Estimating real driving emissions from MAX-DOAS measurements at the A60 motorway near Mainz, Germany

. In urban areas, road trafﬁc is a dominant source of nitrogen oxides ( NO x = NO + NO 2 ). Although the emissions from individual vehicles are regulated by the European emission standards, real driving emissions often exceed these limits. In this study, two MAX-DOAS instruments on opposite sides of the motorway were used to measure the NO 2 absorption caused by road trafﬁc at the A60 motorway close to Mainz, Germany. In combination with wind data, the total NO x emissions for the occurring trafﬁc volume can be estimated. Hereto, the ozone-dependent photochemical equilibrium between NO and NO 2 5 is considered. We show that for 10 May 2019 the measured emissions exceed the maximum expected emissions calculated from the European emission standards ✿✿ for ✿✿✿✿✿✿✿✿✿✿ standardised ✿✿✿✿ test ✿✿✿✿✿ cycles ✿ by a factor of 11 ± 7 . One major advantage of the method used here is that MAX-DOAS measurements are very sensitive to the integrated NO 2 concentration close to the surface. Thus, all emitted NO 2 molecules are detected independently from their altitude and therefore the whole emission plume originating from the nearby motorway is captured which is a key advantage compared to other approaches such as in-situ measurements.


Introduction
Nitrogen oxides (NO x ) is a collective term for nitrogen dioxide (NO 2 ) and nitric oxide (NO). In the troposphere, a photochemical reaction with ozone leads to an equilibrium state between NO 2 and NO (Pandis and Seinfeld, 2006). A large fraction of the global emissions of NO x originates from anthropogenic sources. Therefore, nitrogen oxides do not only play a major role in atmospheric chemistry but are also important in terms of air quality. The World Health Organization reports negative 15 short-term as well as long-term exposure effects in pulmonary function and in other organs (World Health Organization et al., 2000). For this reason, the limitation of the concentration of nitrogen oxides is part of the European programme regarding ambient air quality and cleaner air (European Parliament and Council of the European Union, 2008).
Fossil fuel combustion from road traffic is a major contributor to NO x emissions. Hence, the European emission standards were introduced to regulate the exhaust emissions of new vehicles in the EU since 1998 (European Parliament and Council 20 of the European Union, 1998) and tightened in 2007 by a new regulation bringing into force the so-called Euro 5 and Euro 6 norms (European Parliament and Council of the European Union, 2007). New vehicles sold in the EU need to undergo a typeapproval procedure which verifies the compliance with these regulations. This procedure is standardised by the New European However, various studies (Carslaw et al., 2011;Chen and Borken-Kleefeld, 2014) have shown that the real driving conditions are more dynamic than the tested driving cycles. In addition, it is known that several manufacturers have installed software that manipulates the test results by reducing emissions specifically during the test procedure (Borgeest, 2017). This results in increased exhaust emissions during normal driving operation.
In-situ measurements such as used in vehicle chasing experiments, e.g. performed by Pöhler and Engel (2019), need to 30 convert NO into NO 2 as they directly measure the exhaust plume. Furthermore, this approach is dependent on the exact position of the emission source and the inlet of the measuring instrument. Others use remote sensing techniques (Carslaw et al., 2011;Chen and Borken-Kleefeld, 2014) to measure exhaust gases across-road. However, these require an estimate of the amount of primary NO 2 in the exhaust. Hence, the retrieval of the total amount of emitted NO x is afflicted with large errors.
Moreover, the across-road method can only give a point measurement and is not necessarily representative for the average 35 emission of a vehicle. Both approaches are able to resolve the emission of individual vehicles but are depending on the wind field and the position of the exhaust pipe with respect to the measuring instrument.
Nevertheless, in the atmosphere NO and NO 2 form an equilibrium state which is mainly influenced by the ozone concentration and solar irradiance but not the primary composition and amount of the exhaust gases. Thus, the Multi AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) yields a key advantage when operated at some distance from the emission 40 source. The method is described in more detail in the next section.

Method
The MAX-DOAS method (Platt and Stutz, 2008) allows measuring the differential slant column density (DSCD) of different trace gases (Hönninger et al., 2004). Hereto, spectra of scattered sunlight are recorded at different elevation angles using ground based instruments. To convert the slant column density (SCD), which represents the integrated concentration along the 45 slant light path, into the vertical column density (VCD), the so-called air mass factor (AMF) is needed. For trace gas layers close to the ground the geometric approximation for the AMF can be used (Hönninger et al., 2004). The integrated trace gas concentration along the vertical path is then given by where α is the elevation angle.

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In order to remove the Fraunhofer lines, the logarithm of a so-called Fraunhofer reference spectrum with preferably minimal trace gas absorption is subtracted from the logarithm of the measured spectra. To fulfil this criterion, the reference spectrum is usually recorded with an elevation angle α = 90°, i.e. in zenith direction. Assuming that for a given solar zenith angle the stratospheric absorption is constant for measurements at different elevation angles, the differential SCD yields the integrated tropospheric concentration of a specific trace gas (for an altitude range from the surface up to about 2 to 3 km, Frieß et al.,55 2019, and references therein).
In this study, the MAX-DOAS method is used to measure the NO 2 emissions of vehicles on a motorway. Using two MAX-DOAS instruments, the background NO 2 DSCD is subtracted from the total NO 2 DSCD and thus yields the NO 2 SCD caused by the traffic emissions. In a final step, the derived NO 2 SCD is converted into the NO x emissions by combining it with wind data and assuming a steady state NO x to NO 2 ratio. These steps are described in detail below.

Experimental setup
To retrieve the amount of NO x emitted by road traffic, two Tube MAX-DOAS instruments (Donner, 2016) were set up on both sides of a motorway. With these instruments, it is possible to measure the NO 2 DSCD of the ambient air along the viewing direction. The chosen measurement site is located along the heavily used A60 motorway close to Mainz, Germany, and has a long straight section which provides an advantageous geometry for the measurement setup. The exact alignment of 65 the instruments for the presented measurement day is depicted in Fig. 1 and shows that the viewing direction is northward and parallel to the lane of traffic. On the measurement day, continuous westerly wind was present so that the air mass transport was perpendicular to the motorway as well as to the viewing direction of the instruments. From the difference between the upwind (west side) and downwind (east side) signals, the emissions of the motorway are estimated. The locations of the instruments were about 160 m and 220 m to the west and east side of the motorway, respectively. Therefore, the area enclosed by the two In addition, a camera and a weather station were positioned on the upwind side to obtain further information. Taking videos with this setup makes it possible to observe the traffic density on the motorway. The weather station records the wind direction 80 and wind velocity as well as several other meteorological parameters such as pressure and temperature every second.

Spectral analysis
The spectral analysis of the obtained spectra is performed using the QDOAS software (version 2.112.2, Danckaert et al., 2012). As a reference, a series of 90°measurements were taken simultaneously with both Tube MAX-DOAS instruments at the upwind measurement site. In order to categorise differences between the two instruments (Sect. 2.3), the reference 85 measurements were taken at the same location after the measurement series was completed on both sides of the motorway. The wavelength calibration is accomplished using a high resolution solar spectrum (Chance and Kurucz, 2010). For the analysis, a wavelength range of 400 nm to 460 nm was selected. The DOAS fit includes trace gas absorption cross-sections (NO 2 at 298 K (Vandaele et al., 1998), O 4 at 293 K (Thalman and Volkamer, 2013), O 3 at 223 K (Serdyuchenko et al., 2014), and H 2 O (Rothman et al., 2010)) as well as two ring spectra, calculated with DOASIS (Kraus, 2003) using the reference spectrum, and 90 a polynomial of 5 th order also allowing an intensity offset. The spectral analysis is run separately for each instrument yielding the NO 2 DSCD time series for both measurement sites.

Instrumental differences
To estimate the influence of instrumental differences between the two Tube MAX-DOAS instruments on the NO 2 results, the reference spectra are investigated in more detail. These measurements were taken simultaneously with both instruments on the 95 upwind side with an elevation angle of 90°(zenith view). Fig. 2 shows the time series of the NO 2 results for these spectra. The first 90°measurement of each instrument is taken as a reference.
As can be seen, in the grey shaded area the standard deviation between the measurements of the two instruments only amounts to whereas for the spectra after 15:05 UTC the signal differs widely with a standard deviation of 7.9 × 10 14 molec cm -2 . This increased deviation is due to clouds passing by (see Sect. A1). Thus, the measurements in the grey shaded area show that both instruments measure similar NO 2 DSCDs for the same measurement conditions, i.e. the same setup, viewing direction and cloud conditions. Therefore, these spectra are being integrated to minimise noise and used as fixed references which assures that both instruments are analysed under the same conditions. 105

Integration time
In order to investigate the influence of the integration time on the spectral analysis, the fitting procedure is performed for spectra with different integration times but the same fit settings. Therefore, two or more spectra are added before performing the DOAS fit. The result of the NO 2 retrieval as well as the average root mean square (RMS) over each measurement series is depicted in Fig. 3. The standard error of the average NO 2 DSCD is about 0.006 × 10 16 molec cm -2 and thus not visible in the 110 Figure. The average NO 2 error, which is given by the QDOAS analysis, shows the same trend as the average RMS. Although the average RMS decreases for longer integration times, the NO 2 retrieval yields the same result regardless of the integration time. The standard deviation between the results for different integration times amounts to less than 8 × 10 12 molec cm -2 for the east side and 10 × 10 12 molec cm -2 for the west side measurements which is three orders of magnitude smaller than the NO 2 signal. Consequently, the measurements taken with an integration time of 2 s give sufficient results above the detection 115 limit which is preferable as high temporal resolution is necessary to resolve specific traffic events.

Measurement results
The measurement results for the 10 May 2019 are shown in Fig. 4 A persistent offset is found with a mean value of SCD traffic = (0.185 ± 0.009) × 10 16 molec cm -2 (4) 125 as represented by the orange line. The error is calculated using the error propagation of the standard errors of the mean for both instruments and additionally includes the deviation ∆(NO 2 DSCD) between both instruments as derived in Sect. 2.3.
As there are no large sources of NO 2 other than the motorway close to the measurement site, the background NO 2 DSCDs in both measurements can be assumed to be the same. Therefore, the difference between both sides is most likely due to traffic emissions. There seems to be no significant additional emission due to the passing trains (marked by the dashed grey lines in wind velocity, also the minimum and maximum values over 1 s using a sampling rate of 4 Hz are depicted in grey.

Plume age
For a better understanding of the retrieved signal, the wind field needs further investigation. The quantity of interest is the wind velocity v wind,⊥ perpendicular to the viewing direction of the Tube MAX-DOAS instruments whose viewing directions are assumed to be parallel to the motorway. Thereby, the age of the measured plume can be quantified which is needed to 140 retrieve the total emission (Sect. 3.3). The perpendicular wind velocity v wind,⊥ is shown in Fig. 4 (F) and is calculated using the measured wind velocity and the wind direction. From the alignment of the two Tube MAX-DOAS instruments as depicted in Fig. 1, it can be seen that the viewing direction corresponds to approx. 330°. The perpendicular wind velocity is thus where φ wind,meas is the measured wind direction at the weather station. The error can be calculated using the propagation of uncertainty principle and taking into account the minimum and maximum values of the wind data. An additional error for a possible misalignment of the weather station with regard to the viewing direction of the telescopes of 2°is considered. During the measurement period, the wind velocity perpendicular to the viewing direction is on average 150 v wind,⊥ = (2.8 ± 1.0) m s -1 .
Taking into account the average distance between the motorway and the downwind instrument's viewing direction x = (195 ± 25) m estimated from Fig. 1 within the main area of high sensitivity, an average age of an air parcel of can be obtained. However, variations in the wind velocity and wind direction on short time scales affect the transport of an air 155 parcel. Therefore, the plume age cannot always be correctly represented by Eq. 8. The correlation between the wind field and the measured NO 2 SCDs is further discussed in Sect. A3.

Estimation of real driving emissions
To estimate the real driving emissions, first the mean NO 2 SCD must be converted into a VCD using the geometric approximation as given in Eq. 1. Thus, for the elevation angle of 20 ± 2°, the measurement yields 160 VCD traffic = (0.63 ± 0.07) × 10 19 molec m -2 .
Multiplying this value by the average wind velocity perpendicular to the viewing direction, the measured emission of NO 2 amounts to E meas, NO2 = (1.8 ± 0.7) × 10 19 molec (m s) -1 .
This value now describes the number of molecules emitted per meter and second along the motorway section. It is a direct 165 quantity of the measurements and can be converted into emissions per vehicle per second by dividing by the number of vehicles per length of the motorway.
In combustion processes, N 2 is mainly oxidised into NO and in the atmosphere it is further oxidised into NO 2 and other oxides of nitrogen (Pandis and Seinfeld, 2006) forming an equilibrium between NO and NO 2 . Therefore, to retrieve the total NO x emissions from the observed NO 2 levels, the share of NO 2 in total NO x has to be known.

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In order to estimate the rate of NO to NO 2 conversion, we used the CAABA box-model simulation with representative environment conditions and a road traffic source for the measurement period. CAABA uses the atmospheric chemistry model MECCA that includes the state of the art chemical mechanisms (Sander et al., 2019). A fraction of the traffic-emitted NO is photochemically equilibrated with air NO 2 at the daytime near-surface conditions. We estimate that about two-thirds of the emitted NO is thus converted into NO 2 in about 4 min. After 2 min, about 90% of the traffic-emitted NO is converted into 175 the observed NO 2 enhancement. One important factor regarding the conversion is the ambient ozone level, as it regulates the 6 https://doi.org/10.5194/amt-2020-125 Preprint. Discussion started: 17 June 2020 c Author(s) 2020. CC BY 4.0 License.
photochemical NO x cycling and influences the resulting NO 2 to NO repartitioning dynamics. However, our simulations with CAABA confirm that for the presented measurement the NO 2 to NO ratio is rather stable and yields a ratio of 0.7 ± 0.4 for the time t = (1.2 ± 0.4) min which was estimated above. That is due to sufficiently high ambient ozone concentrations which were measured at local environmental monitoring stations (42 ppb to 44 ppb, Mainz-Mombach, distance to the measurement 180 site approx. 5 km, and Wiesbaden-Süd, approx. 9 km, Umweltbundesamt, 2019).
The corresponding NO x to NO 2 conversion factor, for the time t = (1.2 ± 0.4) min an air parcel needs to get from the vehicle exhaust to the sensitivity region of the Tube MAX-DOAS instrument, can be deduced to be f = 2.4 ± 1.0. The NO x emission is then derived using
In case the equilibrium is already reached, a conversion factor of f eq = 1.5 needs to be applied instead. Then, the total NO x emission would amount to E meas, NOx, eq = (2.7 ± 1.1) × 10 19 molec (m s) -1 .

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The determination of the conversion factor f relies on the rather rough estimate of the age of the air parcel as well as the ozone concentration and chemical processes during the measurement period. Therefore, the equilibrium value gives an estimate which is independent of these factors. However, it can be seen that this is within the error of E meas, NOx . In the following, the more realistic value of E meas, NOx will be taken for the comparison with the expected traffic emissions. To undertake the following calculation, these emission standards need to be converted into limiting values per km. Therefore, the values are multiplied by a conversion factor of 1.5 ± 0.5 kWh l −1 . This is composed of the fuel value 10.4 kWh l −1 of 200 diesel fuel, the efficiency of a diesel engine of about 40 % and an average consumption for trucks of 36 l per 100 km (Hilgers, 2016). The error accounts for varying fuel consumption of ±10 l per 100 km and the uncertainty in the efficiency of the vehicle engine.

Expected traffic emissions and comparison to real driving emissions
For the calculations, the statistical composition of the vehicle fleet is considered (see Table 2 The error estimation accounts for miscounting the number of vehicles on the video e.g. when a truck shields the view of the other traffic lanes. Taking into account the average traffic volume, the expected total emission for the measuring period is given by E calc, NOx = N cars · E limit, cars + N trucks · E limit, trucks which yields 225 E calc, NOx = (0.39 ± 0.07) × 10 19 molec (m s) -1 .
Here, it is used that the NO x emissions are given in NO 2 equivalents and thus 1 mg of NO x emissions correspond to 1.3 × 10 19 molec.
The expected emissions calculated from the European emission standards can now be compared to the measured NO x emissions. Evidently, the measured amount of NO x is by a factor 11 ± 7 larger than expected. Even if an equilibrium state 230 between NO and NO 2 for the measured traffic emissions was assumed, the measured NO x emissions still show a higher value (by a factor of 7 ± 3) compared to the calculated emissions. Moreover, in the very unlikely case that the exhaust gases primarily consist of NO 2 and the measured NO 2 difference directly equals the NO x emissions, this discrepancy remains unexplained.
Possible error sources in the measurement cannot completely explain these differences.
As the traffic volume was relatively constant throughout the measurement period, it is more likely that the statistics do not 235 reflect the vehicle fleet well enough and/or a large part of the vehicles does not meet the emission standards. Here, it should be noted that the deviations of the actual vehicle composition from the assumed one cannot be the sole reason for this factor. which is still lower than the measured emission. As today only a minor fraction of all vehicles is registered as Euro 3 cars and Euro III trucks, this worst case scenario is highly unlikely. Considering that especially non-German trucks more often drive with defective exhaust gas systems, these could lead to large emissions even exceeding the Euro III norm. Thereby, the discrepancy between the expected and measured emissions could be partly explained. However, trucks only account for a small amount of the total traffic volume. This again implies an excess of the European emission standards regarding NO x emissions 245 also for a significant number of passenger cars.

Conclusions
The measurement of NO x emissions at the A60 motorway close to Mainz, Germany, gives an estimate of the real driving emissions. With two MAX-DOAS instruments set up on both sides of the motorway, it is possible to retrieve the NO 2 signal caused by the road traffic and calculate the total NO x emissions for the occurring traffic volume.

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The most uncertain aspect during the analysis of the data was the age of the measured plume at the downwind side. It directly affects the conversion factor f of the NO x to NO 2 ratio and thus the final result of the measured emission (Eq. 11). To further investigate the effect of the plume age, it is favourable to set up several MAX-DOAS instruments downwind with different distances to the motorway. Thereby, the setup of the instruments could be optimised and the equilibrium state of NO 2 for the given weather conditions can be measured. This yields a more accurate conversion factor.

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Other aspects such as the high ozone concentration and relatively constant wind are uncritical for the presented measurement day and allow to apply a constant conversion factor f to the average emission. Although the changing cloud cover caused large fluctuations in the NO 2 DSCDs, filtering the data leads to only slightly lower emissions. Consequently, this effect cannot explain the difference between the measured and expected emissions.
The main possible error source regarding the derivation of the expected NO x emissions is the difference from the assumed 260 vehicle fleet to the measured vehicle fleet. Although the statistics are relevant to the Mainz region, the exact composition remains unknown. However, the worst case calculation showed that the uncertainty of the vehicle fleet cannot explain the deviation from the measured emission. Presumably, a considerable amount of vehicles did not meet the European emission standards. Moreover, it must be assumed that a substantial number of trucks are non-German vehicles. Recent studies showed that a large fraction of these vehicles had conspicuously high emissions which indicate deactivated fuel cleaning units (Pöhler 265 and Engel, 2019). These could also explain the temporal variations in the measured time series. Applying this method at different measurement sites, different driving conditions (e.g. the slope of the motorway section, the allowed speed limit, road works etc.) and the impact of the composition of the vehicle fleet could be investigated in more detail.
It can be concluded that the measured emissions exceed the maximum expected emissions calculated from the European emission standards (Umweltbundesamt) by a factor of 11 ± 7. This observation is in line with the work of other groups (Carslaw 9 https://doi.org/10.5194/amt-2020-125 Preprint. Discussion started: 17 June 2020 c Author(s) 2020. CC BY 4.0 License. et al., 2011;Chen and Borken-Kleefeld, 2014;Pöhler and Engel, 2019). Especially, the whole plume originating from the nearby motorway was measured rather than individual vehicle plumes and hence the possibility that parts of the plume get overlooked can be neglected which is a key advantage compared to other approaches such as in-situ measurements.
Data availability. Measurement data are provided in the supplement.

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A1 Effect of clouds on the reference spectra Clouds can have a great impact on MAX-DOAS measurements. A change of the light path is caused by the increased scattering probability in clouds as there are more particles compared to the ambient air. Furthermore, the wavelength dependency of the scattered light changes for particle scattering processes compared to pure Rayleigh scattering. This effect already occurs for aerosols and is even more pronounced for clouds.

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There are different methods to identify and classify clouds. Here, the temporal variation of the colour index (Wagner et al., 2014) is used. The colour index (CI) is defined as the ratio of two radiance values at different wavelengths. In this case, the wavelengths 320 nm and 440 nm are chosen. Thereby, the wavelengths cover a large range to pronounce the effect of the wavelength dependency.
The CI is calculated for the 90°measurements as shown in Fig. 2 and the obtained temporal evolution is given in Fig. A1. As 285 for cloud free conditions a constant CI is expected, it can be seen that measurements after 15:05 UTC were affected by clouds.
This leads to larger deviations in the retrieved NO 2 signal as shown in Sect. 2.3. Accordingly, the CI analysis also encourages the approach to use only the 90°measurements in the grey shaded area as a reference.

A2 Effect of clouds on the measurement result
Calculating the CI as described in Sect. A1 for all spectra, a characteristic behaviour can be seen (Fig. A2). As high temporal 290 variation indicates cloud cover, all spectra where the CI is below the reference CI ref are filtered. The reference was inferred by fitting a 2 nd order polynomial to the data. The filtered time series are displayed in Fig. A3 where the dashed line indicates the filter threshold. Recalculating the mean difference between the two measurement sites yields SCD traffic, filtered = (0.156 ± 0.005) × 10 16 molec cm -2 (A1) which is about 16 % smaller compared to the unfiltered case.

A3 Correlation to the wind field
Assuming a constant emission, the NO 2 difference is expected to be reciprocal to the wind velocity. However, an air parcel is also affected by obstacles such as trees and follows the turbulent flow of air. Furthermore, the wind varies on time scales of less than 1 min whereas the transport of the air parcel from the emission location to the sensitivity region of the MAX-DOAS instrument happens on larger time scales of 1 min or more. This means that the time of the wind measurement and the time 300 of the NO 2 measurement are shifted by a time difference in which the wind might change strongly. Hence, the age of the air parcel cannot always be correctly represented by the simple calculation in Eq. 8. In Fig. A4 the traffic emission SCD traffic is plotted against the inverse of the wind velocity v −1 wind,⊥ showing no correlation (R 2 = 0.001 1) between the two quantities. To further test this hypothesis, both -the wind measurements and the time series of the NO 2 differences -are averaged over a time period of 12 min. Figure A5 shows a higher correlation between both quantities (R 2 = 0.365). The data points 305 are fitted using the linear least squares method (LLS, orange line) as well as using the orthogonal distance regression (ODR, green line). Here, ODR is able to take into account the standard errors of the mean values in the fitting procedure (Cantrell, 2008). In doing so, the slope of the fit increases and at the same time the intercept decreases. Comparing the fit results with the obtained emission E meas, NO2 over the complete NO 2 measurement series as described in Sect. 3.3, a slope of about 5000 ± 2000 molec (m s) −1 is expected. The fits from Figure A5 show slopes of 4230 ± 208 molec (m s) −1 for the LLS and 310 7539 ± 2013 molec (m s) −1 for the ODR method which are in agreement with the expected value.
Nevertheless, the weak correlation is not completely surprising because of the low variability of the wind velocity. Moreover, a constant wind velocity is generally advantageous for the measurements. Competing interests. The authors declare that they have no conflicts of interests. 18 https://doi.org/10.5194/amt-2020-125 Preprint. Discussion started: 17 June 2020 c Author(s) 2020. CC BY 4.0 License.