Estimates of free-tropospheric NO 2 and HCHO mixing ratios derived from high-altitude mountain MAX-DOAS observations in the mid-latitudes and tropics

In this study, mixing ratios of NO 2 (X NO2 ) and HCHO (X HCHO ) in the free troposphere are derived from two Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) data sets collected at Zugspitze (2650 m a.s.l., Germany) and Pico Espejo (4765 m a.s.l., Venezuela). The estimation of NO 2 and HCHO mixing ratios is based on the modified geometrical approach, which assumes a single-scattering geometry and a scattering point altitude close to the instrument altitude. Firstly, the horizontal optical path length (hOPL) is obtained from O 4 differential slant column densities (DSCDs) in the horizontal (0°) and vertical (90°) viewing directions. Secondly, X NO2 and X HCHO are estimated from the NO 2 and HCHO DSCDs at the 0° and 90° viewing directions and averaged along the obtained hOPLs. As the MAX-DOAS instrument was performing measurements in the ultraviolet region, wavelength ranges of 346-372 nm and 338-357 nm are selected for the DOAS analysis to retrieve NO 2 and HCHO DSCDs, respectively. In order to compare the measured O 4 DSCDs and moreover to perform some sensitivity tests, the radiative transfer model SCIATRAN with adapted altitude settings for mountainous terrain is operated to simulate synthetic spectra, on which the DOAS analysis is also applied. The overall agreement between measured and synthetic O 4 DSCDs is better for the higher Pico Espejo station than for Zugspitze. Further sensitivity analysis shows that a change in surface albedo (from 0.05 to 0.7) can influence the O 4 DSCDs, with a larger absolute difference observed for the horizontal viewing direction. Consequently, the hOPL can vary by about using the 346-372 nm (338-357 nm) fitting window. The estimated monthly values of X NO2 (X HCHO ), averaged over these hOPLs during clear sky conditions, are in the range of 60-100 ppt (500-950 ppt) at Zugspitze and 8.5-15.5 ppt (255-385 ppt) at Pico Espejo. Interestingly, multi-year averaged monthly means of X NO2 and X HCHO increase towards the end of the dry season at the Pico Espejo site, suggesting that both trace gases are frequently lifted above the boundary layer as a result of South American biomass burning.

In this work, MAX-DOAS data sets from observations at two mountain locations are analyzed to obtain NO2 and HCHO mixing ratios in the free troposphere. The analysis is based on a modified geometrical approach proposed by Gomez et al. (AMT, doi:10.5194/amt-7-3373-2014), which assumes a single scattering geometry and a scattering point altitude close to the instrument. The manuscript is well written and provides information on species that have been little studied. Especially the long period of time analyzed make this study interesting. I recommend this manuscript for publication in ACP after minor revisions.
Minor comments: -The field of view of the instrument is not mentioned at all in the paper. This has to be taken into account specially when analyzing data from Pico Espejo.
We have now added some information about the instrument's field of view and added two references for more information about the MAX-DOAS system: "Scattered sunlight entering the telescope, either from the zenith or horizon window, is focused by a lens to reduce the field of view before it reaches the optical fibre mount. During the instrument's operation at the two measurement stations, a field of view with an opening angle of ~1° was achieved (Oetjen, 2009 andPeters, 2013). Consequently, the signal in the horizontal path might be slightly affected by the contribution of trace gas absorption at lower altitudes (up to 500 m below the measurement stations at the end of the hOPL). Nevertheless, the mixing ratios as presented in Sects. 6.3 and 6.4 for NO2 and HCHO, respectively, are still considered to be representative for the free troposphere." -I think Fig. 1 does not add more information than the given in the text. It may be removed. Or, is there an estimation/equation to add?
We partly agree with this comment. However, as we have used these two scenarios for the radiative transfer simulations, and refer two this figure when describing the two scenarios in the text, it might be useful for the reader. We would prefer to keep this figure in the manuscript, although it does not include any equation.
-The symbol for degrees (°) by describing elevation angles is missing in this new version.
This change was introduced during typesetting. There is a symbol for degrees (°) always only after the last value (e.g. 90°). This scheme can also be found in other ACP publications, for example in Gomez et al. (2014).
-Is there any reason why could be or should be BrO included in the HCHO analysis? (apart from the obvious one that BrO absorbs in this spectral range) It is common to include BrO in the HCHO analysis (e.g. Roscoe et al. (2010)) as there is spectral interference between these two species and the presence of BrO in the free troposphere cannot be excluded.
In addition to the reviewers' comments, we have performed some minor changes: -In the ACPD version, References from Table 2 are not included in the reference list. We have now added them to the reference list.
Author's response to comments by referee #2 We would like to thank the reviewer for his / her useful comments.
MAXDOAS data from two high mountain stations at mid and tropical latitudes are analysed to obtain estimations of the background concentrations of NO2 and HCHO in the free troposphere. The analysis makes use of the novel technique MGA extended toward the UV spectral region. Radiation data are compared with synthetic ones to evaluate the accuracy of the measurements and results are discussed considering the aerosol loading (AOD) and the influence of the biomass burning in the area. Results provide new and additional information on the free troposphere minor species chemically active, a region where data are scarce. The manuscript is clearly written and figures are illustrative. I recommend the article for publication after addressing the comments below.

Specific comments:
-The applied technique is quite sensitive to the amount of aerosols present in the air. However, there is little information in the paper on how this has been treated in the data analysis. AOD data based on MODIS (in the visible?) show mean values over 0.2 on 5 out of the 8 months considered in the study. In such conditions the errors of the approach increases notably compared to a Rayleigh atmosphere. In page 31795, lines 10-12 lower limits for considering too much aerosol loading at each spectral range is established. How are these limiting paths calculated?. Is there any "visibility" device at the stations to correlate with the obtained paths? Have the MAX-DOAS data themselves used to retrieve aerosols as part of the rejection criterion? A more detailed description on filtering criterion concerning the atmospheric visibility would be needed. If data with AOD larger than 0.1 passed the filter, it would be useful also to estimate the error in the computed paths.
We agree that aerosols play an important role in this type of measurements. The AOD values are obtained from the MODIS instrument and represent extinction coefficients integrated over a vertical column. As most of the aerosol is expected to be found in the boundary layer, let's assume 80% (see Gonzi et al. (2015) for typical biomass burning injection heights), the values are of course not representative for the level of the measurement instruments. They are too high. If we follow the recommendations made by Gonzi et al. (2015) than we can assume that AODs at the station levels, at least for Pico Especjo, are lower than 0.1. We have added a discussion on this comment: "For example, Gonzi et al. (2015) have estimated biomass burning injection heights using active fire area and fire radiative power from MODIS data in combination with a parameterized plume rise model. They found that 80% of the injections remain within the local boundary layer. Consequently, trace gases and aerosols are only lifted into the free troposphere when the active fire area and convective heat flux exceed a certain threshold. For the Pico Espejo site, it is expected that the possibility of injections reaching the free troposphere increases towards the end of the dry season with increasing fire activity. Due to a lack of ground-based measurements of AOD at the two stations that are representative for the altitude of the station, monthly gridded means of AOD from the MODIS instrument on board Terra and Aqua satellites have been downloaded from ftp://ladsweb.nascom.nasa.gov/allData/51/ (Remer et al., 2008) and averaged over both products and selected regions (see Table 3). The MODIS instruments have 36 channels covering the spectral range from 410 to 14400 nm and representing three different spatial resolutions of 250 m, 500 m, and 1 km. The AOD product used in our study is retrieved at 550 nm and has a spatial resolution of 250 m. Again, the MODIS product provides an extinction coefficient integrated over a vertical column with probably most of the aerosol load being located below the measurement stations. Nevertheless, the effect of aerosols on hOPL can still be quantified for the Pico Espejo site as about 20% of the aerosol load is expected to be found in the free troposphere, following the recommendations made by Gonzi et al. (2015)." Unfortunately, there were no visibility devices at the stations. We therefore filtered the data by making some assumptions on the data. One assumption is to use a lower limit for the hOPL. These lower limits are obtained by testing different values. The values that we propose are a compromise between "loosing not too many measurements" and "still provide clear sky cases". We have added the following text to the manuscript: "As no instruments to obtain information on atmospheric visibility were available at the stations, we have tested different lower limits of hOPL as a filter criterion and found that 17.5 km and 30 km in the 346-372 nm fitting window and 12.5 km and 22.5 km in the 338-357 nm fitting window are good compromises for Zugspitze and Pico Espejo, respectively (see Fig. 7)." As we can only speculate that AOD at the station level and above is smaller than 0.1, we argue that our filter criteria are the only way to remove measurements that are not representative.
-FOV of the instruments is not mentioned in the paper, neither references to previous publicactions. They are relevant for the reasons exposed below (page 31789).
We have now added some information about the instrument's field of view and included two references for more information: "Scattered sunlight entering the telescope, either from the zenith or horizon window, is focused by lens to reduce the field of view before it reaches the optical fibre mount. During the instrument's operation at the two measurement stations, a field of view with an opening angle of ~1° was achieved (Oetjen, 2009 andPeters, 2013). Consequently, the signal in the horizontal path might be slightly affected by the contribution of trace gas absorption at lower altitudes (up to 500 m below the measurement stations at the end of the hOPL). Nevertheless, the mixing ratios as presented in Sects. 6.3 and 6.4 for NO2 and HCHO, respectively, are still considered to be representative for the free troposphere." -31784, line 26. It is more accurate to use "minimize" than "cancel out" since local effects contribute to the hOPL, as well.
We agree with this comment and have now replaced "cancel out" by "minimize" in the text (see Page 3, Line 27).
-31789, line 15. If the average terrain height below the path at Pico Espejo is of only 150 m, and the path length is of 20-30 km, typical FOV of 1° would hit the ground. The quality of the signal should be affected by the contribution of the ground spectrum. A comment on how this geometry affects the measurements should be included in the text.
To our understanding, an opening angle of about 1° (full FOV = 2°) does not hit the ground for the Pico Espejo case. There is a height difference of more than 4500 meters between the mountain station and the terrain height below. At the end of the path length (e.g. 20-30 km), light from a few hundred meters below the level of the mountain station might enter the horizontal light path. This is still clearly above the boundary layer and should not affect our argumentation that elevated values of NO2 and HCHO are found in the free troposphere. We have now added some information in the text (see first comment on FOV above): "Scattered sunlight entering the telescope, either from the zenith or horizon window, is focused by lens to reduce the field of view before it reaches the optical fibre mount. During the instrument's operation at the two measurement stations, a field of view with an opening angle of ~1° was achieved (Oetjen, 2009 andPeters, 2013). Consequently, the signal in the horizontal path might be slightly affected by the contribution of trace gas absorption at lower altitudes (up to 500 m below the measurement stations at the end of the hOPL). Nevertheless, the mixing ratios as presented in Sects. 6.3 and 6.4 for NO2 and HCHO, respectively, are still considered to be representative for the free troposphere." -31794, line 3-6. Measurements of larger paths than those obtained for a Rayleigh atmosphere are also possible due to the use of a room-temperature O4 cross-section. Spinei et al. (AMT, 2015) have shown that too large paths are obtained when using room temperature cross-sections (i.e. Hermans) in low effective-temperature conditions, which I assume is the case at Pico Espejo. I suggest the authors to estimate the error in the path due to the temperature dependence based on the Spinei paper.
Thank you for pointing this out. We have now considered the Spinei et al. (2015) publication and estimated errors that can be expected when a room temperature laboratory-measured O4 cross-section is used for the estimation of optical paths. We have now added the following paragraph: " Recently, Spinei et al. (2015) have shown that too large O4 slant column densities are obtained when using laboratory-measured O4 cross-sections (e.g. Hermans et al. (1999)) in low effective-temperature conditions. They report a temperature dependence in the O4 absorption cross-section from 231 to 275 K at about 9±2.5% per 44 K rate in the 335-390 nm spectral window and suggest a small correction factor of 0.94±0.02 at 231 K when using O4 cross-sections measured at room temperature. Following the recommendations made by Spinei et al. (2015), an overestimation of up to 6% in hOPL and thus, an underestimation in NO2 and HCHO mixing ratios of up to 6% can be expected in our study due to the use of a room temperature O4 cross-section." -31796, line 4-7. I guess the authors make use of MODIS because AOD devices on the stations are lacking. However, since MODIS averages over an area with probably a lower mean heigh than the observing point, the correlation shown in figure 8 and conclusion of table 3 are missundertanding. I suggest explaining this subject in more detail and provide some information on MODIS (size of the footprint, mean altitude, etc). Again, interpretation of section 6.2 (relies on the correlation Xno2-AOD. If AOD is not that above the station, it must be outlined. We agree with this comment and have now added more information on the MODIS AOD product and mean altitude of aerosols (e.g. injection height of biomass burning). We have now outlined that no representative AOD products are available at the mountain stations and thus, we have used a column averaged satellite-derived AOD product. We have now added the following paragraph to the manuscript (see first comment on AOD/MODIS above): "For example, Gonzi et al. (2015) have estimated biomass burning injection heights using active fire area and fire radiative power from MODIS data in combination with a parameterized plume rise model. They found that 80% of the injections remain within the local boundary layer. Consequently, trace gases and aerosols are only lifted into the free troposphere when the active fire area and convective heat flux exceed a certain threshold. For the Pico Espejo site, it is expected that the possibility of injections reaching the free troposphere increases towards the end of the dry season with increasing fire activity. Due to a lack of ground-based measurements of AOD at the two stations that are representative for the altitude of the station, monthly gridded means of AOD from the MODIS instrument on board Terra and Aqua satellites have been downloaded from ftp://ladsweb.nascom.nasa.gov/allData/51/ (Remer et al., 2008) and averaged over both products and selected regions (see Table 3). The MODIS instruments have 36 channels covering the spectral range from 410 to 14400 nm and representing three different spatial resolutions of 250 m, 500 m, and 1 km. The AOD product used in our study is retrieved at 550 nm and has a spatial resolution of 250 m. Again, the MODIS product provides an extinction coefficient integrated over a vertical column with probably most of the aerosol load being located below the measurement stations. Nevertheless, the effect of aerosols on hOPL can still be quantified for the Pico Espejo site as about 20% of the aerosol load is expected to be found in the free troposphere, following the recommendations made by Gonzi et al. (2015)." -31796, line 10. Typo: remove "of" We have now removed "of" in the text (see Page 15, Line 4).
-Check the spectral range in which spectrometers are operating. Different numbers appear along the text.
We have checked the spectral ranges along the text. There are 4 different numbers: 346-372 nm for the NO2 retrieval, 338-357 nm for the HCHO retrieval, 321-410 nm for the spectrometer, and 330-440 nm for the RTM simulations.
In addition to the reviewers' comments, we have performed some minor changes: -In the ACPD version, References from Table 2 are not included in the reference list. We have now added them to the reference list.
Author's response to comments by referee #3 We would like to thank the reviewer for his / her useful comments.
This article reports on MAX-DOAS observations of free troposheric nitrogen dioxide and formaldehyde volume mixing ratios measured from two high-altitude locations: Zugspitze (Germany) and Pico Espejo (Venezuela). Accurate observations of this part of the atmosphere are sparse because with ground-based (i.e. from within the boundary layer) or satellite remote sensing it is almost impossible to do accurate retrievals of this part of the atmosphere. Therefore the study is quite relevant as a first-order quantification of trace gas abundances in the free troposphere, despite the fact that the retrieved values are at best indicative for volume mixing ratios at other locations around the world.
The paper describes the applied methodology in a clear and concise way and the quality of English writing is high.

It would have been nice if the authors would also have reported free tropospheric trace gas partial columns above the location of the instrument. This complementary information would have been equally unique and relevant and is contained in the MAX-DOAS data set used in this work.
A drawback of the work discussed in this paper is the fact that results are almost not compared to other data sets (except for some references to papers reporting similar values for other locations). However, as measurements of tropospheric trace gas abundances with other sensors are so rare, the lack of comparison with other data sets should not be a reason to reject this study.
In my view, the paper can be published after minor changes described below.
-p.31782, l.7: Please replace "close to the instrument" by "close to the instrument altitude". Same for the sentence in the conclusions (p.31799, l.22) We have now replaced "close to the instrument" to "close to the instrument altitude" in the Abstract and Conclusions Sections.
We have now removed "The authors of".
-p.31791: About Fig. 2: The residual spectrum of the HCHO fitting window appears to have a considerable amount of structure in it (it does not look like random noise). Are the residual spectra similar for other cases? What could be the cause of these structures?
We have tried many different settings during the fitting procedure. We found strong correlation between the residual spectra and HCHO differential optical density when using other fitting windows and/or absorption cross sections. The settings used for HCHO retrieval as presented in the manuscript are by far the best. We agree that there is still some structure in the residual spectrum. We do observe similar patterns for other cases. However, the magnitude of the residual spectrum is lower than the magnitude of the differential optical density of HCHO, which makes us confident to use those settings.
-p.31797: First paragraph: I find the reasoning to exclude the month of June not so convincing. I would say that the NO2 life time in July and May is not so very different from June. Did the authors explore back-trajectory calculations to support the hypothesis that air masses measured in June can be linked to different (pollution) source regions?
We agree that June should not be too different from May and July and have followed the suggestion of the referee and checked backward trajectories for the days of measurements that remain after applying the filter criteria and did not find any month-specific patterns or origin of air masses. We therefore can only speculate that in June, air masses with less NO2 crossed the light path of the instrument. We have now rephrased this paragraph to: "This slight deviation could be related to the fact that air masses with less NO2 and/or more aerosols crossed the light path of the instrument in June. However, no significant differences in the origin of air masses between the different months could be found by exploring back-ward trajectories for the days of measurements that remain after applying the filter criteria to the data (not shown)." -p.31797, l.25: Please replace "Due" by "Due to" We have now replaced "Due" by "Due to".
-p.31798, l.1-8: In my view this paragraph should be part of the previous section (as it is about NO2). Please consider to copy it to that section, and then remove the first part of the first sentence: "Before … HCHO," We have now deleted the first part of the first sentence and copied the paragraph to the end of the previous section.
We have now rephrased this sentence to: "This implies that there is sufficient NOx for oxidizing hydrocarbons through photooxidative catalytic cycles. As a consequence, production of some tropospheric ozone (O3) is occurring at mid-latitudes in the free troposphere." In addition to the reviewers' comments, we have performed some minor changes: -In the ACPD version, References from Table 2 are not included in the reference list. We have now added them to the reference list. estimation of NO 2 and HCHO mixing ratios is based on the modified geometrical approach, which assumes a single-scattering geometry and a scattering point altitude close to the instrument altitude. Firstly, the horizontal optical path length (hOPL) is obtained from O 4 differential slant column densities (DSCDs) in the horizontal (0°) and vertical (90°) viewing directions. Secondly, X NO2 and X HCHO are estimated from the NO 2 and HCHO DSCDs at the 0° and 90° viewing directions and averaged along the obtained hOPLs. As the MAX-DOAS instrument was performing measurements in the ultraviolet region, wavelength ranges of 346-372 nm and 338-357 nm are selected for the DOAS analysis to retrieve NO 2 and HCHO DSCDs, respectively. In order to compare the measured O 4 DSCDs and moreover to perform some sensitivity tests, the radiative transfer model SCIATRAN with adapted altitude settings for mountainous terrain is operated to simulate synthetic spectra, on which the DOAS analysis is also applied. The overall agreement between measured and synthetic O 4 DSCDs is better for the higher Pico Espejo station than for Zugspitze. Further sensitivity analysis shows that a change in surface albedo (from 0.05 to 0.7) can influence the O 4 DSCDs, with a larger absolute difference observed for the horizontal viewing direction. Consequently, the hOPL can vary by about 5% throughout the season, for example when winter snow cover fully disappears in summer. Typical values of hOPLs during clear sky conditions are 19 km (14 km) at Zugspitze and 34 km (26.5 km) at Pico Espejo when using the 346-372 nm (338-357 nm) fitting window. The estimated monthly values of X NO2 (X HCHO ), averaged over these hOPLs during clear sky conditions, are in the range of 60-100 ppt (500-950 ppt) at Zugspitze and 8.5-15.5 ppt (255-385 ppt) at Pico Espejo. Interestingly, multiyear averaged monthly means of X NO2 and X HCHO increase towards the end of the dry season at the Pico Espejo site, suggesting that both trace gases are frequently lifted above the boundary layer as a result of South American biomass burning.

Introduction
Tropospheric nitrogen oxides (NO x = NO + NO 2 ) are released from various human activities (e.g. the burning of oil, coal, gas, and wood). Natural sources of NO x include lightning, wildfires, and microbial activity in soils (Lee et al., 1997). Nitric oxide (NO) is the predominant part of NO x released from these sources, but it is quickly converted to nitrogen dioxide (NO 2 ) by reaction with ozone (O 3 ). The major part of NO x emissions remains in the boundary layer (BL). However, in addition to NO x from lightning, significant amounts of NO x from surface sources occasionally reach the free troposphere (FT) due to meteorology, orographic uplift of BL air masses or pyroconvection.
Formaldehyde (HCHO) is the most abundant carbonyl in the atmosphere and a valuable tracer of volatile organic compound (VOC) sources as it is produced from the oxidation of VOCs. Major sources of HCHO include the oxidation of methane (CH 4 ) (Lowe and Schmidt, 1983) and nonmethane hydrocarbons (NMHC) (Fried et al., 2003). While HCHO formation in the remote marine atmosphere is dominated by CH 4 oxidation (Weller et al., 2000), the major precursor of HCHO in the continental BL is isoprene (Guenther et al., 2006). Further sources of HCHO are direct emissions from biomass burning (Andreae and Merlet, 2001), anthropogenic combustion processes (Anderson et al., 1994), and vegetation (Seco et al., 2007).
As NO 2 and HCHO are good indicators of tropospheric pollution, extensive ground-based measurement networks have been exploited in order to monitor their amounts and distributions (WMO, 2010). While ground-based in situ measurements represent rather surface and/or local amounts of NO 2 and HCHO, remote sensing techniques such as the Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) have the potential to derive both horizontal and vertical distributions of these trace gases in the immediate vicinity of the station (Hönninger et al., 2004;Wittrock et al., 2004). There exist some records of NO 2 in the free troposphere from aircraft in situ measurements (Singh et al., 2009), and balloon-borne soundings (Kritten et al., 2010). However, these observations are sparse and mainly performed during short field campaigns. Recently, global free-tropospheric NO 2 mixing ratios have been obtained from satellite data using the cloud-slicing technique (Choi et al., 2014). While the overall order of magnitude of satellite-derived values is similar to those taken from aircraft in situ measurements, the agreement of individual comparisons is not always good. Data records of HCHO in the free troposphere are also rare and deduced at different seasons, regions, and altitudes (Schuster et al., 1990;Arlander et al., 1995;Singh et al., 2001).
Although the number of ground-based in situ and remote sensing instruments to observe tropospheric pollution has increased during the last years, the level of knowledge concerning representative NO 2 and HCHO amounts in the FT is still rather low up to now. There are two reasons for this: Firstly, ground-based in situ measurements performed at high altitude sites are influenced by air masses that are lifted along the mountain slope to the station (Reidmiller et al., 2010) and thus, often represent rather (polluted) BL air. Secondly, MAX-DOAS measurements have been mainly focused on the BL, where the vast majority of tropospheric pollution is found.
Only very recently, a novel approach to estimate NO 2 mixing ratios in the FT from MAX-DOAS measurements was proposed (Gomez et al., 2014). In that study, the retrieval of O 4 and NO 2 differential slant column densities (DSCDs) was performed in the visible part of the electromagnetic spectrum on the basis of data from nine summer days in Izaña having low aerosol levels. The MAX-DOAS observations of that study were performed at a high-altitude site in the subtropics. The great advantage of the method by Gomez et al. (2014) is to average trace gas concentrations over a long horizontal path (in the order of a few tens of kilometers) and thus, minimize local effects of BL air masses that are lifted to the station. A follow-up study to investigate the seasonal evolution of NO 2 in the free troposphere at the Izaña site was carried out by Gil-Ojeda et al. (2015). That study reported background NO 2 mixing ratios in the range of 20-45 ppt, with lowest (highest) NO 2 amounts in winter (summer).
The aim of the present study is to extend these two studies and provide estimates of NO 2 and HCHO mixing ratios in the FT. For this purpose, two long-term MAX-DOAS data sets from two high-altitude sites located in the mid-latitudes and tropics are analyzed. In contrast to Gomez et al. (2014) and Gil-Ojeda et al. (2015), the retrieval of O 4 , NO 2 , and HCHO DSCDs in our study is performed in the ultraviolet range of the electromagnetic spectrum. Here, we obtain monthly means of NO 2 and HCHO mixing ratios during clear sky conditions at the two measurement sites, focus on the seasonal variability, and compare our values with values reported in the literature.
To the best of the authors' knowledge, this is the first study presenting HCHO mixing ratios in the FT based on long-term MAX-DOAS measurements.
In the following Sect. 2, the MAX-DOAS system and the two measurement locations are described. The modified geometrical approach as proposed by Gomez et al. (2014) to estimate horizontal optical path lengths (hOPLs) and mixing ratios of NO 2 from MAX-DOAS DSCDs is briefly summarized in Sect. 3. The simulation of synthetic spectra using the radiative transfer model SCIATRAN is described in Sect. 4. Details about the analysis of measured and synthetic spectra using the DOAS method are given in Sect. 5. The results of this study, including a comparison of measured and synthetic O 4 DSCDs and the analysis of hOPLs, NO 2 and HCHO mixing ratios for both locations, are presented in Sect. 6. A short summary and conclusions are given in Sect. 7.

Instrumentation and location
The MAX-DOAS system, which was operated at the two high altitude stations Zugspitze, Germany (47.5°N, 11°E, 2650 m a.s.l.) and Pico Espejo, Venezuela (8.5°N, 71°W, 4765 m a.s.l.), comprised a temperature stabilized grating spectrometer equipped with a cooled CCD detector.
The spectrometer and CCD detector were housed inside a building and connected to a telescope unit, which was mounted outdoors. In addition to the zenith window, a horizon (off-axis) window was implemented in the telescope to allow for the scanning of different off-axis directions, which were controlled by a motorized mirror. Scattered sunlight entering the telescope, either from the zenith or horizon window, is focused by a lens to reduce the field of view before it reaches the optical fibre mount. During the instrument's operation at the two measurement stations, a field of view with an opening angle of ~1° was achieved (Oetjen, 2009 andPeters, 2013). Consequently, the signal in the horizontal path might be slightly affected by the contribution of trace gas absorption at lower altitudes (up to 500 m below the measurement stations at the end of the hOPL). Nevertheless, the mixing ratios as presented in Sects. 6.3 and 6.4 for NO 2 and HCHO, respectively, are still considered to be representative for the free troposphere. As a result of the wavelength range of the spectrometer covering 321 to 410 nm, HCHO retrieval is possible and the retrieval of O 4 and NO 2 DSCDs is restricted to the UV spectral region in this study (see Sect.

5).
In February 2003, the MAX-DOAS instrument was temporarily set up at the mid-latitude site Zugspitze, Germany, where it performed measurements until the end of July 2003. The underlying intention behind choosing Zugspitze as a measurement location was the fact that MAX-DOAS measurements of NO 2 could be used to validate satellite-derived stratospheric NO 2 columns as most of the NO 2 above this altitude is assumed to belong to the stratosphere. The telescope was orientated at 120° azimuth (east-southeast) throughout the measurement period and elevation angles (α) of 0°, 4°, 7°, 16°, 30°, and 90° (zenith) were selected for the scanning included and thus, less data for both α = 0° and α = 90° are available from that date on (see Sect. 6.2). The meteorological conditions at Pico Espejo with permanent cloud cover during the wet season (from April to November) limit the data analysis to the dry season months December, January, February, and March.
In a recent study by Gomez et al. (2014), a modified geometrical approach (MGA) to estimate long-path averaged mixing ratios of trace gases (e.g. NO 2 ) from mountain MAX-DOAS measurements was proposed.
Briefly, MGA assumes a single scattering geometry and a scattering point altitude close to that of the instrument. In order to validate the former assumption, Gomez et al. (2014) where n O4 is easily calculated by: In our study, the zenith measurements are interpolated between the solar zenith angles (SZAs) of the horizontal measurements. Thus, no further correction with respect to the differences in DSCDs due to a difference in SZA between the sequentially scans is required. The number density of air (n air ) at the altitude of Zugspitze and Pico Espejo is extracted from the respective mid-latitude summer and tropical reference atmospheric model profiles of the Air Force Geophysics Laboratory (AFGL) standard atmosphere (Anderson et al., 1986).
In the second step, the mean mixing ratio of the trace gas (X NO2 and X HCHO ) is estimated for the level of the station by dividing the NO 2 and HCHO DSCD differences by the hOPL and n air :  (2015), an overestimation of up to 6% in hOPL and thus, an underestimation in NO 2 and HCHO mixing ratios of up to 6% can be expected in our study due to the use of a room temperature O 4 cross-section. Gomez et al. (2014) provide a detailed discussion about possible errors that may occur in the MGA. They report an error in the range of 20% for SZAs < 70°, which steeply increases to about 50% towards SZA = 80°. We follow the recommendations made by Gomez et al. (2014) and estimate hOPL as well as X NO2 and X HCHO only for SZAs < 70°.

Simulation of synthetic spectra
In order to determine the effect of altitude settings and surface albedo on the O 4 DSCDs and moreover to compare the measured with simulated O 4 DSCDs at the two high altitude stations, synthetic spectra (intensities) are computed for single clear sky days using the radiative transfer model SCIATRAN, which is applied in the 1-D case (Rozanov et al., 2005).
Briefly, the software package SCIATRAN was developed for modeling radiative transfer processes in the atmosphere and ocean. The simulations can be performed for observations made by ground-based, satellite-based, ship-based, and balloon-borne instruments in the spectral range from UV to thermal infrared. The latest release of SCIATRAN includes multiple scattering processes, polarization, thermal emission and ocean-atmosphere coupling (Rozanov et al., 2014).
The major advantage of 1-D RTMs is their low computation time and their ability to reproduce radiative transfer for clear sky conditions and over flat terrains quite well. For mountainous terrains, however, factors such as altitude and surface albedo are more difficult to treat. The computation of intensities/radiances for ground-based MAX-DOAS instruments using SCIATRAN requires, amongst others, the information on the height above sea level. For a typical measurement station in an urban area, for example, the altitude of the instrument's horizontal path (h path ) does not differ much from the ground level (h ground ) of the surrounding area (Fig. 1,   left). Therefore, h path would be configured by the input for h ground accordingly and the position of the instrument in SCIATRAN would be set to "bottom of the atmosphere". However, for high altitude stations such as Zugspitze and Pico Espejo these settings are no longer valid as they are both located on mountain peaks and information about the atmosphere below would be lost (Fig.   1, right). Therefore, the altitude settings in SCIATRAN are adjusted by assuming that the MAX-  Table 1.

DOAS retrieval of O 4 , NO 2 , and HCHO differential slant column densities
The differential optical absorption spectroscopy (DOAS) method is performed on the measured and synthetic spectra to obtain O 4 , NO 2 , and HCHO DSCDs, which are the parameters used for the MGA-based estimation of hOPLs as well as X NO2 and X HCHO at the two high altitude sites.
Briefly, DOAS is based on absorption spectroscopy following Beer-Lambert's law of absorption and developed for the determination of atmospheric trace gas concentrations from remote sensing measurements of light in the UV, visible, and NIR spectral range (Platt and Stutz, 2008, and references therein). After removing the smoothly varying contributions of Mie and Rayleigh scattering from the signal, DOAS becomes sensitive to variations in absorption with wavelength.
Due to the fact that individual trace gases have characteristic spectral signatures, they can be separated from the signal and quantified in terms of trace gas concentration, integrated along the atmospheric light path.
The trace gases of interest in our study, O 4 , NO 2 , and HCHO have spectral fingerprints in the UV and visible spectral range. As mentioned above, the spectrometer of the MAX-DOAS system at Zugspitze and Pico Espejo collected scattered sunlight between 321 and 410 nm. Therefore, the DOAS fits performed in our study are restricted to the UV.
The DOAS method is performed on the measured and synthetic spectra in the spectral range from 346-372 nm, where O 4 and NO 2 spectral fingerprints are obvious and interference with other trace gases is rather low (Platt and Stutz, 2008, and references therein). For the retrieval of HCHO, the spectral window of the DOAS analysis is shifted to 338-357 nm. Absorption crosssections of O 3 at 223 K, NO 2 at 220 K, O 4 , BrO at 223 K, and HCHO at 297 K, as well as a Ring spectrum and a polynomial of order 4 are included in the non-linear least-squares fitting procedure. For the removal of Fraunhofer lines in the solar spectrum, the measured and synthetic spectra are divided by a reference spectrum (here, a noontime spectrum at α = 90° with the smallest SZA is used). The resulting output of the DOAS fit is the difference in slant column amounts of O 4 , NO 2 , and HCHO between the measured/synthetic and reference spectrum, and thus referred to as DSCD. A summary of fit parameters and cross-sections used for the DOAS analysis is summarized in Table 2.
An example of the spectral DOAS analysis in the 346-372 nm fitting window is shown in Fig. 2 (left) for a single spectrum, which was measured under elevated NO 2 pollution on 16th April 2003 (SZA = 37.86°, α = 0°) at Zugspitze. For the retrieval of O 4 and NO 2 DSCDs on that day, a spectrum in zenith direction (α = 90°) taken during noon (SZA = 37.36°) is used as a reference.
Fit results of the DOAS analysis for the same measurement, but in the 338-357 nm fitting window yield similar values for the residuals and RMS and indicate that HCHO amounts were also higher than usual on that day (Fig.2, right).

Measured and synthetic O 4 differential slant column densities
In this section, two sensitivity tests are carried out with the RTM SCIATRAN to determine the effect of varying altitude settings and surface albedo on the O 4 DSCDs at α = 0° and α = 90° and thus, on the estimation of hOPL. The settings used for the simulation of synthetic spectra are summarized in Table 1.
Two different altitude settings as represented schematically in Fig. 1  For the horizontal viewing direction (α = 0°), the absolute difference of the two scenarios is in the order of 400 x 10 40 molec 2 cm -5 for SZAs between 20° and 70°. The absolute differences are comparatively low for the vertical viewing direction (α = 90°), but increase towards SZA = 70° to about 100 x 10 40 molec 2 cm -5 . Therefore, hOPL is underestimated by about 15% when the atmosphere below is cut off in the RTM.
As the Zugspitze site is located in the northern Alps at an altitude of almost 3000 m a.s.l., snow cover at the mountain peak and at lower altitudes in the immediate vicinity is common during winter and as a consequence, the surface albedo can change significantly throughout the season.
Therefore, another sensitivity test with SCIATRAN is performed to evaluate the effect of a Espejo, the differences are larger at Zugspitze. The better agreement at the former station could be explained by the higher altitude and cleaner atmosphere that is almost solely affected by Rayleigh scattering. In contrast, scattering by aerosol could play an increasing role at the altitude of the latter station. Similar results are obtained for the 338-357 nm fitting window (not shown).

Horizontal optical path length
The Zugspitze was influenced by elevated NO 2 pollution in the afternoon of that day, no significant enhancements in NO 2 DSCDs are observed for Pico Espejo throughout the selected day (not shown). Clearly, the U-shaped curve of the hOPL as obtained from the measured O 4 DSCDs (dotted line) is reproduced by the simulations (solid line) and the agreement of both curves is within 10% for the Pico Espejo case. In general, one would expect smaller hOPLs from the measurements than from the simulations as performed with SCIATRAN without the inclusion of aerosols (see Table 1). One possible explanation for the higher measured values at Pico Espejo could be an aerosol layer below the measurement site. The differences are much larger for the case at Zugspitze. While the differences are about 25% in the morning, they rise to 70% in the afternoon, where NO 2 pollution increased as well (see Sect. 6.1). Again, the better agreement at Pico Espejo might be related to the higher altitude and cleaner atmosphere with negligible Mie scattering. Gomez et al. (2014) have simulated the hOPL for a single wavelength in the visible spectral range (440 nm) and also found a U-shaped curve with higher values of hOPL towards larger SZAs. However, the distances estimated in their study are larger by a factor of about two, although the Izaña station is located at a lower altitude (2373 m a.s.l.) than the Zugspitze and Pico Espejo sites. This means that trace gas concentrations are averaged over a shorter distance in the UV than in the visible, even at higher altitudes. Consequently, MAX-DOAS measurements in the UV are representative of free-tropospheric trace gas concentrations to a lesser extent than in the visible as the influence of BL air masses that are lifted to the station is larger for the shorter horizontal path. Nevertheless, the hOPL in the UV during clear sky conditions is still sufficiently long that NO 2 close to the station is considered to have a negligible influence.
The hOPLs as derived in the 346-372 nm are illustrated in Fig. 7  Terra and Aqua satellites have been downloaded from ftp://ladsweb.nascom.nasa.gov/allData/51/ (Remer et al., 2008) and averaged over both products and selected regions (see Table 3). The MODIS instruments have 36 channels covering the spectral range from 410 to 14400 nm and representing three different spatial resolutions of 250 m, 500 m, and 1 km. The AOD product used in our study is retrieved at 550 nm and has a spatial resolution of 250 m. Again, the MODIS product provides an extinction coefficient integrated over a vertical column with probably most of the aerosol load being located below the measurement stations. Nevertheless, the effect of aerosols on hOPL can still be quantified for the Pico Espejo site as about 20% of the aerosol load is expected to be found in the free troposphere, following the recommendations made by Gonzi et al. (2015). While the estimated hOPLs increase throughout the season at Zugspitze, the results show a decrease of hOPLs towards the end of the dry season at Pico Espejo (Fig. 8). Clearly, AOD seems to be the main driver affecting hOPL in both cases. The decrease in AOD at Zugspitze might be due to an overall decrease in residential wood burning towards summer time in that region (Szidat et al., 2007). On the other hand, the increase in AOD at Pico Espejo is connected to increased biomass burning towards the end of the dry season in that region (Hamburger et al., 2013). Interestingly, there is no relationship between hOPL and AOD observed for the 338-357 nm fitting window (see Table 3). One reason could be the larger uncertainties in O 4 DSCDs, which are used to obtain hOPL.

Long-path averaged NO 2 mixing ratios
The monthly averaged X NO2 as a function of AOD and the multi-year averaged monthly means of X NO2 as a function of fire radiative power (FRP) are shown in Fig. 9 for Zugspitze (left) and Pico Espejo (right), respectively. FRP is defined as the radiant component of energy release from a fire (Kaufmann et al., 1998).
Monthly averaged values of X NO2 at Zugspitze are 93.5±49.8 ppt and 102±60.5 ppt in the spring months April and May, respectively, whereas lower values of 59.6±55.6 and 61.8±28.9 ppt are derived for the summer months June and July. As pollution at the Zugspitze site is mainly anthropogenically induced, the general co-occurrence of higher AOD and higher X NO2 is not surprising. Clearly, higher values of X NO2 are observed during the spring months April and May, which could be explained by both higher combustion due to residential burning and longer life time of NO 2 . While the values of the months April, May, and July are linearly related to a large extend, either AOD is higher or X NO2 is lower than expected from the linear relation in June. This slight deviation could be related to the fact that air masses with less NO 2 and/or more aerosols crossed the light path of the instrument in June. However, no significant differences in the origin of air masses between the different months could be found by exploring back-ward trajectories for the days of measurements that remain after applying the filter criteria to the data (not shown).
The y-intercept of the linear least-squares fit (excluding June) in the order of 20 ppt (not shown) provides some information on the background levels of X NO2 in this region and at this altitude. In comparison, Gomez et al. (2014) and Gil-Ojeda et al. (2015) have reported NO 2 mixing ratios between 20 ppt and 45 ppt for the clean subtropical FT at a similar altitude, which is in good agreement with the background value obtained for Zugspitze, which is located more than 2000 km north of the Izaña station.
The multi-year averaged values of X NO2 for the higher elevated station Pico Espejo are somewhat smaller when compared to X NO2 values at Zugspitze (Table 3). As observed for Zugspitze, there is a positive linear relationship with AOD (not shown), suggesting a background value of 5.5 ppt.
The multi-year averaged values of X NO2 as a function of multi-year averaged FRP is illustrated in Fig. 9. Clearly, X NO2 increases with increasing fire activity towards the end of the dry season. The calculation of a linear least-squares fit reveals a y-intercept of 4 ppt, which is in agreement with the y-intercept as derived for X NO2 vs. AOD.
Although the long-path averaged NO 2 mixing ratios at Pico Espejo are estimated at an altitude of almost 5000 m a.s.l., and thus, clearly above the boundary layer, it seems that the FT is regularly affected by biomass burning emissions in this region.
X NO2 as retrieved in the 346-372 nm fitting window (blue) is compared with X NO2 as derived in the 338-357 nm fitting window (red) for a polluted day at Zugspitze (see Fig. 10). In general, the shape of both curves is similar to a large extend with lowest (highest) values observed in the morning (late afternoon). Although the spectral signatures of NO 2 and O 4 are less pronounced and interference with other gases is stronger in the 338-357 nm fitting window, mixing ratios of NO 2 are still in good agreement with X NO2 obtained in the 346-372 nm fitting window.

Long-path averaged HCHO mixing ratios
The same analysis that was applied to derive NO 2 mixing ratios in the free troposphere was also applied to HCHO. Due to its characteristic spectral signatures at lower wavelengths, the retrieval of HCHO is shifted to the spectral range from 338-357 nm (see Sect. 5 and Table 2).
In Figure 11, the diurnal evolution of HCHO DSCDs as retrieved in the 338-357 nm fitting window for α = 0° (red) and α = 90° (black) is shown for the same day at Zugspitze. As observed for NO 2 , HCHO levels increase in the afternoon. Backward trajectories as calculated with the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) online tool (Draxler and Rolph, 2013) using meteorological data from the NCEP/NCAR 40-year reanalysis project (Kalnay et al., 1996) indicate that air masses from a more densely populated region at lower elevation in the northeast moved along the slope of the Bavarian alps, before crossing the light path of the MAX-DOAS instrument (not shown). While the increase of HCHO DSCD is obvious for α = 0° (red), HCHO DSCD at 90° (black) is relatively stable throughout the day with slightly negative columns obtained in the morning hours.
The filter criteria, as defined in Sect. 6.2 are applied to obtain X HCHO during clear sky conditions.
An exemplary diurnal evolution of X HCHO before (green) and after (black) applying the filter criteria is shown for the polluted day at Zugspitze in Fig. 12. According to the filter criteria, the remaining black dots are observed during clear sky conditions and are in the range of 400-800 ppt.
Monthly means of X HCHO between April and July are in the range of 500-950 ppt at the Zugspitze site (Table 3). Air sampling of HCHO deduced from a flight track of the TROPospheric OZone Experiment (TROPOZ-2) above Northern Spain/Western France reveals HCHO mixing ratios of ~400 ppt at a similar altitude, but in the winter season (Arlander et al., 1995). According to the seasonal variability of HCHO in the mid-latitudes as obtained from satellite measurements, lowest values of HCHO are observed during winter months (De Smedt et al., 2015). Therefore, the higher values observed in our study during spring and summer months are reasonable.
Considerable lower HCHO mixing ratios at Zugspitze are found in April when compared with values in May, June, and July. This is in good agreement with HCHO concentrations as obtained from MAX-DOAS measurements at the high-alpine station Jungfraujoch (Franco et al., 2015). In both cases, the April values are about 35% lower than the average of May, June, and July values.
Multi-year averaged monthly means of X HCHO as obtained during the dry season at Pico Espejo are in the range of 255-385 ppt and thus, well below the values deduced at Zugspitze. The comparison with HCHO deduced from air sampling in this region during TROPOZ-2 is quite revealing, with our values being slightly higher at this altitude. Singh et al. (2001) reported values of HCHO mixing ratios in the range of 100-200 ppt for this altitude. However, they have used data from a larger region (0-30°S, 165°E-100°W) and focused on the tropospheric composition over the tropical Pacific Ocean.

Summary and conclusions
In this study, Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) data sets from two high altitude stations in the mid-latitudes and tropics are analyzed for horizontal optical path lengths (hOPLs) and free-tropospheric NO 2 (X NO2 ) and HCHO (X HCHO ) mixing ratios. The method is based on the modified geometrical approach (MGA), which assumes a singlescattering geometry and a scattering point altitude close to the instrument altitude.
For the estimation of hOPL, X NO2 , and X HCHO , DSCDs of O 4 , NO 2 , and HCHO in the horizontal (0°) and vertical (90°) viewing directions are obtained with a conventional differential optical absorption spectroscopy (DOAS) retrieval between 346 and 372 nm for the NO 2 and between 338 and 357 nm for the HCHO retrieval. In order to compare the O 4 DSCDs with synthetic data and moreover to evaluate the effect of a varying surface albedo on the O 4 DSCDs, the radiative transfer model SCIATRAN is used. As for the retrieval of O 4 DSCDs from MAX-DOAS measurements, the synthetic spectra are also analyzed with the DOAS method.
In general, the measured and synthetic vertical O 4 DSCDs are in good agreement (differences < 20%) during clear sky conditions and for solar zenith angles (SZA) smaller than 70°. While the differences between measured and synthetic horizontal O 4 DSCDs are small at the higher and "cleaner" Pico Espejo site (< 10%), they are between 25% and 70% at Zugspitze. The results of the sensitivity analyses show that a decrease in surface albedo from 0.7 to 0.05 can increase hOPL by about 5%, which can have possible implications for such measurements in mountainous terrains with a seasonal varying snow cover.
Monthly means and multi-year averaged monthly means of hOPL as obtained from the long-term measurements are 19 km (14 km) and 34 km (26.5 km) for the 346-372 nm (338-357 nm) fitting window at Zugspitze and Pico Espejo, respectively. At both high altitude sites, hOPL as derived in the 346-372 nm fitting window decreases as a function of increasing aerosol amounts. In contrast, no relationship is found for the 338-357 nm fitting window, which could be explained by the larger uncertainties in O 4 DSCDs.
Long-path averaged mixing ratios of NO 2 are obtained using the estimated hOPL. The monthly means and multi-year averaged monthly means of X NO2 are in the range of 60-100 ppt and 8.5-15.5 ppt at Zugspitze and Pico Espejo, respectively. A statistically significant linear relationship between aerosol optical depth (AOD) and X NO2 is obtained for the measurements from both measurement sites, suggesting that both NO 2 and aerosols are closely connected to air pollution in these regions and at the respective altitude level. The results of a linear least-squares fit performed on the averaged data show that upper limits for the background free troposphere NO 2 mixing ratios are about 20 ppt and 4.5 ppt for Zugspitze and Pico Espejo, respectively, where the former value is in good agreement with background NO 2 mixing ratios reported by Gomez et al. (2014) and Gil-Ojeda et al. (2015) for a similar altitude at the Izaña station (28.3°N, 16.48°W, 2373 m a.s.l.). The latter site on Tenerife is relatively remote, whereas Zugspitze is farther north but both are probably probing on average similar free tropospheric air masses transported from Tenerife towards Europe. However, the higher values at mid-latitudes in the northern hemisphere as opposed to those close to the ITCZ are probably indicating an anthropogenic influence at midlatitudes in the free troposphere.
The same procedure as for X NO2 is applied to obtain X HCHO , but for an optimized fitting window covering the strong spectral signatures of HCHO. The monthly means of X HCHO at the Zugspitze site are 500-950 ppt, which is reasonable when comparing these values with values obtained from air sampling in winter at similar altitudes and latitudes as well as considering a seasonal variability in this region. At mid-latitudes, the values of HCHO and NO 2 are relatively high for clean conditions. This implies that there is sufficient NO x for oxidizing hydrocarbons through photooxidative catalytic cycles. As a consequence, production of some tropospheric ozone (O 3 ) is occurring at mid-latitudes in the free troposphere. The values of X HCHO are in the range of 255-385 ppt at Pico Espejo and increase towards the end of the dry season. Moreover, multi-year averaged monthly means of X HCHO are linearly correlated with the multi-year averaged monthly means of X NO2 , further supporting the notion that emissions from South American biomass burning clearly reach the free troposphere in this region. This probably also implies some photooxidation of hydrocarbons and production of O 3 is occurring some of the time in the air masses observed in the free troposphere above Pico Espejo.