Studies of the horizontal inhomogeneities in NO 2 concentrations above a shipping lane using ground-based MAX-DOAS and airborne imaging DOAS measurements

This study describes a novel application of an "onion peeling" like approach to MAX-DOAS measurements of shipping emissions aiming at investigating the strong horizontal inhomogeneities in NO2 over a shipping lane. To monitor ship emissions on the main shipping route towards the port of Hamburg, a two-channel (UV and visible) MAX-DOAS instrument was deployed on the island Neuwerk in the German Bight, 6–7 km south of the main shipping lane. Utilizing the fact that the effective light 5 path length in the atmosphere depends systematically on wavelength, simultaneous measurements and DOAS retrievals in the UV and visible spectral range are used to probe air masses at different horizontal distances to the instrument to estimate twodimensional pollutant distributions. Two case-studies have been selected to demonstrate the ability to derive the approximate plume positions in the observed area. A situation with northerly wind shows high NO2 concentrations close to the measurement site and low values in the north of the shipping lane. The opposite situation with southerly wind, unfavorable for the on-site 10 in situ instrumentation, demonstrates the ability to detect enhanced NO2 concentrations several kilometers away from the instrument. To validate the approach, a comparison to air-borne imaging DOAS measurements during the NOSE campaign in July 2013 is performed, showing good agreement between the approximate plume position derived from the onion peeling MAX-DOAS and the air-borne measurements. Combining synergistically information about the plume width from the airborne measurements and about the vertical plume extent from MAX-DOAS, yields NO2 concentrations in the plume from 15 both measurements which agree very well.


Introduction
Over the last decades, there has been a strong increase in ship traffic and shipping emissions of gas phase pollutants but a reduction in their land sources in much of Europe.This has lead to an increasing contribution of shipping emissions to Ortega et al. (2015) probed a circular area with 14 azimuthal viewing directions distributed over a 360°view around the instrument.In the present study, a similar measurement pattern was applied using 5 different azimuth directions distributed over a 120°angle to cover the shipping lane close to the island (see Fig. 1b) with sufficient time resolution to monitor individual passing ships.The onion peeling approach provides additional distance information for the measured NO 2 columns.
This study uses measurements in both the UV (∼350 nm) and blue spectral range (∼450 nm), while Ortega et al. (2015) used additional measurements in the yellow spectral range (∼570 nm) to get an even longer effective horizontal light path and cover a larger region.This is not possible here as the instrument used has a smaller wavelength coverage.
As can be seen from Fig. 1a and b, the measurement site on the island Neuwerk is ideal for applying this measurement principle: The distance between site and shipping lane is on the order of 6 to 10 kilometers, depending on the azimuthal viewing direction, which is in the range of typical UV horizontal effective light path lengths (Seyler et al., 2017).Depending on the azimuthal direction, the additional probing distance gained by measurements in the visible spectral range covers the shipping lane or the region in the north of the ship track.As it is shown in the following, this enables the NO 2 distribution caused by the ship emission plumes over and around the ship track to be determined.In addition even the distance and course of the emitted plumes is observed.This publication is a follow up to an earlier study entitled "Monitoring shipping emissions in the German Bight using MAX-DOAS measurements" (Seyler et al., 2017) where long-term measurements were used to asses the impact of shipping emissions on the regional air quality, while the present study focuses on describing, demonstrating and validating a new method for improved measurements of ship emissions and their localization.
The present study is part of the project MESMART (measurements of shipping emissions in the marine troposphere), a cooperation between the University of Bremen (Institute of Environmental Physics, IUP) and the German Federal Maritime and Hydrographic Agency (Bundesamt für Seeschifffahrt und Hydrographie, BSH), supported by the Helmholtz Zentrum Geesthacht.For further information visit http://www.mesmart.de/.
2 Measurement site and instrumentation

MAX-DOAS instrument
The multi axis differential optical absorption spectroscopy (MAX-DOAS) (Hönninger et al., 2004;Wittrock et al., 2004) is a well-established technique for measurements of trace gases that absorb in the UV and visible spectral range.This passive remote sensing method measures spectra of scattered sunlight in multiple viewing directions and is highly sensitive to absorbers in the atmospheric boundary layer.A two-channel MAX-DOAS instrument was deployed on the island Neuwerk from July 2013 to July 2016.It comprises a telescope unit with a field of view of 1°on a pan-tilt head, an optical fiber cable and two spectrometers with CCD cameras for UV (304.6-371.7 nm) and visible (398.8-536.7 nm) spectral range.This arrangement is optimized for the simultaneous retrieval of NO 2 and O 4 in both spectral domains.
A detailed description of the MAX-DOAS instrument and its components as well as the general measurement geometry for ship emission measurements is given in Seyler et al. (2017).Details of the DOAS fit settings used are given in Table 1.

Measurement site
Neuwerk is a small island in the German Bight, northwest of the city of Cuxhaven at the mouth of the river Elbe, around 9 kilometers off the coast.An overview of the area is shown in Fig. 1a.The main shipping lane into the river Elbe towards the port of Hamburg passes the island in the north in a distance of 6-7 km (see Fig. 1a).The MAX-DOAS instrument was installed on a radar tower in a height of 30 meters above ground level.Additional instrumentation on site included in situ gas analyzers (NO x , SO 2 , O 3 , CO 2 ) in a combined compact housing (Airpointer from MLU-recordum, Austria), a Davis Vantage Pro 2 semi-professional weather station and an automatic identification system (AIS, (IMO, 2002)) receiver.The AIS signal broadcasts various information like identification, position, speed, course and size of the ship.Broadcasting equipment is mandatory for all ships larger than 20 m.In the present study, the AIS information is used to attribute the measurements to

Ring
SCIATRAN (Rozanov et al., 2014) SCIATRAN (Rozanov et al., 2014) * Interpolation in time between the zenith measurements directly before and after the off-axis scan.
individual ships.Wind direction and speed is available with a time resolution of 10 minutes from two stations (see Fig. 1a), one on Neuwerk and one on the neighboring island Scharhörn, operated by the Hamburg Port Authority (HPA).
To sample a larger region, the MAX-DOAS was set up to have five different azimuthal viewing directions: 310°, 335°, 5°, 35°and 65°with respect to north, each pointing towards different sections of the shipping lane (see Fig. 1b).
For further information on the measurement site and instrumentation see Seyler et al. (2017).

Methodology
The quantity retrieved from DOAS measurements is the concentration of an absorber integrated along the atmospheric light path, the so-called slant column density (SCD).To measure the NO 2 absorption inside the ship plumes emitted on the shipping lane, the instrument is pointing in 0.5°elevation towards the horizon.Taking a close-in-time zenith-sky measurement as a reference, in a first assumption only the absorption along the horizontal part of the effective light path is retrieved and the absorption higher up in the atmosphere cancels out.This yields the differential slant column density (DSCD).
For the comparison with in situ measurements the MAX-DOAS horizontal trace gas columns are converted to horizontal path averaged volume mixing ratios (VMR) by using the O 4 scaling approach (see Section 3.1).The onion peeling approach (see Section 3.2) is used to separate NO 2 absorptions at different horizontal distances to derive separate NO 2 VMRs and estimate the distance to the plumes.3.1 O 4 scaling approach -methodology and limitations The oxygen collision complex O 4 absorbs in similar wavelength ranges as NO 2 in the UV and visible.Since the near-surface concentration of O 4 is known, the effective horizontal path length can be calculated by dividing the DSCD of O 4 by its number density n O4 :

5
with n O4 = (n O2 ) 2 , which can be calculated from the measured temperature and pressure.This can be done independently for both UV and visible measurements, giving average light path lengths of L UV = (9.3± 2.3) km and L vis = (12.9± 4.5) km [mean ± standard deviation] for the three years of measurements on Neuwerk, depending on the observational conditions.
Under clear sky conditions, typical light path lengths are 10 km in the UV and 15 km in the visible spectral range (Seyler et al., 2017).
This O4 scaling approach has been successfully applied to MAX-DOAS measurements before, for example in urban polluted areas (Sinreich et al., 2013;Wang et al., 2014) or at high mountain sites (Gomez et al., 2014;Schreier et al., 2016).
For a homogeneous, well-mixed NO 2 field along the light path, this VMR must agree with in situ measurement from the same altitude.For the ship emission case, where emission plumes are filling only a small fraction of the several kilometers long light path, the path-averaged MAX-DOAS VMR will not represent the VMR inside the plume and values will be smaller than in situ measurements inside the plume (Seyler et al., 2017).
However, the different shapes of the atmospheric profiles of NO 2 (emitted and formed close to the surface) and O 4 (exponentially decreasing with altitude) introduce systematic errors as has been shown by Sinreich et al. (2013) and Wang et al. (2014).To account for this, correction factors calculated by radiative transfer simulations are needed.These depend on wellknown quantities such as solar zenith angle (SZA) and relative solar azimuth angle (RSAA) as well as on unknown quantities such as aerosol optical density (AOD), height of the NO 2 box profile and the extent and vertical position of the aerosol layer relative to the NO 2 profile (Sinreich et al., 2013), which are not measured and cannot be easily approximated for the present study.In previous studies, it has been assumed that NO 2 is well mixed within a layer from the surface up to a top layer height and absent above this altitude.This is not a valid assumption in case of horizontally inhomogeneous NO 2 fields such as those probed over the shipping lane.As in Seyler et al. (2017), scaling factors are therefore not considered here, presumably leading to a systematic overestimation of path lengths and thus underestimation of MAX-DOAS VMRs (Sinreich et al., 2013;Wang et al., 2014).

"Onion peeling" MAX-DOAS approach
As mentioned above, the wavelength dependence of Rayleigh scattering results in a wavelength dependence of the light path lengths after the last scattering point.This can be utilized to probe different air masses in the atmosphere by measuring both in the UV and visible spectral range.
The aforementioned O 4 scaling method gives two path-averaged volume mixing ratios for each measurement; one for the shorter UV and one for the longer visible effective horizontal light path, which are shown in Fig. 1b and 2 as a purple and green line, respectively.One can calculate a third volume mixing ratio from the difference of the two DSCDs and path lengths: This yields the average volume mixing ratio VMR @∆L along the path difference ∆L, which is shown as an orange line in Fig. 1b and   As each ship is a moving point source for NO 2 emissions, the NO 2 field over a shipping lane is strongly inhomogeneous.
This means that the NO 2 is in general not distributed evenly along any of the effective horizontal light paths.
Depending on the position of the plume in relation to the UV and visible light path, the path averaged mixing ratios can differ substantially.Figure 2 shows schematically the plume-light-path geometry for three possible observation scenarios and illustrates the expected NO 2 signal for the different horizontal light paths.
In case (a) the plume is close to the instrument and is completely covered by the shorter UV path L UV , i. e. it is closer to the instrument than the (mean) last scattering point in the UV.Although both paths cover the same amount of NO 2 , the retrieved path-averaged concentration is higher for the UV signal because of the higher relative contribution of the fraction of the light path which probes the NO 2 plume.The path difference ∆L incorporates no NO 2 from the emission plume, resulting in zero or background level NO 2 from there.It can be seen from Fig. 1b that this situation occurs for northerly wind directions.Section 4.2 shows example measurement results for such a case.
Case (b) shows the opposite situation, when the plume is further away from the instrument than the UV scattering point and only covered by the visible path L vis .This results in an enhanced signal for the NO 2 retrieved in the visible, and no signal in the UV.The path averaged concentration retrieved for ∆L is even higher, because ∆L is only a segment of the visible path and therefore shorter than the complete visible path.On Neuwerk, such a situation can occur for southerly winds (compare Fig. 1b).Section 4.3 shows example measurement results for this kind of situation.As already discussed in Seyler et al. (2017), the measured column density as well as the path-averaged concentration do not only depend on the emitted amount of NO 2 inside the plume, but also on the angle of intersection between plume and line of sight of the instrument.The smallest absorptions, and thus column amounts, will be retrieved if the plume runs orthogonal to the line of sight, the highest values if the instrument measures along the plume.The latter can occur for certain combinations of wind direction, wind speed and ship movement direction and speed.Because of the movement of the ships (and the shape of the shipping lane), this is in general not the case when the instrument measures in wind direction, as it would be for a stationary point source.
The time span between plume emission and measurement is also important for the measured NO 2 values because of NO to NO 2 titration, as a large fraction of nitrogen oxides (NO x ) is emitted as NO (Alföldy et al., 2013;Zhang et al., 2016), which does not absorb in the spectral range covered and cannot be measured with MAX-DOAS.Therefore, the NO 2 signal increases with distance from the ship and, depending on the wind direction, with distance from the ship track.

Plume trajectories
Here, plume trajectories have been calculated as simple forward trajectories on a 10 s time grid, where each point shaped plume air parcel on each time step is moved from its old position to a new position, depending on wind direction and speed.Each ship emits a new plume air parcel at each time step at the actual ship position.By starting with an initialization period of 90 minutes before the measurements, old plumes from ships that passed by the island before and already left the map can be included in maps as those shown in Fig. 6.The width of the schematic plumes in the maps is not to scale and depends simply on the ship size, with broader plumes drawn for larger ships.Plume broadening and dilution over time is neglected.However, the gray shading of the drawn plumes gets brighter with each time step to indicate the plume age.The trajectories are two-dimensional, vertical wind components were not measured and are therefore neglected.While some weather models provide such vertical wind components, their spatial and time resolution is too low for this application.

Onion peeling approach applied to ship emission measurements
Figure 3 shows the measured NO 2 DSCDs in 0.5°elevation for the 335°azimuth direction (compare Fig. 1b) on 26 May 2014.
The NO 2 shows sharp peaks, which originate from shipping emissions, with rapid changes of NO 2 levels between consecutive measurements of up to one order of magnitude.The small, but non-zero baseline between the peaks shows an ambient NO 2 pollution, which is enhanced in the morning hours.The background NO 2 signal may be originating from land-based sources 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 Time (UTC) As a result of the longer light path, the NO 2 columns measured in the visible range are larger than in the UV.The difference between visible and UV columns, ∆DSCD, shows concurrent peaks for some of the peaks, with varying relative height.The peak at 12:50 UTC is not visible in the ∆DSCD, indicating that the plume must be closer to the instrument than the UV scattering point.
Figure 4 shows the corresponding effective horizontal light path lengths derived from the measured O 4 DSCDs.For a clear sky day like this, path lengths are quite constant over time.Clouds can decrease or increase the light path length (and O 4 absorption) by multiple scattering, depending on the cloud's position and its optical properties, especially its optical thickness (Wagner et al., 2014).As a result, a day with scattered or broken clouds will show much more variation in path lengths even between consecutive measurements by having clouds in either off-axis or reference measurement or both or neither, which makes interpretation of results more difficult.
Figure 5 shows the horizontal path averaged NO 2 volume mixing ratios retrieved from the NO 2 DSCDs by using the O 4 scaling approach with the path lengths for UV and visible shown in Fig. 4, as well as the volume mixing ratio on the path difference calculated via Eq. 1.The baselines of all three curves agree very well, showing that the ambient NO 2 background pollution is well-mixed in the boundary layer and homogeneously distributed along all light paths sections.However, the sharp peaks originating from ship emission plumes have different relative heights, showing that the corresponding NO 2 field is inhomogeneous.The strong NO 2 signal at 12:50 UTC without enhanced NO 2 VMR on the path difference, resembling situation (a) in Fig. 2, will be further investigated in the next section.In Panel 15 the larger ship has moved further away from the instrument, leading for the first time in this sequence to a higher concentration on ∆L, far away from the instrument, than close by.

Southerly wind situations
The second selected case study shows a diametrically opposite situation: For southerly winds the emitted pollution plumes are blown to the north of the shipping lane (compare Fig. 1b), further away from the instruments.As a result, NO 2 concentrations south of the shipping lane, close to the instruments, should be low, resembling situation (b) in Fig. 2. On-site in situ instruments are not able to measure the ship emission plumes.
Figure 6 shows a 12 minute sequence of consecutive measurements on 13 August 2014 starting at 12:35 UTC (14:35 local time).It shows MAX-DOAS path averaged NO 2 VMRs as well as in-situ measurements.
In the map sequence, three ships can be seen on the shipping lane, two large ones (336 m and 365 m) and a smaller one (100 m).As all ships move in the same, eastward, direction, the plume trajectories are almost parallel.Apart from the ship emission plumes, another plume crosses the area of interest, originating from the two directly adjacent coal-fired power plants in Wilhelmshaven, located at 53.57°N, 8.14°E, in a distance of about 50 km, southwest of the measurement site.Using the 10 m a.g.l.wind speed of 7.5 ± 1.0 m s −1 the plume age is estimated to be around 110 minutes, and even shorter taking into account that wind speed increases with height.
Panel 1 shows the MAX-DOAS measurement at 12:35:31 UTC in the 310°azimuth direction.The horizontal path averaged NO 2 VMR along the UV light path is low (∼0.6 ppb) and on ∆L slightly enhanced (∼1 ppb), meaning low NO 2 close to the instrument and enhanced NO 2 further away (than the UV scattering point).The source for the enhanced NO 2 signal on ∆L could either be the small ship's plume or plumes from the more distant power plants.
The next measurement in Panel 2 at 335°azimuth gives similar results.In this viewing direction the plume of the small ship is not in the line of sight of the instrument, indicating that the plume originating from the power plants is the source of the slightly enhanced NO 2 VMR along ∆L.
In Panel 3 (5°azimuth) the MAX-DOAS instrument is measuring towards the two adjacent plumes of the two large ships, one located close to the UV scattering point and the other one further away.NO 2 VMR is high (∼2 ppb) behind the UV scattering point and medium high (∼1 ppb) closer to the instrument.
Panel 4 (35°azimuth) shows again high values far away from the instrument and medium high values close by.
In Panel 5 (65°azimuth), only one of the two plumes is in the line of sight and is further away than the UV scattering point, leading to enhanced NO 2 along ∆L and low (ambient) NO 2 along the UV path.
Panels 6 and 7 are similar to Panels 1 and 2, showing that the situation in these viewing direction has not changed four minutes later.
In Panel 8, four minutes after Panel 3, the plumes of the two big ships traveled a bit further northward, making the gradient between NO 2 VMRs on UV path and ∆L even stronger.
Panels 10 to 12 are similar to Panels 5 to 7.
In Panels 13 to 15, the plumes of the two big ships are now clearly only probed by the visible light path giving enhanced NO 2 concentrations along ∆L and low, ambient NO 2 concentrations along the UV path.To validate the onion peeling MAX-DOAS approach, the NO 2 VMRs retrieved from the MAX-DOAS measurements have been compared to other, independent measurements.As already indicated above, the comparison to on-site in situ trace gas analyzers is well suited for ambient NO 2 background values or specific constellations, but fails for in-plume concentrations in many constellations.For unfavorable wind conditions, like southerly winds, the in situ instrument does not detect the plumes at all.
The spatial resolution of satellite instruments is not sufficient to resolve individual ship plumes, even with the newest Sentinel 5 precursor satellite (3.5 × 7 km 2 , Veefkind et al. 2012).Airborne imaging DOAS measurements are the ideal method to compare to, at least on a campaign base, since they can deliver high resolution NO 2 maps along the azimuthal viewing directions of the instrument.Such measurement have been performed during the NOSE (for german "Nord-Ost-See-Experiment" meaning "North and Baltic sea experiment") campaign on 21 August 2013.

AirMAP instrument and data analysis
The Airborne imaging Differential Optical Absorption Spectroscopy instrument for Measurements of Atmospheric Pollution (AirMAP) is a push-broom imaging DOAS instrument.Scattered sunlight from below the aircraft is collected by a wide-angle objective and coupled into a sorted bundle of 35 sorted optical fibers.The image of the vertically stacked fibers is then dispersed by an imaging grating spectrometer and mapped onto a frame-transfer-CCD.The field of view of around 52°leads to a ground swath width similar to the flight altitude.With this set-up, 35 across track pixels are measured simultaneously with an exposure time of 0.5 seconds, leading to a spatial resolution better than 50 m when the aircraft is flying at 1600 m altitude.For more detailed information on the instrument see Schönhardt et al. (2015) and Meier et al. (2017).
Differential slant column densities of NO 2 were retrieved in a fit window of 425-450 nm using the settings described in Meier et al. (2017).For the retrieval of NO 2 vertical column densities, air mass factors were calculated for an NO 2 box profile in the lowest 500 m, in an atmosphere without aerosols and for a constant surface reflectance of 0.05.

NOSE campaign 2013
The NOSE campaign took place in northern Germany in August 2013 aiming at the measurement of shipping emissions in support of the MESMART project.On 21 August between 9:00 and 12:30 UTC a flight over the Neuwerk region was performed with a flight pattern covering the individual MAX-DOAS azimuthal viewing directions.In addition to that, a low level flight over an individual ship following the emitted plume was performed.For more detailed information on the NOSE campaign see Meier (2018).

Comparison between MAX-DOAS and AirMAP
The combination of ground-based MAX-DOAS with airborne imaging DOAS measurements provides mutual benefits for the interpretation of the measurements: The combination of both methods makes it possible to derive in-plume NO 2 concentrations from each method.
The onion peeling MAX-DOAS approach delivers horizontal path averaged concentrations.As discussed in Section 3.1, ship emission plumes usually fill only a small fraction of these light path segments.The average over the path segment will therefore strongly underestimate the concentration inside the plume.To retrieve the in-plume concentration, the horizontal plume extent has to be known.AirMAP high resolution NO 2 maps can provide this information.
The AirMAP measurements deliver vertical columns of NO 2 between ground and aircraft, but no information about the vertical location of the NO 2 inside the column.By assuming a box profile for the near-ground NO 2 layer, one can derive concentrations from the vertical columns.The MAX-DOAS vertical scan can provide an estimation for the vertical extent of the plume.The crucial differences in viewing geometries are sketched in Fig. 10.The MAX-DOAS instrument scans the plume vertically by using different elevation angles giving (slanted) horizontal transects of the plume.The AirMAP instrument, measuring in nadir direction downward from the aircraft, observes vertical transects of the plume.The plume height h can be roughly estimated from the MAX-DOAS measurements if the distance is known, while the plume position and width b can be obtained from the airborne observations.Hence, the combination of both observation geometries can be used to narrow down the plume's extent in space.along the UV path.The time difference between both measurements of less than 20 seconds is very small as stated in the map, especially considering the integration time of the MAX-DOAS instrument of 10 seconds.The calculated forward trajectory of this plume matches the AirMAP measurements.The plumes further north have been measured by AirMAP around 1 minute later, enough time for the wind to blow the plumes northward so that the positions do not fully coincide with the plume forward trajectories which have been calculated for the MAX-DOAS measurement time.
The calculated plume trajectory matches the AirMAP measurements very well (even better in the second example in Fig. 14) and the plume position derived from the onion peeling MAX-DOAS fits to the AirMAP measurements.These results provide confidence in the calculated plume trajectories, as well as in the onion peeling approach to detect locally enhanced NO 2 levels in the ∆L light path segment.
Figure 12a shows NO 2 VCDs from AirMAP as a function of distance to the radar tower for the flight track section shown in Fig. 11.The 35 individual viewing directions were binned to 5 (1:7, 8:14, 15:21, 22:28 and 29:35) to reduce the noise.
Although additional binning would reduce the noise even further, it would also smear out the plume signal, since the flight track crosses the plume not orthogonally but at an angle of about 70°(see Fig. 11).A strong enhancement of NO 2 is observed at a distance of about 9.1 km to 10.1 km.This interval is covered by the visible light path but not the UV path, which means it is completely inside the path difference ∆L.Along the UV path NO 2 VCDs are significantly lower representing ambient background pollution.There is a slight decrease of ambient NO 2 observed along the UV path from the radar tower towards the UV scattering point.Figure 12b shows the measurements of the plume in more detail, revealing the distance shift of the plume position in the different viewing directions due to the slanted angle between flight direction and plume.The NO 2 enhancement caused by the plume is roughly Gaussian-shaped in all 5 binned viewing directions, although maximum values and peak widths differ sligthly.
The measured vertical columns are total columns between flight altitude and ground level.To retrieve the local enhancement of NO 2 inside the plume, the background (ambient) column is subtracted from the total NO 2 column: The plume width b can be estimated from the measurements as b = 500 m ± 100 m.The three panels in Figure 13 show the MAX-DOAS DSCDs of NO 2 for the lowest 5 elevation angles measured in the UV and visible spectral range, as well as their difference, ∆DSCD.The UV measurements in Panel (a) show the typical elevation angle dependency for tropospheric absorbers, with longest light paths (and therefore highest DSCDs) in the lowest elevation angles.When the instrument points further up (higher elevation angles), the light path lengths through the troposphere decrease giving smaller DSCDs.the instrument is around 1.0°.Thus the plume is observed in a solid angle of 2.0°(see Fig. 10).At a distance of 9.6 km, this corresponds to a plume height of h = 9.6 km • tan 2 • ≈ 335 m.
The plume, as can be seen in Fig. 11 and 12b, is only partly covered by the ∆L light path segment.To retrieve the in-plume NO 2 DSCD, the ambient NO 2 background within ∆L has to be subtracted.This can either be estimated from the measurements in the slightly higher elevations, which presumably do not contain plume NO 2 , assuming constant NO 2 background in the lower altitudes, or from the column along the UV light path.This is not trivial, since the ambient NO 2 is not constant along this path, but increases towards the radar tower, as can be seen in Fig. 12a.Whether this slightly enhanced NO 2 is in the right height to be probed by the instruments field of view, is unknown.Either way, both estimations end up with a similar background column of (6 ± 1) × 10 15 molec cm −2 , the error margin reflecting the underlying uncertainty.This yields: The NO 2 columns measured horizontally (MAX-DOAS) and vertically (AirMAP) through the plume are different.This is expected, because the horizontal and vertical extent of the plume differ -the plume width is larger than its height.For a quantitative comparison, the NO 2 column densities of both measurements need to be converted to VMRs.With the plume height derived from MAX-DOAS measurements the NO 2 VMR inside the plume can be calculated for the AirMAP measurements:

Conclusions
The present study describes a novel application of the "onion-peeling" MAX-DOAS approach to measurements of shipping emissions to estimate the two-dimensional pollutant distribution in the strongly inhomogeneous NO 2 field over a shipping lane.The ability to probe air masses at different horizontal distances to the instrument to derive the approximate ship plume positions in the measurement area is shown on the basis of selected case studies out of the three year measurement period on the island Neuwerk.Located in the German Bight, 6-7 km south of the main shipping lane from the North sea into the river Elbe towards the harbor of Hamburg, the island was selected as an ideal site for the application of the onion peeling approach.
It is located in a suitable distance to the shipping lane for exploiting the use of UV and visible radiation to probe the emission plumes released from the passing ships.
To determine the horizontal light path lengths for the onion peeling, a simple approach using the trace gas column of the oxygen collision complex, O 4 has been applied.To compare the measurements on the shorter UV path with the measurements on the longer visible path, horizontal path-averaged volume mixing ratios have been derived from the measured column amounts of NO 2 .In addition to that, the NO 2 mixing ratio on the path difference, which was usually located over or close to To conclude, the presented measurements provide a real world demonstration that the onion peeling approach works for MAX-DOAS measurments and can successfully be applied to ship emission measurements.

Figure 1 .
Figure 1.(a) Ship traffic density map calculated from all received AIS messages (2013-2016) showing the main shipping lane from the North sea into the Elbe river close to the measurement site on a radar tower on the island Neuwerk (red dot).Wind measurements are available on Neuwerk as well as the neighbouring island Scharhörn (green dots).(b) Effective horizontal light paths in UV (purple line) and visible spectral range (green line) for the five azimuthal viewing directions of the MAX-DOAS instrument (310°, 335°, 5°, 35°, 65°, with respect to north), shown for typical light path lengths of 9 km (UV) and 13 km (vis), respectively.The difference between both paths, ∆L, is highlighted by the orange line.

10
Knowing the horizontal light path length L, the NO 2 DSCD can be divided by L to obtain the average concentration (number density) of NO 2 along the horizontal light path.Dividing the NO 2 concentration by the concentration of air, n air , which can be Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-348Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 11 December 2018 c Author(s) 2018.CC BY 4.0 License.calculated via the ideal gas law from the measured temperature and pressure, yields the average volume mixing ratio (VMR) along L:

Figure 2 .
Figure 2. Plume-light-path geometry and the resulting path averaged NO2 concentrations for three possible cases: When the plume is close to the instrument and completely covered by the UV path (a), when the plume is further away from the instrument than the UV scattering point and is only covered by the visible path (and ∆L) (b) and when the plume is located around the UV scattering point (c) Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-348Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 11 December 2018 c Author(s) 2018.CC BY 4.0 License.In case (c) the plume is close to the UV scattering point.All three light paths see enhanced NO 2 .The relative peak heights depend on the fraction of plume NO 2 probed by the different light paths as well as the total light paths lengths.Situations like this will most likely occur for westerly and easterly winds.

Figure 3 .
Figure 3. Differential slant column densities of NO2 on 26 May 2014 in 0.5°elevation and 335°azimuth for the UV (purple) and visible spectral range (green) and their difference (orange)

Figure 4 .Figure 5 .
Figure 4. Effective horizontal light path lengths on 26 May 2014 in 0.5°elevation and 335°azimuth for UV (purple) and visible spectral range (green) and their difference (orange)

Figure 6 .Figure 7 .
Figure 6.Sequence of maps showing 15 consecutive measurements in 0.5°elevation on 26 May 2014, starting at 12:46 UTC (14:46 local time): The extent of the UV path and ∆L and corresponding path averaged NO2 VMRs are shown as colored lines.In situ NO2 VMRs are shown as a colored dot at the location of the measurement site.Magenta triangles show the ship position and course (sharp tip), with larger triangles for larger ships.Grey point clouds show forward trajectories of the emission plumes calculated from wind speed and direction for the moving ship.Wind direction and speed is shown with meteorological wind barbs.12

Figure 7
Figure 7 shows again in more detail the measurements, ship and plume positions from Panel 10.To highlight the entire retrieved two dimensional NO 2 field in the measurement region along the shipping lane, the four previous MAX-DOAS measurements are shown as well, which were measured between 30 seconds and 3 minutes before.The strong horizontal gradient between enhanced NO 2 concentrations close to the site and low concentrations further away for such a north wind situation is clearly visible in the figure.10

Figure 8 .Figure 9 .
Figure 8. Sequence of maps showing 15 consecutive measurements in 0.5°elevation on 13 August 2014, starting at 12:35 UTC (14:35 local time): The extent of the UV path and ∆L and corresponding path averaged NO2 VMRs are shown as colored lines.In situ NO2 VMRs are shown as a colored dot at the location of the measurement site.Magenta triangles show the ship position and course (sharp tip), with larger triangles for larger ships.Gray stripes show forward trajectories of the emission plumes calculated from wind speed and direction for the moving ship.Wind direction and speed is shown with meteorological wind barbs.15

Figure 9
Figure9shows again in more detail the measurements, ship and plume positions from Panel 15.To highlight the entire retrieved two dimensional NO 2 field in the measurement region along the shipping lane, the four previous MAX-DOAS measurements are shown as well, being measured between 30 seconds and 3.5 minutes before.It highlights the horizontal gradient between low NO 2 concentrations close to the site and enhanced concentrations further away, northward of the shipping lane, demonstrating that with MAX-DOAS it is well feasible to measure ship emission plumes under conditions unfavorable for in situ measurements.
Figure 10.Sketch of the different measurement geometries of ground-based MAX-DOAS and airborne imaging DOAS instrument when measuring a ship plume.While the MAX-DOAS instrument scans the plume vertically, the AirMAP instrument measures in nadir direction.Distances and sizes are not up to scale.

Figure 11
Figure 11 shows MAX-DOAS path averaged VMRs along with AirMAP vertical columns of NO 2 for a ship plume measured on 21 August 2013 around 9:53 UTC (11:53 local time).The Cessna airplane, a research aircraft of the Freie Universität

Figure 11 .Figure 12 .Figure 13 .
Figure 11.Map showing the MAX-DOAS path averaged VMRs (colored lines) and AirMAP vertical columns of NO2 (broad image stripe beneath) on 21 August 2013 around 9:53 UTC (11:53 local time).As the plotted physical quantities are entirely different (VMRs and columns), color scale agreements are not expected (and completely random).Magenta triangles show current ship positions and course.Grey stripes show forward trajectories of the ship emission plumes calculated from wind speed and direction for the MAX-DOAS measurement time.The time difference between AirMAP and MAX-DOAS measurements is indicated in the map at specific parts of the flight track.Wind direction and speed is shown with a meteorological wind barb.

Figure 14
Figure 14 presents another AirMAP overpass over several plumes from ten minutes earlier, again showing good agreement between the measured plume position and the approximate plume positions derived from the onion peeling MAX-DOAS.It shows even better how projected plume trajectories and real plume positions derived from AirMAP fit together.

Figure 14 .
Figure 14.Map showing the MAX-DOAS path averaged VMRs (colored lines) and AirMAP vertical columns of NO2 (broad image stripe beneath) on 21 August 2013 around 9:43 UTC (11:43 local time).As the plotted physical quantities are entirely different (VMRs and columns), color scale agreements are not expected (and completely random).Magenta triangles show current ship positions and course.Grey stripes show forward trajectories of the ship emission plumes calculated from wind speed and direction for the MAX-DOAS measurement time.The time difference between AirMAP and MAX-DOAS measurements is indicated in the map at specific parts of the flight track.Wind direction and speed is shown with a meteorological wind barb.
Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-348Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 11 December 2018 c Author(s) 2018.CC BY 4.0 License. the shipping lane in our measurements, can be calculated from UV and visible measurements, providing the NO 2 concentration several kilometers away from the instrument.For northerly wind directions, the onion peeling MAX-DOAS can detect enhanced NO 2 concentrations close to the instrument south of the shipping lane and low NO 2 concentrations north of the shipping lane.For southerly wind directions, low NO 2 values are measured close to the site south of the shipping lane and enhanced NO 2 values in the north of the shipping lane, demonstrating that the MAX-DOAS instrument can detect pollution several kilometers away from the instrument under wind directions unfavorable for in situ measurements.A comparison to airborne imaging DOAS measurements during the NOSE campaign 2013 shows the validity of the approach.The good agreement of AirMAP measured and MAX-DOAS derived plume positions shows that MAX-DOAS measurements can be used to derive the approximate position of the emission plumes.The good agreement of plume locations calculated from wind and AIS data with the AirMAP measurements shows that simple forward trajectories provide sufficient accuracy to model the two-dimensional NO 2 field over the shipping lane.Combining airborne vertical column and ground based horizontal column measurements provides mutual benefits, enabling the independent derivation of in-plume volume mixing ratios from both measurement techniques.AirMAP and MAX-DOAS in-plume VMR agree well within their error margins, again confirming the validity of the onion peeling MAX-DOAS approach.