4.1 Ozone

For the spatial evaluation, all the aircraft measurements and the extracted model data points are combined regardless of the time of the measurement; observations and models are separated into three altitude layers: the low troposphere layer (0–3 km), the middle troposphere layer (3–9 km) and the upper troposphere–lower stratospheric layer (9–14 km).

The comparison of O₃ between the observation and the reanalyses is shown in Figs. 2, 3 and 4. The tropospheric ozone concentration is higher in the Northern Hemisphere than the Southern Hemisphere because of higher anthropogenic emissions of ozone precursors (air pollution). In the 9–14 km layer, the polar ozone concentrations are very high because the height of the tropopause in that region is lower than at lower latitudes, and as a result, the aircraft penetrated the ozone-rich stratosphere. The comparison between the aircraft observations and the reanalysis values from MACCRA is generally good. In the low troposphere, the biases of the averaged grids are mostly within 20 %. MACCRA underestimates the O₃ concentrations in the Arctic region and in the Southern Hemisphere, while it overestimates the O₃ concentrations in the northern low and middle latitudes, especially over the western Pacific Ocean (over 50 %), the eastern coast of US and the North Atlantic (about 40 %). The biases of MACCRA in the middle troposphere are smaller than those in the low troposphere. The positive biases in the lower layer become smaller with increasing altitude everywhere except in the Arctic, where the negative biases turn to positive values. In the upper troposphere, the agreement is worse than in the lower layers. The biases are mostly positive over the Pacific Ocean and negative in North America.

Figure 2Campaign observations of O₃ (a). (b) The relative difference in percent between MACCRA and the observations (MACCRA – observation). (c) The difference between CIRA and the observations (CIRA – observation). (d) The difference between CAMSRA and the observations (CAMSRA – observation), and (e) the difference between the control run and the observations (control – observation). The data are averaged to $\mathrm{5}{}^{\circ }\times \mathrm{5}{}^{\circ }$ (latitude × longitude) and to the altitude bin of 0–3 km. Note that MACCRA only includes campaigns between 2003 and 2012.

Figure 3Same as Fig. 2, but for the altitude bin of 3–9 km.

Figure 4Same as Fig. 2, but for the altitude bin of 9–14 km.

The agreement of CIRA with the aircraft measurements is similar to the agreement of MACCRA when using the same measurements before 2013. In the lowest layer, however, the mean bias of CIRA is slight smaller than that of MACCRA. The CIRA reanalysis overestimates the observation in the middle of the Pacific Ocean and northwest of the Atlantic Ocean, which is similar to the values derived from MACCRA but with smaller biases; CIRA underestimates ozone concentrations in the rest of the region with biases of less than 20 %. Above the Pacific Ocean, the positive bias, which is small in the lower layers of the atmosphere, increases with height and becomes substantial in the upper troposphere. The patterns of the biases in the CIRA reanalysis in the upper troposphere are similar to those in the middle troposphere layer but with larger values.

In the low troposphere, CAMSRA generally overestimates the O₃ concentration relative to the observation, which is different from the MACCRA and CIRA cases. The biases of CAMSRA are usually less than 15 %, and the relatively larger biases are found in the tropics and Arctic, where the reanalysis overestimates the measurements by about 30 %. In the free troposphere, the biases of the reanalysis become larger than in the low troposphere, especially over the tropical ocean, while the differences are smaller in the western African region. For the comparison above 9 km, the positive biases over the Pacific Ocean are even larger and reach 50 %.

The mean bias of the CAMS control simulation (model run performed without assimilation of observed data) is similar to the bias associated with CAMSRA, but the patterns are different. The bias of CAMSRA is more uniform over the globe, which shows that data assimilation improves the global distribution of the O₃ concentration. In the low troposphere, the bias of the control run is of the order of 15 %. The control run underestimates the measurements on the west coast of US and in the south of the Pacific Ocean, where the ozone concentrations provided by the CAMSRA are higher than the observation. In the polar free troposphere, the control simulation provides concentration values that are lower than suggested by the observations with a bias of about 20 %; in contrast to this, in the tropical region, the control simulation overestimates ozone, which is similar to the corresponding estimates by CAMSRA. In the upper layer, the bias pattern is similar to that in the free troposphere, but the bias values are larger.

Overall, for ozone, the level of agreement between the observations and the three reanalyses and between the observations and the control run are similar, but the biases associated with CAMSRA are more uniform in space. A linear regression was performed between all observed ozone data points and ozone concentrations extracted from the three reanalyses and from the control simulation. Table 4 lists the corresponding linear regression parameters. Fewer data are available when considering MACCRA because MACCRA includes information only until the year 2012. To more directly compare with MACCRA, the regression parameters for the other models runs before 2013 are also given in the table. The correlations of all three reanalysis cases are high, with squared correlation coefficients larger than 0.9. The highest correlation is achieved with CAMSRA. The squared correlation coefficient R² derived for the control simulation (0.89) is not substantially smaller than in the three cases with assimilation (0.93). This suggests that the CAMS model in its control mode has good predictive capability but that, as expected, data assimilation slightly improves the calculated ozone fields. To exclude the contribution of stratospheric ozone values in the statistical analysis, the stratospheric data were filtered out and the statistical parameters recalculated. The squared correlation coefficients decreased from about 0.9–0.95 to about 0.6–0.7.

Table 4Linear regression of ozone between observations and models.

Note: N is the number of points considered for the calculation of the correlation, MB the mean bias (ppb), MAE the mean absolute error (ppb), R the correlation coefficient and RMSE the root mean square error (ppb).

Download Print Version | Download XLSX

4.2 Carbon monoxide

The comparison of carbon monoxide between the observation and the reanalyses is shown in Figs. 5, 6 and 7. MACCRA underestimates the CO concentrations in the Arctic region and Canada (about 30 %), West Africa (about 20 %), and the Southern Ocean (about 10 %). It overestimates the concentrations in the other regions covered by the campaigns, with most of the biases within 15 %. In the middle troposphere, the bias pattern is similar to that of the low troposphere, but the biases are smaller than in the lowest layer, especially in the Arctic. In the upper layer, often located in the stratosphere, the biases become larger at high latitudes (positive in the Arctic and negative in the Southern Ocean), with biases larger than 50 %. In this layer, the patterns of the biases over the Pacific Ocean are different than in the lower layers.

Figure 5Campaign observations of CO (a). (b) The relative difference in percent between MACCRA and the observations (MACCRA – observation). (c) The difference between CIRA and the observations (CIRA – observation). (d) The difference between CAMSRA and the observations (CAMSRA – observation), and (e) the difference between the control run and the observation (control – observation). The data are averaged to $\mathrm{5}{}^{\circ }\times \mathrm{5}{}^{\circ }$ (latitude × longitude) and to the altitude bin of 0–3 km.

Figure 6Same as Fig. 5, but for the altitude bin of 3–9 km.

Figure 7Same as Fig. 5, but for the altitude bin of 9–14 km.

CIRA agrees better with the observations than MACCRA. In the low troposphere, the biases are smaller than those derived with MACCRA, and the large negative biases in the Arctic found in MACCRA disappear with CIRA. The mean bias of CIRA is only of the order of 10 %. CIRA underestimates the CO observation in the region of the northern Pacific Ocean, but MACCRA overestimates the concentrations there. In the middle troposphere, CIRA underestimates CO in most regions in the Northern Hemisphere, while it overestimates CO in the Southern Hemisphere. In the upper layer, the biases of CIRA are also large at high latitudes, but the biases are positive in the both polar regions.

The agreement between the CO measurements and the CAMSRA is generally good, with biases generally smaller than 15 %. In the low and middle troposphere, the CAMSRA behaves similarly to CIRA; however, in the upper layer, the biases are different. The biases in CAMSRA become smaller in the polar region. CAMSRA underestimates CO concentrations in most regions of the low and middle latitudes, with biases less than 20 %.

The bias between the control run and the CO observations is larger than for the CAMSRA. The bias pattern of the control run in the lowest layer is similar to that of CAMSRA, but the positive biases in the Southern Hemisphere are larger (about 30 %). In the free troposphere, the control run underestimates the CO concentration at latitudes north of 40^∘ N, similar to the CAMSRA, but overestimates the CO elsewhere. The positive model biases in the Southern Hemisphere and tropics are efficiently removed by the assimilation of CAMSRA. In the upper layer, the biases are positive in most regions except west of North America. The biases are large in the polar stratosphere, where they reach about 50 %.

When confronted with CO data collected by airborne instrumentation, all three reanalyses provide good results in the low and middle troposphere; however, the two early reanalyses are not successful when considering the field observations made in the polar region, specifically in the upper troposphere–lower stratosphere. The situation is improved with the new CAMSRA reanalysis. The control simulations performed without assimilation overestimate the CO concentration in the Southern Hemisphere. The linear regression parameters of CO are shown in Table 5. For all the data points, the correlations are weak due to the extreme values appearing in localized pollution plumes, which are not captured by coarse-resolution global models. After filtering out these extreme values (values larger than 300 ppb), the correlations of CO between the observations and models improve substantially. The correlation calculated using CAMSRA is the highest, with a correlation coefficient of 0.71 and a slope of 0.78. The mean bias of CAMSRA is reduced with the assimilation resulting from the correction of the positive bias in the Southern Hemisphere.

Table 5Linear regression of CO between the aircraft campaign observations and the reanalyses.

Note: N is the number of points considered for the calculation of the correlation, MB the mean bias (ppb), MAE the mean absolute error (ppb), R the correlation coefficient and RMSE the root mean square error (ppb).

Download Print Version | Download XLSX

Table 6Qualitative summary of the overestimation and underestimation by the CAMSRA for several observed chemicals at four geographic locations and at two altitudes (6 km and the surface).

Note: G = −10 % < bias < 10 %; O = 10 % < bias < 40 %; U = −40 % < bias < −10 %; OO = bias > 40 %; UU = bias < −40 %.

Download Print Version | Download XLSX

4.3 Other chemical species

Spatial distributions of nitrogen oxides (${\mathrm{NO}}_x=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$), the hydroxyl radical (OH), the hydroperoxyl radical (HO₂) and formaldehyde (HCHO) for CAMSRA in the Northern Hemisphere are provided in the Appendix. The CAMSRA reanalysis values are compared with observations from aircraft for three different layers of the atmosphere. Because the measurements of NO_x, OH, HO₂ and HCHO used in the work are only in North America, the Arctic and Korea, the analyses below are for these regions.

In the case of NO_x, the CAMSRA reanalysis underestimates the values measured in the middle and upper troposphere but overestimates the observed values in the lowest layer. There are several possible reasons: (1) the model overestimates the effect of regional pollution sources; (2) the model underestimates the local production (e.g., lightning); (3) the model underestimates the convective transport; (4) the model underestimates the lifetime of the surface emissions. We also compared the NO_x fields produced by CAMSRA and the control run in order to assess the benefit of NO₂ assimilation. Both fields are very similar, which suggests that the assimilation does not significantly improve the reanalysis of NO_x. This is explained by the fact that NO₂ has a short lifetime. Most of the impact of the data assimilation is therefore lost between analysis cycles (Inness et al., 2015). In the case of HCHO, the reanalysis underestimates the observed concentrations at all levels. The negative biases in the low troposphere are between 20 % and 40 %, while those in the higher levels are about 50 %. In the case of OH, the calculated values are overestimated at middle and low latitudes, which may lead to a shorter lifetime of NO₂, consistent with the vertical distribution of NO_x discussed above. CAMSRA underestimates OH concentrations in the Arctic region, which may be related to the overestimation of CO in that region. Finally, no clear pattern is found in the difference between model-simulated values and observations of HO₂.

5.1 Ozone

In the case of ozone in the Arctic (Fig. 9), where the vertical profile is strongly affected by stratospheric processes, the control run underestimates the O₃ concentration above 1 km, particularly above 6 km of altitude. The assimilation brings the profile much closer to the aircraft data. The concentrations calculated by the control and the reanalysis runs in the surface layer below 1 km are almost twice as large as those derived from the observations, which may be affected by the halogen chemical removal in Arctic spring. In the free troposphere and low stratosphere, the agreement is best for CAMSRA. In Bangor (Fig. 10), the control and reanalysis simulations underestimate the aircraft observations in the upper troposphere, while they overestimate the measurements near the surface.

Figure 9Averaged profiles of the trace constituents over the Arctic during the ARCTAS campaign from April to July 2008. The black lines are the observations, the red lines correspond to the CAMSRA reanalysis, and the blue lines are the control run (only shown for O₃, CO and NO_x). The error bars represent the standard deviation of the data and model.

Download

The low-latitude ozone profiles (Figs. 11 and 12) are well reproduced by the reanalysis. However, the control run tends to overestimate ozone in Mexico City and to a lesser extent in Hawaii. In this last region, the agreement of O₃ between the observations and models is quite good below 7 km: the biases are positive and smaller than 10 %, which is opposite to what is found in the Arctic. The reanalysis provides slightly better results than the control run. At higher altitudes the positive biases get larger and the CAMSRA data become worse than in the control run, which is surprising since the model with assimilated ozone should be better constrained. This result may be due to the fact that the constraint on tropospheric ozone is weak and the bias correction may be distributed incorrectly in the vertical. In Mexico City, the model represents the ozone bulge that is detected by the airborne instruments at 2 to 3 km and is observed for most chemical species. At higher altitudes, the control model overestimates the ozone concentration; however, the bias is reduced by the CAMSRA assimilation.

5.2 Carbon monoxide

In the case of Arctic CO (Fig. 9), the general agreement between the control and reanalysis runs and the observed profile is very good. The control run, however, slightly underestimates the CO concentration in the troposphere but overestimates it in the stratosphere. The assimilation does not change the simulation significantly as MOPITT observations with latitudes higher than 65^∘ were excluded in the CAMS assimilation. It increases the biases in troposphere CO in CAMSRA but decreases the positive biases in the stratosphere. In Bangor (Fig. 10), both the control and the reanalysis simulations underestimate the observed concentrations by typically 10 ppb above 3 km of altitude but underestimate the surface concentrations. At low latitudes (Hawaii and Mexico; Figs. 11 and 12), the control simulation overestimates the concentrations by about 10 ppb in the free troposphere, while CAMSRA underestimates the values observed from the DC-8 by 10 ppb. In Hawaii in the first 2 km above the surface, the control run provides concentrations that are about 10 % lower than the aircraft observation. In Mexico, the control model provides surface values that are 30 % higher than the observation. The bulge observed at 2–3 km of altitude is not reproduced by the model.

Figure 10Averaged profiles of the trace constituents over Bangor during the INTEX-A campaign from July to August 2004. The black lines are the observations, the red lines correspond to the CAMSRA reanalysis, and the blue lines are the control run (only shown for O₃, CO and NO_x). The error bars represent the standard deviation of the data and model.

Download

5.3 Nitrogen oxides

In the Arctic (Fig. 9) the control run underestimates NO_x, especially above 8 km, i.e., in the layers strongly influenced by the injection of stratospheric air. The assimilation process does not substantially reduce the discrepancy, since the CAMS model does not include a detailed representation of stratospheric chemistry and NO_x in the stratosphere is strongly underestimated because of this. In Bangor (Fig. 10), the models underestimate NO_x above 2 km as in the Arctic but overestimate NO_x below 2 km. In the low-latitude regions (Mexico and Hawaii; Figs. 11 and 12), the calculated profiles are in rather good agreement with the observations, except below 2 km, where the influence from local air pollution is not well captured by the control and reanalysis simulations. In Hawaii, the model tends to slightly underestimate the observation. As in the Arctic, this underestimation is larger in the case of the reanalysis. In all regions except the Arctic, the models provide higher surface concentrations than suggested by the measurements.

Figure 11Averaged profiles of the trace constituents over Hawaii during the INTEX-B campaign from March to May 2006. The black lines are the observations, the red lines correspond to the CAMSRA reanalysis, and the blue lines are the control run (only shown for O₃, CO and NO_x). The error bars represent the standard deviation of the data and model.

Download

Figure 12Averaged profiles of the trace constituents over Mexico during the INTEX-B campaign from March to May 2006. The black lines are the observations, the red lines correspond to the CAMSRA reanalysis, and the blue lines are the control run (only shown for O₃, CO and NO_x). The error bars represent the standard deviation of the data and model.

Download

5.4 Hydroxyl and hydroperoxyl radicals

In the Arctic (Fig. 9), the model underestimates OH concentrations by about 0.02 ppt at all altitudes (of the order of 50 %), which may be linked to the slight overestimation of calculated stratospheric CO. In the reanalysis, the concentrations of HO₂ are overestimated by about 1 pptv between 4 and 8 km of altitude. In Bangor (Fig. 10), the reanalysis overestimates OH by about 0.2 pptv, which is coincident with the underestimation of the CO concentration at this location. The HO₂ concentrations are overestimated by 3–5 pptv. In Hawaii, the simulations made for the reanalysis overestimate the OH concentrations below 6 km but underestimate them above 8 km, which is consistent with the overestimation of high-altitude CO in the control run. In Mexico City, the simulated OH concentrations are larger than the measurements below 8 km but smaller above 8 km. The reanalysis overestimates HO₂ by about 4 pptv or 20 %.

5.5 Hydrogen peroxide

In the Arctic (Fig. 9), where the calculated concentrations of HO₂ are too high in CAMSRA, the concentration of hydrogen peroxide is overestimated by typically a factor of 2. In Bangor (Fig. 10), the overestimation is of the order of 20 %. The agreement between the reanalysis and observations is generally good in Hawaii (Fig. 11) and Mexico City (Fig. 12), except in the lower levels of the atmosphere, where the model overestimates the concentrations.

5.6 Nitric acid

Nitric acid concentrations are strongly affected by wet scavenging in the troposphere and, at high latitudes, by the downward flux of stratospheric air (Murphy and Fahey, 1994; Wespes et al., 2007). The reanalysis generally underestimates the concentration of HNO₃ above 2 km of altitude. This is the case in the Arctic (Fig. 9), Bangor (Fig. 10) and Hawaii (Fig. 11). The discrepancy is particularly large in the upper levels of the Arctic, which implies that (1) scavenging of HNO₃ is too strong, and (2) the reactive nitrogen (e.g., NO_x) in the stratosphere is too low due to missing stratospheric chemistry. The model accounts for the high concentrations observed in the lowest levels of the atmosphere, specifically in Mexico City (Fig. 12) and to a lesser extent in Bangor and Hawaii.

5.7 Peroxyacetyl nitrate (PAN)

The agreement between the calculated and observed PAN vertical profile is good in the Arctic (Fig. 9), even though the concentrations are slightly underestimated between 2 and 8 km of altitude. The agreement is also good in Hawaii (Fig. 11) below 5 km of altitude, but a discrepancy of about 50 % is found above this height. In Bangor (Fig. 10), PAN concentrations are overestimated by about 25 % in the free troposphere and by as much as a factor of 2 below 3 km of altitude. The calculated concentrations are slightly too high in Mexico City (Fig. 12). The model shows the presence of a peak in the PAN concentration at 3 km, but the calculated concentration values are somewhat too low.

5.8 Primary organic compounds: ethene (C₂H₄), ethane (C₂H₆) and propane (C₃H₈)

In most cases, the model underestimates the measured concentrations of the primary hydrocarbons, which indicates that the emissions are too low. The discrepancy is substantial at all altitudes, for example for C₂H₄ in Hawaii (Fig. 11), as well as C₃H₈ in the Arctic (Fig. 9) and in Bangor (Fig. 10). Calculated C₂H₆ is substantially lower than suggested by the observations at all four locations. In Mexico City (Fig. 12), the model rather successfully reproduces the vertical profile of C₂H₄ but underestimates C₃H₈ below 5 km of altitude. This last compound is well represented in Hawaii in the upper troposphere but is underestimated by the model below 7 km.

5.9 Secondary organic compounds: formaldehyde (HCHO), methanol (CH₃OH), acetone (CH₃COCH₃), ethanol (C₂H₅OH) and methyl hydroperoxide (CH₃OOH)

As should be expected from the underestimation by the reanalysis of the atmospheric concentration of the primary hydrocarbons, the model also underestimates the abundance of oxygenated organic species in the troposphere. This is the case in the Arctic (Fig. 9), where the abundances of formaldehyde, acetone and ethanol are underestimated by typically factors of 3 to 8. Methanol is too low by about 30 %. Large discrepancies are also found in Bangor (Fig. 10) where methanol and acetone are underestimated by a factor of 2 and methyl peroxide by a factor of 5. In Hawaii (Fig. 11), the concentration of formaldehyde is slightly underestimated in the middle and upper troposphere, but the discrepancy reaches a factor of 2 at 2 km of altitude. Methanol is underestimated by 30 %, but acetone and ethanol are underestimated by a factor of 2. The model is in better agreement with the observations in Mexico City (Fig. 12): this is the case for formaldehyde (except below 4 km where the calculated concentrations are a factor of 3 too low), methanol (except at the surface) and methyl hydroperoxide except below 4 km. Ethanol is underestimated by a factor of 2.

To summarize the discussion, we have qualified the degree of success of the reanalysis model versus the observational vertical profiles in the four regions of the world that are considered in the present study. The results, based on a subjective comparison between the vertical profiles derived from the CAMSRA and the profiles measured independently by airborne instruments, are presented in Table 6 for the altitudes of 6 km above the ground and at the Earth's surface, respectively. The symbols used in this table are the following: G for good agreement (bias < 10 %), O for overestimation by the reanalysis model (10 % < bias < 40 %) and U for underestimation (−40 % < bias < −10 %). Double symbols (i.e., OO or UU) indicate from a subjective analysis that the disagreement is large (bias > 40 %).

5.10 Concentration ratios

In order to analyze the performance of the reanalysis and to reproduce the observed relationships between different reacting species, we present and discuss the vertical distribution of the concentration ratio between photochemically coupled chemical compounds. In order to avoid the chemically and dynamically complex situation encountered in the boundary layer, we limit this analysis to results (models and observations) obtained above 4 km of altitude. We focus here on the NO∕NO₂, PAN∕NO₂, HNO₃∕NO₂ and HO₂∕OH concentration ratios (Fig. 13).

Figure 13Concentration ratios of NO∕NO₂, HO₂∕OH, HNO₃∕NO₂ and PAN∕NO₂ derived from aircraft measurements (black curves), control runs (blue curves), reanalysis (red curves) and simple equilibrium relations (except in the case of the PAN∕NO₂ ratio; green curves). The values are shown in the Arctic, Bangor, Hawaii and Mexico. Note that, in most cases, the blue and red curves cannot be distinguished.

Download

We first examine for the four locations considered in the present study (Arctic, Bangor, Hawaii and Mexico) the NO∕NO₂ concentration ratios derived from the aircraft observations of NO and NO₂, respectively, as well as the similar ratios produced by the control case (blue curves), reanalysis models (red curves) or derived from an approximative expression based on the photochemical theory of the troposphere (green curves). We note at all locations that the value derived from the reanalysis (with a detailed chemical scheme included) is in good agreement with the value derived from the simple photostationary expression:

where $J_{{\mathrm{NO}}_{\mathrm{2}}}$ (about 10⁻² s⁻¹ in the entire troposphere for a solar zenith angle of 45^∘) represents the photolysis coefficient of NO₂, and k₁ and k₂ are the rate constants of the reaction of NO with ozone and the hydroperoxy radical (HO₂), respectively (Burkholder et al., 2015). The symbol X accounts for the effects of additional conversion mechanisms of NO to NO₂. Note that, as the temperature and the ozone number density decrease with height in the troposphere, the NO∕NO₂ ratio tends to increase with altitude. In the lower stratosphere, the ratio is expected to decrease as the ozone concentration rapidly increases with height above the tropopause.

In the Arctic, the ratio derived from observations (typically equal to 1; see the black curve in Fig. 13) is about a factor of 2 smaller than the calculated ratio between 6 and 10 km of altitude. In Bangor, its value (about 2 to 3) is higher than the model calculations. Perhaps the most interesting point is the substantial discrepancy between the models and the observations in the upper troposphere of the tropics (Hawaii and Mexico). One notes, for example, that the observed ratio does not increase as expected from theory, and at 11 km, for example, the calculated ratio of close to 1 when derived from the observations reaches a value of the order of 4 or 5. Among possible causes for this discrepancy is an underestimation of the correction factor X due to reactions not considered in the models. Possible mechanisms include the reactions of NO with the methyl peroxy radical (CH₃O₂) and with BrO (Sasha Madronich, personal communication, 2019). CH₃O₂ plays a significant role in the NO to NO₂ conversion. The BrO radical is expected to affect the NO to NO₂ ratio if the BrO concentration becomes larger than 2–5 pptv. Another point to stress is the large uncertainty that results from dividing two mean concentration values to which substantial uncertainties are attached so that the stated ratio derived from mean observations may be subject to a large error.

Figure 13 also shows the concentration ratio between PAN and NO₂ and between HNO₃ and NO₂. In the first case, the ratios derived from the models (control run and reanalysis) are in fair agreement with the ratios derived from the measurements of NO₂ and PAN concentrations. The ratio decreases with height in the Arctic and Bangor but is relatively constant with height (typically 10–20), with some elevated values at some specific altitudes. In the case of the HNO₂ to NO₂ ratio, the differences between ratios derived from the models and the aircraft observations can be substantial. The control and reanalysis runs (blue and red curves) underestimate the ratio in the Arctic and in Bangor. The agreement is somewhat better in Hawaii and in Mexico, even though large differences exist at specific altitudes. These discrepancies can probably be explained by the role played by the heterogeneous conversion of nitrogen oxides to nitric acid, which depends on the chaotic behavior of clouds and aerosols in the troposphere. The green curve provides an estimate of the ratio derived from the following expression (assuming equilibrium) that ignores any heterogeneous conversion but is calculated using the observed values of OH:

Here, $J_{{\mathrm{HNO}}_{\mathrm{3}}}$ (about $\mathrm{6}\times {\mathrm{10}}^{-\mathrm{7}}$ s) is the photolysis coefficient for nitric acid, while k₃ and k₄ are the kinetic coefficients for the reactions between NO₂ and OH and between HNO₃ and OH, respectively (Burkholder et al., 2015).

Finally, we show in Fig. 13 the concentration ratio between HO₂ and OH, which is influenced by carbon monoxide, nitric oxide and ozone that, to a good approximation, can be expressed as

Here k₅ and k₆ refer to the reactions of OH with carbon monoxide and ozone, respectively, and k₇ and k₈ to the reactions of HO₂ with nitric oxide and ozone, respectively (Burkholder et al., 2015). The ratio derived from observations (black curves) follows the vertical distribution of the ratios derived by the model (reanalysis, red curve) and calculated by the above equilibrium relation with observed values of CO, NO and ozone (green curve). The value of the ratio decreases from about 100±25 at 4 km (all sites except the Arctic) to about 30–40 at 12 km in the tropics (Hawaii, Mexico) and to 10–20 at high latitudes (Bangor and the Arctic).