Sensitivity coefficients towards domain-wide emissions (i.e., emissions across the entire simulation domain) calculated by HDDM are shown in Fig. 1; these values represent monthly means and in turn are computed from hourly sensitivity coefficient output by the CMAQ model configured with HDDM. Generally, the response of O3 to NOx emissions exhibits positive first-order sensitivities (Fig. 1a) and negative second-order sensitivities (Fig. 1c) because of the concave response of O3 to NOx emissions. Exceptions are found over eastern China to the Korean Peninsula, some parts of Europe, and some cities in the western US (e.g., Seattle, San Francisco, and Los Angeles), around the Great Lakes, and the northeastern US (e.g., New England region). These regions show negative first-order sensitivity to NOx emissions due to the NO titration effect by dense NOx emission sources. Note that due to the use of a coarse horizontal grid resolution to cover the entire Northern Hemisphere, the simulation may not adequately capture the chemical regime in urban areas where O3 chemistry is VOC sensitive. The values of sensitivity coefficients to VOC emissions (Fig. 1b and d) are small compared to those to NOx emissions. In addition, the second-order sensitivity coefficients of O3 to VOC emissions are also smaller, indicating that the nonlinear response of large-scale O3 distributions to VOC emissions is negligible. A positive second-order cross sensitivity of O3 to domain-wide NOx and VOC emissions (Fig. 1e) demonstrates O3 will become less responsive to NOx emissions with a concurrent reduction of VOC emissions, and vice versa. While these sensitivities were calculated towards total (i.e., both anthropogenic and biogenic) emissions, the main interest from a policy-making perspective is on the sensitivities towards anthropogenic emissions. To estimate these sensitivities, we recalculated sensitivity coefficients of O3 to isoprene emissions as a proxy for biogenic emissions (Fig. S1 in the Supplement). By comparing these sensitivities to isoprene emissions (Fig. S1) to the sensitivities towards all emissions (Fig. 1), it can be concluded that O3 is more sensitive to NOx emissions than to biogenic VOC emissions during April 2010. It should be also noted that the positive first-order and negative second-order sensitivities to VOC found near the lateral boundary with ring shape in the modeling domain could be the perimeter sensitivity. In this H-CMAQ modeling system, the boundary conditions are taken from the clean tropospheric background values with updates to the physical and chemical sinks for organic nitrate species (Mathur et al., 2017). For these boundary conditions, the NO concentration was set to zero, the NO2 concentration was set to 10-5 ppmv, and the O3 concentration was set to 30 ppbv. These low-NOx boundary conditions likely caused the perimeter sensitivities to VOC, although it should also be noted that the absolute values of these sensitivities are small. The effect of boundary conditions is further discussed later in Sect. 4.3.

Determining the O3 sensitivity regime can provide useful information to policy makers designing emission reduction strategies by clarifying the relative importance of precursor emissions. Based on the relationships between the sensitivity coefficients, we determined O3-sensitivity regimes from threshold values revised from previous studies (Wang et al., 2011; Itahashi et al., 2013) as follows. 10ppbv<SVOCs(1),SNOx(1)<SVOCs(1):VOC sensitive10ppbv<SNOx(1),SVOCs(1)<SNOx(1):NOxsensitive Grid cells meeting neither of these two criteria are considered to be in a transition regime. This classification is applied to all hourly HDDM results during April 2010 and then averaged. The O3-sensitivity regimes obtained through this analysis are shown in Fig. 2. The shading of NOx (purple) or VOC sensitive (green) indicates the high frequency of occurrence of sensitivity to NOx or VOC regime. As already suggested by the relative magnitudes of the sensitivity coefficients towards NOx and VOC emissions shown in Fig. 1, O3 during April 2010 is in a NOx-sensitive regime over the midlatitude Northern Hemisphere with the exception over the locations that had negative first-order sensitivity to NOx emission and were classified as VOC sensitive. Therefore, controls on NOx emissions can be an effective way to reduce surface O3 across almost the entire Northern Hemisphere but it may cause an increase of O3 mixing ratios over eastern China and some areas in Europe and the US. Due to the coarse grid resolution, H-CMAQ could partly missed the VOC-sensitive regime characterized over urban areas, and our previous study reported the dependency of photochemical indicators to judge the O3 regime (e.g., H2O2/(O3+NO2)) on model grid resolution (Zhang et al., 2009). Through the analysis of HDDM results for domain-wide emissions, this section provided an overview of O3 sensitivities and the response of O3 to precursor emissions over the Northern Hemisphere. The following section further investigates the sensitivity of surface O3 over the US by defining different emission source regions over the US and east Asia.

To investigate the emission impacts from the US and east Asia, we defined two source regions as shown in Fig. 3a. In this study, east Asia includes China, Taiwan, Mongolia, the Korean Peninsula (North and South Korea), and Japan. We conducted additional HDDM simulations using these two source regions and then calculated their sensitivity coefficients, which are shown in Figs. S2 and S3. The sensitivities from other regions except the US and east Asia are illustrated in Fig. S4. Based on these sensitivity coefficients, ZOCs of emissions from the US and east Asia are derived according to Eq. (5) and the resulting emission impacts are shown in Fig. 3b and c. The ZOCs of emissions from the US show more than 10 ppbv over the southeastern US and relatively small impacts around 2–8 ppbv in the western US. In some areas over the US that are characterized by a weak VOC-sensitive regime in Fig. 2 (e.g., Seattle, San Francisco, Los Angeles, around the Great Lakes, and New England regions), emissions from the US have small negative impacts. The US emission impacts extend to the Atlantic Ocean with impacts of more than 2 ppbv, which are comparable to those found over the western US, and then decrease over Africa. The ZOC of emissions from east Asia also shows positive impacts greater than 10 ppbv over China, Taiwan, Japan, and the western Pacific Ocean, with the exception of negative impacts over eastern China. These negative impacts indicate that the elimination of emissions can lead to O3 increase, because NO titration works to reduce the O3 mixing ratio over these areas, which have a high emission density. The analysis of the ZOC from east Asian emissions clearly illustrates the presence of trans-Pacific transport of O3. This transport on a monthly mean basis is estimated to be more than 2 ppbv over almost the entire Pacific Ocean and reaches many parts of North America, i.e., almost the entire US and Canada and western Mexico.

Detailed analyses of these impacts over the US are conducted by focusing on longitudinal differences. In this study, we use four time zones of Pacific, Mountain, Central, and Eastern Standard Time (abbreviated as PST, MST, CST, and EST, respectively) in the US and investigate O3 mixing ratio and ZOC of emission from the US and east Asia in these zones. Results for monthly and daily means are shown in Fig. 4. Consistent with previous studies (e.g., Simon et al., 2015), O3 mixing ratios have a longitudinal gradient with lower values in the west and higher values in the east (modeled monthly mean concentrations are 35.8, 39.3, 39.1, and 40.6 ppbv over PST, MST, CST, and EST, respectively). The results of the ZOC analysis reveal varying impacts from US and east Asian emissions across the four regions. For the US on a monthly mean domain-wide basis, the impact of domestic emissions surpasses that of east Asian emissions. Over the PST region, the monthly averaged impact of domestic emissions is 3.2 ppbv, while that of east Asian emissions is 2.8 ppbv; i.e., the impacts from both source regions over the PST zone are comparable. It should be noted that the daily averaged impact of east Asian emissions can exceed that of US emissions on some days (e.g., in early April and during 27–30 April), suggesting the significant role of episodic trans-Pacific transport on air quality over the western US. In contrast to the situation over the PST zone, the impact from domestic emissions always clearly exceeds the impact from east Asian emissions in the MST, CST, and EST zones; this feature strengthens towards the east. For example, the temporal variations of daily averaged O3 mixing ratios and the impacts of domestic emissions are well correlated over the EST zone. The impact of east Asian emissions is small compared to that of US emissions over the CST and EST zones, but it is not negligible. These impacts are 2.1 ppbv on a monthly average basis (ranging between 1.2 and 3.0 ppbv on a daily basis) over CST and 1.9 ppbv on a monthly average basis (ranging between 1.2 and 2.8 ppbv on a daily basis) over EST through April 2010.

To illuminate the relationship between surface O3 mixing ratio and impacts from US and east Asian emissions, in Fig. 5, scatter plots were constructed using model-derived estimates at all CASTNET sites and at elevated CASTNET sites only (refer to Fig. 10 of Itahashi et al., 2020). The statistical analysis of R and its significance level by Student's t test between surface O3 mixing ratio and these impacts by emissions is listed in Table 1. At all CASTNET sites, the relationship between the modeled MD8O3 and the impact of emissions from the US shows a positive slope with R of 0.63 and p<0.001, confirming that domestic emissions are generally the cause of high surface O3 mixing ratios. On the other hand, the relationship between modeled MD8O3 and the impact of emissions from east Asia is flat, with R of -0.03 and no significance, suggesting that constant impacts are found in the US but do not directly relate to high surface O3 mixing ratios. A noticeable result is that the relationship varies across the regions. Each point in the scatter plots is shaded by time zone, and it can be seen that high O3 mixing ratios over the CST and EST zones (darker black in Fig. 5c) are not linked to the impacts of east Asian emissions (R of 0.06 and -0.03, respectively, and not significant), while moderately higher O3 mixing ratios found over PST and MST (lighter black in Fig. 5c) appear to be linked to higher impacts from east Asian emissions (R values were 0.36 and 0.36, respectively, and p<0.001). These analyses are repeated using data from sites with an elevation higher than 1000 m (see Table S1 in the Supplement). At this subset of stations, the O3 mixing ratio shows a positive relationship with emissions from both the US (R of 0.52 with p<0.001) and east Asia (R of 0.22 with p<0.001). This might be partly because most of the elevated CASTNET sites are located in the western US (17 of 21 elevated sites are located in the PST or MST zones). Since long-range transport occurs aloft and since changes in pollutant concentrations influence their ground-level values (e.g., Mathur et al., 2018b), in the next section, we specifically investigate the impacts of emissions from different source regions on O3 aloft.

In this section, we focus on the impacts of US and east Asian emissions on O3 distributions through the troposphere over the US. Monthly averaged O3 mixing ratios and ZOCs of emissions from the US and east Asia at different altitudes in the free troposphere are shown in Fig. 6. As the reference, monthly averaged ZOCs of domain-wide emissions at different altitudes at surface and in the free troposphere are shown in Fig. S5. Throughout this study, we define the free troposphere as ranging from 750 to 250 hPa and refer to pressure levels of 750, 500, and 250 hPa as the bottom, middle, and top of the free troposphere, respectively. The results of this analysis are also summarized in Table 2. O3 mixing ratios are larger over continents from the surface to 750 hPa (i.e., boundary layer) but are more dispersed over midlatitudes to high latitudes at 500 and 250 hPa (Fig. 6). O3 mixing ratios at the surface exhibit a longitudinal gradient with lower values over the western US and higher values over the eastern US, and the same gradient is seen at 750 hPa. However, there are no longitudinal gradients at 500 hPa with 54 ppbv over the entire US, and a reversed longitudinal gradient with western highs and eastern lows is found at 250 hPa (Table 2).

Once O3 is lofted to free troposphere, its sinks are not effective, and consequently it can be transported further. For ZOC of US emissions, the largest contribution is found over the southeast US at 750 hPa but the impacts of US emissions stretch far across the Atlantic to Europe, north Africa, Eurasia, and even Japan with values above 2 ppbv. Areas where the impact of US emissions exceeds 2 ppbv are shown over the entire Northern Hemisphere at 500 and 250 hPa (Fig. 6). It should also be noted that the impacts of US emissions on the US remained constant or declined with increasing altitude. In particular, constant impacts from US emissions with increasing altitude are found over the PST zone, whereas decreasing impacts are found over the MST, CST, and EST zones. From the middle to the top of the free troposphere, the impacts of US emissions on the US are around 2–3 ppbv (Table 2). For ZOC of east Asian emissions, extended impacts on the US when increasing altitude are shown (Fig. 6). At 750 hPa, the impacts are found over the entire Pacific Ocean with more than 10 ppbv around Hawaii and contribution as high as 4–8 ppbv over the entire US. At 500 hPa, its impacts are smaller over the Pacific Ocean with less than 8 ppbv; however, the impacts are above 6 ppbv almost across the entire US, surpassing the impacts found at 750 hPa. At 250 hPa, the impacts are slightly decreased beyond the US but stretch across a broader range to Europe and western Russia (Fig. 6). It is shown that the impacts of east Asian emissions are around 5 ppbv or more over the entire free troposphere over the US (Table 2). From the middle to the top of the free troposphere, the impacts of emissions from east Asia are twice or more those of US emissions over the eastern and western US, respectively.

In characterizing the dominant sources of O3 aloft, the role of stratospheric air masses also needs to be considered. In our Part 1 paper, we developed an air mass characterization technique, but it was limited to estimate the air mass burden on column O3. In this Part 2 paper, to unify the methodology investigating sensitivities to model parameters, the sensitivity towards O3 specification near the tropopause based on a potential vorticity scaling, hereafter referred to as O3VORT, is directly calculated. The results of the O3 sensitivity towards O3VORT are shown in Fig. 7 at the surface, 750, 500, and 250 hPa with different color scales. Not surprisingly, the sensitivity of O3 to O3VORT shows increasing values with increasing altitude. At the surface level and on a monthly averaged timescale, the impact of STT is less than 1 ppbv, except over the Tibetan Plateau because of its elevation. In other regions, smaller impacts of STT are noted over the western US and north Africa; the former is due to the high elevation of the Rocky Mountains, whereas the latter may be related to active convection. Impacts of STT exceeding 1 ppbv are found over midlatitudes areas at 750 hPa, and stronger impacts exceeding 5 ppbv are found at 500 hPa. At 250 hPa, the impacts of STT are shifted towards high latitudes and exceed 25 ppbv, reflective of the lower tropopause height at higher latitudes (Fig. 7). Over the US, the monthly averaged impacts of STT are below 1 ppbv at the surface and 750 hPa and increase from around 2 ppbv at 500 hPa to more than 10 ppbv at 250 hPa (Table 2). At 250 hPa, the impacts of STT range from more than 20 ppbv in the west and a low of around 10 ppbv in the east; therefore, these differences partly account for the longitudinal gradient of the O3 mixing ratio modeled at the top of free troposphere.

Note that O3 concentration fields and the sum of sensitivities do not generally equal each other because of nonlinearities in O3 formation. Moreover, the zero-out contributions for US and east Asian emissions represent only a portion of the total emissions burden, and the emissions' sensitivity calculations can also be affected by initial and boundary conditions. To investigate this further, the temporal evolution of O3 concentrations and sensitivities towards O3VORT, O3IC, O3BC, and domain-wide emissions' ZOC are presented in Figs. S6–S9. The figures show time series of these contributions averaged over the PST, MST, CST, and EST areas in the US at the surface, 750, 500, and 250 hPa, corresponding to the results presented in Table 2. These figures show that the domain-wide emission zero-out contributions (Fig. S5) are larger than those of zero-out contributions from the US and east Asia (Fig. 6 and Table 2), pointing to the impact of emissions from other regions on simulated ozone concentrations. As expected, the impact of O3BC is small over the US due to the distance from the equatorial boundaries. At the beginning of the simulation, O3 concentrations are dominated by initial conditions, as shown by the close agreement between the O3 concentration and O3IC curves during the first half of March. The sensitivity towards O3IC declines throughout the simulation, while O3VORT and ZOC increase and begin to dominate the O3 variation by April. However, even after the 1-month spin-up period, O3IC is still present over all time zones and all altitudes. In this study, we initiated the H-CMAQ simulation from the prior model simulation for 2010 (Hogrefe et al., 2018); however, this result suggest that spin-up periods longer than 1 month may be necessary to fully capture the effects of emissions and O3VORT contributions through calculating HDDM sensitivities over a hemispheric-scale modeling domain. Finally, Figs. S6–S9 still show differences between simulated concentrations and the sum of O3VORT, O3IC, O3BC, and ZOC. Aside from the nonlinearities and interactions mentioned above, this likely is also caused by contributions of initial conditions of species other than O3 (e.g., PAN or N2O5) to the simulated O3 levels.

To illustrate altitude dependencies of the impacts of US and east Asian emission and STT, vertical cross sections (“curtain plots”) of these impacts at six ozonesonde sites across the US are examined in Fig. 8 (refer to Figs. 4 and S5 of Itahashi et al., 2020). In these curtain plots, the pressure levels of 750, 500, and 250 hPa are marked to indicate the representative altitude of the bottom, middle, and top of the free troposphere. The comparison of the ZOCs from US and east Asian emissions clearly shows the differences of their vertical structures. Over these ozonesonde sites, except Hilo (Fig. 8a), the emission impacts from the US greater than 10 ppbv are mostly confined to below 750 hPa (within the boundary layer) and occasionally extend into the free troposphere. In contrast, the emission impacts from east Asia can predominantly be found in the free troposphere and sometimes extend into the boundary layer (below 750 hPa) and/or the upper model layers (above 250 hPa). These patterns further confirm that pollution lofted to the free troposphere over Asia can undergo efficient transport across the Pacific and entrain to the lower troposphere and boundary layer over the US. The sensitivity towards O3VORT is the dominant factor over the upper model layers (above 250 hPa) and downward into the upper part of the free troposphere, but most of its episodic impact does not reach the middle of the free troposphere (500 hPa) or below. The strong STT events seen in these cross sections, i.e., the events in early and late April at Trinidad Head (Fig. 8b), early April at Boulder (Fig. 8c), late April at Huntsville (Fig. 8d), and mid-April at Wallops Island (Fig. 8e) and Rhode Island (Fig. 8f), are generally consistent with the results inferred from the air mass classification technique presented in the Part 1 paper. It should be however noted that a more robust quantification of the fraction of ground-level O3 that originated in the stratosphere and its seasonal and spatial distributions would require conduct of longer-term sensitivity simulations than those examined here.

As has been shown in previous studies and affirmed in the current work, trans-Pacific transport can impact air quality in the US. April 2010 was used as the target period for our analysis because El Niño conditions during that time period favored trans-Pacific transport. In this section, we estimate the variation of trans-Pacific transport caused by recent emission changes. According to the NOAA Climate Prediction Center (CPC), strong and long-lasting El Niño conditions occurred from late 2014 to the middle of 2016 (NOAA and CPC, 2018). Observed average MD8O3 over the US was 46.9 ppbv in April 2015, a decline from its April 2010 values of 52.2 ppbv, and the number of sites exceeding the NAAQS declined from 39 sites in April 2010 to 7 sites in April 2015. From 2010 to 2015, annual NOx (VOC) emissions in the US decreased from 13.4 (13.6) Tg to 10.6 (12.9) Tg (see Fig. S1 of Itahashi et al., 2020). These emission reductions likely contributed to the decline of the observed O3 mixing ratios relative to the 2010 values. How about the trans-Pacific transport? Anthropogenic emissions in China grew during the 2000s (Itahashi et al., 2014) and reached the highest levels in the world in 2010; however, substantial reductions have been measured by satellites since then (Irie et al., 2016; Krotkov et al., 2016; van der A et al., 2017; Itahashi et al., 2018). In addition, bottom-up emission inventories indicate that Chinese NOx emissions were reduced as a consequence of clean air actions (Zheng et al., 2018). In particular, Zheng et al. (2018) report that annual NOx emissions were reduced from 26.5 Tg in 2010 to 23.7 Tg in 2015, while annual VOC emissions increased from 25.9 Tg in 2010 to 28.5 Tg in 2015. While NOx emissions have been regulated and subsequently declined after reaching a peak of 29.2 Tg in 2012, the situation is more complex for VOC emissions which show decreases from the residential and transportation sectors but increases from the industrial sector and solvent use. Applying the percentage changes in Chinese emissions from 2010 to 2015 to the HDDM sensitivities for east Asian emissions (assuming that changes in east Asian emissions are dominated by changes in China), we estimated their impacts on tropospheric O3 mixing ratios.

The changes in O3 mixing ratio caused by emission changes between 2010 and 2015 over the US and east Asia can be investigated via Eq. (4). Based on the emission changes noted above, the resulting values of εi and εj in Eq. (4) are -20.9 % and -5.1 % for NOx and VOC emissions from the US, and -10.6 % and 10.0 % for NOx and VOC emissions from east Asia, respectively. The estimated spatial changes in O3 mixing ratios at the surface and aloft are shown in Fig. 9, and estimates for monthly and daily means over four time zones in the US are shown in Fig. 10 in a similar manner to Fig. 4. The US emission reductions between 2010 and 2015 resulted in generally reducing surface O3 mixing ratios with changes of at least -0.5 ppbv across the entire US and up to -5.0 ppbv over the southeast US. Exceptions are found over Seattle, San Francisco, Los Angeles, around the Great Lakes, and in New England regions that were characterized as VOC sensitive in Sect. 3.2. These changes are expected because reductions in NOx emission were greater than those in VOC emissions across the US. It is also shown that the US emission reductions cause a reduction of O3 mixing ratio over the free troposphere. On the time-zone-averaged basis, the changes in monthly mean O3 mixing ratios are -0.5, -1.1, -1.8, and -1.5 ppbv over PST, MST, CST, and EST, respectively (Fig. 10). The maximum reductions are found over CST because EST contains the complex sensitivity over New England regions. In contrast, the changes in east Asian emissions between 2010 and 2015 do not cause a noticeable reduction in surface O3 mixing ratios over the US, while they led to O3 mixing ratio increases of more than 1 ppbv over eastern China, the Korean Peninsula, and some parts of Japan on a monthly average basis (Fig. 9). These increases are expected both because these areas were shown to be VOC sensitive in Sect. 3.2 and because of the increase in VOC emissions. On a time-zone-averaged basis, changes in east Asian emissions between 2010 and 2015 are estimated to change the monthly mean O3 mixing ratio across the US by about -0.1 to -0.3 ppbv. The corresponding changes in daily average surface-level O3 mixing ratio were also less than -0.5 ppbv (Fig. 10). A slight reduction in monthly mean O3 mixing ratios of around -0.5 ppbv was estimated across large parts of the Northern Hemisphere free troposphere, indicating that the reductions in east Asian emissions that occurred between 2010 and 2015 can partly contribute to a weakening of trans-Pacific O3 transport over the free troposphere. However, the reductions in Asian emissions during 2010 and 2015 did not appear to alter the monthly mean surface-level O3 mixing ratio across the US.