Before perturbing the inputs and running the model, the next step was to create the uncertainty distributions for the prescreened model inputs using the uncertainties listed earlier in the methods section and in Tables  and . For the majority of the factors, we used lognormal uncertainty distributions where the standard deviations were determined by σ=(f-1/f)/2 where f is the published uncertainty factor. Normal distributions were used for some meteorological factors (relative and specific humidity, soil wetness, and temperature). To allow model perturbations' time to spread globally, all runs in the model ensemble were spun up 9 months before the first flight for the respective campaigns.

RS-HDMR sensitivity indices were calculated using graphical user interface – HDMR (GUI-HDMR), a free MATLAB package (http://www.gui-hdmr.de) . As in , in running GUI-HDMR, the inputs were scaled according to their percentiles within their respective uncertainty distributions and the correlation method option was applied .

For ozone and OH, GEOS-Chem modeled mixing ratios were consistently higher than measurements (Fig. ). Throughout the vertical column, GEOS-Chem modeled ozone was around 10 ppb greater than measurements. For OH, modeled and measured values were similar close to the surface, but the disagreement widened higher, with modeled values being a factor of ∼ 1.6 greater than measurements around 6 km. Unlike GEOS-Chem, the box model generally agreed with the measured OH profiles, suggesting that the model errors for OH are likely arising outside of the chemical mechanism, such as emissions sources. In contrast to ozone and OH, measured HO2 profiles were generally greater than the model ensemble, with the widest disagreement coming close to the surface. Unlike OH, HO2 profiles modeled by the box model generally agreed with GEOS-Chem more than they did with the measurements. This model–model agreement suggests that either the model errors may be arising from the largely similar chemistry of the two models or the measurements are incorrect, perhaps due to peroxy radical interference. The agreement between GEOS-Chem and ATHOS HOx profiles presented here is different than in due to errors found in the calibration of the measurements . At all altitudes, there were small differences between the finer 2∘×2.5∘ and the coarser 4∘×5∘ ensemble. Specifically, these differences were less than 4 ppb for ozone, a few hundredths of a ppt for OH, and less than 1 ppt for HO2.

Part of this disagreement in mixing ratios could be attributed to uncertainties in the modeled values. We find 1σ uncertainties for the modeled oxidant mixing ratios to range from 19 to 23 % for ozone, 27 to 36 % for OH, and 18 to 37 % for HO2 in the different vertical bins. When taking into account both uncertainties in model input factors and measurements, we find there to be overlap between all the oxidant profiles. This overlap shows that the uncertainties in the model and measurements can explain the difference between the model and measured profiles.

The vertical profiles for ozone, OH, and HO2 all follow a similar pattern: general agreement between measured and modeled mixing ratios near the surface turning to model overestimation above 4 km or so (Fig. ). In the case of ozone, the model–measurement gap persists even when accounting for measurement uncertainty, especially from 5 km higher. As a consequence of this model overprediction of ozone, OH and HO2 both are also overpredicted by GEOS-Chem above 4–5 km, but unlike ozone, there is overlap at all levels between the measured and modeled values when uncertainties in both are taken into account. Generally, there are small differences between the median of the 4∘×5∘ model ensemble and a finer resolution 2∘×2.5∘ run; however, there are some larger differences between these two possibilities, with ozone mixing ratios being reduced by 7–9 ppb above 5 km in the finer resolution. Conversely, below 5 km, the finer resolution run produces higher OH mixing ratios (about 0.06 ppt or ∼ 30 % higher), roughly on the order of the 1σ model uncertainty. Differences between HO2 profiles using either model resolution were within a few ppt at all altitudes and within 1 ppt in most of the vertical bins.

Unlike GEOS-Chem, the box model tended to better agree with measurements higher in the troposphere for OH (Fig. ). In the case of OH mixing ratios, the box model was around a factor of 2 greater than measurements in the first vertical bin and around 30 % greater up to 4 km. Higher than 4 km, the box model and measurements largely agreed. For HO2 mixing ratios, the box model was greater than observations at all heights but was marginally closer than GEOS-Chem to the measured profile.

Model ozone uncertainty was largely altitude independent, running between 19 and 21 % below 8 km. Uncertainty in modeled OH was between 28 and 40 %, with uncertainty on a percentage basis ranging highest near the surface and above 7 km (Fig. ). Model HO2 uncertainty followed a similar vertical pattern to OH with the highest uncertainty coming near the surface (∼ 30 %) and lower in the middle troposphere (18–20 % from 3 km up to 8 km).

Vertically, uncertainty in ozone is nearly altitude independent, ranging between 17.5 and 20.5 % (1σ) (Fig. ). While GEOS-Chem on average comes close to the average measured values, the model fails in matching the measured profile shape. Near the surface, GEOS-Chem is around 12 ppb less than measured values. This underprediction shifts to overprediction around 4 km, with the model overpredicting 25–30 ppb around 9–10 km. This under- and overprediction by the model at low and high altitudes is outside the model and measurement uncertainties. Differences between the finer 2∘×2.5∘ and the coarser 4∘×5∘ ensemble were smaller than these model–measurement disagreements. At nearly every altitude, the ozone mixing ratios were within 10 ppb with no consistent positive or negative bias.

In contrast to ozone, the uncertainty in OH mixing ratios is high and vertically variable (Fig. ). From 0 to 3 km, uncertainty is roughly around 32–36 % before increasing through the middle troposphere to 38–40 %. For all altitudes, measured and model values were within each other's uncertainty range. The box model agreed well with OH measured mixing ratios, especially above 5 km with more modest agreement and slight overprediction below. Between the finer 2∘×2.5∘ and the coarser 4∘×5∘ ensemble we found generally higher OH mixing ratios but within a few hundredths of a ppt.

Compared to OH, uncertainty in HO2 mixing ratios is lower but follows the same pattern of increasing with altitude (Fig. ). We find uncertainty rising from 16–20 % between the surface and 4 km to between 23 and 30 % from 5 km higher. Generally, GEOS-Chem replicated the measured HO2 mixing ratio profile within a couple ppt. Differences between the finer and coarser resolution choices resulted in differences around or less than 2 ppt below 9 km. Like OH, the box model generally agreed well with measured HO2 mixing ratios. The overall agreement between the oxidant profiles in this domain may be attributable to the reduced surface emissions sources in this remote central Pacific domain.

In contrast to the previous regions analyzed here, measured ozone, OH, and HO2 mixing ratios were generally greater than GEOS-Chem modeled values in nearly every vertical bin (Fig. ). Ozone mixing ratios were underpredicted by the model around 10 ppb, with the difference between modeled and measured values maxing out at 17 ppb around 4 km. Except for near the surface where the model was around 0.04 ppt too high and above 8 km, GEOS-Chem generally underrepresented OH by a couple hundredths of a ppt. These differences are within the model and measurement uncertainty. HO2 mixing ratios showed some of the widest disagreement between modeled and measured values, with the model being anywhere from 1.6 ppt short near the surface to upwards of 6.8 ppt between 3 and 4 km. In this domain, we found small differences in oxidant mixing ratios between the finer 2∘×2.5∘ and the coarser 4∘×5∘ ensemble. Specifically, modeled ozone was around 0–4 ppb higher in the fine resolution case, OH 1–3 hundredths of a ppt higher in the fine resolution case, and HO2 mixing ratios within a few tenths of a ppt.

Compared to GEOS-Chem, the box model performs better in matching the measured OH and HO2 mixing ratio profiles. In particular, while still somewhat underpredicting HO2 mixing ratios, the box model does match the shape of the measured HO2 profile unlike GEOS-Chem (Fig. ). Because of this relatively close match between the box model and the measurements, the disagreement between GEOS-Chem and the measurements could be arising outside of the chemical kinetics. Conversely, the box model may be better matching the measured profile just due to its lack of aerosol uptake of HO2. In the Arctic, the aerosol uptake of HO2 is a major loss pathway for HO2 . Without this loss pathway, the box model may have artificially high HO2 mixing ratios.

Uncertainty in modeled ozone mixing ratios was relatively low, ranging between 13 and 20 %. In contrast, uncertainties in both OH and HO2 mixing ratios were considerable, ranging between 34 and 57 % for OH and 21 and 40 % for HO2 (Fig. ). This higher uncertainty is in part a product of the very low mixing ratios modeled in this northern domain with OH mixing ratios being less than a tenth of a ppt for most of the vertical column and modeled HO2 mixing ratios in a range between 6 and 9 ppt.

Despite the geographic range of the regions presented here, there are many similarities to highlight. For instance, uncertainties in GEOS-Chem modeled mixing ratios for ozone, OH, and HO2 were largely similar. As a rule of thumb, uncertainties in ozone mixing ratios were around 20 %, OH between 25 and 40 %, and HO2 between 20 and 35 %. Also, for most regions, when uncertainties in both GEOS-Chem and measurements are taken into account, there is general agreement between oxidant mixing ratios with the exception of ozone profiles in the higher-altitude Houston-based INTEX-B flights and ozone in a few other vertical bins in the Pacific INTEX-B flights.

Generally, ozone was most sensitive to emissions, particularly NOx and isoprene (Fig. ). Near the surface, ozone was most sensitive to the EPA-NEI (Environmental Protection Agency – National Emissions Inventory) NOx emissions and isoprene (Si=0.21 and 0.20, respectively). A few kilometers up, this sensitivity to surface NOx emissions is replaced by sensitivity to lightning NOx (Si=0.28 and 0.30 for 3–4 km and 7–8 km, respectively). Sensitivity to chemical factors such as the NO2 + OH reaction rate and the NO2 photolysis rate were largely altitude independent (Si between 0.08 and 0.13 for k[NO2 + OH]; Si=0.07-0.08 for j[NO2]).

Sensitivities for OH largely mirrored those of ozone (Fig. ). As photolysis of ozone in the presence of water vapor leads directly to the production of OH, this is unsurprising. In addition to NOx and isoprene emissions mentioned with ozone, we also find OH above 3 km to be sensitive to CO emissions, especially from biomass burning (Si=0.16 between 3 and 4 km and Si=0.10 between 7 and 8 km).

Near the surface where modeled aerosol concentrations are greatest, HO2 is most sensitive to the aerosol uptake of HO2 and isoprene emissions (Si=0.28 and 0.25, respectively) (Fig. ). This sensitivity to aerosol uptake is reduced higher in the troposphere with biomass CO (Si=0.26 at 3–4 km and Si=0.18 between 7 and 8 km), lightning NOx (Si=0.12 at 7–8 km), and isoprene emissions (Si= 0.15 between 3 and 4 km and Si=0.26 between 7 and 8 km) being the dominant sources of the uncertainty above 3 km. As uncertainty in gamma HO2 is not limited to just the rate of the reaction but also to the product, we examined the modeled profiles in a model run having gamma HO2 producing H2O2 rather than H2O. With small differences generally around or less than half a ppt for HO2 and likewise small differences for OH and ozone, HO2 and the other oxidants are rather insensitive to this difference. Sensitivity to isoprene emissions is roughly altitude independent. As isoprene's lifetime is shorter than the timescales to allow consequential transport past the boundary layer, the sensitivity of HO2 to isoprene emissions in the middle to free troposphere is almost certainly due to chemistry relating to secondary and higher-order isoprene products such as the photolysis of formaldehyde and acetaldehyde.

As with INTEX-A, ozone is largely sensitive to NOx emission inventories, specifically soil NOx near the surface and lightning NOx from 3 km higher (Fig. ). In contrast to the height dependencies in the emissions inventories' sensitivities, sensitivity to chemical factors was generally altitude independent with sensitivities to k[NO2 + OH] ranging between Si values of 0.07 and 0.09, and j[NO2] and j[O3] between 0.03 and 0.08. For emission factors, in the lowest 1 km, apart from soil NOx emissions (Si=0.28), we also find isoprene emissions (Si=0.08) and EDGAR NOx emissions (Si=0.07) having Si values greater than 0.05. From 3 to 4 km higher, lightning NOx becomes the dominant source of uncertainty, with Si values of 0.30 around 4 km and higher between 7 and 8 km (Si=0.41). In these higher-altitude bins, we also find ozone to have greater sensitivity to biomass CO emissions with Si values of 0.07 between 3 and 4 km, and Si=0.09 between 7 and 8 km.

Similar to ozone, while we find OH to be most sensitive to emissions sources, the sensitivity to these sources is altitude dependent (Fig. ). Near the surface, OH is most sensitive to isoprene and soil NOx emissions sources (Si values of 0.21 and 0.15, respectively). Chemical factors such as k[NO2 + OH], aerosol uptake of HO2, and j[NO2] also had Si values greater than 0.05 (0.09, 0.08, and 0.07, respectively). Higher, lightning NOx becomes the dominant source of uncertainty for OH mixing ratios with Si values of 0.21 in the 3–4 km bin and 0.54 for the 7–8 km bin.

For HO2 mixing ratios, near the surface, we find gamma HO2 to be responsible for about half of the model uncertainty (Si=0.51), with isoprene emissions being the only other factor with Si>0.05 (Si=0.16) (Fig. ). This dominance by gamma HO2, though, is restricted to near the surface where aerosol concentrations are highest. In fact, higher than 3 km, we find biomass CO emissions to become the dominant source of uncertainty (Si=0.27 for 3–4 km, Si=0.38 for 7–8 km). Sensitivity to isoprene emissions is similar between 3–4 and 7–8 km with Si values of 0.13 and 0.14, respectively.

For the flights based out of Honolulu, near-surface ozone was most sensitive to surface emissions sources in the first vertical kilometer with ship NOx (Si=0.27) and methyl bromoform emissions (Si=0.07) and a variety of chemical factors such as the ozone photolysis rate (j[O3] (Si=0.14), k[NO2 + OH] (Si=0.06), j[HOBr] (Si=0.05), j[NO2] (Si=0.05)) (Fig. ). Higher, ozone becomes sensitive to other emissions sources, especially lightning NOx (Si=0.11 and 0.25 at 3–4 km and 7–8 km, respectively), and to a lesser extent, soil, and east Asian NOx and isoprene emissions. These latter emissions sources are noteworthy as they illustrate the sensitivity of this region to nonlocal upwind emission sources, as there are not any appreciable isoprene or soil NOx emissions over the remote north-central Pacific. In addition to emissions sources, ozone also showed moderate sensitivity to chemical factors. In particular, the photolysis rate of ozone, in spite of its low uncertainty (20 %), had sensitivity indices ranging between 0.10 and 0.15 between the surface and 5 km. The NO2 + OH reaction rate also had sensitivity indices at about 0.07 at most altitudes.

OH mixing ratios were largely sensitive to the same factors as ozone (Fig. ). Near the surface, OH was largely sensitive to ship NOx emissions (Si=0.38), both biomass and east Asian CO, j[O3], k[NO2 + OH], and j[NO2] (Si=0.09, 0.08, 0.08, 0.06, and 0.05, respectively). Above 3 km, there is no single factor that overwhelmingly contributes to the uncertainty, but CO and NOx emissions, along with the photolysis rate of ozone and the NO2 + OH reaction rate, all had Si values greater than 0.05 for the higher-altitude bins.

Like the Houston flights, HO2 mixing ratios were largely sensitive to CO emissions, NOx emissions, and aerosol uptake of HO2; only sensitivity to aerosol uptake is reversed vertically with higher sensitivities coming in the upper troposphere rather than near the surface (Si=0.10, 0.16, and 0.30 for 0–1, 3–4, and 7–8 km vertical bins) (Fig. ). This is a result of the modeled aerosol concentrations being highest near the surface for the Houston flights and highest in the upper reaches of the troposphere for the Honolulu flights.

Near the surface, ozone sensitivity was dominated by ship NOx emissions (Si=0.52) and to a much lesser extent photolysis of HOBr (Si=0.06). Higher, a host of emissions factors become more important, with bromoform emissions (Si=0.11 for 3–4 km and Si = 0.09 for 7–8 km), soil NOx (Si=0.10 and 0.11 for 3–4 and 7–8 km, respectively), and lightning NOx (Si=0.13 at 7–8 km) (Fig. ). Chemical factors such as k[NO2 + OH] and j[NO2] also were responsible for between 6 and 8 % of the uncertainty for both the 3–4 km and 7–8 km altitude bins.

Like ozone, OH was overwhelmingly sensitive to ship NOx emissions (Si=0.50), with this one factor being responsible for around half the model uncertainty (Fig. ). At 3–4 km, this sensitivity to ship NOx emissions is replaced by CO emissions from east Asia and biomass burning and soil NOx (Si=0.11 for east Asian CO, Si=0.09 for biomass CO and soil NOx). From 3 km higher, OH mixing ratios are most sensitive to the aerosol uptake of HO2 (Si=0.14 at 3–4 km, Si=0.29 at 7–8 km).

At all but the highest altitudes, modeled HO2 mixing ratios were overwhelmingly sensitive to the aerosol uptake of HO2 (gamma HO2) with this one factor contributing around half the model uncertainty (Si=0.49 at 0–1 km, Si=0.57 at both 3–4 and 7–8 km) (Fig. ). This dominance of gamma HO2 on HO2 mixing ratios has been noted before in the similar ARCTAS-A (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) domain .

For all the regions presented here, GEOS-Chem modeled and measured ozone and OH profiles have closer agreement with lower lightning NOx emissions than those emitted by default. In examining the closest 25 model ensemble members for each region and oxidant, we find reductions in their lightning NOx emissions anywhere from ∼ 25 % for Anchorage INTEX-B ozone and OH, INTEX-A ozone, and Honolulu INTEX-B OH, to around a factor of 2 reduction for INTEX-A OH, Houston INTEX-B ozone and OH, and Honolulu INTEX-B ozone. Considering GEOS-Chem tended to overpredict ozone and OH, especially at higher altitudes, it is unsurprising there is better agreement with lower lightning NOx emissions.

The vertical profiles of NO and NO2 (Fig. S5) somewhat corroborate this overestimation of NOx emissions in INTEX-A and can explain the overestimate of ozone. In INTEX-A, we found modeled NO2 to be consistently greater than their respective measured values. Near the surface, this difference can be anywhere between 50 % and factor of 2 or greater for NO2 with the greatest difference on an absolute basis near the surface (0–1 km) and on a percentage basis in the middle troposphere (between 5 and 7 km). In contrast to INTEX-A NO2 mixing ratios, NO was underpredicted by the model with the exception of the first vertical kilometer. With high NO2 and low NO, the model steady-state ozone concentrations would be elevated, as ozone concentrations are generally proportional to the [NO2] / [NO] ratio e.g.,. In the Houston-based INTEX-B flights, we found NO2 to have modeled mixing ratios greater than those measured between the surface and 1 km and above 5 km (Fig. S6). Between 5 and 9 km, NO and NO2 mixing ratios are between 10 and 25 ppt too high in the model compared to measurements.

This model NOx overestimate is similar to results found in for the SEAC4RS campaign. In the case of , GEOS-Chem more closely matched observations when the United States regional NOx emissions were reduced by a factor of 2. The blue lines in Figs.  and illustrate the better model–measurement agreement, especially for ozone, when both EPA-NEI and lightning NOx emissions are reduced by a factor of 2 for INTEX-A and Houston-based INTEX-B flights. In the case of lightning NOx, this factor of 2 reduction is similar to the difference between modeled lightning NOx production in the tropics vs. the midlatitudes (north of 23∘ N for North America).

For the INTEX-A flights, this reduction in NOx emissions eliminates much of the model–measurement disagreement, especially for ozone, but unlike INTEX-A, the Houston-based INTEX-B GEOS-Chem model–measurement disagreement is not fully bridged for ozone, especially in the upper troposphere. This persistent disagreement suggests that lightning NOx emissions are not solely to blame for the upper altitude disagreement in ozone mixing ratios for the Houston-based INTEX-B flights.

In addition to lightning NOx, the Pacific flights of INTEX-B were also sensitive to ship NOx emissions, especially for the near-surface vertical bins. For ozone, the 25 best-matching model ensemble members had higher ship NOx emissions (65 % greater for Honolulu and 25 % greater for Anchorage flights). Since ozone was underpredicted by the model in conjunction with NOx (Figs. S7 and S8), increasing NOx emissions would presumably ameliorate some of this model–measurement disagreement. While this strong sensitivity to shipping emissions was not found during the ARCTAS campaign, this difference is likely a result of the more southerly direction, and thus more maritime domain, of the INTEX-B flights out of Anchorage, rather than the more continental flights of the ARCTAS campaign. Model treatment of ship emissions is unique in comparison to other anthropogenic sources. In order to approximate the complex and nonlinear chemistry within ship exhaust plumes, NOx emissions are modified and partitioned via the PARAmeterization of emitted NOx (PARANOX) scheme into not only NOx emissions but also directly as ozone . Clearly, both the ship emissions and their immediate treatment are an important consideration, especially for near-surface ozone and OH over remote maritime domains such as the northern Pacific Ocean.

Underprediction of ozone and HOx is a persistent problem in this northern domain and largely mirrors previously published studies involving the ARCTAS campaign, a field campaign that took place over the North American Arctic in April of 2008 . For the same flights, we similarly find model underprediction of NOx mixing ratios, especially above 2 km (Fig. S8). Underprediction of NOx mixing ratios would explain some of the underprediction of ozone mixing ratios.

As for the aerosol uptake of HO2, the sensitivity of HO2 mixing ratios to this factor has been noted before but mostly in the Arctic where low NOx mixing ratios and lower temperatures lead to longer HO2 lifetimes. Indeed, we found greater sensitivity to this factor in the Anchorage-based INTEX-B flights, the northernmost domain analyzed here. However, we also find similar sensitivities for HO2 mixing ratios in different vertical bins for the other regions presented here. Like a similar study for a North American Arctic campaign , we also consistently find better agreement between HO2 modeled and measured mixing ratios when aerosol uptake of HO2 rates is reduced from its default rate of 0.20. In the case of the 25 best-fitting ensemble member profiles, we find rates of anywhere between 0.133 for Honolulu INTEX-B, 0.085 for Houston INTEX-B, 0.069 for INTEX-A, and 0.064 for Anchorage INTEX-B. For most of these cases, where we found greatest sensitivity to gamma HO2, we also found HO2 underprediction by GEOS-Chem. Thus, lower uptake rates alleviate some of this difference.

It is also possible that some of the underprediction of HO2 by the model could be attributed to missing HO2 sources or interferences in the measurements from peroxy radicals . As this interference requires the presence of alkenes or aromatics, it is more of a consideration near the surface and VOC emissions sources. While this is a consideration for the near-surface HO2 model underestimation in INTEX-A, it is not a major consideration for INTEX-B since much of that campaign took place over more remote maritime regions.