The mini-DOAS instrument records scattered skylight in the ultraviolet/visible/near-infrared wavelength ranges in nadir and limb direction . Here, solely the data collected in limb direction (telescope elevation angle 0°) are reported.

The interpretation of air-borne mini-DOAS observations requires the DOAS analysis of the measured skylight spectra, radiative transfer modeling of the observation conditions with a Monte Carlo model such as McArtim , and the conversion of inferred differential slant column densities (dSCDs) retrieved with the DOAS technique into VMRs using the scaling method . In this study, the focus is on limb geometry measurements of NO2, HCHO and HONO, which were performed during 25 scientific flights of the EMeRGe (e.g. https://acp.copernicus.org/articles/special_issue1074.html, last access: 10 April 2026, ) and CAFE-Africa (e.g. ) missions during 2017 and 2018.

The attribution of the determined SCDs to VMRs of the targeted gases in space and time in the atmosphere is performed using the scaling method (e.g. ). The scaling method relies on information about the radiative transfer inferred from co-measured or calculated absorption of a gas with a known concentration or extinction [P]i in an atmospheric layer i. Weighting factors, i.e. relative detection sensitivities of the targeted gas [X]i and the scaling gas [Y]i (further on called α factors), are determined by combining air mass factors calculated by the radiative transfer model McArtim and the chosen a priori profiles for both gases.

The radiative transfer model is provided the time and the geolocation of the measurements and in-situ temperatures and pressures provided by the aircraft's navigation and monitoring system, climatological aerosol profiles as well as a priori profiles of the target and scaling gas.

Climatological aerosol profiles are determined from the stratospheric aerosol and gas experiment (384 and 520 nm) instrument from the international space station and the lidar climatology of vertical aerosol structure (355 and 532 nm) light detection and ranging instrument, while parameterization of the single scattering albedo and Henyey-Greenstein phase function are also included.

The a priori extinction profiles of the O4 collisional complex are calculated from the oxygen concentration and the collisional absorption cross-section. The a priori profile of ozone is determined from in situ ozone measurements and ozone mapping and profiler suite satellite data. The a priori profiles of the target gases are taken from the EMAC or MECO(n) models, where available.

Previously, the sensitivity of inferred VMRs with respect to uncertainties related to the a priori profile was studied (see Fig. 1 in ), and it was found that after a few iteration steps (i.e. the inferred profile of the targeted gas in step i are used as a priori for the retrieval of step i+1), a priori profiles converge to a final profile. This is corroborated by another sensitivity study, an investigation of the erroneous retrieval of HONO VMRs in the free troposphere above a layer of intense air pollution in the boundary layer. It was found that the scaling method robustly avoids mis-attributing absorption from the boundary layer to higher altitudes as long as the a priori information captures the general shape of the trace gas profile (see Fig. ).

Furthermore, the scaling method converts a detection limit defined by the DOAS retrieval error into VMRs which vary with altitude. The detection limit for HONO for example ranges from 1 to 15 ppt from the boundary layer to the upper troposphere.

The precision of the scaling method is primarily limited by the signal to noise ratio of the DOAS retrieval of the target gas. Other sources of error include the determination of the SCD_ref of the scaling gas, differences between a priori and measured profiles, and misalignment of the telescopes during flight. For details see , .

The integration of spectra in the UV lasts 30 s on average – during which the aircraft moves at 100 ms-1 – while the mean path length at 360 nm increases with altitude. The retrievals of the mini-DOAS instrument represent averages over a volume, the horizontal area of which ranges from dozens to hundreds of square kilometers.

The interpretation and contextualization of the measurements of the mini-DOAS instrument require observations of complementary instrumentation operated on board the HALO aircraft, although the package of instruments varied between the different missions. Those instruments which were present for the EMeRGe mission as well as the CAFE-Africa mission are listed in Table , as well as those instruments which were present only for one mission or the other. Further details of the instruments are provided in the respective publications listed in the last column of Table .

In the absence of an in situ instrument which measures HONO, or satellite measurements thereof, the VMRs of HONO observed by the mini-DOAS instrument are compared to the simulations of atmospheric chemistry models. Model outputs are also compared to the measured HCHO and NO2 VMRs. These simulations are used to construct a priori profiles of the target gases for the scaling method. The two models used in this study are the EMAC and MECO(n) chemistry climate models. Neither model is suited for fine spatial (and temporal) scale comparison of parameters measured from the aircraft, in particular with the VMR ratios measured by our instrument near emissions or around the boundaries of air masses with different trace gas concentrations. This is not due to a deficiency of either model per se, but rather that the concentrations of the investigated gases may vary near strong sources of pollution on spatial and temporal scales which in these cases neither model resolves (see below). However, model predictions should still be broadly representative of atmospheric composition, and capture the general spatial distribution of the target gases in the free and upper troposphere.

The EMeRGe mission investigated the composition, transport and transformation of pollution plumes from mega-cities and major population centers. Airborne measurements of relevant atmospheric parameters, trace gases, and aerosols were made on board the HALO aircraft at different altitudes over Europe in July 2017 and the East China and South China Seas between the Philippines and Japan in spring 2018 (during the inter-monsoon period, which favors the outflow of pollutants from East Asia). These airborne observations were complemented by a suite of ground- and satellite-based measurements, as well as photochemical transport and chemistry climate modeling (e.g. EMAC, MECO(n), …) . The field observations concentrated on the characterization of different air mass types downwind from various emission sources (e.g., those of anthropogenic, biogenic, and biomass burning origin as well as background air). The transformation of the suite of trace gases and radicals as well as aerosol parameters (e.g., particle number, size distribution, and chemical composition) has been used to provide insights into chemical processing (and mixing) of these air masses during their atmospheric transport . Of particular importance are the measurements of peroxy radicals RO2*, which are strongly influenced by the OH produced from the photolysis of HONO . A detailed description of the objectives, instrument payload, and findings of the EMeRGe mission is found in publications of the ACP/AMT inter-journal EMeRGe special issue (https://acp.copernicus.org/articles/special_issue1074.html, last access: 10 April 2026), specifically in the EMeRGe-EU overview paper by .

During both EMeRGe phases, the measurement flights had a duration of 8 h on average. The take off was typically in the mornings and landings occurred in the afternoon, i.e. flights were exclusively during daylight. While the flight levels spanned measurement altitudes from a few dozen meters above sea level to up to 12 500 m, 72 % of the air masses analyzed were within the lowermost 4 km of the atmosphere, i.e. in the boundary layer and free troposphere. As a consequence of the altitude range and season, the ambient temperatures were mostly above 0 °C; the high ambient temperatures and associated cabin temperatures reduced the data coverage of the DOAS instrument during some flights. The measurement flights sampled large geographical areas, spanning continental Europe and East Asia.

Detailed flight tracks together with air mass tags (see Sect. ) are shown in Fig. . During the European deployments, most of the flight time was spent over land, in contrast with deployments in Asia, where much of the flight time was spent over the East China Sea and South China Sea. Various atmospheric conditions characterized each flight, such as the occurrence of thunderstorms in Southern Europe, as well as the presence of anthropogenic pollution plumes.

The CAFE-Africa (https://mpic.de/4130589/cafe-africa, last access: 10 April 2026) mission was based in Sal, Cape Verde and took place in August and September of 2018. The area of study was the tropical troposphere over the Atlantic Ocean and western Africa. Of the 14 scientific flights, 12 are analyzed here since the transfer flights are excluded. The scientific objectives of CAFE-Africa included the study of oxidation chemistry, thunderstorm effects, radiative forcing, and long-range transport of pollutants from biomass burning. The investigated region overlaps with the inter-tropical convergence zone, while the maximum flight altitude was around 15 km. The flight tracks are shown in Fig. .

The measurement flights took off in the mornings, landed in the evenings and were primarily conducted during daylight (except for the flight on 26.08.2018, which continued past sunset). Most of the flight time was spent at high altitudes, over the Atlantic Ocean. The ambient temperature was therefore usually well below 0 °C, enhancing the temperature stability of the mini-DOAS instrument.

During the CAFE-Africa mission, simultaneous measurements of OH, NO, and JHONO allow the quantification of gas phase HONO formation. Airborne measurements of HONO within the same region (and at similar altitudes) the following year, reported by , largely corroborate the HONO reported by this study.

The origin and composition of an air mass may determine the concentrations of trace gases sampled from the HALO aircraft. In keeping with the scientific objectives of the EMeRGe mission, the air masses probed are characterized with plume tags, which are interpolated to a one-second resolution from the volatile organic compound (VOC) measurements of the HKMS instrument . Elevated VMRs of acetonitrile (above 145 ppt) are indicative of biomass burning influence, whereas VMRs of benzene (above 19 ppt) are indicative of anthropogenic pollution. Across all flights, 34 % of air masses observed during the EMeRGe missions are tagged with anthropogenic influence, 14 % contain signatures of biomass burning, and the remaining 51 % are assumed to be otherwise aged background air. These percentages vary from flight to flight and across mission phases. As expected, less biomass burning influenced air was found during the deployments in Europe, compared to those probed over Asia . Since the HKMS instrument was not part of the CAFE-Africa mission, the same thresholds were applied to the acetonitrile measurements of the MMS instrument to differentiate biomass burning (BB) air masses accordingly . Fine and coarse aerosol surface area (SA) and volume (V) data calculated from the measurements of the Sky-OPC instrument may also be used to identify dust events .

The measurements reported here are derived from several thousand limb spectra successfully recorded with the mini-DOAS instrument. Rarely, there are periods during some flights when skylight could not be collected, or when measured skylight spectra cannot be analyzed. The former includes highly variable cloud conditions, when the aircraft flew inside or next to bright clouds, since then the spectrometers tend to become over-saturated (in the post-flight analysis such periods are identified by inspecting images captured with the IDS uEye camera). The latter occurs when the detector and/or spectrometer temperature increase beyond approximately 4 °C, since increasing detector temperatures increase the dark current and changing spectrometer temperatures degrade the imaging of the spectrometers (by broadening the instrument's spectral response function). Temperature stability for some flights lasted up to 9 h, while when flying for longer periods at higher ambient temperatures (i.e. at low altitudes), the stable measurement interval lasted only 3 h in some cases (particularly during the EMeRGe mission). Spectra recorded during sharp turns of the aircraft are also discarded from analysis. Communication problems between the BAHAMAS and mini-DOAS instruments during four flights of the EMeRGe mission prevented the live alignment of the telescopes with the horizon, rendering the correct attribution of observed absorption to a particular layer in the atmosphere practically impossible. Therefore, the affected flights on 26 July 2017, 28 July 2017, 22 March 2018, and 3 April 2018 are excluded from the analysis.

Unfortunately, not only failure or malfunctions of the mini-DOAS instrument restrict our analysis, but also the availability of the necessary data measured by the complementary instruments operated on board the HALO aircraft. For example, during the EMeRGe mission, measurements of VOCs made by the HKMS instrument (and consequently the air mass characterizing plume tags) are not available on 17 July 2017, while RO2* measured with the PERCEAS instrument is not available on 17 March 2018. During the CAFE-Africa mission, measurements of NO, OH, and HO2 are unavailable on 10 August 2018, while measurements of HNO3 with the CIMS instrument are not available for the first four flights of the mission on 10 August 2018, 12 August 2018, 15 August 2018, and 17 August 2018.

The HONO VMRs retrieved from the mini-DOAS observations made on board HALO are high in the PBL and free troposphere (FT) (up to 150 ppt) for every flight of the EMeRGe mission (see Fig. ) compared to our expectations from known homogeneous sources (Reactions R1 to R3). In addition, in the upper troposphere (UT), mixing ratios of up to 75 ppt were observed during the two flights of the EMeRGe-Asia mission which probed those altitudes. Comparatively little HONO is observed in the free troposphere (FT) (less than 50 ppt) in all missions. In comparison to the EMeRGe mission, where the flight tracks passed through highly polluted air masses, during the CAFE-Africa mission, which took place over the Atlantic Ocean, lower HONO VMRs are retrieved in the FT. Nevertheless, some tens of ppt are still observed within the MBL. In the UT, the HONO VMRs are elevated: more than 100 ppt during all flights of the CAFE-Africa mission. In summary, the HONO VMR measurements in EMeRGe-EU, EMeRGe-Asia and CAFE-Africa are consistently found to be in excess relative to the expectations based on the known gas phase formation mechanisms and thus model predictions (see below).

, , , , measured HONO from aircraft and a Zeppelin in disparate regions: over a forested region in North Michigan, over the Po Valley of Northern Italy, in a convective cloud over the Caribbean Sea, over the North Atlantic Ocean, over the southeastern US, and in the remote Atlantic troposphere, respectively. Given the individuality of each set of HONO observations, our measurements compare reasonably well, except for some peculiarities addressed below.

Figure  compares the HONO measured by the mini-DOAS instrument with the predictions of the EMAC and MECO(n) models. So far the EMAC and MECO(n) simulations only include the known gas phase formation mechanisms of HONO (Reactions  to ).

For EMeRGe-EU, the EMAC model predicts at most 35 ppt of HONO along the flight track of the HALO aircraft in the boundary layer. The MECO(n) model, by comparison, predicts up to 60 ppt of HONO along the HALO flight track. Neither model predicts appreciable VMRs of HONO in the FT. During EMeRGe-Asia, the EMAC model predicts at most 16 ppt HONO in the PBL along the flight track. The MECO(n) model, by comparison, predicts up to 127 ppt of HONO there. While the MECO(n) model predicts only 2 ppt of HONO in the UT, the EMAC model predicts up to 10 ppt of HONO at 12 km altitude for the HALO flights from Taiwan towards Japan.

During both phases of EMeRGe (over Europe and Eastern Asia), the observed HONO VMRs exceed both models' predictions throughout the probed altitude ranges (see Fig. ). During the European phase, the observations are in excess of model predictions by at least a factor of two, and up to a factor of five. During the Asian phase, the excess relative to predictions is model and altitude dependent and may exceed one order of magnitude. For the CAFE-Africa mission, only the EMAC model simulations are available for comparison. The retrieved HONO VMRs are here, again, much larger than the model predictions. The EMAC model correctly predicts the general shape of the retrieved HONO profiles, but on average predicts VMRs in the single digits (ppt), and never more than 18 ppt along the flight track of the HALO aircraft (at 12.5 km altitude).

Since there is general agreement between model predictions and observations of the mini-DOAS instrument for HCHO and NO2 (see Figs.  and in the appendix), the discrepancies between model predicted HONO and the observations of the mini-DOAS instrument are unlikely to be due to the model resolution, instrumental or methodological issues. Rather, HONO formation in the troposphere (especially the UT) may act via a mechanism (or mechanisms) which are altogether not represented in the models.

While during the CAFE-Africa campaign, in situ measurements of OH, NO, and JHONO are available to quantify [HONO]PSS, the measured HONO is still in excess of what would be expected based on those measurements (see below).

The excess HONO VMRs observed with the mini-DOAS instrument require explanation. In the low-NOx marine boundary layer (MBL), our observations largely corroborate previous HONO measurements performed with another technique (see ), and thus also serve to validate both sets of measurements (see Sect. ). The latter provides consistent evidence on the importance of particulate nitrate photolysis as the cause for observed HONO in the MBL (see Sect. ). In the polluted PBL and FT more broadly, we investigate heterogeneous formation of HONO (Sect. ). In the cold upper troposphere (UT), we suggest that a heretofore unknown gas-phase mechanism may produce HONO (Sect. ).

Within the low-NOx regime of the marine MBL, a growing body of research attempts to account for observed HONO VMRs by invoking the photolysis of particulate nitrate . While the photolysis frequency of particulate nitrate is not measured directly, it has been argued that it is possibly up to two orders of magnitude larger than the photolysis frequency of gaseous nitric acid . The enhancement factors (EF) for nitrate photolysis, defined as 2EF=JNO3-JHNO3 which are derived from field measurements have been significantly different from those determined in laboratories . Recently, speculated that this discrepancy may arise from a saturation effect, whereby the EF decreases with increasing particulate nitrate concentration in the aerosols, although details of the underlying processes are unclear. Here, we follow the approach of and construct the photolysis EF necessary to explain our HONO observations using measured quantities from around the Cape Verde Islands during the CAFE-Africa mission. In the low-NOx environment of the MBL, HONO production may be assumed to be largely driven by particulate nitrate photolysis. Under this assumption, as well as the assumption of a photo-stationary state, the EFs can be derived from the following: 3EF=JHONO⋅[HONO]JHNO3⋅[pNO3-]. Here, we only consider the HONO production channel from the photolysis of particulate nitrate.

During CAFE-Africa, the C-ToF-AMS instrument measured NO3- in sub-micron aerosol, which is unlikely to constitute the whole aerosol nitrate load, due to an unknown fraction tied in coarse mode aerosols . Unfortunately, even though information on the aerosol mass in the micron range is available from the SKY-OPC instrument, the nitrate fraction across different size regimes cannot be assumed to be constant and therefore total particulate nitrate cannot be inferred. However, other quantities (NO, NO2, HONO, SAtotal, and JHNO3) measured from the HALO aircraft during the CAFE-Africa mission are largely in range of and thus corroborate the measurements of for the MBL around the Cape Verde islands in summer.

Assuming that either (a) all aerosol nitrate resides in the sub-micron aerosols or that (b) only a fraction of total nitrates are found in the sub-micron aerosol modulates the resultant EFs (panel a versus panel b in Fig. ).

In both cases, a decrease in EFs with the particulate nitrate concentration is observed, in agreement with the findings of . Further, a more consistent picture arises compared to the findings of when coarse mode nitrate is taken into account (panel b in Fig. ). The missing HONO source strength and rate of particulate nitrate photolysis also then match better with those observed by and .

Moreover, the degree to which particulate nitrate photolysis can contribute to HONO formation can also be inferred from HNO3 as measured by the CIMS instrument and the photolysis frequency measured by the HALO-SR-A instrument. Note that the CIMS instrument was designed to measure PAN rather than nitric acid and (through use of a thermal dissociation inlet) not only measures gaseous nitric acid, but also detects some particulate at the same mass-to-charge ratio (62 and 190) if the nitrate is thermally labile (i.e. ammonium nitrate or HNO3 weakly bound to black carbon).

If all the HNO3 measured by the CIMS instrument were actually in particulate form rather than gas phase, the resulting high levels of particulate nitrate would mean that no enhancement in the frequency of particulate nitrate photolysis (relative to the frequency of gaseous nitric acid photolysis) would be necessary to explain our HONO observations. However, this is unlikely, as the HNO3 detected by the CIMS instrument exceeds the particulate nitrate measured by the C-ToF-AMS instrument by orders of magnitude, and the two are not strictly correlated.

Nevertheless, it can be seen that measured HNO3 concentrations only fit into the overall picture with EFs which reach unity under the assumptions that the measured HNO3 is actually particulate nitrate, and that the photolysis of particulate nitrate exclusively produces HONO. Otherwise, the quantum yield for HONO formation by HNO3 photolysis is much less than one, and it is unlikely that it contributes to re-noxification (or HONO formation) in the MBL.

The air masses sampled during EMeRGe-EU were primarily confined to the PBL and FT, particularly to less than 6 km altitude . EMeRGe-EU is characterized by mostly continental background air, with some instances of anthropogenic influence ; many of the air masses sampled were in high-NOx environments. The HONO VMRs observed in the PBL and FT during the EMeRGe-EU mission exceed predictions of the EMAC and MECO(n) models, which are based on gas phase production. Therefore, we next consider possible heterogeneous sources of HONO. Like the EMeRGe-EU mission, the -Asia mission was largely confined to the PBL and FT, with exceptions only during the final two flights leading from Taiwan towards Japan at high altitudes. The air masses sampled were high-NOx environments, and there was regular detection of benzene from anthropogenic plumes. In addition, the air masses sampled during EMeRGe-Asia were often influenced by biomass burning . Here, as before, HONO VMRs observed with the mini-DOAS instrument exceed model simulations. This excess HONO certainly requires heterogeneous sources beyond the photolysis of particulate nitrate.

In order to investigate if either (a) a specific parameter directly or (b) which of the many proposed HONO formation mechanisms listed in Table  correlates well with the observed HONO VMRs, for both options the Spearman correlations are investigated (Fig. , left column for case a and right column of case b). For case (b) the reactants from each formation mechanism are multiplied and their product is correlated with the observed HONO (Fig. , right column). Correlations are determined with the Spearman correlation coefficient rather than the Pearson coefficient, to account for the case that the relationship is non-linear (for example due to saturation effects). While the HONO formation rate necessary to match its loss via photolysis is what should be correlated with the reactants of these mechanisms, many include photolysis frequencies themselves. Therefore, the correlation analysis is performed against the retrieved HONO VMRs to avoid a correlation between photolysis frequencies measured by the HALO-SR-A instrument. Similarly, the correlations are determined between VMRs instead of concentrations to avoid correlations as a function of atmospheric density. Several of the in situ instruments have time resolutions of only 15, 30, or 60 s, so for each spectrum recorded by the mini-DOAS instrument, all data reported by the in situ instruments are averaged over the integration time of the mini-DOAS spectra (30 s). This down-sampling avoids interpolation or repeated values, which may lead to spurious or diluted correlations, respectively.

The observed HONO VMRs may however also be correlated directly with other gases and atmospheric parameters simultaneously observed on board the HALO aircraft. The trace gases retrieved with the mini-DOAS usually share a strong correlation (ρ>0.7). While the correlation between HCHO and HONO is not necessitated by their photochemical relationship, also observed a strong correlation of HONO with NO2. Since most of the heterogeneous sources of HONO proposed in Table  require NO2 as a reactant, the correlation between HONO and NO2 is to be expected. However, any correlation between the observed HONO and some other gas, parameter, or the product of the reactants of some hypothetical formation mechanism should ideally correlate more strongly than this threshold, i.e. the correlation with NO2 (0.7).

Furthermore, not all species listed in Table  were measured during the EMeRGe mission (for details see ). Indeed, no instrumentation to detect nitro-phenols was available for any of the three missions, so Mechanism 2 is left out of this analysis entirely. Nitric acid data is unavailable during the EMeRGe mission, therefore a proxy (NOz) is constructed by subtracting NOx (NO + NO2) from the NOy measured by the AENEAS instrument. OH was measured during the CAFE-Africa mission but not during both EMeRGe missions, precluding analysis of Mechanism 1 for the latter, while measured RO2* may only serve as a proxy for HO2 during the EMeRGe missions.

The observed HONO correlates with several other simultaneously measured species, as well as with the formation mechanisms proposed in Table  (see Fig. ). Unsurprisingly, the proposed formation mechanisms are correlated to varying strengths with the observed HONO. The strength of the Spearman correlation coefficient varies with air mass type (anthropogenic, biomass burning, background), so filtering the lower tropospheric EMeRGe data further according to air mass type yields different correlations.

Across the EMeRGe mission, in high-NOx air masses, nearly every mechanism correlates with the observed HONO. Separating the observations according to their air mass tags reveals that some correlations are weaker in the biomass burning plumes probed during EMeRGe-Asia and in anthropogenic air during EMeRGe-EU (see Fig. ). The proposed formation mechanisms all have some humidity dependence, since water vapor is likely a necessary, but not sufficient, component of the formation of HONO in the PBL and FT.

Generally, Mechanisms 5, 7 and 12 are correlated best with the observed HONO in all probed environments, while Mechanisms 9, 10 and 11 only correlate with the observed HONO in the polluted high-NOx air masses during the EMeRGe mission. The lack of correlation between the observed HONO and Mechanisms 8 and 13 may arise from underestimation of measured particulate nitrate and gaseous nitric acid. Otherwise, the use of NOz as a proxy for HNO3 for the EMeRGe mission may obscure any correlation. The dependence of the EF for the photolysis of particulate nitrate on the nitrate load (see Sect. ) may also confound a simple monotonic relationship between the observed HONO and the components of Mechanism 13. The observed HONO is correlated with the presence of NO2, daylight, and some catalytic surface (i.e. soot, mineral dust, organics) in all air masses, as well as with haze aerosol water reactions in polluted air masses and to a lesser extent with the photolysis of nitrates in pristine air masses.

Previous studies have found similar relationships between NO2, aerosol and HONO. found that the heterogeneous reaction of NO2 on aerosols produces HONO. The photolytic nature of heterogeneous HONO production has also been reported previously: found a HONO source from NO2 requiring sunlight. , and describe photo-enhanced heterogeneous conversion of NO2 to HONO on aerosol surfaces. found during eclipse conditions that the HONO source must be photochemical. speculated that the conversion of NO2 on BC enhanced by light may be a likely heterogeneous source of HONO, along with the photolysis of particulate nitrate.

This analysis is limited by the spatial and temporal resolutions of the mini-DOAS instrument, as well as those of the in situ instruments: the necessary down-sampling of parameters reported by in situ instruments may obscure correlations. Chemical interferences of the in situ instruments also obscure a precise attribution of observed HONO formation to a particular mechanism or even phase (Mechanisms 8 and 13). The suitability of proxies also limits the scope of the analysis, e.g. whether black carbon mass (or number) is a suitable proxy for the presence of soot, particularly fresh soot (Mechanism 5). NOz may be also a poor proxy for HNO3 (Mechanisms 8 and 9), while although HCHO is indicative of active VOC chemistry, it does not represent total VOCs (Mechanism 9). Moreover, volume, mass, and number of particles with a diameter larger than 500 nm are the only quantities available to determine the presence of dust (Mechanism 7).

We also lack any measurements of aerosol pH, while the aerosol water content is represented only by relative humidity. These variables are not directly interchangeable, but instrumentation to observe aerosol water content and pH directly were not present, and attempts to model aerosol water content and pH with ISORROPIA led to nonphysical results. Moreover, the amount of particulate ammonium is not synonymous with that of gas phase ammonia (Mechanism 10). Nor does the amount of aerosol sulfate equal that of gas phase SO2 (Mechanism 11). Indeed, the C-ToF-AMS instrument analyzes only non-refractory sub-micron aerosol and thereby presents an incomplete picture of the aerosol composition; a more complete aerosol chemical composition would be necessary to investigate Mechanisms 10, 11, 12, and especially 13 in more detail.

Moreover, the pH of haze is not well understood , though sub-micron aerosol is generally acidic . Aerosol acidity is lower in China than in Europe , in large part due to the partitioning of gas phase ammonia and particulate ammonium . Without measurements of these quantities (aerosol pH, gas phase ammonia), we can only observe the output of the aerosol chemistry. Further, the products of aerosol nitrate photolysis seem to also be pH dependent .

describe modeling of heterogeneous reactions on surfaces producing HONO, and reports improved model performance for O3 and PM_2.5. In another modeling study, found that HONO produced by heterogeneous reactions increased the concentration of OH by a factor of two, increased aerosol nitrate via the conversion of NO2, and increased SOA formation via reactions of OH with VOCs (see also ). Heterogeneous HONO formation mechanisms have also been implemented in a chemistry-climate model , where the heterogeneous formation reactions were found to contribute more to HONO formation than direct emissions, particularly those on aerosol surfaces. Heterogeneous HONO formation mechanisms in the LT then represent a critical subject in the understanding of tropospheric oxidation capacity.

In summary, because of the lack of data and/or the weak correlations inferred from the relevant parameters, we cannot firmly conclude on or reject any of the proposed heterogeneous HONO formation mechanisms listed in Table . Further, it is also likely that some HONO formation mechanisms act in parallel, though at varying strengths over time, which complicates deciphering the relevant HONO mechanisms from field data.

However, the field data easily allow inferring the necessary source strength for closing the excess HONO budget. The necessary source strength reaches up to 0.3 ppbh-1 in the MBL, up to 1 ppbh-1 in the polluted PBL, up to 0.6 ppbh-1 in the FT and ranges from 0.3 to 1.6 ppbh-1 in the UT. This may represent a significant modification to the oxidation capacity of the PBL and the lower part of the FT. Previously reported daytime heterogeneous HONO sources in the NOx polluted atmosphere include those reported by (0.77 ppbh-1), (1 ppbh-1), (0.64 ppbh-1), and (0.65 ppbh-1), albeit at lower altitudes.

HONO VMRs in the tropical UT inferred from the mini-DOAS measurements during the CAFE-Africa mission are largely more than (about a factor of five) what may be expected according to the known gas phase formation mechanisms and what is predicted by the EMAC model. While the presence of enhanced NOx and HOx from lightning are likely at these altitudes , the in situ measurements of NO and OH by the MPIC and of JHONO by the HALO-SR from on board the HALO aircraft allow us to quantify the gas phase formation of HONO and thus excess HONO (see Fig. ). Meanwhile, heterogeneous formation of HONO by one of the processes listed in Table  can largely be excluded based on the low aerosol surface and the necessary HONO formation rates which are in the range of hundreds of ppth-1.

Unexpectedly high HONO SCDs have also previously been observed using DOAS measurements in the limb direction from a balloon in the vicinity of a cumulonimbus cloud reaching the tropopause over Northeastern Brazil on 13 June 2005, but due to some clouds within the line of sight, [HONO] could not be inferred . Further, reported increased amounts of HONO (∼ 160 ppt) (and of HCHO and NOx) in a thunderstorm cloud probed by the CARIBIC flying laboratory (Civil Aircraft for the Regular investigation of the atmosphere based on an Instrument Container) over the Caribbean Sea in August 2011. Recent studies highlight that oxidants and indeed HONO may be produced by lightning. Such extreme HONO production events in the vicinity of thunderstorm clouds may explain the variable HONO VMRs retrieved by the mini-DOAS at constant altitude, given the averaging volume of the scaling method compared to the in-situ measurements of NO, OH, and JHONO.

In contrast, a preliminary analysis of spectra collected in polar air-masses in the low-NOx UT indicates only 15 ppt of HONO, an order of magnitude less than the VMRs observed during CAFE-Africa. The excess HONO observed in the UT during CAFE-Africa as well as EMeRGe-Asia (see Fig. ) then indicates the necessity of sufficient NOx precursors.

Another indication of the present deficit in our understanding of the coupled NOx and HOx cycles in the UT comes from two findings. First, it has been known for some time that in the UT, the measured (Leighton) ratio NO2/NO is often much larger than modeled when accounting for all known NO oxidants . Second, also based on measurements of OH and HO2 (or HOx in the UT at twilight), speculated on a photolytic pathway for HO2 production by peroxynitric acid (HNO4) photolysis in the wavelength range 650≤λ≤1250 nm.

Here, we suggest and investigate in some detail another explanation to reconcile our findings and the findings listed above, i.e. the existence of peroxynitrous acid (HOONO) in the cold UT, a potential intermediate candidate to form HONO and a so far overlooked species in the coupling of the NOx and HOx cycles.

Based on the suggestion of that peroxynitrous acid (HOONO) may be present in the UT, we investigated its potential role to explain (a) our observation of excess HONO, (b) help to close the gap between measured and modeled NO2/NO and (c) provide a source for additional HO2 at twilight in the UT.

Unfortunately, to date there are no reported measurements of HOONO in the atmosphere, but there are a wealth of experimental and theoretical studies on HOONO available, from which some information can be gained for our study . Unfortunately, most studies involve warmer (ambient) temperatures than relevant for the upper troposphere ≤220 K, which at present may limit a further quantification of the role HOONO may play in the UT.

Given the body of information already available on HOONO, there are several open questions regarding its potential role in UT photochemistry: (1) which reactions produce and destroy HOONO in the cold UT? (2) what are their temperature and pressure dependencies? (3) how much HOONO can be expected to be found in the cold UT? (4) may photochemical reactions of HOONO with oxidants efficiently produce HONO?

Accordingly, in the following we briefly review several theoretical and experimental studies of HOONO to determine what is known or controversial about the formation of HOONO in the atmosphere (for a possible reaction diagram see Fig.  in the appendix).

From theoretical and laboratory studies, it is known that HOONO forms in a side channel (8 %) of the well studied reaction of OH and NO2 which otherwise forms nitric acid : R4OH+NO2+M→HOONO+M Moreover, suggested that again in a side channel (or as an intermediate) the reaction of HO2 and NO into OH and NO2: R5HO2+NO→OH+NO2 may not only produce nitric acid, R6HO2+NO+M→HNO3+M, while ab initio and master equation studies suggest that Reaction () may proceed via HOONO as an intermediate. R7HO2+NO+M→HOONO+M These reactions are summarized in Fig.  in the appendix.

While unimolecular thermal decay is rapid at room temperatures, under the temperature and pressure conditions of the UT, the loss coefficient for thermal decomposition recommended by the IUPAC is 10⁻⁶ s-1 . While such a slow decay could lead to some 80 ppt of HOONO in the UT, this is very much an upper bound and will be reduced by UV photolysis and reaction with OH .

Of note is that since most if not all laboratory studies of HOONO were conducted at room temperature, the short lifetime of HOONO may have obscured details of its unimolecular decay, unlike the information provided by theoretical studies. However, these theoretical studies suggest that in the cold UT, the known thermal decomposition of HOONO into its products OH and NO2 may take up to 14 d, and therefore sizable amounts of HOONO would build up in this part of the atmosphere.

More recent studies also calculated the photolysis frequency of HOONO in the IR or UV. It was found that the lifetime of HOONO against photolysis may be limited to 45 h in the IR and 30 min in the UV .

Noteworthy is also, that neither unimolecular decay nor photolysis of HOONO would produce HONO, since besides being thermo-chemically unfavorable, it would require a rearrangement of the host molecule.

Further, since all reactive nitrogen may not build up as HOONO, it must be removed from the UT by either photolysis, or oxidation or both (see below). However, unless the photolysis rate of HOONO proceeds apace of the HONO photolysis rate, it cannot explain our HONO observations.

Instead, we further discuss thermo-chemically favorable loss mechanisms of HOONO, specifically three reactions which on paper lead from HOONO to HONO.

In order to investigate the steady state abundance of the relevant species (HOONO, HO2, NO, NO2, HONO, …) from which the required reaction rate coefficients for both the formation and destruction of HOONO can be estimated, we use on board measured photolysis frequencies and VMRs of OH, NO, HO2, NO2, HONO, and O3 .

By considering a PSS, we quantify the reaction rate coefficients needed for the formation of relevant amounts of HOONO and oxidation into HONO at UT temperatures. From the known HONO destruction rate (JHONO [HONO]) of hundreds of ppth-1, we can determine the required production rate of HONO and hence the production rate of HOONO (k(R7) [HO2] [NO] + k(R4) [HO] [NO2]) and finally the reaction rate with an unknown oxidant (X) leading to HONO.

In consequence, the necessary production rate of HONO is JHONO⋅[HONO]=k(R7)⋅[HO2]⋅[NO]4+k(R4)⋅[OH]⋅[NO2]5=kX⋅[X]⋅[HOONO] Since in the UT, [HO2] is much more abundant than [OH], the reaction of OH with NO2 can be discarded in this context.

In the following, we consider three potential oxidants: O3, OH, and NO (=X), of which the reactions with HOONO are all exothermic (see Table ). R8HOONO+O3→HONO+2⋅O2R9HOONO+OH→HONO+HO2R10HOONO+NO→HONO+NO2

In the absence of kinetic data or quantum chemical calculations regarding the reaction of HOONO with X and by rearrangement of Eq. (), we estimate the necessary reaction rate coefficients as a function of HOONO, for each JHONO⋅[HONO][X] (see Fig. ).

It is unlikely that the reaction of HOONO with OH may explain our HONO observations (see Fig. ), since the necessary reaction rate coefficient exceeds the maximum possible gas phase reaction rate coefficient for most measurements of OH, unless more than 1 ppb HOONO is assumed (which would often exceed the NOy budget in the UT ).

Meanwhile, the necessary reaction of HOONO with NO could explain a HONO source term if HOONO is found in the tens of ppt, as is predicted by , and O3 is abundant enough to explain a potential HONO source term, provided that HOONO exists only in the parts per trillion. However, both reactions would have a significant effect on the nitrogen and ozone budgets of the UT, which for ozone is unlikely based on field observations. Here, the necessary reaction of HOONO with O3 would create an unlikely several ppb per day loss term for O3 in the UT (0.2ppts-1⋅43200s≈9ppbd-1), which is not observed . Also, Reaction () would require a rearrangement of intramolecular (bonded) O atoms through potentially large energy barriers, which is rather unlikely. Both arguments practically exclude Reaction ().

The proposed reaction of HOONO with NO would produce NO2, creating a net-zero effect on the nitrogen budget by substituting Reactions () and () for Reaction (), followed by the photolysis of HONO into OH and NO.

In this way, HOONO would act as a reservoir of NO2 (and HOx), biasing atmospheric measurements of NO2 at temperatures sufficient to thermally dissociate HOONO (see ). Since OH would be recycled in the photolysis of HONO, the formation of HOONO and reaction with NO would also not have an impact on HOx in the UT, but HOONO would simply serve as a temporary reservoir for OH.

Figure  indicates plausible pathways for the production of HONO from HOONO. However, there remain some open questions:

Past laboratory studies of the HO2 + NO reaction have been performed at or near room temperature , where HOONO would thermally decompose faster than the time frame given by the experiment, which would preclude HOONO detection. Further, the presence of NO in the reaction chamber would potentially destroy HOONO. On the other hand, only measure some of the relevant species, precluding the detection of intermediates entirely. To what extent could the formation/presence of HOONO have been overlooked in these experiments? To date, only conducted experiments at these cold temperatures of the UT, and their results remain uncorroborated.