We focused on the spatial domain of 5–15∘ E and 47–55.5∘ N, particularly over Germany. Near-surface NO2 and O3 data from measurement stations across Germany were used in this study. However, not all measuring stations collect data on both pollutants; there are fewer stations measuring O3 than those measuring NO2. There were also temporal gaps in the measurement data. Therefore, we only considered stations that had more than 80 % data coverage during the study period. In the end, we considered 321 stations for modeling NO2 and 256 stations for modeling O3. The selected measurement stations are located throughout the entire country and are situated in high-traffic, industrial, and background locations (Fig.  and Table A1).

Predictor variables or input features for the ML models include satellite column measurements of air pollutants and meteorology and auxiliary data containing information on the area of interest.

The study period was chosen to be between 30 April 2018 and 1 July 2021, which corresponds to the availability of TROPOMI data retrievals with the same processing version. Despite the fact that satellites pass over the study area between 13:00 and 14:00 LST, we found that the satellite data represent the daily mean of air pollutants well. Therefore, we considered the daily 24 h mean for near-surface NO2 and the daily maximum 8 h mean (i.e., the mean of the eight highest hourly values during a day) for near-surface O3 as our variables of interest (dependent variables to model), as these are commonly used metrics in air quality research .

Because each data set has a different spatiotemporal resolution, we resampled all of the data to the same spatial (0.1∘×0.1∘) and temporal (daily) resolution. The 0.1∘ (≈10 km) resolution was chosen because it corresponds to the resolution of the main features, such as road density (spatial resolution of 8 km), TROPOMI satellite measurements (spatial resolution of 7km×3.5km), and concurrent high-resolution (0.1∘) air quality forecasts from CAMS (Copernicus Atmosphere Monitoring Service). We computed the daily 24 h mean for near-surface NO2 and the daily maximum 8 h mean for near-surface O3 for each in situ measurement station and then calculated the mean of all stations that fell within the 0.1∘ grid. The mean of surface elevation, NDVI, EVI, TROPOMI (NO2, HCHO, and O3), and road density for each day were then calculated for the corresponding 0.1∘ grids. The surface elevation and road density were assumed to be constant during the study period. The ERA5 meteorology product was resampled to 0.1∘ resolution using the nearest-neighbor method, and the 24 h mean was computed.

We primarily used the gradient-boosted tree (GBT) machine learning algorithm, XGBoost , to model near-surface NO2 and O3 concentrations. The GBT algorithm is a gradient-boosted decision-tree-based algorithm that is expected to outperform deep-neural-network-based algorithms for structured data . Furthermore, tree-based models are more interpretable and require less time to train than deep neural network algorithms. However, for comparison, we also used the multi-layer perceptron (MLP; neural network) algorithm . The GBT and MLP algorithms were implemented using scikit-learn, a Python module (https://scikit-learn.org/stable/, last access: 10 March 2023). When training the MLP model, we normalized the discrete feature variables between 0 and 1. The corresponding predictor variables and data flow for the NO2 and O3 ML model is shown in Fig. .

To evaluate the ML model, we used the R2 (coefficient of determination) and RMSE (root mean square error) metrics. We split the available data into training (70 % of the data) and testing (the remaining 30 %). The training data set was used to iteratively vary the hyperparameters (combinations) and select the best set of hyperparameters using a 5-fold CV (cross-validation). The hyperparameters used in this study are shown in Tables A2 and A3. We also evaluated the ML model using three different 5-fold CV testing strategies (random 5-fold CV, time-leave-out 5-fold CV, and location-leave-out 5-fold CV) with 100 % of the data . In the random 5-fold CV testing strategy, the data were randomly split into five parts, four of which were used for training and one for testing. This procedure was repeated until all five parts had been used as test. The mean (and standard deviation) of R2 and RMSE from the 5-fold CV were then computed. In the time-leave-out 5-fold CV testing strategy, the 5-fold CV procedure was the same, but the data were split based on time period (by date; i.e., from the start of study period to the end of study period). Similarly, in the location-leave-out 5-fold CV testing strategy, the data were split based on location (by latitude). Figure A1 shows the first 1-fold step in a 5-fold CV for time-leave-out and location-leave-out testing strategies. To interpret the importance of feature variables in the fitted model, we use SHAP (SHapley Additive exPlanations) values. The SHAP method (https://christophm.github.io/interpretable-ml-book/shap.html, last access: 10 March 2023) is the most commonly used method for interpreting ML model output, which calculates the contribution of each feature variable to the final prediction. Thus, higher SHAP values indicate greater feature importance.

We obtained near-surface NO2 and O3 air quality forecasts from CAMS in order to compare the performance of our ML model to that of the chemical transport model. This data set is based on a data assimilation technique that combines real-time measurements with an ensemble of 11 air quality models to provide air quality data with high spatial resolution (0.1∘) and 1 h temporal resolution over Europe; however, it is only available for 3 years in the rolling archive. We used data from 17 July 2019 to 31 January 2020. We did not use data after 31 January 2020 due to COVID-19 lockdown restrictions, during which many anthropogenic emission activities were limited, and CAMS had not adjusted the emission inventory for changes in emissions. This is because NO2 has a short lifetime, so the effect of assimilated observations is minimal, and the CAMS-forecasted NO2 product mostly reflects emissions prescribed in the inventory .

In this study, GEOS-Chem (Goddard Earth Observing System with Chemistry; hereafter GC) chemical transport model simulations were used to normalize the meteorology effects when estimating the influence of the COVID-19 lockdown restrictions on air pollutant concentration changes. The GC simulations over the study area were obtained with a spatial resolution of 0.5∘×0.625∘ and 1 h temporal resolution for the 2020 strict COVID-19 lockdown period (21 March to 31 May) and the same period in 2019. Identical anthropogenic emissions from the 2014 Community Emissions Data System (CEDS) inventory were used for both 2020 and 2019 but with the corresponding meteorology, natural, and fire emissions in the respective years. Therefore, the difference in GC-simulated species (X) concentrations between 2020 and 2019 results from changes in meteorology, natural, and fire emissions between 2020 and 2019 (GCX2020–2019); here, X refers to either NO2 or O3. Then, we subtracted the GCX2020–2019 from the observed near-surface X2020–2019 to estimate the changes in the concentrations of species X due to changes in anthropogenic emissions in the 2020 lockdown period (refer to the studies of , for detailed descriptions of the method).

The trained GBT model with 70 % of the data (78 433) for NO2 reproduced the observed NO2 concentration well in the test case (33615), with an R2 of 0.88 and RMSE of 4.77 µgm-3 (Fig. a and Table ). The random 5-fold CV results were in the same range (R2=0.89±0.002 and RMSE=4.65±0.034 µgm-3). The other two testing strategies (time-leave-out 5-fold CV and location-leave-out 5-fold CV) showed slightly worse agreement (Table ), indicating that different validation strategies should be performed to interpret the ML model capability. Otherwise, it may result in an overoptimistic view of ML models . Furthermore, the worse agreement in the location-leave-out 5-fold CV testing strategy suggests that there is less confidence in modeling the near-surface NO2 over new locations that the GBT model has not been trained on before. However, these results outperformed the MLP model trained by another study (; R=0.8 and RMSE=6.32 µgm-3 obtained for the testing strategy of the random split of 90 % of the data used for training and 10 % of the data used for testing) for near-surface NO2 over Germany. Feature importance, based on the SHAP values, indicates that road density is the most important feature in the fitted model for NO2 (Fig. c) because traffic is the main source of near-surface NOx in urban areas. The next most important features were TROPOMI NO2, boundary layer height, and elevation. Because the majority of NOx sources are present at the surface, tropospheric column NO2 data play an important role in explaining near-surface NO2. Near-surface NO2 typically has a negative correlation with the boundary layer height, as an increasing BLH disperses more, and vice versa . Therefore, BLH is one of the most important features. It is unexpected that elevation was an important feature. The cause could be that the surface elevation varies greatly across Germany, influencing the total tropospheric column of NO2 and thus serving as a link between the tropospheric column of NO2 and near-surface NO2. A previous study also found that elevation was an important feature in the fitted MLP model for near-surface NO2 over Germany.

The GBT model trained with 70 % of the data (65 705) for O3 also had a good representation of the observed O3 concentrations in the test case (28 160), with an R2 of 0.92 and RMSE of 8.53 µgm-3 (Fig. b). Similar to the NO2 GBT model findings, time-leave-out 5-fold CV and location-leave-out 5-fold CV testing strategies showed less agreement than the random 5-fold CV testing strategy (Table ). In comparison to our NO2 GBT model, our O3 GBT model demonstrated greater confidence in modeling near-surface O3 over locations that the model was not trained on. According to SHAP values, the five most important features were DUV, T, RH, BLH, and season, with DUV having the greatest influence (Fig. d). Because ozone is formed in the atmosphere from the photolysis of NO2, DUV plays a significant role in the fitted model that explains near-surface O3. Temperature is the second most important feature, which is also not surprising, as it drives biogenic VOC emissions (an important precursor to O3). Previous studies also show similar findings . GBT-modeled near-surface NO2 was the sixth most important feature in the fitted model, according to the SHAP values, and it was also more important than TROPOMI NO2.

Figure A2 shows the results obtained from the MLP model. Both the NO2 and O3 MLP models performed worse than the NO2 and O3 GBT models, respectively (Table A4 vs. Table ). In particular, the MLP model findings showed poorer agreement in the time-leave-out 5-fold CV and location-leave-out 5-fold CV testing strategies. This supports previous studies and shows that the MLP model is unlikely to outperform tree-based models for tabular data. Because the GBT model outperforms the MLP model, we only considered the GBT model results in the following.

It is important to note that deep learning models are data intensive, and their performance and generalization capabilities tend to improve with larger amounts of data. In our study, we utilized the simplest deep learning algorithm known as MLP. However, it is essential to explore the capabilities of other deep learning algorithms, such as the CNN (convolutional neural network) and LSTM (long short-term memory), in future studies to gain further insight. Additionally, employing multiple ML models through bagging techniques could potentially lead to improved performance, despite the computational expense involved .

To evaluate how well our GBT model performs compared to CAMS, we compared the high-resolution near-surface NO2 and O3 forecasts from CAMS with observations and GBT-simulated near-surface NO2 and O3 with observations for the period between 17 July 2019 and 31 January 2020 (i.e., CAMS comparison period; Fig. ). Please note this time period was not used for training the GBT model for this comparison. Our NO2 GBT model reproduced the observed near-surface NO2 concentrations well during this comparison period, with an R2 of 0.82 and RMSE of 5.76 µgm-3, while CAMS NO2 forecasts showed poor representation (R2=0.37 and RMSE=14.96 µgm-3). However, CAMS O3 forecasts agreed slightly better with the observed concentrations (R2=0.93 and RMSE of 9.2 µgm-3) when compared to our O3 GBT model (R2=0.85 and RMSE=13 µgm-3). Our NO2 GBT model outperforms CAMS due to the fact that the effect of the data assimilation on the CAMS NO2 forecast product is minimal, with CAMS simulations mostly reflecting the emissions provided in the inventory. Additionally, it should be noted that our GBT model requires less computational effort than the CAMS model.

After the discussed model evaluation, we trained the GBT model using 100 % of the data and modeled the near-surface NO2 and O3 concentrations over the study domain at 0.1∘ resolution and daily (24 h mean for NO2 and 8 h maximum mean for O3) intervals. The averaged GBT-modeled near-surface NO2 concentrations over the study domain during the study period are shown in Fig. a. The spatial variability in the near-surface NO2 correlates with Germany's population density, and the main hotspots correspond to Germany's major metropolitan areas (Fig. A3). The study domain's main hotspot is western Germany (North Rhine-Westphalia; a federal state of Germany), which is Germany's industrial heartland. The number of days (%) that exceeded the 2021 World Health Organization (WHO) NO2 limit (24hmean>25µgm-3) over major metropolitan areas in Germany was more than 50 %, with western Germany (North Rhine-Westphalia) experiencing the most days of exceedance during the study period (Fig. ). Around 36 % of people live in locations where more than 25 % of the days exceed the WHO NO2 limit during the study period (Fig. ). The GBT-simulated near-surface O3 showed a distinct spatial variability compared to NO2, with high O3 concentrations over southern Germany and low O3 concentrations over northern Germany (Fig. ). This could be due to the fact that O3 is a secondary pollutant that is primarily driven by photochemical reactions influenced by meteorology, DUV, and temperature values, which were the factors with the most influence on photochemical reactions; accordingly, the most important features fitted in the O3 GBT model were higher in southern Germany than northern Germany (Fig. A4). During the study period, more than 50 % of the study days in southern Germany exceeded the 2021 WHO O3 limit (maximum 8hmean>100µgm-3). Nearly 90 % of people live in locations where more than 25 % of the study days exceed the WHO O3 limit (Fig. ). Another interesting fact is that southern metropolitan areas and high NOx regions have fewer days that exceeded the WHO O3 limit than southern rural regions (Fig. ). It is a well-known fact that rural regions have higher ozone levels than urban regions . It could be because NO is a significant O3 scavenger in higher NOx (NO2 is a proxy for NOx) regions or because NO is in a NOx-saturated regime. Furthermore, it is due to the fact that rural regions are the downwind locations of emission plumes and are the primary source of biogenic VOC emissions .

We also evaluated the model's capability to capture the exceedance events (above the WHO limit) using time-leave-out evaluation strategy. The exceedances of NO2 and O3 events simulated by the GBT model were compared with ground truth events in each iteration. This allows us to assess the model's ability to reproduce the exceedance events that have not been used in the training process. In total, 82 % of the WHO NO2 and O3 exceedance events in the whole data set (ground truth) were correctly identified as WHO NO2 and O3 exceedance events (true positives) in both the NO2 and O3 GBT models (Table A5). This indicates that our GBT model might slightly underestimates the exceedance events for both NO2 and O3. It could be due to unknown drivers that are not included in the model. However, we also noted that 6.6 % and 7.3 % of the data were incorrectly identified as exceedance events (false positives) by our NO2 and O3 GBT models, respectively.

The GBT-simulated near-surface NO2 showed seasonal variations, as expected, with higher values in the winter season (Fig. ). This is because of the high residential heating demand and favorable meteorology (e.g., a low boundary layer height) for pollutant accumulation and less NO2 photolysis due to low solar radiation in the winter. The near-surface NO2 hotspots were the same in all seasons, as seen in the overall study period average. In contrast, near-surface O3 showed strong seasonal variations, with high values in the spring and summer due to high solar radiation (Fig. ). It is worth noting that, as seen in the overall study period average, O3 values in southern Germany were significantly higher in spring and summer than in northern Germany. Because near-surface O3 is mainly driven by meteorology (DUV and temperature, which drive photochemical reactions and precursor emissions), the spatiotemporal variability is attributed to changes in meteorology. We also compared the spatial variability in the GBT-simulated near-surface NO2 and O3 to the CAMS forecasts product for the period between 17 July 2019 and 31 January 2020 (Figs. A5 and A6). The spatial variability in the GBT-simulated near-surface NO2 and O3 agreed well with the CAMS model. This implies that the ML model can supplement or replace the computationally expensive chemical transport models.

Due to the COVID-19 outbreak, many nations, including Germany, announced a lockdown in the spring of 2020. During that time period, various anthropogenic emission activities were restricted, particularly affecting traffic-related emissions. To estimate the influence of the lockdown restrictions on air pollutant concentration changes, we compared the GBT-simulated 2020 lockdown concentration with the same period in 2019. The 2020 lockdown period measurements were not used for GBT model training in this comparison. This can also be regarded as the critical performance evaluation of the GBT model.

When comparing different time periods, it is crucial to normalize the meteorology effects when estimating the impact of anthropogenic emission reductions (i.e., lockdown effects) on changes in air pollutant concentrations. Therefore, as described in Sect. 2, we used GC simulations to normalize the meteorology effects from GBT-simulated concentrations. After normalizing the meteorology effects, it is noticeable that high near-surface NO2 levels decreased primarily over the previously observed hotspots (Fig. ). The near-surface O3 increased over western Germany, while decreasing elsewhere, particularly over low NOx regions. We already observed that western Germany was a NOx hotspot, possibly due to being a NOx-saturated regime, so a reduction in NOx increases ozone. Also, we could see that changes in near-surface O3 were either negligible or slightly increased over metropolitan areas. The meteorology-normalized mean lockdown near-surface NO2 decreased by about 23 % (± 5.3 %), while the meteorology-normalized mean lockdown near-surface O3 increased by 1 % (± 4.6 %), over 10 major metropolitan areas (Berlin, Bremen, Cologne, Dresden, Düsseldorf, Frankfurt, Hamburg, Hanover, Munich, and Stuttgart) when compared to 2019. It increased by about 9 % in the Cologne and Düsseldorf metropolitan areas (located in western Germany) and slightly increased or decreased (between -3 % and +2 %) in other metropolitan areas when compared to 2019. This finding is consistent with other studies that found a decrease in the meteorology-normalized lockdown near-surface NO2 and the small increase in the lockdown near-surface O3 over German metropolitan areas when compared to 2019, using in situ measurements . We also evaluated our GBT model's ability to represent different emission scenarios by comparing weekends and weekdays; typically, anthropogenic NOx emissions on weekends are lower than on weekdays due to reduced vehicle transportation. Our GBT model was also able to distinguish between the weekend and weekday emission scenarios; weekend near-surface NO2 was lower than weekday near-surface NO2, and as expected, there were no or only slight changes in weekend near-surface O3 when compared to weekdays, with slight increases particularly over metropolitan areas (Fig. A7).

Although our study domain also covered parts of other European countries, we trained our GBT model using data from German measurement stations only. Therefore, comparing our trained GBT model simulations with measurements in other countries demonstrates how well our GBT model can model near-surface NO2 and O3 concentrations in neighboring parts of the world (similar to the location-leave-out testing strategy). We chose five major cities (Salzburg, Prague, Strasbourg, Liège, and Groningen) in different European countries covered by our study domain and compared their measured NO2 and O3 concentrations with GBT-modeled NO2 and O3 concentrations (Fig.  and Table A6).

Our trained NO2 GBT model based on German measurement stations explained 32 %–64 % (R2 ranges between 0.32 and 0.64; RMSE ranges between 9.76 and 13 µgm-3) of the near-surface NO2 measured in five metropolitan areas located outside of Germany, while the O3 GBT model simulations agreed well with the observations (R2 ranges between 0.87 and 0.94; RMSE ranges between 9.55 and 14.32 µgm-3). Since near-surface O3 is mainly driven by meteorology, the O3 GBT model trained using German measurement stations explains a large portion of near-surface O3 in other locations. The worse agreement between the NO2 GBT model predictions and NO2 observations in other European countries suggests that information is lacking in the NO2 GBT model to enable better representations of other locations, similar to location-leave-out 5-fold CV, which also showed poorer agreement for the NO2 GBT model when modeling new locations (Table ). Differences in the vehicle fleet composition and emission standards across different countries and locations would have an impact on our NO2 GBT model predictions when applied to other countries or locations. In future work, other features and proxies besides road density could be considered to represent traffic emission.