For the car DOAS zenith-sky and tower DOAS off-axis observations of tropospheric NO2 in Vienna, a DOAS system was used to measure scattered sunlight from directly overhead and from the horizon, respectively. A cardboard box was built to house a commercial Avantes miniature spectrometer (AvaSpec-ULS2048x64) and a notebook. The AvaSpec-ULS2048x64 is small in size (175×110×44 mm), robust, and lightweight (855 g). The instrument performs spectral measurements between 290 and 550 nm at a spectral resolution of 0.65 nm (see Table 1). Both the spectrometer and notebook were supplied with electricity from the car battery and from the existing tower power circuit during the measurements.

An optical fiber was connected to the spectrometer and threaded through an aluminium bracket to the outside of the car, where it was fixed to a small aluminium plate by duct tape. In order to prevent direct sunlight from entering the optical fiber, a cylindrical plastic tube was used for shading the entrance. The field of view of the optical fiber was characterized in the laboratory to be about ±5∘. As the telescope was directed to the zenith, no large errors are expected for the retrieval of tropospheric vertical NO2 columns in this case as light path length is relatively insensitive to small deviations of the pointing from the zenith direction. For stability reasons, the bracket was clamped by the two door windows of the rear area. The geographical position of the car was recorded by a GPS receiver, which was connected to and powered by a USB port of the laptop computer.

The overall approach was to keep the measurement system simple. Therefore, only the zenith direction was implemented, which is insensitive to changes in pointing as from telescope misalignments or car movements. Pointing the instrument closer to the horizon increases the sensitivity to tropospheric NO2, but introduces an additional complication as pointing accuracy in a moving car becomes an issue. Experience also showed that in a city environment, a large fraction of the measurements at 22∘ or 30∘ elevation, for example, are affected by blocking from houses, trees, or other vehicles. As shown in previous studies (e.g., Wagner et al., 2010; Shaiganfar et al., 2011), the air mass factor for measurements at 22 and 30∘ depends on the relative azimuth between the telescope orientation and the sun, necessitating computation of the car heading from GPS data, which can be complex in typical city traffic situations. In summary, the choice was made to use a simple and robust method at the expense of reduced sensitivity.

A total of 20 identical car circuits around Vienna were performed on nine days in April, September, October, and November 2015 within the metropolitan area of Vienna (see Table 3). Each drive spanned about 110 km and lasted about 1.5 h. In order to minimize the effect of clouds and wind speed, measurements were performed in the morning rather than in the afternoon. After a successful test phase of the car DOAS zenith-sky measurements on 10 April 2015, more days were planned in fall of the same year, including working days and days on weekends as well as days with different wind conditions. Measurements between April and September, e.g., during the summer season, were unfortunately not possible due to other priorities and due the fact that the authors were not located in Vienna during that time.

Figure 1 illustrates an exemplary overview of a single car journey performed on 10 April 2015 between 05:27 and 06:59 UT. The starting point of each drive was within the municipality of Wolkersdorf im Weinviertel (48∘22′59′′ N, 16∘31′05′′ E), a small city located in Lower Austria, about 10 km north of Vienna and away from large sources of NOx. From there, the journey was planned to cover one of the busiest motorways in Austria, pass by known emission sources (e.g., power plants), and drive around one of the largest inland refineries in Europe, before heading back to the starting point on a different route. Also shown in Fig. 1 are the air quality monitoring stations that are used for comparison purposes (see Sect. 3.3) as well as the location of the Danube Tower, from which horizon measurements were performed (see the following Sect. 2.3).

The same DOAS instrument was used for the measurements performed from the café at the Vienna Danube Tower (48∘14′25′′ N, 16∘24′36′′ E), which rotates at about 160 m above ground (https://www.donauturm.at, last access: 29 April 2019). Due to its geographical location (about 4.5 km to the northeast of the city center), it is possible to scan both urban and rural areas during a single counterclockwise 360∘ rotation (duration = 26.5 min). In contrast to the car DOAS zenith-sky measurements (see Sect. 2.2), the telescope was directed towards the horizon at an elevation angle of 0∘. An optical lens was placed in front of the light fiber entrance to reduce the field of view of the instrument to about 0.8∘. Both the lens and the entrance of the optical fiber were protected from direct sunlight by purpose-built cardboard. Because the scattered sunlight was passing through a thick glass window, no UV spectra could be recorded by the DOAS instrument from the rotating tower platform.

Tower DOAS off-axis observations were performed on five days in April and May 2016. More than thirty 360∘ scans of Vienna were recorded, each of them for an individual rotation of the café. For reasons of simplicity and accessibility, zenith-sky measurements were only taken afterwards from the open terrace, which is located a few meters below.

As the Vienna Danube Tower does not provide information on the exact orientation of the platform, and due to the fact that the signal of the GPS receiver was not accurate enough to reliably determine the position along the circle, the horizontal viewing angle was determined with the following approach: the Donau City Tower 1, the tallest skyscraper in Austria, which is located about 1 km from the Vienna Danube Tower, comes into field of view once every rotation and considerably reduces the signal (see Fig. 2). According to Google Earth, the position of the Vienna Danube Tower relative to this skyscraper is 167∘ (nearly south). Due to the constant rotation speed of the platform, which can be calculated from the DOAS observations, the horizontal viewing angle can be determined from the periodic sharp reduction in intensity.

The spectral measurements as obtained during the individual car journeys and tower platform rotations are analyzed using the DOAS technique applying a nonlinear least-squares fitting algorithm. The spectral retrieval of NO2 differential slant column densities (DSCDs) is based on a fitting window between 425 and 490 nm, a polynomial degree of 5 (car DOAS zenith-sky) and 7 (tower DOAS off-axis), and a wavelength calibration using data from the solar atlas of Kurucz et al. (1984). These general settings have been commonly used in recent studies for the retrieval of NO2 DSCDs from ground-based DOAS-type measurements (e.g., Roscoe et al., 2010). High-resolution absorption cross sections of O3, NO2, O4, H2O, and a pseudo-cross section accounting for rotational Raman scattering as computed with QDOAS (Danckert et al., 2015) have been included in the two retrieval settings (see Table 2). The motivation for using a higher polynomial degree in the analysis of the horizon measurements is large broadband residuals found in the data. These residuals are attributed to the fact that the horizon measurements were taken through thick multilayer glass while the zenith-sky measurement was taken outdoors.

Exemplary car DOAS zenith-sky fit results, recorded on 10 April 2015 (SZA = 47.68∘) under elevated NO2 pollution (DSCD = 4.03×1016 mol cm-2), are shown in Fig. 3a, c. In some parts of the route, the zenith view of the instrument is obstructed by tunnels, bridges, or other objects. These measurements were identified using an intensity criterion and removed from the data set. However, some outliers having unrealistically high values of NO2 are still present in the data set, which strongly correlate with exceptional high chi-square values. Consequently, we only consider NO2 DSCDs with chi-square values < 2.5×10-3 for further analysis. Noontime measurements of three selected days, taken in rural areas and close to air quality monitoring stations, are used as reference measurements (see Sect. 3.2.4 and Table 3).

Exemplary tower DOAS off-axis fit results obtained from a spectrum recorded on 29 April 2016 (SZA = 66.99∘) under elevated NO2 pollution (DSCD = 1.46×1017 mol cm-2) are shown in Fig. 3b, d. When comparing the two fit results, it becomes clear that the absorption by NO2 in the horizontal path is larger by a factor of 3.6 in this case. This is because most of the NO2 in urban environments is found in the boundary layer, close to the ground. In contrast, to the car DOAS zenith-sky measurements, no filtering was applied to the tower DOAS off-axis measurements.

The uncertainty of the retrieved unfiltered NO2 DSCDs was calculated from the fit. For car DOAS zenith-sky and tower DOAS off-axis measurements, this error is generally less than 0.75×1015 and 1.5×1015 mol cm-2, respectively

For the estimation of residual amounts in SCDref as well as for the comparison of NO2 VCDtropo obtained from car DOAS zenith-sky (see Sect. 4.4) and NO2 mixing ratios from tower DOAS off-axis measurements (see Sect. 4.5) with in situ NO2 concentrations, data from 23 air quality monitoring stations in and around Vienna, provided by the Environment Agency Austria, UBA (Umweltbundesamt), are used (see Fig. 1). For the detection of NO2 concentrations, Horiba APNA-370 and API M200E (NOx) instruments are currently used at most of these stations. In addition, TEI 42i and Horiba APNA-360E instruments are operated at individual stations (Spangl, 2017). The combined measurement uncertainty for these instruments is about 10 % (W. Spangl, personal communication, 2018).

Residual amounts in SCDref are calculated by converting simultaneous in situ NO2 measurements from the air quality monitoring stations in Gänserndorf (10 April 2015) and Wolkersdorf (27 September and 23 October 2015) into VCDtropo applying the empirical relationship between concurrent MAX-DOAS and urban background in situ measurements (Kramer et al., 2008): 2y=0.036x+0.018, where y is the tropospheric NO2 VCD (residual amounts in SCDref in our study) in units of 1016 mol cm-2 and x denotes the in situ NO2 mixing ratios in units of parts per billion. The conversion of in situ NO2 concentrations (µg m-3) into in situ NO2 mixing ratios (ppb) in our study is described in Sect. 3.5.

The residual amounts in SCDref as determined with Eq. (2) are estimated at 1.3×1015, 1.1×1015, and 2.2×1015 mol cm-2 on 10 April, 27 September, and 23 October, respectively. We note that the extrapolation of the empirical relationship to our measurements is critical in a sense that meteorological conditions and emissions are not the same in Leicester and Vienna. Due to the fact that SCDref measurements were taken outside of Vienna in our study, with in situ measurements of NO2 being in the range of 2.5 to 6 ppb on those three days and indicating rather low residual amounts, the error is assumed to be likewise low in this case.

For the comparison of car DOAS zenith-sky and in situ NO2 observations, we have selected half-hour averages of NO2 concentrations from seven stations in Lower Austria and eight stations in Vienna that are within 5 km of the car route (see Fig. 1). The selection of appropriate in situ NO2 observations for the comparison with tower DOAS off-axis measurements is described in Sect. 4.5. For both cases, half-hour averages of NO2 concentrations are converted into mixing ratios (see Sect. 3.5).

The conversion of VCDtropo into mixing ratios as described in the following Sect. 3.5 requires, in addition to meteorological measurements of pressure and temperature, information on the planetary boundary layer depth (also known as mixing height). The Austrian official weather service, ZAMG (Zentralanstalt für Meteorologie und Geodynamik), performs operational aerosol-layer height measurements with a Vaisala CL51 ceilometer at the Hohe Warte site in the northwest of Vienna (48∘14′55′′ N, 16∘21′23′′ E). Mixing-height (MH) time series are obtained from these measurements by removing unrealistic nocturnal aerosol-layer height values, avoiding outliers, filling data gaps by linear interpolation, and smoothing (Lotteraner and Piringer, 2016). Mixing-height data at a temporal resolution of 5 min were provided by ZAMG for those days when car DOAS zenith-sky measurements were carried out.

The comparison between the two independent NO2 observations (car DOAS zenith-sky versus in situ) is based on gridding the data of both measurement techniques onto a 0.01∘×0.01∘ spatial resolution. For a better comparison, NO2 VCDtropo as obtained from car DOAS zenith-sky measurements as well as in situ NO2 concentrations are converted into mixing ratios. The former conversion is based on recommendations made in Knepp et al. (2013). The authors of that study have converted Pandora tropospheric NO2 values into mixing ratio values by applying a planetary boundary layer (PBL) height correction factor. Although this approach assumes a constant mixing ratio in the PBL, which is not necessarily correct in an urban environment, it accounts for the variability in MH throughout the day. We follow their approach and estimate boundary layer mixing ratios of NO2 (XNO2) via the following equation: 3car  DOASBLXNO2=VCDtropoMH⋅na, where MH is the mixing height (PBL in their study) and na denotes the number density of air (N in their study). Here, we use lap averages for MH as calculated from the data in 5 min resolution provided by ZAMG (see Sect. 3.4). The standard deviation of these lap averages generally ranges between 10 and 50 m but can be as high as 200 m when wind speeds are high (see Table 3). The number density of air, which is related to the atmospheric pressure by the ideal gas law, is also averaged over the individual car laps. Meteorological measurements of pressure (p) and temperature (T) used for the calculation of na are provided by the BOKU (Universität für Bodenkultur) weather station, located in the northwest of Vienna (48∘14′16.45′′ N, 16∘19′54′′ E). We note that the weather station is located about 100 m higher than the altitude level of the car route. Thus, pressure might be slightly lower when compared to the pressure level 100 m below. Conversely, the weather station is also located outside of the city center, at the foot of the hills in the northwest and in a less densely populated residential area with many green areas, resulting in slightly cooler temperatures than expected for other places along the car route. Following this reasoning, it becomes clear that the altitude difference might cancel in the calculation of na (see Eq. 3) and also in the following Eq. (5).

Recently, Dieudonné et al. (2013) highlighted the fact that large vertical gradients of NO2 concentrations exist over urban areas. The authors of that study suggest that the averaged concentration within the PBL is only about 25 % of NO2 surface concentration measurements when NO2 profiles from chemistry transport models are assumed for the PBL. Following this reasoning, car DOAS (BL) XNO2 as estimated via Eq. (3) does not represent NO2 near-surface mixing ratios sufficiently well and a comparison with NO2 as obtained from air quality monitoring stations and converted into in situ XNO2 (see Eq. 5) is not yet reasonable. Consequently, an empirical approach for estimating near-surface NO2 mixing ratios from the car DOAS zenith-sky measurements is introduced in our study, in addition to car DOAS (BL) XNO2.

In order to achieve optimal agreement between car DOAS zenith-sky measurements and in situ observations in our study, we include four parameters that are expected to affect the vertical NO2 gradients and conduct a linear regression analysis as follows: 4Y=β0+β1X1+β2X2+β3X3+β4X4+ε, where Y is the expected value of the dependent variable in situ XNO2 (see Eq. 5) and X1, X2, X3, and X4 are the independent variables VCDtropo NO2, MH, wind speed, and na, respectively (see Table 3).

The conversion of in situ NO2 concentrations (cm) into mixing ratios is based on the equation 5in situXNO2=cm1Mi⋅RTp, where Mi is the molecular weight of NO2 and R denotes the universal gas constant. As for the calculation of na, p and T measurements at a 10 min resolution are taken from the BOKU weather station and averaged for the individual car laps.

All NO2 mixing ratio values within individual grid cells are averaged and then compared with each other.

Most of the emission sources other than traffic are located in the southeast of Vienna. The wind blew exactly from this direction on several days when car DOAS zenith-sky measurements were carried out. In addition, the car journey was planned to include the motorway along the Danube River, spanning a distance of about 20 km from the northwest (48∘21′25′′ N, 16∘18′25′′ E) to southeast (48∘12′32′′ N, 16∘26′24′′ E). These are prerequisites for the optimal analysis of the evolution of NO2 in space and time, in particular on days when wind was blowing from either the northwest (NW) or southeast (SE). As there are no large sources of NOx located in the NW, we rather focus on days when wind was blowing from the SE.

Data on wind direction and wind speed are provided by ZAMG. We have selected such data from four stations in Lower Austria and five stations in Vienna that are in close proximity to the car route (see Table 5). The temporal resolution of these measurements is 10 min. Instead of attempting to map the wind direction to the car route in time, we have averaged these measurements over the period between the start and end time of each car journey and calculated the standard deviation (see Table 3).

As the car DOAS zenith-sky measurements provide, in addition to the temporal distribution, the horizontal variation in NO2, the method described in Sect. 3.2.1 is applied to the car DOAS zenith-sky observations to determine horizontal gradients of NO2.

In Fig. 9, typical examples of such horizontal gradients are presented for 27 September (Sunday), 6 October (Tuesday), and 3 November (Tuesday) 2015 – three days with different wind conditions, temperature levels, and tropospheric NO2 amounts (see Table 3). In general, an increase in absolute NO2 differences with increasing distance from the individual starting points is found. While absolute NO2 differences sharply increase within the first one or two kilometers for most of the journeys, the increase significantly weakens during the remaining kilometers. During the first kilometer, absolute NO2 differences increase by a factor of 1.5 to 4, depending on the overall NO2 level on the investigated days. While the absolute NO2 differences rise by a factor of about 2 within the first two kilometers on 27 September, an increase by a factor of almost 4 is found for the same distance on the more polluted 6 October 2015.

The results imply that the magnitude of absolute NO2 differences is linked to the magnitude of tropospheric NO2 amounts observed. Conversely, it is difficult to detect the factors affecting the shape of the derived curves. Interestingly, we found only small differences in the shape and magnitude of horizontal NO2 gradients when comparing individual car journeys of single days with each other. Only for days with significant changes in wind direction (e.g., 27 September 2015) are the differences in magnitude obvious, when the single laps are compared with each other. While the curves of 10 April (not shown) and 6 October are similar in shape, the typical sharp increase within the first two kilometers is not observed for 3 November, although average values of wind speed, wind direction, and mixing height were similar on those days (see Table 3). It is not clear why the shape of NO2 as a function of distance observed on 3 November differs from those found on the other two days. One reason could be variations in photochemistry and/or emissions and/or dilution of NOx. It is interesting to note that 3 November 2015 was clearly the coldest day with temperatures below 5 ∘C (see Table 3). As a result, we argue that the characteristic horizontal NO2 scale of the observed NO2 fields in Vienna is on the order of 1 to 2 km.

Figure 10 shows typical car DOAS zenith-sky measurements of NO2 performed on 10 April 2015. The black and red curves represent DSCDmeas and VCDtropo, respectively. The stratospheric NO2 amounts as simulated by B3dCTM and scaled to GOME-2 observations (see Sect. 3.2.2) are illustrated by the blue line. Clearly, stratospheric NO2 is relatively low in this case of increased tropospheric NO2 levels when compared to VCDtropo. The relatively small diurnal increase in NO2 in the stratosphere can hardly be seen for the 6 h period. There are individual peaks in NO2 throughout the morning of 10 April 2015. While the longer lasting NO2 peaks are probably connected to pollution from traffic, sharp peaks rather indicate some outflow of NO2 from the refinery and/or other local static emission sources. The magnitude of observed NO2 VCDtropo is in good agreement with measurements performed around the German cities Mannheim and Ludwigshafen as well as in the Romanian city Braila (Ibrahim et al., 2010; Dragomir et al., 2015). As expected, significantly higher values of NO2 VCDtropo were observed by Wang et al. (2012) in the central urban area of Shanghai, China.

In the following, the small-scale transport of NO2 is evaluated along the Donauufer motorway (A22) in more detail. The A22 motorway, which is identifiable in Fig. 1 by azure and turquoise dots (NW to SE), is one of the busiest roads in Vienna, in particular in the southeastern area, where many commuters take the Südosttangente motorway (A23) at the motorway junction Kaisermühlen. The A23 is another busy road in Austria having about 160 000 passenger cars driving on it every day on average (https://www.vcoe.at, last access: 29 April 2019). As a consequence, NO2 levels are expected to be significantly increased in this area, in particular during the morning and evening rush hours.

The NO2 variation along the A22 motorway is shown in Fig. 11 for Friday, 10 April and Friday, 3 November 2015 as a function of cumulative distance, where the starting and end points are in the NW and SE of the A22 motorway. The red, blue, and green curves represent NO2 VCDtropo during the first, second, and third drives, respectively. In order to not confuse the reader, the first and second rounds of days with measurements taken only during two rounds are here referred to as rounds two and three, starting approximately at 07:00 and 08:30 UT, respectively (see Table 3). While wind was blowing from the SE on both days, averages of wind speed were slightly higher on 3 November.

On 10 April, the highest NO2 VCDtropo is observed in the SE rather than in the NW during the first drive. This seems reasonable as the traffic volume is generally largest in this area, in particular during the morning rush hour, which is captured by the first drive of that day. NO2 loads then move to the NW of the A22 motorway because air masses are transported from the SE. A clear shift of NO2 pollution from the SE to the NW is observed on 10 April 2015. The highest NO2 VCDtropo values during the first (> 1.5×1016 mol cm-2), second (< 2.0×1016 mol cm-2), and third drives (> 2.5×1016 mol cm-2) are located around 19.5, 18.5, and 8.5 km away from the starting point in the NW, respectively. Interestingly, the observed NO2 peak during the last drive is very pronounced. We attribute this to the NO2 formation via the chemical reaction of NO with ozone towards noontime. The topography in this area could also be responsible for these high NO2 levels. There are two hills east (Bisamberg, 358 m a.s.l.) and west (Kahlenberg, 484 m a.s.l.) of the Danube River. As a consequence, the pollution load could be channeled between the two hills, leading to a localized increase in NO2 amounts in this area.

The distance of NO2 transport appears larger between the second and third drives when compared with distances of NO2 transport between the first and second journeys. This might be related to the increase in average wind speed throughout the morning (see Table 3). Overall, the distance of NO2 transport on 10 April 2015 is in good agreement with average wind speed. Due to higher wind speeds on 3 November 2015, the expected peaks of NO2 in the NW during the third journey cannot be seen anymore. This might be related to the high averaged wind speeds during the second and third drives (between 8 and 10 km h-1) and thus a distance of transport exceeding the area of evaluation. Conversely, a clear shift of elevated NO2 amounts into the NW is also observed for the second round on 3 November 2015. It is interesting to note that the horizontal extent of elevated NO2 amounts during the third round of 10 April and during the second round of 3 November 2015 spans about 8 km in both cases – under similar wind speeds. We argue that this is a characteristic horizontal extent of a NO2 plume resulting from morning rush-hour traffic in Vienna under calm southeasterly winds.

The spatial and temporal variation in tropospheric NO2 amounts is also evaluated by analyzing the tower DOAS off-axis measurements. In order to correct light path lengths in the troposphere, NO2 DSCDs are normalized with O4 DSCDs. When looking at the time series of intensity (see Fig. 2), NO2, and O4 (Fig. 12), it becomes apparent that these parameters show variations as a function of azimuth angle. This variation is repeated with each further tower platform rotation. Although some similarity is found between DSCD NO2 and O4, the highest and lowest amounts of both trace gases are somehow shifted on the x axis. Some similarity between DSCD O4 and NO2, which is observed on all five days (not shown), is attributed to changes in the light path. Interestingly, the normalization with O4 slightly changes the azimuthal position of the pollution peaks towards the city center.

The geographical distribution of DSCD NO2 and O4 is shown in Fig. 13 for 10 May 2016, when tower DOAS off-axis measurements during nine platform rotations were collected. The values plotted on the map are mean NO2/O4 values and the radius is the O4 column. On that day, wind was mainly blowing from easterly to southeasterly directions. As a result, the highest NO2/O4 ratios are observed towards the city center.

The spatial and temporal variability of DSCD NO2/O4 as obtained from tower DOAS off-axis measurements is shown in Fig. 14 for 9 and 10 May 2016. As already identified from the analysis of the car DOAS zenith-sky measurements, the highest tropospheric NO2 over Vienna is found in the early morning – a consequence of both a lower (nocturnal) mixing height and emissions of NOx from morning rush-hour traffic. The highest NO2 amounts on both days are generally observed over the city center of Vienna, which is located to the southwest of the Vienna Danube Tower. A closer look suggests that DSCD NO2/O4 is about a factor of 2 larger on 9 May than on 10 May. While wind was constantly blowing from the SE on both days, the explanation for this is most likely the higher wind speeds on 10 May.

The spatial and temporal evolution of NO2 on 10 April 2015 in Vienna as observed by car DOAS zenith-sky (dots) and in situ measurements (squares) is shown in Fig. 15. Wind direction and wind speed obtained from local weather stations are indicated by white arrows. The geographical maps illustrate the spatial distribution of tropospheric NO2 during the three performed journeys on that day. As already highlighted in Sect. 4.2, a clear change in the amount of NO2 throughout the morning is observed along the motorway A22. A large proportion of observed NO2 amount is produced from traffic emissions of NOx during the morning rush-hour traffic, in particular in the area southeast of the city center. During the time period of about 4.5 h between the starting and end points of the measurements performed on that day, NO2 is transported over a distance between 10 and 15 km. Another hot spot of increased NO2 levels is observed close to an oil refinery in the SE. The outflow of the refinery is in good agreement with wind direction on that day. As already mentioned in Sect. 4.2, such peaks of NO2 amounts as a result of local static emission sources are sharper than those originating from typical rush-hour traffic. There is a clear decrease in tropospheric NO2 throughout the morning (see also Table 3), most likely as a consequence of dilution and/or the reaction of NO2 with the hydroxyl radical (OH), which is the largest NOx sink during daytime.

Overall, averages of tropospheric NO2 observations were highest on 10 April and 3 November 2015. We attribute this behavior to the comparatively low wind speeds, and consequent low dilution.

As outlined in Sect. 3.5, the correlation of the two data sets (car DOAS zenith-sky versus in situ) uses data converted into NO2 mixing ratios, which are values gridded onto 0.01∘×0.01∘ cells. The correlation is performed for each single day when car DOAS zenith-sky measurements were carried out. The scatter plots including statistics about slope, intercept, and correlation coefficient are illustrated in Fig. 16. Each of the diamonds represents a grid box average of XNO2 from car DOAS zenith-sky measurements as a function of averaged XNO2 from in situ monitors. The correlation coefficient on 10 April 2015, for example, is 0.83, suggesting a close linear relationship of the two independent NO2 measurements on that day (see also Table 3). The apparent negative offset implies that in situ XNO2 is higher than XNO2 estimated via Eq. (3). While this is the case for the grid box averages calculated from measurements taken during the second and third journeys of that day, XNO2 values from car DOAS zenith-sky observations seem to be overestimated during the first journey. A similar result with slightly lower values for R and slope is observed on 2 October, the second day, when early morning measurements were performed and when wind was also blowing from the southeast. The reason for the better agreement in the early morning (e.g., during the first car journey) could be the lower MH and lower wind speed, resulting in a better vertical mixing within the shallow boundary layer. The increase in both MH and wind speed throughout the morning might counteract a vertical mixing of NO2 loads.

Another explanation of the rather underestimated mixing ratio values obtained from car DOAS zenith-sky measurements observed on the other days is a possible overestimation of tropospheric AMFs, which are used for the conversion of NO2 DSCDs (see Eq. 1). Wang et al. (2012) have reported total uncertainties of tropospheric AMFs in the range of 20 %–30 % for SZAs < 40∘. With increasing SZA towards sunrise and sunset the uncertainties further increase. We note that most of our car DOAS zenith-sky measurements were performed for SZAs larger than 40∘.

Kramer et al. (2008) performed a comparison between data from a concurrent MAX-DOAS (CMAX-DOAS) instrument and in situ instruments in the city of Leicester, England. They highlighted the fact that the relative positions of the in situ instruments to the streets affect the comparison. In contrast to their study, car DOAS zenith-sky measurements were performed along motorways in our study. Therefore, this effect can be partly ruled out for the comparison presented in our study. Difficulties rather arise from losing some of the NO2 signal at the surface levels because of the zenith-sky geometry applied for our car DOAS measurements.

Nevertheless, large correlation coefficients (R = 0.72–0.93) are also observed on the other days with wind coming from the SE (6, 27 October and 3 November). In contrast, weak correlation between the two data sets is observed on days when wind was blowing from the NW (27 September, 19 and 23 October). The reason for the weak correlation on those days is not entirely clear. However, a closer look reveals that the variability of NO2 levels between the performed car journeys on a single day is only low on days with winds from the NW (see Table 3). This might be related to the high traffic volume but also most of the in situ monitoring stations used in this study are located rather in the SE of the city center than in the NW and thus the peak of rush-hour traffic does not show up in the measurements of most of the in situ monitoring stations on those days.

As XNO2 values estimated via Eq. (3) represent averages within the PBL and thus values are rather underestimated when compared to the values obtained from air quality monitoring stations (see Table 3), a linear regression analysis is introduced (see Eq. 4). The motivation behind this approach is related to the findings of Dieudonné et al. (2013). The authors of that study highlighted the fact that the vertical distribution of NO2 within the PBL over an urban area is not homogenous. They also suggested considering the effect of wind speed on the vertical gradient. Therefore, we also include wind speed in the linear regression analysis.

The lap averages of car DOAS (surface) XNO2 are given in Table 3. Overall, the values are in good agreement with the lap averages obtained from the air quality monitoring stations. For a better view, the modeled mixing ratios are plotted against mixing ratios obtained from in situ measurements in Fig. 17. The grey dotted lines represent the ±25 % level, meaning that all the values estimated via Eq. (4) are within ±25 %, with the exception of values lower than 10 ppb. The reason for these larger differences could be a reduced signal-to-noise ratio of the car DOAS zenith-sky measurements and consequently larger errors in the NO2 DSCDs. Nevertheless, the high correlation coefficient of the linear relationship (R = 0.94) is promising, in particular when thinking of applying this method to NO2 VCDtropo obtained from long-term MAX-DOAS measurements, which provide better statistics.

Although the NO2/O4 ratio gives an overall impression of spatiotemporal changes of NO2 amounts over Vienna, an absolute quantification of NO2 amounts (e.g., the conversion into mixing ratios) is not possible with this approach. Therefore, another method is used for the estimation of path-averaged NO2 mixing ratios at 160 m altitude of the rotating tower platform (see Sect. 3.7.2).

Estimated horizontal optical path lengths as a function of the azimuthal viewing direction obtained from measurements taken on 29 April (blue) and 9 May (red) 2016 are shown in Fig. 18. Both curves represent the last round measurements recorded during those days, when the reference zenith-sky measurement was taken shortly afterwards. Overall, higher hOPLs are observed on 9 May, which was a day with wind speeds reaching up to 15 km h-1. The exceptionally low wind speeds observed on 29 April (< 5 km h-1) explain the lower values of hOPL on that day. Low values of hOPL are generally linked to low visibility, which is the result of an increased aerosol accumulation over emission hot spots on that otherwise cloudless day. As aerosols largely affect hOPL under such conditions (Sinreich et al., 2013), it is reasonable that the lowest values (5–6 km) are preferably found in off-axis directions between the eastern and southern directions, which include areas with high traffic roads and industry. In contrast, the highest hOPLs are observed in the north of the Vienna Danube Tower on both days (10–11 km). This is reasonable because those regions are known as rather rural areas without significant emission sources. The highest hOPLs estimated in our study are slightly lower than the mean value (12.9 km) reported in Seyler et al. (2017), but still within the standard deviation.

Although our assumption made on the limitation of the horizontal light path length towards the hill might be critical, we argue that the distance of 6.95 km between the Vienna Danube Tower and the summit of that hill is still lower than 12.9±4.5 km and thus seems to be optimal for this normalization approach.

Estimated path-averaged NO2 mixing ratios are shown for 29 April (blue) and 9 May (red) 2016 in Fig. 19. Again, only the last rotations of those days are presented in the graph. As expected from the observed wind conditions and estimated hOPLs, path-averaged XNO2 is higher on 29 April. Over rural areas, which are located in the north of the Vienna Danube Tower, values are lowest (2.5 to 4 ppb) on both days. In contrast, the highest values (up to 9 ppb) are again observed towards the SE. We note that path-averaged mixing ratios are only shown for two tower rotations, which took place shortly before noon – at a time when the peak in NO2 amounts over the city is past.

For a better illustration, XNO2 as a function of hOPL obtained from the last rotation of tower DOAS off-axis measurements and XNO2 values calculated from simultaneous in situ measurements are plotted on a geographical map in Fig. 20 for 29 April (a) and 9 May 2016 (b). We note that the NO2 mixing ratios estimated from tower DOAS off-axis measurements are averages over several kilometers at 160 m above ground, whereas NO2 mixing ratios from in situ stations rather represent point measurements at the surface level. The comparison therefore implies that the variability of NO2 as observed at 160 m above ground is much less pronounced than that between the individual ground stations. Moreover, horizontal gradients at 160 m above ground are small. As already outlined above, the highest NO2 amounts obtained from both measurements are generally found over the city center and over high-traffic roads in the southeast of the city center on 29 April, a day with very low wind speeds (< 5 km h-1). The picture looks different for 9 May, when wind was blowing from the southeast and wind speeds reached values of up to 15 km h-1. The highest NO2 amounts from tower DOAS off-axis observations are found in parallel to the wind direction in this case.

For a better quantification, XNO2 from tower DOAS off-axis measurements as well as XNO2 from in situ observations are averaged and compared with each other (Fig. 21). While the mean and standard deviation are calculated by including all individual measurements of the last tower rotations in the former case, these parameters are computed by including measurements of XNO2 from air quality monitoring stations that fall within the outer circle of tower DOAS off-axis measurements as determined by hOPL in the latter case. For both tower DOAS off-axis and in situ measurements, averaged XNO2 values are larger by a factor of 2 on 29 April than on 9 May. On both days, averaged NO2 mixing ratios are about a factor of 6.5 larger at the surface level when compared with averaged path-averaged values at 160 m above the ground. This difference is much larger than the 25 % difference reported in Dieudonné et al. (2013), who compared surface concentrations with in situ concentrations at 300 m above ground in Paris. One reason for the larger factor found in our study might be an overestimation of mean XNO2 at the surface level due to the relatively large number of air quality monitoring stations close to the city center, where higher pollution levels are expected. Conversely, low values of mean XNO2 at 160 m above ground arise from the long light paths, which partly include areas with lower traffic density, especially in the north of the Danube River. Although a quantification and comparison is challenging for this case study with only a small number of data, interesting insights into NO2 distributions in the boundary layer above the urban area of Vienna can be gained.