Simulations described here have been performed using the MicroHH LES model . The LES implementation of MicroHH uses a surface model that is constrained to rough surfaces and high Reynolds numbers, which is a typical configuration for atmospheric flows. This model computes the surface fluxes of the horizontal momentum components and the scalars (including thermodynamic variables) using Monin–Obukhov similarity theory (MOST) . To parameterise the anisotropic subfilter-scale kinematic momentum flux tensor, MicroHH uses the Smagorinsky–Lilly model . For our simulations, we use a domain size of 50–100 km with grid cells of 100 m × 100 m in the horizontal and 25 m in the vertical dimension. MicroHH uses an adaptive time step depending on the local flow conditions that typically amounts to 1–5 s in the current simulations. The emission of scalars from point and line sources is described in . The coupling of MicroHH with meteorological reanalysis data from ERA5 using the open-source “the Large-eddy simulation and Single-column model – Large-Scale Dynamics ((LS)2D)” Python package is described in . The simulations will focus a point source (stack) within a domain. Next to CO2, the stack emits prescribed amounts of NOx and other pollutants. These latter species are involved in atmospheric chemistry. The next section describes the implementation of atmospheric chemistry in MicroHH.

One of the aims of the CoCO2 project (https://coco2-project.eu/) is to build a library of plumes. To that end, simulation protocols have been designed (https://coco2-project.eu/sites/default/files/2021-07/CoCO2-D4.1-V1-0.pdf, last access: 10 July 2024). Here, we present results of four cases listed in Table  that address emissions from point sources.

The Jänschwalde Power Station (JAE) is a coal-fired power station near Cottbus, Germany, close to the Germany–Poland border. The Jänschwalde Power Station has nine cooling towers (120 m high) in groups of three, of which only two towers per group are active. This facility has been studied in a couple of recent papers .

The Bełchatów Power Station (BEL) is also a coal-fired power station near Bełchatów, in central Poland. Emissions are released from two 299 m high stacks. CO2 emissions from this facility have been addressed in and .

The Lipetsk steel plant (LIP) is owned by the NLMK group, the largest steelmaker in Russia. This facility has been identified in earlier studies .

Finally, the Matimba Power Station (MAT) is a dry-cooled, coal-fired power plant in the north-east of South Africa, approximately 300 km north of Johannesburg. The power plant has two 250 m high stacks. This case is based on and is also addressed in publications such as , , and .

Emission details of these four cases are summarised in Table . These facilities are all major emitters of CO2, with emission strengths ranging from 16 to 28 kmol s-1. For chemical compounds, Matimba is clearly emitting more NOx, whereas Lipetsk is a very strong emitter of CO.

The emissions are based on the CoCO2 intercomparison protocol (https://coco2-project.eu/sites/default/files/2021-07/CoCO2-D4.1-V1-0.pdf). For JAE and BEL, these emissions are based on reported yearly total values in the European Pollutant Release and Transfer Register (E-PRTR). For MAT, we use the emissions averaged over the year 2018, based on the monthly reports provided by the responsible company – Eskom (https://www.eskom.co.za, last access: 10 July 2024). For LIP, the emissions are obtained from the 2019 annual report of the NLMK group (https://nlmk.com/en/ir/reporting-center/annual-reports/, last access: 10 July 2024). We have smaller confidence in these emissions, because it remains unclear whether the reported emissions can be fully ascribed to the Lipetsk facility.

Concerning emission heights, we prescribed fixed emission profiles that account for plume rise. For JAE and BEL, these were calculated using the empirical equations recommended by the Association of German Engineers, which are based on the original work of . Typical stack parameters were obtained from , considering typical power plant capacities and fuel types, and from site descriptions. For LIP and MAT, the emission heights recommended by the CAMS emission dataset for the Industry and Public Power sectors were used.

Depending on the wind direction during the selected time periods and visual inspection of the TROPOMI NO2 plumes, a modelling domain was set up around the point source. JAE, BEL, and LIP were modelled on a 51.2 km × 51.2 km domain, whereas a domain of 102.4 km × 102.4 km was selected for the MAT case. All simulations employed a horizontal resolution of 100 m × 100 m. In the vertical, the domain size was 4000 m, with an equidistant grid of 25 m resolution. We tested the effect of model resolution on the simulation results (see Supplement). We found that the conversion of NO to NO2 proceeds slower and the NOx : NO2 ratios are larger at a finer horizontal model resolution of 25 m. At a resolution of 100 m used here, a substantial instant dilution error is still present, which can lead to errors in simulated NO2 columns as large as 20 % up to 10 km downwind of the stack.

At the top of the domain, a buffer layer starting at 3250 m was used to damp gravity waves . Radiative transfer was calculated every 60 s using the Radiative Transfer for Energetics (RTE) and Rapid Radiative Transfer Model for Global circulation models applications Parallel (RRTMGP) radiative transfer model . At the surface, we employed an interactive land surface model based on HTESSEL . We initialised our simulations using CAMS (composition) and ERA5 (meteorology) using LS2D . During the simulations, boundaries were nudged towards time-varying profiles of CAMS and ERA5. For temperature, humidity, and momentum, circular boundary conditions were used. To avoid re-entering of emissions from the point source, we employed free-outflow conditions for tracers, as described in . As the current focus is on stack emissions, surface fluxes of CO2 and other tracers were ignored.

Simulations were performed on the Dutch national supercomputer Snellius, using 1024 cores (8 nodes). Typical run times of the simulations ranged from 2 d (JAE, BEL, and LIP) to 5 d (MAT).

We compare the results of our simulations to TROPOMI satellite data. We downloaded level-2 TROPOMI NO2 data from the Copernicus Open Access Hub (https://scihub.copernicus.eu, last access: 4 September 2023). For consistency, we selected the product that was reprocessed (RPRO) with processor version 2.4.0. For JAE, orbits 3136 (22 May 2018) and 3150 (23 May 2018) were downloaded; for BEL, orbits 3349 (6 June 2018) and 3363 (7 June 2018) were downloaded; for LIP, orbits 8611 (12 June 2019) and 8626 (13 June 2019) were downloaded; and for MAT, orbits 14402 (24 July 2020) and 14416 (25 July 2020) were downloaded. The latter two orbits provide data at nadir on a 5.5 km × 3.5 km resolution, whereas the nadir resolution of the other orbits is 7 km × 3.5 km. The uncertainty in a single TROPOMI tropospheric column due to albedo, clouds, and aerosol amounts to 20 %–30 % .

Figure  displays the tropospheric NO2 columns in the TROPOMI product on the selected days and on the MicroHH modelling domains. Wind speed and direction as calculated with MicroHH are also shown in the panels. We selected only column retrievals with a quality assurance (QA) value > 0.75.

First, the resolution of the TROPOMI product strongly depends on the satellite viewing angle. Second, for all cases, clear NO2 plumes are visible. Only for the LIP case on 12 June 2019 is the spread of the plume limited due to low wind speeds. Moreover, many TROPOMI pixels are flagged on this day, likely due to aerosol and/or clouds. Finally, as expected and analysed later, the TROPOMI NO2 columns depend strongly on the wind speed. A clear effect of wind speed is seen on the second day of the JAE case (23 May 2018), when columns are clearly reduced compared with the first day (22 May 2018).

In the further analysis of TROPOMI data, we will remove inconsistencies in the model–satellite comparison caused by the use of vertical NO2 profiles from the coarse-grid TM5 model in the satellite product. This global chemistry transport model runs on a resolution of 1° × 1° and does not resolve the highly localised plume simulated by MicroHH. As the sensitivity of the satellite measurement drops significantly for NO2 that resides near the surface, mainly due to Rayleigh scattering, it is important to correct for the differences in NO2 profile shape and NO2 amount between MicroHH and TM5. Previous studies have shown strong impacts of the NO2 profile and amount on satellite retrievals .

The TM5 information about the vertical NO2 distribution is stored in the TROPOMI data product in the form of a tropospheric averaging kernel (AK) and air mass factor (AMF). We employ the method outlined in and applied in for the Ozone Monitoring Instrument (OMI). To this end, we sample the MicroHH NO2 profile, augmented with the CAMS profile above 4 km, on the pressure grid of the TM5-based tropospheric AK, and calculate a correction to the tropospheric AMF as follows: 4Mtrop,MHH=Mtrop,TM5×∑l=1LAtrop,lxl,MHH∑l=1Lxl,MHH. Here, Mtrop is the tropospheric AMF of the MicroHH model (MHH) or the TM5 model (stored in the satellite product), Atrop,l is the tropospheric averaging kernel element for layer l (also stored in the satellite product), xl,MHH is the modelled NO2 column density sampled on the TM5 pressure grid, and L is the uppermost TM5 layer in the troposphere. In Sect. , we will compare MicroHH tropospheric NO2 columns to corrected and uncorrected TROPOMI tropospheric NO2 columns.

Simulations started at 00:00 UTC and lasted for 48 h. Figure  shows the simulated wind speeds below 1000 m, averaged over the model domains. Also indicated are the TROPOMI overpass times. These wind speeds are strongly determined by the boundary conditions that are provided by ERA5. Driven by the synoptic situation, winds in the lower boundary layer vary considerably. We often observe a slowdown of the wind prior to TROPOMI overpass (vertical lines). This is related to the growing convective boundary layer in the morning that propagates surface friction to higher altitudes. For LIP, winds are calm prior to the TROPOMI overpass on day 1, whereas the wind speed increases to more than 8 m s-1 prior to the TROPOMI overpass on day 2. This is clearly reflected in the TROPOMI data in Fig. . Likewise, the lower TROPOMI columns for JAE on the second day are caused by the higher wind speeds on day 2.

To analyse the situation further, Fig.  shows profiles of wind speed, turbulent kinetic energy (TKE), and potential temperature (θ) sampled 30 min around the TROPOMI overpasses. TKE (m2 s-2) is calculated from the variances of the three wind components: 5TKE=12σu2+σv2+σw2.

In all cases, a well-mixed boundary layer is visible up to the inversions layer, with logarithmic profiles close to the surface. For instance, the boundary layer depth of the JAE1 case amounts to roughly 2500 m. We expect that, due to convective mixing, emissions from the stack will be distributed over the well-mixed boundary layer. Above the inversion layer wind speeds either increase or decrease, while the wind directions change considerably with height (not shown). Despite the low wind speed, TKE is substantial in the Lipetsk day-1 (LIP1) case, pointing to strong buoyancy. Turbulent mixing within the boundary layer is smallest in the Bełchatów day-1 (BEL1) case.

To derive a representative wind direction for plume dispersion, we determine this direction by weighting the wind-profile with the mean NO2 profile. We subsequently rotate the MicroHH domain around the stack location using the plume direction angle, shown in Fig. , such that the plumes are aligned along the positive x axis.

Figure  displays the simulated NO2 mole fractions, averaged over the boundary layer at the times of TROPOMI overpass (see Fig. ). All plumes are aligned along the x axis and share the same colour scale. Except for the LIP1 simulation, which will be excluded in further analyses, the plumes stay within the Gaussian-type plume depicted by the black lines, which indicates that the winds are relatively stable in direction. The NO2 abundance in the plume is mostly determined by the emission strength and the wind speed. However, as will be shown later, chemistry also plays and important role. The Jänschwalde day-1 (JAE1) and Bełchatów day-2 (BEL2) plumes show more wavy lateral displacements compared with the other plumes, while the Matimba plumes reveal a slight curvature, possibly due to effects of the Coriolis force .

To investigate the chemistry in the plume, cross-sections up- and downwind of the stacks are analysed for the NO2 and NOx lifetime, the mixing of NO2 within the plume, and the abundance of OH. For all plume slabs downwind of the stack, averages are taken within the Gaussian-shape black lines in Fig.  and bounded by the height of the boundary layer. Outside the plume upwind of the stack, the full domain up to the boundary layer height is considered. The lifetimes of NOx and NO2 are calculated by moles of NOx (NO + NO2) or NO2 (mol) divided by NO2 loss in the reaction between NO2 and OH (mol s-1). The mean OH mole fraction represents the volume mean OH in these slabs. The mixing of NO2 is quantified by calculating the intensity of segregation between OH and NO2 in the slabs, which is defined as follows: 6Is,NO2,OH=NO2-NO2‾OH-OH‾‾NO2‾OH‾. Here, the bar represents a volume average. Thus, Is represents the scaled covariance between two reactive compounds in a volume . Generally, a negative value of Is signals a situation in which the concentrations of two reactants are negatively correlated, which implies that the chemical reaction between these species proceeds more slowly compared with a well-mixed situation. In contrast, a positive value of Is indicates that the reacting species are spatially correlated in a volume.

Thus, the Is concept quantifies the effect of assuming a well-mixed situation, e.g. in coarse-grid models. Specifically, if kNO2,OH represents the reaction rate between NO2 and OH under well-mixed conditions, the modified reaction rate in a heterogeneously mixed air volume becomes the following: 7kNO2,OH′=kNO2,OH×1+Is,NO2,OH.

Figure  shows the calculated lifetimes of NO2 (panel a) and NOx (panel b) in the simulated plumes. Figures S15 and S16 show the lifetimes of NO2 and NOx degraded to the TROPOMI resolution. Right after emission, lifetimes show a clear spike. This is caused by the switch from a low or intermediate chemical NOx regime to a high-NOx regime in the plume . In this regime, NO2 becomes the main sink for OH (Reaction R12 in Table ). Moreover, the concentration of O3 drops to low values because of the reaction between O3 and NO (Reaction R6 in Table ). Note that 95 % of the NOx is emitted as NO.

Further downwind in the plumes, mixing of the plume with ambient air leads to a recovery of the NOx and NO2 lifetimes. Even further downwind, lifetimes may become substantially shorter compared with ambient conditions. For instance, NO2 lifetimes converge to 1.5 h for JAE1, JAE2, BEL2, and LIP2. This shorter NOx lifetime within the plume corresponds to findings in , who report faster removal of hydrocarbons in pollution plumes. The lifetime reduction depends strongly on the strength of mixing and the amount of NOx that is emitted at the stack. For Matimba, NOx emissions are very high (Table ), which leads to a stronger perturbation of the plume chemistry and a slower recovery of the lifetimes. For Bełchatów, the BEL1 plume stays intact longer compared with the BEL2 plume, driven by weaker mixing of the BEL1 plume (Fig. ). As a result, BEL1, MAT1, and MAT2 lifetimes remain longer than the background over the entire plume length.

Chemically, the behaviour of the lifetimes can be explained by the strong non-linear relation between the NO2 abundance and its main sink OH. OH levels show a maximum at NO2 mole fractions of 1–10 nmol mol-1 due to recycling of OH (e.g. Reaction R11) . Indeed, we observe this relation in our simulations, with low OH in the core plume (high NOx) and high OH concentrations at the plume edges, where (due to intermediate NOx levels) OH recycling is efficient.

To separate the effects of OH and mixing effects on the simulated lifetimes, Fig.  shows slab-averaged Is,NO2,OH (panel a) and OH (panel b) for the simulations. Figure S17 shows Is,NO2,OH degraded to the TROPOMI resolution. Is values vary strongly downwind of the stack. Starting from values close to zero outside the plume, values turn negative first, signalling anti-correlations between NO2 and OH, in line with the high-NOx regime. For JAE1, JAE2, BEL2, and LIP2, Is values turn positive after ≈ 10 km. This implies a positive correlation between NO2 and OH due to the strong recycling of OH in the chemical oxidation chain . In contrast, the BEL1, MAT1, and MAT2 plumes show negative Is values, although values become gradually less negative at larger downwind distances and turn positive for the Matimba case at large distances from the stack. The split between intact and well-mixed NO2 plumes also appears in mean OH mole fractions. In well-mixed plumes, mean OH in the plume is substantially enhanced further downwind of the stack, while OH stays roughly invariant in the BEL1, MAT1, and MAT2 simulations. For the latter plumes, the enhanced lifetimes (Fig. ) are therefore mostly determined by Is, while a combination of higher mean OH and Is is responsible for the lifetime behaviour in the other plumes. Note that background lifetimes show large variations that are driven by differences in OH values outside the plume. For instance, the background NO2 lifetime is ≈ 11 h for LIP2, corresponding to an OH mole fraction of ≈ 0.1 pmol mol-1. In contrast, values for MAT1 amount to ≈ 3.5 h and ≈ 0.35 pmol mol-1.

In a next step, we connect to methods that have been developed with the aim of quantifying plume emissions from satellite data. For instance, in the cross-sectional flux (CSF) method described by , the emission (in mol s-1) is derived from the integrals of the cross-section of the plume perpendicular to the wind direction (i.e. line density in mol m-1) multiplied by an effective wind speed (in m s-1). To investigate the validity of the underlying assumptions in these methods, Fig.  shows column densities (0–4 km) of CO2, NO, NO2, and NOx (NO + NO2), calculated as the mean in the cross-wind direction (y = [-10 km, 10 km], in molec. cm-2) on the 2 Jänschwalde simulation days. Columns have been averaged during 1 h around the TROPOMI overpass, and the shaded areas denote 1σ variability (NO, NO2, and CO2). To allow comparison to NOx, the right CO2 axes have been scaled such that the CO2 and NOx maxima match. As a result of the higher wind speed during the second day of the simulation, both y axes in panel (b) have smaller values (Fig. ).

First, variability in the columns during this sampling hour is large, indicating a large role of turbulence. Due to turbulent eddies that are aligned with the wind direction, downwind transport of species from the stack is irregular, resulting in persistent high-concentration patches that move downwind (e.g. Fig.  and ). Second, variability downwind of the stack decays on day 1 but remains sizable on day 2. Third, CO2 columns in the plume are not constant on day 1, which shows that the gradual slowing down of the winds (see Fig. ) has had a noticeable impact on the simulated columns. Assuming a mean wind speed of 5 m s-1 in the atmospheric boundary layer (Fig. ), the NOx and CO2 as sampled 40 km downwind of the stack was emitted more than 2 h prior to the TROPOMI overpass. Fourth, because of chemical removal of NO2, NOx columns decay faster than CO2 columns. Figure  shows that this lifetime is not constant but, rather, gets substantially shorter at larger distances from the stack, a feature that also shows up in Fig. . Finally, the NOx:NO2 ratio varies considerably along the plume. This is further corroborated in Fig. , which shows the ratios for all simulations, except for LIP1. Figure S18 shows the NOx:NO2 ratio at the TROPOMI resolution.

For all plumes, NOx:NO2 ratios quickly rise from a background value of 1.3–1.5 to values of 3–5. Within the first 10 km, values decline to below 2, with further declines to background values further downwind of the stack. Interestingly, the downwind decay of NOx:NO2 ratios is slower for BEL1, MAT1, and MAT2, compared with the faster decaying plumes (JAE1, JAE2, BEL2, and LIP2). Thus, slow decaying plumes are characterised by persistent negative values of Is, longer NO2 and NOx lifetimes, and larger NOx:NO2 ratios. Both chemical factors (i.e. the size of the perturbation of the background chemistry) and mixing factors (i.e. mixing with ambient air) play a role is determining the plume behaviour.

In the next section, we will compare the simulated NO2 columns to TROPOMI and evaluate the NOx emissions that were applied in the simulations.

As a first comparison between TROPOMI and the simulations, Fig.  shows the model results at the TROPOMI overpass time plotted on top of the TROPOMI NO2 columns. As the simulations are on a 100 m resolution, more detail is visible in the simulations, and the NO2 columns (even considering only z = 0–4 km) are often outside the maximum colour range. Generally, the simulated plumes align well with the observations. However, for BEL1 and MAT2, the simulated plume direction differs by roughly 10 ° from the observed plume direction. For LIP1, the plume direction is ill-defined due to low wind speeds. Our simulations use meteorological boundary conditions from ERA5, and biases in ERA wind direction have been reported . However, the way we impose the ERA5 boundary conditions using one time-dependent profile for the winds, also likely plays a role. As a consequence, when wind curvature is present in the ERA5 forcing fields, this curvature is currently not propagated to the MicroHH simulations. At larger scales, curvature due to the effect of the Coriolis force have been identified in TROPOMI images .

The next steps in the comparison between TROPOMI and simulated NO2 plumes are a mapping of the simulated NO2 fields to TROPOMI pixels, an extension of the simulated profiles to the tropopause, and an AMF correction of the TROPOMI columns using Eq. (). We will present results for the JAE1, JAE2, BEL2, LIP2, and MAT1 cases, based on the favourable match between the model and TROPOMI. We focus on NO2 enhancements above the background and filter for simulated mean column mole fractions (0–4 km) smaller than 0.28, 0.25, 0.25, 0.15, and 0.28 nmol mol-1 for JAE1, JAE2, BEL2, LIP2, and MAT1, respectively. These values differ slightly per case, because background NOx and winds vary in the simulations. To compare only the highly concentrated plume, we further discard TROPOMI tropospheric columns smaller than 2 × 1015 molec. NO2 cm-2. To extend the simulated columns to the tropopause, CAMS NO2 profiles are used. This extension adds a small and relatively constant amount of roughly 0.3 × 1015 molec. NO2 cm-2. As the number of TROPOMI pixels that overlap with the simulated plumes is rather limited (e.g. only ≈ 17 for BEL2), we also use simulated fields 15 min before and after the TROPOMI overpass.

Figure  shows the comparison between TROPOMI and the simulations for the BEL2 case and illustrates the effects of (i) adding free tropospheric columns from CAMS and (ii) the AMF correction of the TROPOMI columns with Eq. (). The blue points denote the uncorrected TROPOMI NO2 columns with the uncorrected simulations, while the orange points denote the corrected values. Corrected and uncorrected values are connected with a thin grey line.

When comparing simulations to TROPOMI, it should be realised that the simulations represent a highly turbulent field with large variability (e.g. Fig. ) and that TROPOMI takes a low-resolution “snapshot” of this turbulent field. A clear one-to-one comparison is therefore not expected. Yet, the integrated or average columns should indicate whether the simulated NO2 columns are systematically too high or too low. For this reason, we calculated a linear fit (forced through the origin), and the resulting slopes are given in Fig. . Moreover, we calculated the mean of the TROPOMI and MicroHH plumes, and results are given by the blue and orange crosses in Fig. .

While the uncorrected slope would indicate a 29 % overestimate of NO2 columns in the simulation (i.e. overly high NOx emissions), the corrected slope of 0.93 points to a slight underestimate. The change in slope is mostly caused by the AMF correction of the TROPOMI tropospheric NO2 columns. The correction factor is on average 1.40 (range 1.13–1.68), and corrections are larger for enhanced NO2 columns. This is caused by the fact that, under polluted conditions, a larger fraction of the NO2 column resides close to the surface in a high-resolution model like MicroHH, compared with the coarse-scale TM5 model that is used in the TROPOMI product (see Eq. ). A similar conclusion can be drawn from the plume-mean columns: without correction, MicroHH overestimates the mean TROPOMI column by ≈ 23 %, whereas the mean TROPOMI column is underestimated by ≈ 11 % after correction.

Figure  shows the results for all simulations. As for BEL2, the calculated slopes decrease considerably when the AMF correction is applied. Except for LIP2, slopes are within 20 % of the 1 : 1 line, which would indicate that NOx emissions in the LIP simulation are too high. In Sect. , we indeed expressed less confidence in the emissions used for the LIP simulation. Results for JAE1 and JAE2 are rather consistent with slopes of ≈ 1.1, while applied emissions for Matimba might be slightly too low. The inset in Fig.  shows the plume-mean columns. Again, the AMF correction generally improves the agreement between the simulations and TROPOMI, with signs of overly high (low) emissions for the LIP2 (MAT1) simulation.

We note, however, that the spread of the individual pixels around the 1 : 1 line is considerable, with systematic model overestimates for high TROPOMI columns and model underestimates for intermediate tropospheric NO2 columns (specifically for BEL2 and MAT1). This could point to either deficiencies in the model chemistry/transport or to potential biases in the TROPOMI columns. For instance, close to the stack, aerosols and clouds may have influenced the TROPOMI retrievals . Potential model deficiencies include a rather simple approach for plume rise. For both BEL1 and MAT1, winds aloft are stronger (see Fig. ) and if plume rise would loft the emissions more, near-stack NO2 columns would decline while downwind columns would increase, potentially explaining some of the biases in Fig. . In general, however, a comparison between a turbulent plume and TROPOMI poses substantial challenges that need to be addressed in the future. For instance, slight rotations or plume-matching algorithms might allow for a more in-depth evaluation of the emissions. For now, we conclude that the emissions that are used in the simulations are likely within 20 % of the true emissions, except for Lipetsk. Deviations might be explained by the use of yearly average emissions in the simulations, while emissions may vary considerably due to varying demand . In the next section, we will summarise and discuss our main findings.

Our simulations show that large NOx emissions in a background atmosphere lead to strong non-linear effects, in which the abundance of NOx strongly influences the NOx and NO2 lifetimes, the NOx:NO2 ratio, and the duration over which a plume stays chemically intact. This latter effect is most clearly observed for the Matimba simulation in which the largest amount of NOx is emitted (Table ). The intensity of segregation between OH and NO2 (Is,NO2,OH; Eq. ) stays negative over more than 75 km downwind of the emission point, signalling plume regions that remain in the high-NOx chemical regime for a long time. Other plumes (JAE1, JAE2, BEL2, and LIP2) show a high-NOx regime only in the first 5–10 km of the plume. At a larger distance from the stack, a different chemical regime is present, with enhanced OH levels, positive Is,NO2,OH values, and NOx and NO2 lifetimes that are shorter than outside the plume (Fig. ).

Next to the NOx emission strength, 3D turbulence in the atmospheric boundary layer determines the dynamical and chemical behaviour of the simulated plumes. Although most simulated cases show well-mixed profiles of wind, TKE, and potential temperature in the boundary layer, some plumes are clearly more turbulent than others. For instance, the BEL1 simulation shows less turbulent mixing compared with the BEL2 simulation (Fig. ). As a result, less ambient air is entrained in the plume, and the plume remains intact for longer, with persistent negative Is values and longer NOx and NO2 lifetimes.

Another important meteorological factor is wind speed. We have identified that wind speed changes affect columns of an inert tracer like CO2 substantially downwind of the plume (Fig. ). For instance, the JAE1 simulation shows a substantial slowing down of the wind speed prior to the TROPOMI overpass time (Fig. ), which increases the CO2 column by roughly 30 % close to the stack location. To reduce errors in simplified methods that aim to quantify plume emissions from satellite data , these methods should ideally account for these wind speed changes. On top of that, 3D turbulence in the boundary layer leads to large temporal variations in the simulated plumes. Simulated 1σ variations (1 h averaging time) in CO2 columns can easily reach 30 %, with highest variability close to the stack location. This behaviour of turbulent plumes is well documented . Satellite images from polar-orbiting platforms, like TROPOMI and the upcoming CO2M mission , take only a snapshot of the turbulent plume, leading to uncertainties in simplified emission estimation methods . Large-eddy simulations, as presented in this paper, help to identify the main factors that influence temporal variations in the plume and to design strategies to reduce errors in emission estimation methods.

Overall, we find a favourable comparison between the simulated plumes and TROPOMI (Fig. ). The Lipetsk simulation on day 1 had low wind speeds, which makes the comparison with TROPOMI difficult. Two other simulation days, BEL1 and MAT2, show that the simulated plumes are rotated clockwise compared with the observations. Biases in simulated wind direction have been identified as a major source of uncertainty in other studies as well . To allow a direct comparison between simulation and TROPOMI, the implementation of a plume-matching algorithm would be useful e.g.. As our simulations are nudged to a single time-dependent wind profile, wind rotation on the synoptic scale can currently not be resolved. Curvature observed in TROPOMI images has been attributed to effects of Coriolis forces . Efforts are ongoing to embed MicroHH within ERA5 and CAMS on larger domains with spatially varying forcing fields.

One of the largest challenges that has been identified in this study is that temporal variability in turbulent plumes is typically large, making a one-to-one comparison to satellite images difficult. TROPOMI samples in an afternoon orbit (13:30 LT, local time), while CO2M will have an overpass time of 11:30 LT . An earlier overpass may avoid some of the strong turbulent plumes that we simulated here. However, other challenges remain.

In a simplified emission estimation procedure, we found that tropospheric TROPOMI columns should be enhanced by ≈ 40 % due to different NO2 amounts and profile shapes in the simulations (Eq. ). Also here, however, there is no one-to-one match between a TROPOMI pixel and the simulation, which makes the applied correction uncertain. By averaging over several simulation snapshots 15 min apart and by calculating the plume-mean enhancements, we tried to account for the modelled variability (Fig. ). Comparisons showed that NOx emissions used in the simulations were likely correct within 20 %, except for Lipetsk, for which the NOx emission in the model was ≈ 40 % too high based on the comparison with TROPOMI. However, we also noticed systematic overestimates in the simulated columns close to the emission location and systematic smaller columns at intermediate distances from the stack. Such biases may point to errors in our simplified chemistry and/or TROPOMI retrievals and AMF correction. The latter might be due to the occurrence of plume-generated clouds and aerosol in the stack plume. One interesting finding that needs further exploration is the possible effect of plume rise on the vertical extend of the plume and its subsequent transport in the atmosphere. Simulated wind profiles (Fig. ) show complex vertical structures. Better characterisation and evaluation of the meteorological situation associated with point source emissions is therefore needed e.g..

In the sections above, we identified the main factors that need to be accounted for in simulating plumes and comparison to satellite images.

First, wind speed and direction as well as their variations in space and time drive how plumes are transported after emission. Associated with that, plume emission height and plume rise are important factors that have been identified before .

Second, we found that the NOx emission strength strongly determines the subsequent fate of the NOx plume. The large NOx emissions of the Matimba stack lead to a chemical perturbation that keeps the plume chemically intact for almost 100 km after emissions. Additionally, the turbulent mixing that mixes the plume with ambient air also plays a role, as shown for the Bełchatów simulation. We also identified plumes (JAE1, JAE2, BEL2, and LIP2) that quickly move out of the high-NOx regime and move into a regime with short NOx and NO2 lifetimes. Accounting for proper NOx lifetimes and NOx:NO2 ratios is important to use NO2 as an additional tracer to constrain CO2 stack emissions.

Third, the AMF correction of TROPOMI data is an important factor. However, variability in the simulated NO2 distribution makes a one-to-one comparison to TROPOMI images, and hence a proper AMF correction, difficult. New data-assimilation techniques to better constrain 3D turbulence are being developed but require time-resolved observations of 3D turbulence. One option to explore is the use of data from recently reported time-resolved imaging spectroscopy . Our chemistry-enabled MicroHH simulations in combination with these detailed observations may improve methods to quantify emissions from large point sources.

Our study also has some shortcomings. First, our chemistry is simplified and does not account for possible impacts of heterogeneous reactions on aerosol surfaces. In highly concentrated plumes, these processes may be important . Second, we performed our simulations according to the CoCO2 simulation protocols (https://coco2-project.eu/sites/default/files/2021-07/CoCO2-D4.1-V1-0.pdf) that only crudely account for plume rise. In the future, we could add heat and moisture stack emissions to the simulations to account explicitly for plume rise. Third, next to applying inflow due to CAMS boundary conditions, we only accounted for emissions from the stack, ignoring possible surface emissions. As a result, concentration fields might be less realistic, specifically in the downwind domain outside the plume. Fourth, the use of 100 m resolution LESs at night is insufficient to resolve small-scale turbulence in the nocturnal boundary layer. As a result, transport will be driven by the sub-grid model, leading to an overestimation of mixing. However, the impact on the development of a convective boundary layer on the next day was shown to be limited . As further outlined in the Supplement, a horizontal model resolution of 100 m also proves barely sufficient to properly account for mixing and plume chemistry. Finally, our boundary conditions consist of single time-dependent columns. Thus, the simulations cannot account for commonly observed rotation in the wind fields. Future developments of the MicroHH code will account for these shortcomings. Moreover, we are extending our method to more complicated emission hot spots, like cities.

In general, our simulations provide new insights into the factors that are important for the interpretation of satellite-observed NO2 plumes. Although it is impractical to run the model for each observed plume, it is likely that the main impacts can be parameterised in light-weight methods, as recently shown in .

In conclusion, we presented LESs of NO2 plumes from four large emitters world-wide. To this end, we implemented a simple chemistry scheme in the MicroHH model. Simulations showed generally good agreement with TROPOMI images as well as the need to account for the strongly non-linear NOx chemistry in concentrated plumes. LESs with chemistry are useful to test less-involved algorithms to derive emissions from large point sources. For a start, the use of a fixed NO2 lifetime and NOx:NO2 ratio can be replaced by values derived from our high-resolution plume simulations.