A sketch of the viewing geometry is shown in Fig. . AirMAP observes from an aircraft nadir port downwards, measuring the solar electromagnetic radiation that is backscattered by the ground or atmosphere to the entrance objective. Radiation from a field of view (FOV) of around 48∘ across track is observed simultaneously. From the fibre bundle with an entire height of 8.5 mm, the radiation from 35 of the 38 individual fibres is recorded by the CCD with a chip height of 8.2 mm. Thus, a maximum of 35 individual viewing directions can be separated at a time. The instantaneous FOV (IFOV) along track is around 1.2∘, while the effective FOV along track is given by the convolution of the IFOV with the travelled distance (i.e. the product of flight speed and exposure time). The along-track IFOV projected onto the ground is usually smaller than the travelled distance during the exposure time and is therefore neglected in the trace gas maps. The length of displayed ground pixels in flight direction is determined here by the travelled distance during one exposure, also taking into account the aircraft attitude at the start and end of an exposure.

Typical flight speed during the central flight pattern (i.e. the flight path above the power plant area) is around 60 m s-1. With an exposure time of 0.5 s, a ground pixel size of 30 m along track is achieved.

The lines of sight, LOS, across track are spread between ±24∘ at level flight. With respect to flight direction, positive LOS values point to the right. At a typical flight altitude of around 1100 m a ground swath width of nearly 1000 m is covered. Averaging over neighbouring viewing directions and/or over time along track may be applied during post-processing depending on the respective research focus, e.g. depending on the spatial extent of observed sources and required signal-to-noise ratio. All values reported in the present study are derived from the original 0.5 s exposures without temporal averaging. Specifications for ground resolution and spatial imaging quality follow below in Sect. .

Under flight conditions, the viewing geometry as described above is impacted by the aircraft attitude, i.e. the pitch, roll and yaw (heading) angles. For an accurately computed geolocation, required for source assignment and the determination of distances, it is essential to take into account the aircraft orientation and its altitude in addition to the latitude and longitude positions. Positioning information is either taken from the AirMAP GPS and AHRS, or it is received from the AIMMS-20 AHRS on board the research aircraft. The latter is used in the current study. By convention, the pitch angle is positive when the aircraft nose is pointing upwards, the roll angle is positive when the right wing is down and the yaw angle is counted positive from north (0∘) in clockwise direction, i.e. towards the east.

The information of the aircraft positioning is read twice, viz. at the start and the end of each exposure. To map the trace gas amounts, the coordinates of the four corners of each ground pixel are computed – two corners for conditions at the exposure start, and two for the end conditions. Linear variation of all parameters during the fairly short exposure time of 0.5 s is assumed, so that the ground pixel is a tetragon. The across-track limits of an individual ground pixel are given by two individual LOS angles, θi, with respect to the centre of the entire FOV. From the pitch (αp) and roll (αr) angles, the spatial displacements of the corner ground locations along (L) and across (d) flight direction can be calculated, whereby H denotes the flight altitude above ground level (a.g.l.). L=H⋅tan⁡(αp)d=Hcos⁡(αp)⋅tan⁡(θi-αr) Starting from the aircraft location with latitude ϕ0 and longitude λ0, a corner coordinate (ϕ,λ) deviates from the centre by ϕ′ and λ′ and is calculated at a given time instance for each individual corner by using the above displacements, the aircraft yaw angle (αy) and the Earth radius R0: λϕ=λ0ϕ0+λ′ϕ′ with λ′ϕ′=180∘πR0cos⁡αycos⁡ϕ0sin⁡αycos⁡ϕ0-sin⁡αycos⁡αydL. This results in λ′=180∘⋅HπR0cos⁡ϕ0cos⁡αytan⁡(θi-αr)cos⁡αp+sin⁡αytan⁡αpϕ′=180∘⋅HπR0-sin⁡αytan⁡(θi-αr)cos⁡αp+cos⁡αytan⁡αp. During most survey flights, where the pitch angle and altitude do not change much, the roll angle has the largest influence on the spatial displacement. Also during straight flight legs, the aircraft is often not exactly levelled. For the example flight discussed in Sect. , the average displacement magnitude over fairly straight tracks (with αr≤5∘) lies around 60 m, while for curved tracks (with αr>5∘), the displacement mostly lies between 300 and 400 m with maxima up to between 700 m (central viewing direction) and 1200 m (sideways viewing direction). Application of the above correction is hence essential for accurate geolocation.

For part of the flight described in Sect. , Fig.  shows an image of the recorded radiation intensity mapped onto the ground (left) together with a Google Earth image (right). The image contains a piece of a motorway, which is visible in the measurements by the enhanced intensity. The intensity map is a composite of several passes over the motorway in different orientations, at different locations, and also during fairly curved paths. Nevertheless, the motorway, i.e. the enhanced intensity, shows a continuous course and is positioned at the correct location, demonstrating the good performance of the computed geolocation.

Following from the field of view described in Sect. , a flight altitude of typically around H=1100 m above ground level yields a swath width of 980 m and an individual pixel size of 28 m across track using full resolution. When combining spectra from adjacent fibres, e.g. to a number of nine LOS (8×4 fibres and one LOS with three fibres at the upper CCD edge), the effective ground pixel size is increased to around 110 m while improving the SNR by about a factor of 2. In order to further improve the SNR, subsequent detector read-outs may be averaged, increasing the integration time, e.g. from 0.5 to 2 s. This increases the ground pixel size to 120 m along track and the SNR again by a factor of 2. As the entire pixel-by-pixel read-out of each CCD exposure is stored, spatial and temporal averaging and choices of viewing directions may be performed during post-flight data evaluation, depending on the respective research question.

The instrument's optics have been carefully adjusted for the imaging of distant objects (practically close to infinity) before flight in the laboratory. An example image on the CCD chip is shown in Fig. . On the left, the scene photograph in black and white is shown; the simultaneous CCD image of the DOAS measurement is shown on the right. In the CCD image, the horizontal axis contains the spectral information, while spatial information is distributed along the vertical axis. The blue box in the photograph marks the field of view for the DOAS observation. The CCD figure shows 35 illuminated stripes from the 35 glass fibres. The strongly reflecting motorway in the centre of the photograph causes high intensity only in one fibre, i.e. within one stripe on the CCD. Other features such as the smaller road above the motorway and the bright area towards the bottom of the picture can also be distinguished in the CCD image. The good imaging quality also allows the fine mapping of the motorway seen before in Fig. .

Due to image aberrations for off-axis object points, the SRF has a different shape and width for the different viewing angles. In addition, the image quality along the spatial axis is slightly degraded towards the detector edges. However, the individual spatial directions remain well separated. The narrowest SRF is that one of the central viewing direction with a FWHM (full width at half maximum) of 0.5 nm, while the outermost viewing directions have an SRF with a FWHM of around 1.0 nm. The experimental SRF measured at 435.8 nm with a HgCd calibration lamp is displayed in Fig. . From the centre to the outer directions, lighter colours are used. The viewing directions to the right are drawn as solid lines; directions to the left are drawn as dotted lines. With a sampling of 512pix/41nm=12.5pix/nm, i.e. between 6 and 12pix/FWHM, the Nyquist sampling theorem is well fulfilled. The broadening of the point spread function towards the outer directions is clearly visible. The central directions reveal good symmetry, while the two outermost viewing directions (VD 01 and 09) show some deviation in form of a dent to the right of the SRF centre. Most importantly, the SRF shape and width for each individual viewing direction are reasonably constant along the wavelength axis (not shown). Such a dependency may in general occur and would become more important for larger CCD chips. However, no variations in the SRF spectral shape were detected in laboratory tests with the AirMAP. This stability is required for accurate and consistent trace gas retrieval results.

For the retrieval of NO2 slant column densities, the spectral region from 425 to 450 nm is used as a fitting window. As a background reference, spectra that only slightly differ in time are used, averaged over a 1 min time period from above a rural region. Therefore, the retrieved NO2 amount is a differential slant column density (dSCD, hereafter SC) amount with respect to this background column. This approach effectively removes the absorption of any NO2 in the upper troposphere or stratosphere, where the NO2 is well mixed over horizontal scales of 50 km as a result of the high wind speed, mean free paths and related mixing. Using SCIAMACHY satellite data , also available at http://www.iup.uni-bremen.de/doas/data_products.htm, the NO2 product indicates that the stratospheric NO2 amount was about 4.0×1015 molecules cm-2 for the time and location of the research flight. The small diurnal variation of this stratospheric NO2 column and the effect of changing the solar zenith angle (SZA) close to local noon are negligible. This is also because of the short time between the actual and the background measurement, which is 1 h at maximum for the measurements discussed in this study.

In addition to the NO2 absorption cross section (293 K, , ) the absorption signatures of O3 (241 K, , ), O4 (296 K, , ) and H2O vapour (HITRAN 2004 data base, ) are taken into account. A quadratic polynomial accounts for the broad-band spectral structures, and a constant intensity offset is fitted. In order to account for the in-filling of Fraunhofer lines in scattered light measurements, the Ring effect spectrum determined by radiative transfer calculations is also fitted as a pseudo-absorber. Prior to the actual retrieval procedure, all reference spectra are convolved with the instrument's SRF, individually for each viewing direction.

During the measurement flight, the retrieved SC of NO2 varies between values around 0 for areas which are similarly unpolluted as the rural reference region, and 5× 1016 molec cm-2 for locations most strongly affected by local NOx emissions. Small negative SC values in some locations indicate cleaner conditions and thus lower NO2 amounts than in the reference region average. All results in this section refer to division of the field of view into nine viewing directions (referred to as LOS09 retrieval) at 0.5 s exposure time. A short part of the NO2 slant column time series is shown in Fig. , covering a 24 min period from 09:51 to 10:15 UTC for three viewing directions, the furthest right (VD 01), centre (VD 05) and furthest left (VD 09) with respect to flight direction. Results of VD 01 and VD 05 are offset against VD 09 for better visibility by 2×1016 molec cm-2 and 1×1016 molec cm-2, respectively. With an exposure time of 0.5 s this high-resolution time series shows significant spatial variations along flight direction, i.e. along the time axis, as well as considerable spatial variation in across-flight direction, visible through the differences between the three viewing directions. Some of the variation is due to noise, which is in the range of a few times 1015 molec cm-2 for the slant columns as discussed below. The observed variations along and across flight direction are clearly larger than the noise alone.

Example fit results for the measurement time 10:11:47 UTC are shown in Fig.  for the same selected viewing directions. For the given location, all three viewing directions show enhanced NO2 amounts with slant column densities of SCVD01=2.6±0.2×1016 molec cm-2, SCVD05=4.0±0.1×1016 molec cm-2 and SCVD09=3.6±0.2×1016 molec cm-2, respectively. Individual relative fitting errors range between 3 and 9 % for the given examples. The root-mean-square (RMS) value of the residual optical depth gives a measure of the fit quality and of the detection limit. Typical RMS values of the residual are in the range of (1.5–2.0)×10-3. As the spectral sampling is larger than necessary, the RMS may be improved by coadding along the spectral axis. However, such a procedure has no effect on the noise of the retrieved NO2 amount.

The detection limits and uncertainties of the column results are better estimated from the retrieved NO2 amounts and their noise. For this purpose, the spread of NO2 values is analysed, taken from an area with small relative abundances . In the present case, a suitable area is the reference location, from where the 1 min average reference spectrum I0 for the DOAS analysis is obtained. For better statistics, a 3 min section from the flight is used for the error analysis. Figure  shows the results for viewing directions VD 01, 05 and 09. The relative occurrence of the given NO2 column densities is plotted in a histogram with a bin width of 0.5×1015 molec cm-2. The mean and the width of the distributions are found in each case by a fitted Gaussian function. The mean is slightly positive but close to 0 in all three cases (0.5–0.6×1015 molec cm-2) due to residual background NO2. With 95 % probability, values lie within 2 times the standard deviation, 2σ, of 4.4, 3.5 and 5.5×1015 molec cm-2 for VD 01, 05 and 09, respectively. These values give a meaningful measure for the slant column detection limit and uncertainty for individual detections. With typical air mass factors of around 2.2 (Sect. ), the vertical column detection limit and uncertainty lie between 1.6 and 2.5×1015 molec cm-2 for a single observation, assuming a normal distribution and using 2σ to cover the range of possible values. As a result of some real variability in the NO2 amounts, these values represent an upper limit of the experimental uncertainty.

At a typical speed of 60 m s-1 and 1100 m flight altitude, averaging over four subsequent measurements leads to nearly quadratic ground scenes with an area of 110×120 m, and the fit RMS is improved by nearly a factor of 2 as expected. In areas affected by anthropogenic activities, NO2 enhancements are clearly above the detection limit of the AirMAP instrument.

For the central flight pattern above the power plant area, the map in Fig.  shows the spatial distribution of NO2 slant column amounts. The column density is colour-coded according to the legend given in the map. For the analysis of the AirMAP observations no post-processing in the form of destriping has been applied. Such a procedure would be necessary in case of irregular viewing angle dependencies in the trace gas results, i.e. non-uniformities in the slant column values (Dobber et al., 2008; Popp et al., 2012). The LOS correction applied in the next section takes into account only the smooth viewing angle dependency due to a slightly longer light path for observations at the sensor edges. The single viewing directions of AirMAP yield consistent results, which do not exhibit stripy features, i.e. in the sense that certain viewing directions would have the tendency to always show larger values than others, neither in the instrument calibration parameters nor in the retrieved NO2 column amount.

The location of the power plant is marked in the figure by a black dot. Enhanced amounts of NO2 are observed downwind of the power plant stack, while surrounding areas have much lower NO2 amounts than within the exhaust plume. The average wind direction is indicated in the map (see also Sect. ). For single measurements, maximum slant columns reach 5.0×1016 molec cm-2. Typical amounts within the power plant plume are between 1.2 and 4×1016 molec cm-2. This is much smaller than values measured by above the huge South African Highveld power plants. In comparison, they observe slant columns up to 1.1×1017 molec cm-2 for the coal and syngas-fired Majuba power station (around 4100 MW nominal capacity), and observe vertical columns of up to 8×1016 molec cm-2 above the lignite-fired Monticello power station (Texas, USA, around 2000 MW nominal capacity).

In order to transfer the retrieved NO2 slant columns into vertical column amounts, air mass factors (AMF) are computed by radiative transfer (RT) calculations. For this purpose, the SCIATRAN code is used . The AMF takes care of the relative light path length through the absorber layer, and the vertical column (VC) is determined by VC=SCAMF(p). The AMF depends on a set of parameters p which determine the radiative transfer scenario. This is influenced, e.g. by the wavelength, ground reflectance, the absorber profile, SZA and aerosols. The sensitivity of the measurements in dependence of the altitude location of the absorber is given by the Box-AMF, which is the respective AMF in a defined altitude range. For a scenario of 40∘ SZA and a wavelength of 425 nm, the Box-AMF is plotted in Fig.  for different values of the ground reflectance and considering a flight altitude of 1100 m and direct nadir LOS. SZA values for the campaign flight lie between 32 and 57∘, and for the central flight pattern, between 39 and 50∘. The flight took place on a clear summer day with good visibility; i.e. aerosols are not considered in these examples. The measurement sensitivity changes from 2.6 directly below the aircraft to values between 2.55 (20 % albedo) and 1.65 (5 % albedo) close to the ground. The sensitivity for NO2 observation therefore depends on the trace gas altitude profile.

The path length of solar electromagnetic radiation through the layers below the aircraft also depends on the respective viewing angle, which for the AirMAP instrument reaches up to ± 24∘ for level flight and even larger angles when the aircraft is banking and turning. The LOS influence on the AMF determined by RT calculations is only slightly different (<1%) from the geometrically calculated factor. The AMF for nadir view (AMF0 for LOS α=0∘) is computed with SCIATRAN, and the correction for LOS angle θi is then based on the geometric AMFs, AMF^0 and AMF^θi. With SZA θs and LOS θi, the corrected VCθi for slant viewing directions is determined by VCθi=SCθi⋅1AMFθi≈SCθi⋅1AMF0⋅AMF^0AMF^θi with the geometric air mass factor AMF^θi=1cos⁡(θs)+1cos⁡(θi). For evaluations of the observed NO2 and calculation of VC amounts, a boundary layer box profile of well-mixed NO2 in the lowest 1 km altitude is assumed, and the albedo is set to 5 %. In the vicinity of emission sources, the NO2 will not be well mixed below the aircraft. Using Gaussian plume dispersion, corresponding vertical profiles within an exhaust plume have been computed, and differences between plume profile AMFs and the Box-AMF have been investigated. The AMF for a plume at 6 km distance used below for emission estimates (Sect. ) differs less than a few percent from the Box-AMF within the relevant SZA range, whereas for profiles closer to the emitting stack, the plume is more confined and may cause a difference of about 5 % in the AMF.

It is worth noting that neither SCIATRAN nor the geometric approximation take 3-D effects into account. The importance of such 3-D effects increases for increasing SZA, increasing LOS angle and for a plume which is horizontally confined as well as situated at high altitudes directly below the aircraft. For such a case, an individual light beam may travel through the plume only once, e.g. either on the way from sun to the ground or from the ground to the instrument. In this case, the AMF would be overestimated and the resulting vertical column would be underestimated. In addition, the assignment of the measured trace gas amount to the ground pixel may be affected. Multiple scattering, however, reduces the influence of 3-D effects.

Close to the stack, 3-D effects might be present in our case; further away from the stack, however, the plume has already spread in horizontal and vertical directions, so that the influence of 3-D effects becomes less relevant.

The same observations as in Fig.  with nine viewing directions are depicted in Fig.  (top) now for the NO2 vertical columns in the area of the Ibbenbüren power plant. In order to assess the capability of AirMAP of monitoring NO2 columns at even better spatial resolution, the full 35 viewing directions have been analysed individually (LOS35 retrieval). For direct comparison, the full resolution retrieval result is plotted right below in Fig.  (bottom). The resulting NO2 column amounts from the two different resolution cases are consistent. Consistency has been checked also by comparing the NO2 VC in one viewing direction from the LOS09 retrieval with the average of the contributing viewing direction from the LOS35 retrieval. For example, comparing VD 09 of the LOS09 retrieval to the average of VD 32 to 35 of the full resolution LOS35 retrieval, the difference is as small as 0.4±8.5×1014 molec cm-2 within the central flight pattern.

The VC amounts of NO2 are strongly enhanced within a confined plume downwind of the power plant stack, as seen before. Maximum VC amounts reach up to 2.4×1016 molec cm-2, while typical values within the exhaust plume lie between 0.6 and 2.0×1016 molec cm-2. NO2 amounts in overpasses closer to the stack are lower than in the overpasses further downwind, because emissions of nitrogen oxides first occur as NO which is converted into NO2 during the transport in the plume. The most distant overpass at around 6 km reveals the largest NO2 amounts. In addition, the plume broadens while it is transported away from the stack, and the integrated VC across the plume increases with distance from the stack. This is shown in more detail in the following section. In comparison to the NO2 amounts within the plume, surrounding NO2 values are rather small and variable below (4±2)×1015 molec cm-2.

One flight segment in a north–south direction shows lower NO2 amounts than the other flight paths. The respective segment was flown latest in the pattern and at lower altitude; therefore the track is rather narrow. The later time means that the SZA and the influence of stratospheric NO2 have changed. This effect is noticeable but is too small to entirely explain the observed change in the background NO2. The lower flight altitude might cause some NO2 to be missed by the measurements. Additional effects probably influence the measurements in this flight path, which is however not further used in this study.

Figure  demonstrates some further features of the imaging DOAS aircraft measurements. A comparably large area is covered with trace gas observations within a relatively short time interval at fine spatial resolution. The flight pattern above the target area with several partly overlapping flight legs was, e.g. completed within about 80 min. Hence, the observations with AirMAP are useful for the analysis of small-scale trace gas variability above extended areas with several tens of kilometres' side length.

Information on wind speed and direction is received from the COSMO-DE regional model from the German Weather Service DWD . Observational data are assimilated, and the output grid size is 2.7×2.7 km2. The altitude grid has 12 levels in the lowest kilometre. For the closest grid points around the target area, wind profiles (speed and direction) have been extracted. The wind speed on the campaign day was moderate, increases with altitude in the boundary layer and drops to smaller values above. Figure  shows the altitude profile of the wind speed (left) and direction (middle) for a location close to the power plant (7.67∘ E, 52.28∘ N) for three hourly time steps at 09:00, 10:00 and 11:00 UTC. Vertical changes in wind speed and direction are less pronounced at plume overpass time after 10:00 UTC than earlier in the morning. The diagram on the right shows measurements of moisture mass mixing ratio (m.r.) and potential temperature Θ. These measurements were taken about 15 km south of the example plume overpass during a descent into a regional airport at around 10:46 UTC. For each parameter, two curves for the descent and the subsequent ascent are shown. The potential temperature as well as the moisture profile is fairly constant within the mixed layer, while vertical gradients increase strongly above. From these measurements, a mixing layer height of about 1300 m is estimated, and spreading of the NO2 plume takes place in this altitude range.

Assuming Gaussian plume dispersion for the shape and development of the NO2 emission plume emerging at the stack altitude of 275 m a.g.l., the vertical plume extent can be estimated. Considering that the atmospheric stability class valid for the present campaign day was rated as slightly unstable , dispersion leads to a substantial spreading of several hundred metres within the boundary layer at a distance of 6 km from the stack. From this perception and the measurements of the vertical mixing layer extent, a homogeneous distribution of NO2 below the aircraft is assumed for the wind averaging at this location. Below the aircraft, the wind speed varies between 6.1 and 9.2 m s-1 with an average of 8.3 m s-1. A small bias of +0.7 m s-1 in the COSMO-DE wind speed data for the respective time and region has been identified by in comparison to the AIMMS-20 wind probe. Taking the bias into account, a wind speed of 7.6 m s-1 is used. The wind direction varies between 61 and 75∘ with an average of about 68∘. The AIMMS-20 wind probe on the aircraft yields a direction of 78∘ which is turned clockwise at the higher altitude of the aircraft position above the plume in agreement with the COSMO-DE profiles. The apparent plume transport from the measurements is consistent with a wind direction of around 70∘. For calculations, the 68∘ angle is used, and uncertainties on this value are around ±5∘.

The aircraft measurements integrate over the vertical dimension, so that the flux calculation considers the horizontal component F=VC⋅u of the 3-D vector field of NO2 transport. VC is the NO2 vertical column and u is the effective horizontal wind vector. The source strength (emission rate) Q is thus determined from the vertical NO2 columns measured within the exhaust plume. The divergence theorem yields Q=∫A∇FdA=∮L(F⋅ndl)=∮LVC⋅u⋅ndl. The integral runs over an area A enclosed by the surrounding line L. The calculated flux thus contains the emissions from all sources enclosed by L. For calculation of Q from the experimental discrete data, the integral in Eq. () converts into a sum over the observed ground pixels i: Q=∮LVC⋅u⋅dl≈∑iVCi⋅u⋅Δli⇒Q=∑iVCi⋅u⋅Δlicos⁡(β). In the last step, β is the angle between the wind vector u and the normal vector n of the line element along flight direction Δl (or along any other selected transect). The product vanishes for pieces of the boundary L which are parallel to the wind direction. Figure  illustrates the determination of Q from the aircraft measurements with a simplified sketch of a plume overpass, including the parameters that enter the above calculation. When closing the integral over the surrounding line around the power plant on the upwind side of the power plant, positive NO2 amounts lead to a reduction of the resulting emission rate as the wind and line normal vectors are antiparallel.

The cross section through the plume along flight direction for one example viewing direction (VD 09 from the LOS09 retrieval) is seen in Fig. . The cross section shows enhanced NO2 amounts at around 10:12 UTC up to 1.9×1016 molec cm-2, clearly above the background amount in a compact shape. Immediately to the sides of the central plume, a mean vertical NO2 column of VCB=2×1015 molec cm-2 is observed, resulting from background NO2 concentrations and outflow from the city of Ibbenbüren. Parts of the city of Ibbenbüren are close to the power plant and are therefore enclosed by any possible flight path. The additional sources can influence the emission estimate if the closed line integral is determined. Alternatively, the background NO2 is assumed constant across the plume and subtracted from the observed NO2 in order to effectively remove additional emission sources. The emission rate is then determined by the downwind part of the line integral over the background corrected NO2 column VC-VCB. Calculated this way, the emission rate is slightly smaller than from the closed integral; however, the differences are not significant. Other local sources can therefore be concluded to be small. Figure  shows the computed emission rates with respect to the distance from the power plant location for the nine viewing directions, i.e. nine independent results for Q. From this, the average emission rate and standard deviation is Q¯=(1.1±0.3)×1024 molec s-1. The standard deviation of the derived values for Q is of the same magnitude as the error of the mean when considering the uncertainties on the individual results of Q. The uncertainties on all involved quantities making up for the error bars in Fig.  are discussed in Sect.  below.

The determined emission rates correspond to 82±20 g s-1 NO2. For the conversion into a NOx emission rate, a value for the [NO] / [NO2] ratio r needs to be assumed. The ratio r is the inverse of the well-known “Leighton ratio”, which is the ratio [NO2] / [NO] in photo-stationary state. The NOx emission rate QNOx is then given by QNOx=(1+r)⋅QNO2. A value of r=0.25 is used , which is reasonable as soon as steady state is achieved; see discussions below. Following from this, the NOx emission rate QNOx is 103±25 g s-1 NOx in mass of NO2. The error does not include uncertainties of the ratio r. Reports issued in the E-PRTR state an emission rate of 3060 t a-1 NOx in mass of NO2. Extrapolating the instantaneous observations from the individual overflight to an entire year, the observed annual emission rate would be 3240±800 t a-1, consistent with the reported amounts. The extrapolation is only reasonable either if the emission rate is constant over the course of the year, or if the individual day was a representative situation of typical conditions, which is both not necessarily the case. However, the comparison shows that the plume estimate of NOx emissions and the reported annual average are consistent.

At example locations closer to the stack, the analysis leads to lower NOx emission rates. The reason for this is that less of the emitted NO has been converted to the measured NO2 . For application of the divergence theorem, chemical inertness of the compound or a stationary state condition needs to be assumed. However, NO2 is not inert at atmospheric conditions. For a meaningful reasoning, the distance of the NO2 measurement from the power plant needs to be sufficiently large so that the photochemical stationary state can be assumed as implied above. Stationary state will evolve over the first few tens of kilometres of an exhaust plume . The actual distance required depends on wind speed and atmospheric stability as well as chemical conversions mainly driven by reactions with O3 and photolysis. Wind speed is moderate, and at around 6 km distance, an air parcel has travelled for nearly 15 min from the stack. At large NO concentrations, O3 can be entirely depleted in the plume centre. NOx emissions are smaller in the present case as compared to . If O3 is not entirely depleted, conversion to NO2 and achievement of a steady state evolves faster. If a steady state has not been reached, the factor r and hence also QNOx would be larger than estimated above. In conclusion, estimates of the NOx emission rate are derived here under these limitations.

The NO2 amounts within the emission plume do not show a smooth and uniform distribution. The emission rates plotted in Fig.  represent nine independent results for Q at different distances from the stack, i.e. different times since emission. The approximate time difference between two adjacent viewing directions, taking the locations and wind speed into account, is about 13 s; the difference between the outermost directions is about 2 min. Even from this short excerpt of the emission plume, its variability becomes clear. Possibly the NO emissions in the first place, but mainly the chemical conversions and the transport process are presumably non-uniform. The particularly inhomogeneous structure of the plume was addressed in Figs.  and , where overpasses closer to the stack are included as well. In this respect, observations made with the AirMAP instrument provide a good opportunity to study these plume processes within short time and spatial scales and covering distances of many kilometres.

The NO2 DOAS retrieval exhibits fitting errors around 5 % for large NO2 values within the plume. Naturally, the relative error becomes bigger for small NO2 abundances to the sides of the plume. Absolute errors lie in the range of 2×1015 molec cm-2. The same absolute uncertainty applies for the background NO2 amount, determined next to the emission plume. Systematic errors induced by the choice of NO2 cross section are in the range of a few percent, e.g. the temperature dependence causes an uncertainty of <2% for a temperature change from surface to 2 km of about 15 K (from 297 to 282 K, based on COSMO-DE data), when using a 293 K reference cross section.

Main uncertainties of the NO2 VC arise from assumptions necessary for the calculation of the AMF, e.g. through influences from aerosol scattering, the vertical NO2 profile and ground albedo. While aerosol above a remotely sensed NO2 layer tends to shield part of the trace gas, mixed aerosol with NO2 may also lead to enhanced sensitivity, e.g. shown for satellite-specific studies . The campaign day was a fairly clear and sunny day with good visibility. Therefore, the error from assuming there to be no aerosol scattering in the radiative transfer is not large. Conversely to the NO2 vertical profile, which in general is not known, the emission plume injection height and the height of the mixed layer are approximately known. AMFs for different profiles, box-shaped and Gaussian plumes, as well as for different ground albedo values, have been computed (Sect. ). From the related uncertainties, deviations of the AMF in the range of 25 % are considered.

Factors influencing the calculation of the length of the path element in the line integral include the timing of the GPS signal, the uncertainties in the GPS positioning itself and in the aircraft orientation and altitude. In comparison to the precision and accuracy of the GPS position and its timing, which lead to an uncertainty of a few metres only, the influence of the aircraft angles are the dominant ones. Also, the inaccuracy of the altitude is small in comparison. Uncertainties in the pitch and roll angles, of around 0.5–1∘ each, cause displacements on the ground, leading to an overall error of around 30 m for the geolocation in our case, i.e. when flying at the main altitude of around 1100 m. However, it is the difference in geolocation between the start and end of the measurements that is entered in the emission calculation in Eq. (), which causes a major part of the systematic uncertainty of the angles to be cancelled out. A curvature in the flight path during overpass (cf. Fig. ) induces an inaccuracy as the path is approximated by straight segments leading to a systematic but small underestimation of the track length. Overall, the influence of the path length uncertainty is minor in comparison to the other error sources.

The wind speed and direction imply errors (a) due to uncertainties and inaccuracies in the model data itself, (b) due to the finite grid size and (c) due to uncertainties in the vertical expansion of the emission plume. Depending on the time of day and the lifting of the boundary layer, the variation of the wind speed and direction with altitude can be fairly strong. From estimates of the plume vertical location and extension, related uncertainties on the order of 10 % for the wind speed and 5 % on the cosine of relative wind angle β are reasonable. The latter is true as long as β<30∘, which is the case for the analysed overpass.