemistry (WRF-Chem) model. The CAPE-PR parameterization with a regional scaling factor of 0.5 in the southeastern US, is coupled 5 with Kain Fritsch convective scheme (KF/CAPE-PR) to generate lightning for the continental US. We show that the KF/CAPEPR scheme yields an improved representation of lightning flashes in WRF when comparing against flash density from the Earth Networks Total Lightning Network. Compared to the cloud top height (CTH) lightning parameterization coupled with Grell 3D convective scheme (G3/CTH) used in WRF-Chem, simulated NO2 profiles using the KF/CAPE-PR parameterization exhibit better agreement with aircraft observations in the middle and upper troposphere. Using a lightning NOx production rate of 500 10 mol NO flash−1, the a priori NO2 profile generated by the simulation with the KF/CAPE-PR parameterization reduces the air mass factor for NO2 retrievals by 16% on average in the southeastern US on the late spring and early summer compared to simulations using the G3/CTH parameterization. This causes an average change in NO2 vertical column density four times higher than the average uncertainty.

In Figure 3, is the cloud fraction threshold of 0.2 used as in Figure 4? If so, please add this information to the caption The cloud fraction threshold of 0.2 is also used in Figure 4. We modified the caption of Figure 4: "Relative change in BEHR NO 2 VCD over the southeastern US switching the source of a prior NO 2 profiles from WRF-chem outputs using G3/CTH to one using KF/CAPE-PR lightning parameterization. (a) shows the mean spatial distribution of the changes from Aug 01 to Sep 23, 2013 and (b) shows the temporal variation over urban and rural areas. Only observations with cloud fraction less than 20% are included. Medium to large cities, including Atlanta, GA; Huntsville, AL; Birmingham, AL; Tallahassee, FL; Orlando, FL; and Baton Rouge, LA, are marked by stars in panel (a)." On page 10, line 2, you cite  for the statement that "uncertainty due to AMF calculation for BEHR v3.0B is smaller than 30%. I couldn't find the corresponding statement in that paper and think that more qualification is needed? which parts of the uncertainty do you consider in this number? The way this number is used suggests that you exclude uncertainty from the vertical profile used? Why is it OK to assume that AMF uncertainties (which are strongly related to knowledge of surface reflection) are reduced like a random uncertainty when averaging?
The uncertainty evaluation of BEHR v3.0B is in the Section 6 of supplementary from . Summarized in Table S4 from , the uncertainty in AMF due to surface reflectance, surface pressure, tropopause pressure, cloud pressure, cloud radiance fraction, and a priori profiles is determined by perturbing each parameter and re-retrieving the NO 2 VCD with the perturbed values. The calculated AMF uncertainty is less than 30% except for the winter.
Note that the uncertainty from the vertical profile is also included in the estimated AMF uncertainty. By improving the lightning parameterization in the models, we expect the uncertainty from the vertical profiles is lower than the previous calculation. The uncertainty in AMF of 30% is a very conservative estimate.
According to Figure S12 in , the a priori profile is the largest contributor to the AMF uncertainty, and tropopause pressure and cloud pressure are the next two largest contributors. Given that the uncertainty due to surface reflection is very small in general (<4%), we can treat daily AMF and VCD as independent variables and calculate the uncertainty duo to AMF calculation as random uncertainty. We add the following text to point out the sources of uncertainty: "We follow the same algorithm used in  to determine if the result is significant. The overall uncertainty due to AMF calculation for BEHR v3.0B is smaller than 30% during the study period (Sec 6 in supplementary from ).Over 90% of the uncertainty attributes to the a prior NO 2 profiles, the tropopause and cloud pressures. As each grid in Fig. 3(a) is the average of 45±9 pixels, the reduced uncertainty is less than 4.5%." In order to better understand the reason for the large changes over urban areas when changing the lightning parametrisation it would be good to add figures showing vertical profiles of NO2 for the three cases of no lightning, old parametrisation and new parametrisation as well as the scattering weights for the two cases of August 24 and September 10 that you discuss We add Fig. S3 (also labeled as Fig. R1 in this response) in the supplementary. Note that we did not include the NO 2 profiles from WRF-Chem without lightning NO x emissions, which are similar to the NO 2 profiles from WRF-Chem using KF/CAPE-PR with little NO 2 in the middle and upper troposphere over both urban and rural areas. For both days, switching from G3/CTH to KF/CAPE-PR parameterization in WRF-Chem substantially lowers the NO 2 in the upper troposphere. The di↵erence in the relative change of VCD between two days is mainly due to the sensitivity in AMF to the erroneous high peak of NO 2 caused by G3/CTH parameterization in the middle and upper troposphere. We expand the discussion of the VCD changes on Sep 10 and Aug 24: " Table 2 presents the AMF and VCD obtained from using a priori profiles with G3/CTH or KF/CAPE-PR lightning parameterizations as well as the relative changes on Sep 10 and Aug 24, 2013. The corresponding a priori NO 2 profiles and scattering weights over urban and rural areas are shown in Fig. S3. Sep 10 is an example of one day when the change in NO 2 profiles has a very large impact on the NO 2 VCDs. The WRF-Chem using G3/CTH parameterization places a large amount of NO 2 between 200-600 hPa with the maximum value comparable to the near surface NO 2 over the urban areas. The calculated AMF is predominantly determined by lightning NO 2 due to the combination of higher scattering weight and larger NO 2 in the middle and upper troposphere. The change in AMF is -56.0% over urban areas and -32.0% over rural areas; the corresponding VCD increases by 134.9% and 44.9%, respectively. In contrast, Aug 24 is an example where the lightning parameterization has very little e↵ect. While the positive bias in NO 2 aloft is also observed by using G3/CTH parameterization, the amount of NO 2 in the middle and upper troposphere is smaller than Sep 10. It leads to lower sensitivity in AMF to the erroneous NO 2 caused by the lightning parameterization. With smaller relative change in AMF, the relative change in VCD is 3.1% over urban areas and -4.6% over rural areas. " Please change the labels in Fig. 4 from "change in" to "di↵erence in" The figure is modified accordingly.
Please check again if the figures really show BEHR-WRF-Chem as stated in the text and in the caption. Judging from the numbers, I would guess that in fact WRF-Chem -BEHR is shown.
The figure shows WRF-Chem minus BEHR. We add it into the caption: "Di↵erence in NO 2 VCD between BEHR retrievals and WRF-Chem ("WRF-Chem" "BEHR"). (a) excludes LNO x in model simulation, (b) adds LNO x emission with production rate of 500 mol NO flash 1 . (c) includes the same LNO x emission as (b) but uses NO 2 profiles scaled upward by 60% at pressure lower than 400 hPa. The average time covers May 13 to June 23, 2012. Pixels with cloud fraction larger than 0.2 are filtered out in the analysis." Why is the spatial pattern of lightning ( Fig. 1d) not reflected in Figure 4a? Figure 1 and 4 average the datasets during the same study period. "The Ozone Monitoring Instrument (OMI) is an ultraviolet/visible (UV/Vis) nadir solar backscatter spectrometer launched in July 2004 on board the Aura satellite. It detects backscattered radiance in the range of 270-500 nm and the spectra are used to derive column NO 2 at a spatial resolution of 13 km⇥24 km at nadir  We thank the reviewer for the positive response of the main article. Below we respond to the individual comments. The reviewer's comments will be shown in red, our response in blue, and changes made to the paper are shown in black block quotes. Unless otherwise indicated, page and line numbers correspond to the original paper. Figures, tables, or equations referenced as "Rn" are numbered within this response; Figures, tables, and equations numbered normally refer to the numbers in the original discussion paper.
The abstract, the results, and the conclusions need to be enhanced to indicate the relative amounts of improvement due to changing convective schemes and changing lightning schemes. Table 1 shows that in the southeastern US just changing from G3 to KF produces the bulk of the improvement in slope and R2. With the KF scheme, changing from CTH to CAPE-PR only makes a small incremental improvement in slope and R2. Elsewhere, the change from G3/CTH to KF/CTH makes a 50% greater improvement in R2 than changing from KF/CTH to KF/CAPE-PR. So, the bottom line is is that the convective scheme was more important than lightning scheme in yielding improved lightning prediction. The paper needs to say this.
Thanks for the suggestion. We modify the abstract to: "Lightning is an important NO x source representing˜10% of the global source of odd N and a much larger percentage in the upper troposphere. The poor understanding of spatial and temporal patterns of lightning contributes to a large uncertainty in understanding upper tropospheric chemistry. We implement a lightning parameterization using the product of convective available potential energy (CAPE) and convective precipitation rate ( In the Section 3.1, we rewrite the discussion on the comparison between modeled and observed lightning flash densities: "Both models using the KF/CTH and KF/CAPE-PR parameterizations improves the correlation between modeled and observed lightning flash densities over the US domain. In the southeastern US, changing from G3 to KF convective scheme substantially increases the R 2 from 0.30 to 0.67 and reduces the slope from 2.08 to 0.94. Switching from CTH to CAPE-PR lightning parameterization only contributes a slight increment on the correlation. While the slopes close to unity both for KF/CTH and KF/CAPE-PR, we note that the improved scaling of the slope in KF/CAPE-PR is mainly caused by the scaling factor of 0.5 applied to the southeast region. In this simulation, a constant linear coe cient for CAPE-PR is not adequate to represent the observed lightning over CONUS, in contrast to the finding of Romps et al. (2014). Elsewhere in CONUS, both the changes in convective scheme and lightning parameterization yield a better representation of lightning flash densities compared to the observation. The R 2 for KF/CAPE-PR improves significantly to 0.62 compared to both G3/CTH and KF/CTH. The slope for KF/CAPE-PR is 1.19, which is within the uncertainty of the detection e ciency of ENTLN. In general the KF/CAPE-PR lightning parameterization captures the day-to-day variation in flash densities better than the G3/CTH and KF/CTH parameterizations as shown by the improved R 2 values." The conclusion is also modified accordingly: "We implement an alternative lightning parameterization based on convective available potential energy and precipitation rate into WRF-Chem and couple it with Kain Frisch convective scheme. We first validate it by comparing against lightning observations and find that the switch of convective scheme reproduces day-to-day variation of lightning flashes in the southeastern US and the switch of lightning parameterization contributes to the improvement on lightning representation elsewhere in the US. We also compare the simulated NO 2 profiles against aircraft measurements and find that the simulated NO 2 using KF/CAPE-PR is more consistent with observations in the mid and upper troposphere." We thank the reviewer for the positive response of both the main article and the supplement. Below we respond to the individual comments. The reviewer's comments will be shown in red, our response in blue, and changes made to the paper are shown in black block quotes. Unless otherwise indicated, page and line numbers correspond to the original paper. Figures, tables, or equations referenced as "Rn" are numbered within this response; Figures, tables, and equations numbered normally refer to the numbers in the original discussion paper.
(1) The reason that I suggest deleting the statement? The model-satellite NO2 column comparison suggests 500 mol NO flash 1 is too high for the estimate of lightning NOx production rate, but demonstrates that the uncertainty in the modeled UT [NO2]/[NOx] ratio is a key limiting factor in constraining production e ciency over CONUS in the far-field approaches in the conclusion section is not because I think far-field observations are unimportant for constraining LNOx. But how well we understand NO/NO2 ratio in the upper troposphere (with or without fresh lightning) shouldn't be mixed with LNOx constraints. Since most of NOx is in form of NO, high-quality NO measurements are su cient to constrain LNOx using far-field measurements. Even if we understand and can simulate NO2/NOx ratios in the upper troposphere well, the fact is that NO2 is lower than NO and is arguably more di cult to measure. This last statement of the paper is rather odd to me. So for a third time, I?d suggest either deleting this sentence or providing detailed discussion of the need and application of having both in situ NO and NO2 measurements as constraints of LNOx.
We agree with the reviewer that the error in [NO 2 ]/[NO x ] ratio is limited for constraining LNO x if accurate NO measurement is available. Our statement is based on the fact that OMI only observes NO 2 columns from the space. We decide to delete the statement in the conclusion.
(2) FYI, the R values listed in Table 1 of Luo et al.?s work is for 5-min flash rate comparison between the observations and model results. The correlation values in this work are for daily rates. More averaging can substantially improve R values.
We recognize the di↵erence in the time resolution of lightning datasets between  and this study. The rough comparison of correlation coe cients between this study and  in my last response is inappropriate.
(3) The authors should add some general comments on the di↵erences between G3 and GF schemes in WRF-Chem to (1) explain the di↵erences in the resulting LNOx distributions and (2) compare with the MM5 di↵erences found by .
We add it in Section 3.1: "...The G3/CTH parameterization fails to reproduce the spatial pattern of flashes observed by ENTLN over the CONUS. Compared to the G3/CTH, the KF/CTH parameterization improves the spatial correlation in the southeast region of US and yields a lower amount of lightning flashes. It indicates that KF convective scheme produces smaller cumulus cloud top heights than G3 scheme by including entrainment and detrainment processes during the convection. The result is consistent with . The KF/CAPE-PR parameterization better captures the spatial distribution of flash densities both in the southeast region and elsewhere in CONUS." (4) I suggest adding more discussion details on the di↵erences between ENTLN and NLDN flash rate observations. Some of the details are already in the response. The absolute counts of flash rates by LIS are also uncertain and it should be mentioned. Since the authors have ENTLN and NLDN datasets, doing a direct comparison with LIS data (accounting for detection e ciencies) would seem straightforward. Why is it not included in the paper?
Among three lightning observation datasets, NLDN only observes CG lightning; ENTLN and LIS measure the total lightning flashes but LIS couldn't distinguish IC and CG lightning types. As we use ENTLN as the lightning observation reference, we intend to evaluate it by comparing against LIS and NLDN. The former one is already included, here we add the comparison between ENTLN and NLDN into the supplementary: " 1 Comparison between ENTLN and NLDN While both NLDN and ENTLN have high detection e ciency (>90%) for CG flashes, we recognize that ENTLN observes more CG flashes than NLDN. Shown in Fig. R1, we average the flashes density over CONUS both from ENTLN and NLDN between May 13 to June 23 2012. The daily averaged CG flash density from ENTLN is tightly correlated with those from NLDN with slope of 1.5. It can be explained by discrepancy in the grouping criterions applied to produce flash counts between NLDN and ENTLN. ENTLN groups all pulses within 10 km and 700 ms of each other as a single flash, and NLDN uses 10 km and 1000 ms as the threshold. In consequence, for the same amount of CG pulses measured by both lightning observation network, ENTLN produces more flashes than NLDN according to the grouping algorithm. " (5) In Figure 3, the large urban VCD change is not due to lightning over Orlando. What is the reason then? The authors don't have ENTLN data for that period, can they look at NLDN data to see how well the model simulates lightning flash distribution over urban regions? There are only 4 figures in this paper; adding more discussion cannot hurt. Figure 3 shows the VCD changes by switching a priori profiles produced from WRF-Chem using G3/CTH to the one using KF/CAPE-PR. Since this is a model-model comparison the accuracy of the lightning observations is not especially useful. The area with large VCD di↵erence is also much larger than Orlando from Fig 3 (a).

Introduction
Nitrogen oxides (NO x ⌘ NO + NO 2 ) are key species in atmospheric chemistry, affecting the oxidative capacity in the troposphere by regulating the ozone and hydroxyl radical concentrations (Crutzen, 1979). Anthropogenic sources (mainly fossil fuel 20 combustion) are the largest contributor to the NO x budget on a global scale. Natural sources of NO x are also nonnegligible (Denman et al., 2007). While anthropogenic emissions of NO x are intensively studied, natural sources are less understood (e.g. Delmas et al., 1997;Lamsal et al., 2011;Miyazaki et al., 2012). Lightning contributes to~10% of NO x budget on a global scale and represents over 80% of NO x in the upper troposphere (UT) (Schumann and Huntrieser, 2007;Nault et al., 2017). Over the 1 US, the anthropogenic NO x emissions have been decreasing rapidly (Russell et al., 2012;Lu et al., 2015), making lightning an increasingly important source of NO x and an increasingly large fraction of the source of column NO 2 . Ozone (O 3 ) in UT has long lifetime and leads to a more pronounced radiative effect than ozone elsewhere in the troposphere. Varying lightning NO x emission (LNO x ) by a factor of four (123 to 492 mol NO flash 1 ) yields up to 60 % enhancement of UT O 3 and increases the mean net radiative flux by a factor of three (Liaskos et al., 2015). This range in the lightning NO x production rate is similar to 5 the current uncertainty of estimated lightning emission rates. Further, incorrect representation of LNO x in a priori profiles for satellite NO 2 retrievals leads to biases in the retrieved NO 2 columns. This is exacerbated by the greater sensitivity of UV/Vis NO 2 retrievals to the UT (e.g. Travis et al., 2016). When lightning occurs, NO is emitted as a result of high temperatures and NO 2 forms through rapid photochemistry. Studies report the estimated LNO x production rate ranges widely from 16 to 700 mol NO flash 1 (DeCaria et al., 2005; Hudman et al., 10 2007; Martin et al., 2007;Schumann and Huntrieser, 2007;Huntrieser et al., 2009;Beirle et al., 2010;Bucsela et al., 2010;Jourdain et al., 2010;Ott et al., 2010;Miyazaki et al., 2014;Liaskos et al., 2015;Pickering et al., 2016;Pollack et al., 2016;Nault et al., 2017).
Two categories of methods, one emphasizing the near-field of lightning NO x and the other the far-field, have previously been applied to estimate LNO x . In near-field approaches the total NO x from direct observation close to the lightning flashes 15 is divided by the number of flashes from a lightning observation network to yield the NO x per flash (e.g. Schumann and Huntrieser, 2007;Huntrieser et al., 2009;Pollack et al., 2016). Near-field estimates of LNO x per flash have also been made through use of cloud-resolved models with LNO x constrained by observed flashes and aircraft data from storm anvils (e.g. DeCaria et al., 2005;Ott et al., 2010;Cummings et al., 2013). In contrast, the far-field approach uses downwind observations to constrain a regional or global chemical transport model. The emission rate of lightning NO x is varied in the model (either ad 20 hoc or through formal assimilation methods) until the modeled NO x agrees with the measurements of total NO x at the far field location (Hudman et al., 2007;Martin et al., 2007;Jourdain et al., 2010;Miyazaki et al., 2014;Liaskos et al., 2015;Nault et al., 2017). In general, far-field approaches yield estimates of LNO x at the upper end of reported range, while estimates from the near-field studies are typically at the lower end of the range. Nault et al. (2017) showed that a large part of this discrepancy is because prior near-field studies assume a long NO x lifetime in the UT, while active peroxy 25 radical chemistry in the near field leads to a short NO x lifetime (~3 h). Without accounting for this chemical loss, the near-field and far-field estimates are biased low compared to each other. However, this effect cannot completely reconcile the discrepancy between LNO x reported from near-and far-field studies.
In chemical transport models, LNO x production is modeled by assuming a fixed number of moles of NO are produced per lightning flash, typically 250 or 500 mol NO flash 1 Allen et al., 2010;Ott et al., 2010). This presents 30 an additional challenge to the far-field approaches to constrain LNO x , as errors in the simulation of lightning flashrate will propagate into errors in the LNO x production per flash. However, explicitly simulating the cloud scale processes that produce lightning is generally too computationally expensive to be applied in a regional or global model as it requires spatial resolution at the scale of cloud processes. Instead, the convection is parameterized using simplified convection schemes. Lightning is then parameterized by a suite of convection parameters. The most prevalent lightning parameterization relates lightning to the cloud top height (CTH) (Price and Rind, 1992;Price et al., 1997). Price and Rind found a consistent proportionality between cloud-to-ground (CG) lightning flashes and the fifth power of cloud top height. Other meteorological variables, including upward cloud mass flux (UMF), convective precipitation rate (CPR), convective available potential energy (CAPE), cloud ice flux (ICEFLUX) have been suggested as alternative lightning proxies for CG flashes or in some cases total flashes (Allen and Pickering, 2002;Choi et al., 2005;Wong et al., 2013;Romps et al., 2014;Finney et al., 2014). When CG flashes are predicted, 5 the total lightning rate, including CG and Intra-Cloud (IC) flashes, is derived by defining a regional dependent CG:IC ratio (Boccippio et al., 2002).
Several previous studies have evaluated the performance of these lightning parameterizations in regional and global models. Tost et al. (2007) concluded none of them accurately reproduce the observed lightning observations even though some are inter-comparable. Wong et al. (2013) showed that a model using the Grell-Devenyi ensemble convective parameterization In this study, we implemented the CAPE-PR lightning parameterization (Romps et al., 2014) into WRF-Chem and assess the performance in reproducing lightning flash density. Our motivation is to produce a better representation of a proxy-based lightning parameterization in the regional chemistry transport model. We also evaluate the effect of modeled lightning NO x on both the a priori profiles used in satellite NO 2 retrievals and the retrievals themselves.   (Guenther et al., 2006)). We use a customized version of the Regional Atmospheric Chemistry Mechanism version 2 (RACM2), the details are described by Zare et al. (2018).

3
The default lightning parameterization used in WRF-Chem is based on cloud top height (CTH). The parameterized lightning flash rates are proportional to a power of cloud top height with linear scaling varied by region: where f is the CG flash rate in each grid and H is the colocated cloud top height in units of kilometers.

5
We also implement an alternative lightning parameterization where lightning flash rates are defined to be proportional to the product of the convective available potential energy (CAPE) and precipitation rate (PR).
where f the CG flash rate in each grid cell, E the convective available potential energy and P R the convective precipitation rate. Southeastern CONUS in the context is the region between 94 W to 76 W and 25 N to 37 N. This parameterization  Romps et al. (2014) and Tippett and Koshak (2018). We also apply a regional scaling factor of 0.5 to the southeastern US (See Sec 3.1).
We analyze WRF-Chem outputs from three model runs. The first run, referred as "G3/CTH", is consistent with Laughner and Cohen (2017); it selects the Grell 3D ensemble cumulus convective scheme (Grell, 1993;Grell and Dévényi, 2002) and the 20 CTH lightning parameterization. The Grell 3D convective scheme readily computes the neutral buoyancy level which serves as the optimal proxy for cloud top height (Wong et al., 2013). The "G3/CTH" is the only option for the coupled convectivelighting parameterization used in WRF-Chem at a non-cloud resolving resolution (12 km). In addition, we run WRF-Chem with the CTH lightning parameterization coupled with the Kain-Fritsch cumulus convective scheme (Kain and Fritsch, 1990;Kain, 2004) ("KF/CTH") to test the effect of switching convective schemes. In the "KF/CTH" parameterization, the cloud top 25 height is the level where the updraft vertical velocity equals to zero. Another run, referred as "KF/CAPE-PR", selects the Kain-Fritsch cumulus convective scheme and the CAPE-PR lightning parameterization described above. Compared to the Grell 3D convective scheme, the Kain-Fritsch uses the depletion of at least 90% CAPE as the closure assumption and calculates CAPE on the basis of entraining parcels instead of undiluted parcels, which also improves the calculation of precipitation rate (Kain, 2004). The lightning NO x production rate is defined to be 500 mol NO flash 1 . The CG:IC ratio and the LNO x post-convection 30 vertical distribution are the same as used by   Fig. S2, we matched the ENTLN data to LIS flashes both in time and space after the 10 correction of LIS data based on its detection efficiency (Cecil et al., 2014) during May 13-June 23, 2012. It shows a median correlation (R 2 = 0.51) with the slope of 1.0, indicating the ENTLN data during the study time period is in agreement with the LIS observation. We use the ENTLN for analysis as reported and consider the detection efficiency of ENTLN as a source of uncertainty when comparing the modeled lightning flashes.

Satellite Measurements
The Ozone Monitoring Instrument ::::: (OMI) is an ultraviolet/visible (UV/Vis) nadir solar backscatter spectrometer launched in July 2004 on board the Aura satellite. It detects backscattered radiance in the range of 270-500 nm and the spectra are used to derive column NO 2 at a spatial resolution of 13 km⇥24 km at nadir . ::: The ::::: OMI ::::::: overpass :::: time :: is ::::::: ⇠13:30 25 :::: local :::: time. : We use the Berkeley High Resolution (BEHR) v3.0B OMI NO 2 retrieval . The air mass factor (AMF) is calculated based on the high spatial resolution a priori input data including surface reflectance, surface elevation and NO 2 vertical profiles. In this study we apply an experimental branch of the BEHR product which differs from v3.0B in several ways.
First, instead of calculation based on temperature profiles from WRF-Chem, the tropopause pressure is switched to GEOS-5 30 monthly tropopause pressure which is consistent with NASA Standard Product (SP2) (Mak et al., 2018). Analysis shows the algorithm used in BEHR v3.0B to calculate the WRF-derived tropopause pressure is very much dependent on the vertical 3 Results

Comparison with observed lightning flash density
The lightning parameterizations are compared against observations from ENTLN in Fig 1. Each of the datasets is averaged 5 from May 13 to June 23, 2012, covering DC3 field campaign. The ENTLN data is summed to the 12 km⇥12 km WRF grid. The G3/CTH parameterization fails to reproduce the spatial pattern of flashes observed by ENTLN over the CONUS.

Comparison with observed vertical profiles
We compare the WRF NO 2 profile to the average vertical profile of NO 2 measured during DC3 and SEAC4RS in

Impact on BEHR NO 2 retrievals
In space-based retrievals of NO 2 , the AMF is required to convert the slant column density (SCD) obtained by fitting the observed radiances into a vertical column density (VCD). The AMF depends on scattering weights (which describe the sensi-  tivity of the measurement to different levels of the atmosphere) and an NO 2 profile which is either measured or simulated by a chemical transport model, such as WRF-chem. Over a dark surface, the scattering weights in the UT are up to 10x greater than near the surface, due to the greater probability that a photon that reaches the lower troposphere will be absorbed by the surface. Therefore, errors in the UT NO 2 profile can have large effects on the AMF (e.g. . Here, we investigate how the NO 2 profiles simulated by the KF/CAPE-PR parameterization affect the BEHR NO 2 retrievals. the a priori profiles from the model using G3/CTH to the one using the KF/CAPE-PR lightning parameterization. The relative enhancement of VCD is 19% on average over southeast US but it varies significantly.
The spatial pattern in Fig. 3(a) suggests that the magnitude of the improved representation of lightning is quite different in urban and rural areas. The cities indicated by stars and their vicinity regions are associated with substantial increase in NO 2

Discussion
Here, we apply the improved KF/CAPE-PR simulation to the problem of constraining LNO x production over CONUS. To do so, we vary the lightning NO x production rate prescribed in WRF-Chem to produce the simulated map of NO 2 VCD, and compare against OMI NO 2 retrievals using a priori profiles from model simulations with the same LNO x production rate.
In our model-satellite comparisons the averaging kernel is applied to remove the representative errors introduced by a priori knowledges of NO 2 vertical profiles (Boersma et al., 2016). Figure 4 shows the difference between satellite retrieved NO 2 VCD 5 and model simulated NO 2 VCD without lightning NO x (a) and with lightning NO x production rate of 500 mol NO flash 1 (b) averaged between May 13 to June 23, 2012. Figure S4 shows difference plots with varied lightning NO x production rates (400 and 665 mol NO flash 1 ). The corresponding root-mean-square errors (RMSE) are included in Table S1. LNO x production rate of 500 mol NO flash 1 yields the lowest RMSE of 0.41⇥10 15 mole cm 2 between modeled and observed NO 2 VCD over CONUS. This is at the high end of previous estimates of the lightning NO x production rate (16-700 mol NO flash 1 ). 10 The RMSE for urban areas (top 5% of NO 2 VCD simulated by WRF-Chem without LNO x ) remains at high value (~0.9-1.3⇥10 15 mole cm 2 ) when switching the LNO x production rate. It indicates that the bias in the modeled VCD over urban areas is more likely due to surface NO 2 . The RMSE for non-urban areas shows pronounced change with varied LNO x production rate. Excluding urban areas lowers the RMSE to 0.37⇥10 15 mole cm 2 for LNO x production rate of 500 mol NO flash 1 . The RMSEs are significant considering the uncertainty for retrievals. During the average time period, 32 ± 6 pixels 15 contribute to each value in the plots. While the global mean uncertainty for tropospheric NO 2 VCD retrievals is 1⇥10 15 mole

Conclusions
We implement an alternative lightning parameterization based on convective available potential energy and precipitation rate 5 into WRF-Chem and couple it with Kain Frisch convective scheme. We evaluate its performance in simulating lightning .
The improved lightning NO 2 simulation has significant impact on AMFs and VCD of NO 2 . Over the southeastern US the AMF is reduced by 16% on average leading to a 19% increase in the NO 2 VCD. The effects on AMF and on VCD are very locally dependent. The VCD increase over urban areas is more pronounced and can be up to over 100%. This study emphasizes 15 the importance of including reliable lightning NO 2 in a priori profiles for satellite retrievals.
The model-satellite NO 2 column comparison suggests 500 mol NO flash 1 is too high :: the :::::: upper ::::: bound : for the estimate of lightning NO x production rate, but demonstrate that the uncertainty in the modeled UT /ratio is a key limiting factor in constraining production efficiency over CONUS in the far-field approaches..