EURAD-IM (EURopean Air pollution Dispersion – Inverse Model) is a three-dimensional high-resolution Eulerian CTM simulating air pollution in the troposphere at continental to regional scales. It has been used for several scientific studies for air quality forecasting, episode scenarios, data assimilation, and inverse modelling . EURAD-IM is part of the regional Copernicus Atmosphere Monitoring Service (CAMS), providing daily air quality forecasts and reanalysis over Europe which enable continuous quality assurance using observations and inter-model evaluation .

Table  presents a summary of the specific model settings and modules utilised in the EURAD-IM configuration employed in this study. EURAD-IM describes the transport by diffusion and advection of various trace-gas components emitted both by anthropogenic and biogenic sources and considers the gas-phase chemical transformation of about 110 chemical species with 265 reactions. The MADE (Modal Aerosol Dynamics model for Europe) module is employed to investigate aerosol dynamics within EURAD-IM, providing information on aerosol size distribution and chemical composition. This module simulates the formation and transformation of both primary and secondary aerosols, considering the interactions between the gas phase and aerosols. EURAD-IM accounts for the loss of chemical components through wet and dry deposition, as well as aerosol sedimentation. Moreover, EURAD-IM includes a 4D-Var assimilation system, as described in the subsequent section, along with the adjoint code derived from the forward code detailed in . The adjoint model incorporates the transport, diffusion, and gas transformation processes of the chemical species as well as secondary inorganic aerosol formation.

The CTM is driven by meteorological fields from the Weather Research and Forecasting (WRF) model (version 3.7; ) as thermodynamical forcing. The ECMWF (European Centre for Medium-Range Weather Forecasts) IFS (Integrated Forecasting System) global analysis (ERA5) is used for initialisation and boundary conditions for the WRF simulations. Chemical boundary conditions are generated by the CAMS global reanalysis data set (EAC4) that is produced by the ECMWF Composition Integrated Forecasting System (C-IFS). Anthropogenic emissions used for this study are provided by the German Environment Agency (Umweltbundesamt, UBA) for Germany and by the TNO-MACC_II inventory for the rest of Europe. The emission data set is subject to processing in the EURAD Emission Module (EEM) for seasonal and diurnal redistribution, as well as attributions to working days and weekends. The emission data are divided into point and area sources. The data contain emissions of gaseous air pollutants, i.e. carbon monoxide (CO), nitrogen oxides (NOx), sulfur dioxide (SO2), total non-methane volatile organic compounds (NMVOCs), and ammonia (NH3), as well as the aerosols PM10 (particulate matter with a diameter < 10 µm) and PM2.5 (particulate matter with a diameter < 2.5 µm). Biogenic emissions are calculated online using the Model of Emissions of Gases and Aerosols from Nature (MEGAN), while wild-fire emissions are not considered here and did not play a role in the investigated case.

The EURAD-IM data assimilation system is based on the 4D-Var method as described in and . The 4D-Var approach aims to determine the optimal model state by combining the prior information (e.g. provided by a forecast) with observational data over an assimilation window through the minimisation of the following cost function J: 1J(x0,e)=Jb(x0)+Jo(x0)+Je(e)=12x0-xbTB-1x0-xb+12∑i=0nyi-HiMix0TRi-1yi-HiMix0+12e-ebTK-1e-eb. Here, the optimisation is subject to the initial conditions x0 and the emission correction factor e. The cost function equation includes an additional element (in contrast to the usual 4D-Var used for NWP) that accounts for emissions (Je (e)). The model state is mapped from the model space to the observation space by the observation operator Hi and the model operator Mi, producing the model equivalents of each observation yi. The matrices B, R, and K represent the error covariance matrices associated with the a priori state vector xb, the observations yi, and a priori emissions eb, respectively. The matrix R considers only diagonal elements (i.e. it ignores any error correlation between different observations) while accounting for the uncertainties in the measurements and model representation error. The matrix B is estimated using error variances and the diffusion operator proposed by . Thus, B can be factorised as B=B1/2BT/2 for use in the preconditioning of the highly underdetermined data assimilation system. The matrix K is defined as block diagonal, with non-zero entries for correlations between species and nearby emissions. The variance and correlation values are provided in . The minimisation of the cost function J is performed through an iterative process using the quasi-Newton limited-memory L-BFGS algorithm , which includes the iterative integration of the forward and adjoint EURAD-IM.

The MesSBAR field campaign took place near Wesseling, Germany, on 22–23 September 2021. During these 2 d, a multicopter system composed of a drone and a set of low-cost air quality monitoring instruments was used to carry out vertical profile measurements of air pollutants during the morning hours. Among the instruments loaded on the multicopter, electrochemical sensors were used to monitor nitrogen oxide (NO), and a personal ozone monitor (POM) was deployed for assessing ozone (O3) concentrations. The NO drone observations have an accuracy of 35 % at 40 ppbv with a precision of ± 2.5 ppbv (1σ at 30 s time resolution). POM provides an accuracy of 1.5 ppbv and a precision of 1.5 ppbv (1σ at 10 s time resolution) in the observed O3 mixing ratio range. The feasibility of using these sensors for measurements in the PBL was discussed in and . A detailed description of the development, technical characteristics, and calibration of the multicopter system can be found in . The campaign's base was located within the proximity of the A555 highway, which is a much-frequented connection between the German cities of Cologne and Bonn. The measurements were conducted above agricultural land located about 1 km south of the town of Wesseling. The city centres of Cologne and Bonn are about 15 km north and 10 km south of the measurement location, respectively (Fig. ). The Wesseling region is located within the Rhineland chemical region and is widely recognised as a leading chemical hub in Europe. Wesseling, in particular, hosts a remarkable level of industrial activity attributed to the presence of major companies operating in the chemical and petroleum sectors (source: https://www.chemcologne.de/en/investments/the-rhineland-chemical-region, last access: 21 February 2024).

The objective of this campaign was to capture the early-morning evolution of air pollutant concentrations with the development of the PBL. Furthermore, the proximity to the highway allows for measurements of pollutants specifically originating from traffic sources.

The drone is operated by an autopilot system that uses an inertial navigation solution with an earth-related position based on GNSS (Global Navigation Satellite System) data. During the measurements, the autopilot controls a constant lateral position and a constant vertical climb rate of approximately 1 ms-1. Wind affects only the attitude of the copter, but given the low-wind situations during this campaign, the effect on the attitude can be neglected. The drone reached a maximum altitude of 350 m. This altitude limitation was imposed by air traffic restrictions in the area due to its proximity to the Cologne Bonn Airport. During each drone flight, two profiles were acquired: one ascending profile and one descending profile were done in a short period of time. For the assimilation experiments carried out with EURAD-IM, only the ascending profiles were utilised due to their higher accuracy . The measurements during the descending flights are strongly influenced by the turbulence generated by the drone's propellers, which reduces the data quality. In this study, the vertical profiles of O3 and NO obtained from the multicopter are utilised and assimilated within EURAD-IM. The vertical resolution of these profiles is approximately 10 m, with 254 data points assimilated on 22 September 2021 and 257 on 23 September 2021 for both O3 and NO. Additionally, observations from two ground-based stations situated on both sides of highway A555 (Fig. ) are used to validate the simulation results. Furthermore, meteorological observations from an automatic weather station, located approximately 1 km southeast of the measurement site, are employed for comparing meteorological data, especially the wind fields.

The objective of this study is to investigate the impact of O3 and NO drone profile assimilation on the air quality analysis using high-resolution EURAD-IM simulations. The model grid has a horizontal resolution of 5 km × 5 km and is vertically divided into 30 layers defined by terrain following sigma coordinates between the surface and 100 hPa, with about 19 layers covering the lowest 1 km of the atmosphere. The EURAD-IM domain covers central Europe, including Germany with 271×298 grid points. The model output is adjusted to provide forecasts with a temporal resolution of 60 s, allowing for a more precise comparison with the high-resolution drone observations. To assess the impact of drone data assimilation on air quality forecasts, simulations are conducted both with and without data assimilation (Table ). The joint initial value and emission rate optimisation mode of EURAD-IM is activated for this purpose. Two 24 h experiments are performed without assimilation: one on 22 September 2021 and the other on 23 September 2021. For these experiments, the model is initialised from a climatological chemical state with a spin-up simulation of 6 d (16–21 September 2021) prior to the campaign dates in order to establish a chemically balanced initial state. Moreover, two additional simulations focusing on O3 and NO data assimilation are performed for 24 h on 22 and 23 September 2021. The assimilation window is deliberately selected to coincide with the availability of observations, aiming to minimise computational time in the simulations while also ensuring a meaningful lead time for emission optimisation. For drone data assimilation, the observation error is considered as the sum of measurement and representativeness errors. The measurement error for O3 is taken as the standard deviation of the measurements. For NO, the error ϵmeas is estimated according to by defining a relative error ϵrel and a minimal absolute error ϵabs: 2ϵmeas=max⁡(ϵabs,ϵrel⋅y), where y is the individual observation. The absolute error used for NO is 2 ppbv, and the relative error is considered to be 20 % of the observed values.

The representation error is calculated by applying the corresponding formula from , which considers the grid cell spacing (Δx), the representativeness length of the measurement location (Lrep), and an absolute error specific to the measured species. The formula is expressed as 3ϵrep=ΔxLrep×ϵabs. The grid cell spacing (Δx) corresponds to the spatial resolution of the measurement grid, while the representativeness length (Lrep) indicates the effective range over which the measurement is considered representative. In this case study, Lrep is set to 3 km. The absolute error (ϵabs) varies by species: it is 2 ppbv for O3 and 3 ppbv for NO. For the estimation of background errors, horizontal correlation lengths of 2.5, 10, and 20 km are employed at the surface, at the top of the PBL, and at the upper model levels, respectively.

The wind is a critical parameter that governs the dispersion of air pollutants and their transport, with a direct influence on emission optimisation within the framework of inverse CTMs. The wind conditions at the observation site are evaluated for two purposes: firstly to validate the suitability of the measurement site location for measuring local traffic emissions and secondly to assess the horizontal wind for applications to emission optimisation.

Figure a and b show the surface wind speed and direction observed by the nearby weather station during the flights' operation hours. The dominant wind direction is primarily from the southeast on 22 September 2021, with a maximum speed of 1.3 ms-1, while it comes from the south to southeast in the morning hours of 23 September 2021, with a maximum recorded speed of 2.0 ms-1. This indicates that the observation point is strategically located downwind of the nearest traffic emission source, which enabled the multicopter to successfully capture the emissions from the highway.

Apart from the surface conditions during the measuring period, each of the 2 d is characterised by a distinct wind situation, as shown in the horizontal wind profiles extracted from the WRF simulations in Fig. c and d. On 22 September 2021, the wind patterns exhibit vertical wind shear throughout the day and across all levels, changing direction from the east-southeast at lower altitudes to the west-northwest at higher altitudes. However, the wind intensity remains relatively low, measuring less than 3.0 ms-1. On 23 September 2021, the surface wind direction aligns with the observations during the campaign period. Nevertheless, at higher levels and beyond the campaign period, westerly and southwesterly winds dominate, and their speed increases with height. The maximum speed of 12.0 ms-1 is reached at 450 m between 05:00 and 07:00 UTC. The difference in the wind profiles between the 2 d may result in variations in the assimilation results, particularly with respect to emission optimisation.

In order to evaluate the impact of the drone data assimilation on the air pollutants' vertical distribution and given the lack of independent vertical profiles, the simulation results are first compared to the drone observations that are assimilated. Figure  presents the observed O3 and NO drone profiles as well as vertical profiles resulting from the 4D-Var assimilation and the reference simulations. For both days, the 4D-Var analyses agree better with the drone observations in comparison to the reference forecast for both species, which indicates the successful assimilation of the drone observations. On 22 September 2021, an underestimation by the reference simulation is observed for the O3 levels at altitudes above 200 m, with discrepancies reaching up to 15 ppbv, especially for the first three flights (F1, F2, and F3). The assimilation of drone profiles significantly reduces this underestimation. The bias was reduced by 98 % (-4.58 ppbv) for F1, 36 % (-0.74 ppbv) for F2, and 41 % (-1.44 ppbv) for F3, with an average reduction of 30 % (-0.73 ppbv) across all flights (Table ). On 23 September 2021, the reference model run overestimates O3 concentrations at both ground and near-surface levels. The most pronounced overestimations occur during the first three flights of the day (F7, F8, and F9), with discrepancies reaching up to 20 ppbv. Following the 4D-Var assimilation, the O3 bias is reduced by more than 82 % (-12.49 ppbv) for F7, 56 % (-2.86 ppbv) for F8, and 25 % (-0.96 ppbv) for F9. As a result, the overall O3 bias on the second day is reduced by approximately 55 % (-3.46 ppbv) (Table ).

On both days, the reference simulations underestimate the NO vertical distribution at all heights, with the strongest discrepancies at ground level. Improvement due to the assimilation is accomplished mostly at surface and near-surface levels for the initial three flights of each day (F1, F2, F3, F7, F8, and F9), with more pronounced adjustments on the second day at ground level, while at higher levels during these same flights, the impact of the assimilation is minimal to non-existent, for instance, for flights F7 and F8 above 150 m. Overall, bias reductions of 24 % (6.78 ppbv), 33 % (11.61 ppbv), and 23 % (8.91 ppbv) were observed for F1, F2, and F3, respectively. On the second day, greater improvements were achieved, with reductions of 30 % (4.17 ppbv) for F7, 49 % (10.1 ppbv) for F8, and 57 % (15.29 ppbv) for F9. Because the pollutant concentrations are well-mixed in the PBL, a uniformly positive impact throughout the vertical can be seen in the NO analyses of the later flights of the day (F4, F5, F6, F10, and F11). The bias is reduced by 38 % (-10.81 ppbv) for F4, 54 % (-15.26 ppbv) for F5, and 49 % (-14.66 ppbv) for F6. On the following day, the bias reduction is smaller, with a 27 % (-7.48 ppbv) reduction for F10 and 18 % (-5.58 ppbv) for F11. Overall, the 4D-Var assimilation of drone observations leads to a substantial reduction in NO biases, with a 36 % reduction (-11.34 ppbv) on the first day and a 35 % reduction (-8.52 ppbv) on the second day, between the reference model forecast and observations (Table ).

These results highlight the successful assimilation of drone observations by the EURAD-IM 4D-Var system. The accuracy of these findings is further examined and discussed in Sect.  through a validation process using independent observations.

The 4D-Var data assimilation method applied here aims at finding the best representation of the pollutants combining the knowledge provided by the EURAD-IM simulations and the drone O3 and NO profile observations. The method relies on the assumption that the largest uncertainties in the modelled pollutant concentrations are based on uncertainties in initial values and emission rates. Emission correction factors for 25 anthropogenic pollutants can be deduced from the analysis. Consequently, it is worth looking at the emission factors being analysed to gain a first insight into the potential to retrieve detailed information about emission assessment by applying this inverse modelling technique. However, their generalisation and significance should be carefully evaluated, mainly because of the limited number of drone profiles available, their unequal distribution during the course of the day, the resulting short assimilation windows, and the lack of a long-term statistical analysis.

The assimilation experiments performed with the O3 and NO drone observations result in significant corrections of NO and NO2 emission rates in the grids surrounding the observation site. The resulting emissions factors, which represent the ratio between the optimised emission rates and the input emission rates for each species, have variability that ranges from 1 to 4 for NO and from 1 to 6 for NO2 in the DA_22SEP experiment. In contrast, the variability extends from 1 to 14 for both NO and NO2 in the DA_23SEP experiment (Fig. ). This indicates that an increase in emissions is analysed in the studied region. Figure  (first row) displays the original daily NOx emissions rates and the analysed emission changes on 22 and 23 September 2021. A significant increase in NOx emissions is obtained in the DA_22SEP results, with changes in emission rates reaching up to 16 Mgd-1 in the grid cells located north and northwest of the observation site. The emission of 16 Mgd-1 represents approximately 3.46 % of the total daily NOx emissions in the analysed region, which is about 462 Mgd-1. For DA_23SEP in contrast, the emission rates increase by up to 10 Mgd-1 in the grid cells surrounding the observation site. Based on the chemical coupling with NO and O3, carbon monoxide (CO), sulfur dioxide (SO2), and sulfate (SO4) emissions are optimised, resulting in emission correction factors between 1 and 3 (not shown).

To interpret the results and to investigate this discrepancy between the 2 d, the changes in NOx emissions are evaluated according to the emission source sectors. Figure  additionally shows the original NOx emissions and the analysed emission changes for three dominant polluter sectors in this region: power production, industry, and road transport. The original emission data set includes in total 12 GNFR (gridded nomenclature for reporting) sectors, while only these three sectors are substantially affected in the analysis. The DA_22SEP results indicate that 75 % of the emissions increase can be attributed to power generation and industrial activities. The remaining emission increase is mainly attributed to the road transportation sector. For the DA_23SEP results, almost half of the analysed emissions come from the road transport sector. In some grid cells, the additional road emissions of DA_23SEP are twice as high as those of DA_22SEP, reaching up to 6 Mgd-1 compared to 1.5 Mgd-1, respectively.

The area affected by the emission corrections differs for the two consecutive analysis days. This disparity lies in the different meteorological conditions, particularly in the variation in wind patterns, that occur during these days. As shown in Fig.  the prevailing winds in the studied region have low intensity and significant variability at the ground and high altitude on 22 September 2021, while on 23 September, the wind is more intense and predominantly originating from the west. This causes different dispersion situations for the pollutant during the 2 d.

This can be seen in Fig. , which shows tropospheric NO2 columns observed by TROPOMI (Tropospheric Monitoring Instrument) on board the Sentinel-5 Precursor (Sentinel-5P) satellite. These data highlight that the accumulation of pollutants resulting in high NO2 concentrations is very distinct for each individual day. On 22 September 2021, TROPOMI data show a highly polluted area north and northwest of the observation site, which does not persist on 23 September 2021. This might explain the increase in emissions rates seen in the DA_22SEP results to the north and northwest of the observation site. However, it is unfortunately not possible to directly obtain information about the NO2 emissions from the TROPOMI data. Nevertheless, the 4D-Var assimilation algorithm seems to react to the high concentrations by attributing corrections to emission increases.

These results indicate the strong effects of the wind condition on the observability of the drone measurement. Nevertheless, it shows the potential that the drone observations have for emission optimisation, especially for emissions that are emitted at higher altitudes, such as power plants and industries. Drawing definitive conclusions regarding the accuracy of emissions changes is consistently challenging, primarily due to the scarcity of emissions observations. Consequently, we will validate the 4D-Var analysis using independent ground-based observations, and we will analyse the contribution of emission changes to the observed improvements in order to evaluate the potential of drone observations in optimising emission rates.

The analysis of the DA_22SEP and DA_23SEP experiments shows that the assimilation of drone observations has a positive impact on the vertical distribution of O3 and NO and on the daily cycle of O3 and NOx at ground level. These promising results underscore the significant potential of drone data assimilation in enhancing regional air quality analysis. Moreover, the assimilation process provides optimised emissions rates for each day. To investigate the role of emission optimisation in the analysis improvement, Table  presents the cost reduction for O3 and NO, as well as the partial costs attributed to the optimisation of the initial values (IVs) Jb(x0)J(x0,e) and the emission correction factors (EFs) Je(e)J(x0,e). For both assimilation experiments, the costs are reduced by more than 30 %, which confirms the successful assimilation of the drone profiles. In particular, the O3 costs of DA_23SEP are highly reduced by 80 %, resulting in a precise alignment between the 4D-Var analysis and the O3 observations. The partial costs vary between the 2 d. For DA_22SEP, the costs associated with IV are more than twice those of EF, which indicates important IV adjustments and a minimal impact of the emission changes in the cost minimisation. In contrast for DA_23SEP, the effect of optimising the emissions is higher. This indicates that a significant part of the improvement observed in the analysis is due to the optimisation of EF. Therefore, the drone observations may also have significant potential for assessing local emissions. In a recent study by , it was demonstrated that for high-altitude observations, the efficiency of emission rate optimisation is conditioned by favourable wind conditions and strong vertical diffusion.

Despite the observed improvements in the analysis, some limitations are noted. Firstly, the results reported in Sect.  show a limited impact on the NO vertical profiles on 23 September 2021. Although effective correction is achieved at the ground and near-ground levels, limited improvements are obtained for the NO concentrations at higher altitudes (above 150 m) for the first three profiles of the day. Figure  illustrates the vertically resolved analysis increment (4D-Var analysis – reference run) for O3, NO, and NO2 on 23 September 2021. A negative O3 increment alongside a positive NO2 increment is noted, both exhibiting a well-developed vertical spread. The NO increment is constrained near ground level during the early hours of the day. The reason behind this is the NOx titration process, where freshly emitted NO, including additional NO emissions resulting from emission optimisation, reacts with O3 to produce NO2. To achieve better results, a larger NO increment is needed. However, the NO observations from the drone exhibit high measurement errors compared to the background errors, which limits the effectiveness of assimilating these data.

Secondly, some suboptimal outcomes are observed in the free run, namely for O3 and NO2 ground concentrations, suggesting that the advantage of the drone data assimilation is limited to the assimilation window (Figs. , , and ). Nevertheless, this result is not surprising and is completely explainable. Initially, it is important to note that the reference model simulation already provides underestimations of O3 peaks during the afternoon and nighttime, which may be linked to uncertainties in the boundary layer height at night, vertical diffusion, and/or emission profiles. Through the 4D-Var assimilation of drone data, adjustments are made to the NOx emissions. However, in regions characterised by high NOx emissions, O3 formation exhibits reduced sensitivity to NOx emissions but increased sensitivity to VOCs . Thus, the inability to adjust O3 concentrations and, consequently, NO2 in our simulations is not a limitation specific to drone data assimilation.