Tables 1 and 2 display the statistical model performance metrics for daily maximum 8 h (DM8HR) O3 and daily mean NOx mixing ratios over the domain and each analysis region for all four model cases in July 2011 (Base, mNLDN, hNLDN, and pNLDN). The best performance metrics among the model cases are highlighted in bold. As shown in Table 1, for DM8HR O3, the Base simulation has the lowest MB and NMB values over the domain, while hNLDN produced the smallest RMSE and NME values. The mNLDN generated the largest values for both error (RMSE and NME) and biases (MB and NMB), followed by pNLDN, and all model cases with LNO exhibit slightly higher correlation coefficients than the Base simulation. Additionally, the hNLDN simulation exhibited higher correlation and lower bias and error relative to the measurements indicating the value of higher-temporal-resolution lightning activity for representing the associated NOx emissions and their impacts on tropospheric chemistry.

Examining the regional results for DM8HR O3 in Table 1, the statistical measures indicate that in the northeast (NE), hNLDN outperformed all other model cases with the lowest errors and biases and highest correlation coefficient. In the southeast (SE), the Base simulation performed better with the lowest errors and mean biases, but the correlation coefficient (R) value for hNLDN is slightly higher. Among all the LNO cases, mNLDN produced the worst statistics in this region. Historically, CTMs tend to significantly overestimate surface O3 in the southeast US (Lin et al., 2008; Fiore et al., 2009; Brown-Steiner et al., 2015; Canty et al., 2015), and this is partially driven by a likely overestimation of anthropogenic NOx emissions (Anderson et al., 2014). Thus, even though lightning is known to impact ambient air quality, including this additional NOx source can worsen biases in model O3 in some locations and time periods due to other errors in the modeling system. As noted in Table 1, compared to the Base, the MB values in the SE increased by about 1.6 ppb with mNLDN and increased by less than 1 ppb with hNLDN and pNLDN. Nevertheless, the correlation coefficients for mNLDN and pNLDN were almost the same with the Base, and hNLDN was slightly higher (0.77 compared to 0.76). These correlations indicate that even though additional NOx increases the mean bias, when it is added correctly in time and space, as with the case of hNLDN, the spatial and temporal correlation are slightly improved. In the Upper Midwest (UM), the lowest errors and biases among the model cases are associated with hNLDN, while the worst performance is with mNLDN. In the Lower Midwest (LM), hNLDN performed comparable with the Base, with hNLDN having the highest correlation and lowest mean errors, while the Base has the lowest mean biases. The Rocky Mountain (RM) region is the only region that shows an underestimation of DM8HR O3. In this region all the model cases with LNO outperformed the Base case in all the metrics. Among the three model cases with LNO, mNLDN produced the lowest MB and NMB values, while hNLDN had the lowest RMSE and NME, and the highest correlation. In the Pacific Coast (PC) region, lightning activity is generally very low compared to other regions (Kang and Pickering, 2018). All model cases with LNO outperformed the Base case, especially hNLDN which had the lowest mean error and bias and highest correlation among all the cases.

Most of the NOx produced by lightning is distributed in the middle and upper troposphere with only a small portion being distributed close to the surface. As a result, the impact on ground-level NOx mixing ratios is small. Table 2 shows all the model cases produced similar statistics for the daily mean NOx mixing ratios at AQS sites across the domain and within all the subregions. Although the changes in model performance are small, the model cases with LNO exhibit similar or slightly better performance than the Base case.

Figure 2 presents time series of regional-mean observed and modeled DM8HR O3 for the entire domain and the SE and RM regions during July 2011. Over the domain and in SE, all the model cases overestimate the mean DM8HR O3 mixing ratios on all days with the Base being the closest to the observations. The hNLDN is almost the same as the Base with slightly higher values on some days. Among all the cases, mNLDN produced the highest values on almost all days through the month, on the order of 1–2 ppb higher than the Base. In contrast, in the RM region, the Base significantly underestimates DM8HR O3 mixing ratios on all the days during the month, while all model cases with LNO improved model predictions relative to observations in the region. Among the three model cases with LNO, mNLDN produced the lowest bias for all the days, closely followed by hNLDN.

Figure 3 displays the average daily mean NOx mixing ratios at AQS sites over the same regions as in Fig. 2. On most of the days in July 2011, over the domain and in the SE, the model overestimate NOx values, and on almost half of the days the overestimation is significant (up to 100 %). As noted in Table 2, on average, the overestimation is ∼17 % over the domain and ∼43 % in SE. However in RM, the predicted NOx mixing ratios closely follow the daily observations and on average the modeled and observed magnitude is almost identical (∼3 % difference). All the model cases, with or without LNO, produced almost the same mean NOx mixing ratios at the surface. However, the different cases produce different levels of LNO in the middle and upper troposphere, resulting in differences in O3 production and transport which impact radiative forcing and also downwind ground-level O3 levels. We further explore these features in Sect. 3.2 which presents evaluation of modeled vertical pollutant distributions.

Diurnal plots are used to further examine differences in model evaluation for O3 and NOx. Figure 4 shows the mean diurnal profiles for hourly O3 and NOx over the entire domain, SE, and RM. On a domain mean basis, all model cases overestimate O3 during the daytime hours, while in the SE the overestimation spans all the hours. In RM, the model cases significantly underestimate O3 across all the hours except for a few early morning hours, when the model predicted values are very close to the observations. Among all the model cases, as expected, the most prominent differences occurred during the midday hours when the photochemistry is most active. However, the difference between hNLDN (and mNLDN) and the Base is also significant during the night in the RM region, even though the O3 levels are low. This may be attributed to NOx-related nighttime chemistry in part caused by freshly released NO by cloud-to-ground lightning flashes. The diurnal variations of NOx are similar over the domain and in the regions for all model cases. Appel et al. (2017) reported a significant overestimation of NOx mixing ratios at AQS sites during nighttime hours and underestimation during daytime hours. The bias pattern is identical for all of the LNO model cases evaluated here (Fig. 4).

Figure 5 shows the impact of the different LNO schemes on model performance for DM8HR O3 at AQS sites. The spatial maps show the difference in absolute MB between the cases with lightning NOx emissions and the Base and is calculated as follows. First, the absolute MB was calculated at each site for each case, e.g., |MB[Base-Obs]|, then the difference in absolute MB was calculated between model cases, e.g., |MB[hNLDN-Obs]|–|MB[Base-Obs]|. The histograms of the differences in absolute MB between model cases in Fig. 5 are provided to show the distribution of the change in model performance across space, i.e., the frequency of an improvement in model performance versus a degradation in model performance between cases. As shown in Fig. 5, the mNLDN shows increased model bias in the east US and along the California coast, but reduced model bias in the RM. At a majority of the AQS sites, it increases the model bias (only decreases at 26.8 % (346) of the sites). The hNLDN also significantly reduces model bias in the RM with a moderate increase in the SE. Overall, in the hNLDN, the mean bias decreased at 61.2 % (791) of AQS sites. Similar to mNLDN, increases in mean bias are noted at 29.3 % (378) of the AQS sites in the pNLDN simulation. As noted in the histograms, the distribution of the model bias in the pNLDN is much narrower than both mNLDN and hNLDN, eliminating the large bias increases in mNLDN and the significant bias decreases in hNLDN.

A large source of uncertainty in the specification of LNO is its vertical allocation, which can impact the model's ability to accurately represent the variability in both chemistry and transport. To further assess the impact of the vertical LNO specification on model results, we compared vertical profiles of simulated model O3 with extensive ozonesonde measurements available during the study period. Figure 6 presents the vertical profiles for O3 sonde measurements and paired model estimates of all model cases at Beltsville, MD, and Edgewood, MD. At each location, observations from multiple days are available (one or two soundings per day) during the 2011 DISCOVER-AQ campaign in July 2011. The model evaluation was limited to days where the inclusion of LNO has an obvious impact (the mean vertical profiles of LNO cases are separable from that of the Base case) on the model estimates (21, 22, 28, and 29 July at Beltsville, and 21, 22, 28, 29, and 30 July at Edgewood). We paired the observed data with model estimates in time and space and averaged the model and observed values at each model layer. Only data below 12 km altitude are plotted in Fig. 6 to exclude possible influence of stratospheric air on O3. As can be seen in Fig. 6, at both locations the Base case underestimates O3 mixing ratios above about 1 km, but overestimates values closer to the surface. When LNO is included in the simulations, the predicted O3 mixing ratios increase relative to the Base case starting around 2 km, with greater divergence from the Base case at higher altitudes. The two model cases, hNLDN and mNLDN, produced similar O3 levels from the surface to about 6 km, but above that altitude the mNLDN ozone mixing ratios were higher. All the model cases with LNO performed much better aloft than the Base case. Near the surface, all the model cases overestimated O3, however hNLDN had smaller bias than the other simulations. This may be attributed to the fact that only hNLDN used the observed lightning flash data directly, and as a result, LNO was estimated more accurately in time and space. This improvement in model bias at the surface is further investigated in the next section using evaluation against P-3B measurements.

Extensive measurements of lower tropospheric chemical composition distributions over the northeastern US are available from instruments onboard the P-3B aircraft on 14 d of the DISCOVER-AQ campaign. We utilize measurements from one of the days (28 July 2011) with noticeable (the mean vertical profiles of LNO cases are separable from that of the Base case) lightning impacts, to evaluate the model simulations. Figure 7 shows measured O3 mixing ratios overlaid on the modeled vertical time section for 10:30–17:30 UTC. The color-filled circles represent measured O3 mixing ratios averaged over 60 s and the background is the model estimated vertical profiles from the grid cells containing the P-3B flight path for that hour and location. As indicated in the Base case (Fig. 7a), the model tends to overestimate O3 mixing ratios from the surface to about 2 km, but it tends to underestimate at altitudes above 2 km. The hNLDN reduced the overestimation below 2 km, e.g., fewer grid cells with mixing ratios above 90 ppb (shown in red). The other two cases (mNLDN and pNLDN) did not produce the same improvement near the surface. The hNLDN also decreases the underestimation aloft compared to the Base case with O3 mixing ratios in the 55–65 ppb range (light blue colors), better matching the measured values. This decrease in underestimation aloft is also seen in the mNLDN case, but to a lesser degree while the pNLDN case shows only slight improvement aloft over the Base simulation.

To further differentiate the three LNO model cases, Figs. 8–10 show the difference in the time sections between each of the model cases with LNO and the Base for NO, NOx, and O3 from all the model layers along the P-3B flight path on 28 July. As seen in Fig. 8, the hNLDN scheme injected most NO above 5 km with a peak between 13 and 14 km and only a small amount near the surface. After release into the atmosphere, NO is quickly converted into NO2 in the presence of O3, and these collectively result in the NOx vertical time section (local production plus transport) shown in the middle panel of Fig. 8. NOx is further mixed down through the time section and is more persistent along the flight path near the surface than NO is. As a result, significant O3 is produced above 3 km, and the maximum O3 difference appears between 9 and 14 km during the early afternoon hours (from 13:30 to 17:30 Eastern Daylight Time). However, from surface to about 2 km, O3 is reduced consistently across the entire period, and this is the result of O3 titration by NO from cloud-to-ground lightning flashes that must have been transported to this layer by storm downdrafts. Since O3 is significantly underestimated above 3 km and overestimated near the surface by the Base model, the inclusion of LNO greatly improved the model's performance under both conditions.

Comparison of Fig. 9 (mNLDN) with Fig. 8 (hNLDN) reveals that the time sections of NO and NOx are similar above 5 km but dramatically different near the surface. The near-surface increase in ambient NO noted in the hNLDN is absent in mNLDN, and in fact there are some small decreases in NO, although the reason for this is unclear. The increase in O3 aloft in the mNLDN case is similar to that seen in the hNLDN case. However, the near-surface reduction in O3 is almost absent. In the pNLDN case (Fig. 10), NO mixing ratios are much less than those in hNLDN and mNLDN in the upper layers as a result of less column NO being generated by the linear parameterization. The resulting NOx time section is also smoothed. The pNLDN time sections for NO, NOx, and O3 near the surface are similar to the mNLDN case with no change or small decreases compared to the Base case. O3 mixing ratios increase by more than 30 ppb during the afternoon hours between 10 and 13 km in the pNLDN case, however the increase is not as intense and widespread as the other cases. In summary, the hNLDN scheme produces estimates that are more consistent with measurements at the surface and aloft, compared to the other simulations, reflecting the advantage of using the spatially and temporally resolved observed lightning flash data. The model performance improvement for simulated O3 distributions also suggests robustness in the vertical distribution scheme when LNO is generated at the right time and location.

To corroborate the above time section distributions of NO, NOx, and O3 in the lightning cases, the lightning NO emissions are traced back to 28 July for each case. It is found that in all cases, the lightning NO was injected approximately 200 km upwind (northwest) of the flight path. The hNLDN case captured two injections: one occurred during the morning hours (05:00 to 07:00 EDT) and the other happened during the afternoon hours (after 02:30 EDT). Both mNLDN and pNLDN captured the afternoon lightning event at the later time (after 03:30 EDT for mNLDN and after 04:30 for pNLDN) with varying intensity, but neither captured the morning lightning event, which explains why the increase in NO and NOx in the hNLDN case (Fig. 8) did not occur in the mNLDN and pNLDN cases (Figs. 9 and 10). Also note that the significant increase of NO during the time period from 11:00 to 13:00 EDT occurred about 5 h after the lightning NO was injected at about 200 km upwind in the hNLDN case.

To expand on the evaluation in Figs. 7–10 which focused on measurements from 28 July 2011, we retrieved all the P-3B measurements on days with noticeable lightning impact (21, 22, 28, and 29 July). The 3-D paired observation–model data were grouped together by spiral site and the mean biases (model – observation) were plotted in Fig. 11 (a and b) for O3 and NO, respectively. The boxplots for O3 in Fig. 11a suggests that the Base exhibited larger bias with greater spread (i.e., larger interquartile range) than other model cases incorporating LNO at most of the locations where aircraft spirals were conducted. At all locations except Aldino, the lowest mean biases in simulated NO and O3 are noted in the hNLDN simulation.