NOODLESALAD PM_2.5 retrievals are obtained applying a deep learning based post-process correction approach to the MERRA-2 AOD-to-PM_2.5 conversion ratio. The post-process corrected AOD-to-PM_2.5 conversion ratio is utilized to map high resolution POPCORN SENTINEL-3 SYNERGY AOD estimate to high resolution PM_2.5 estimate. The post-process correction of MERRA-2 AOD-to-PM_2.5 conversion ratio is carried out deploying an ensemble of fully-connected feed-forward neural networks and a fusion of surface in-situ PM_2.5 observations, MERRA-2 reanalysis model AOD and PM_2.5 data, spectral AERONET AOD, satellite-observed spectral top-of-atmosphere reflectances, meteorology data, and various high-resolution geographical indicators. The ensemble technique leads to a distribution of predictions for a single PM_2.5 estimate. The median of the ensemble is considered as the PM_2.5 estimate and the width of the distribution is regarded as an uncertainty related to the machine learning model training (model uncertainty). NOODLESALAD PM_2.5 offers high resolution on a grid with cell size 100 m × 100 m and is currently available for Sentinel-3A and 3B overpasses, covering Central Europe for the year 2019. The two Sentinel-3 satellites currently flying provide revisit times of less than two days for OLCI and less than one day for the SLSTR instrument at equator. Swath width of the OLCI instrument is 1270 km. SLSTR swath width is 1420 km for the nadir view and 750 km for the oblique view.

Evaluation metrics for PM_2.5 at satellite overpass (R2=0.55, RMSE = 6.2 µg m⁻³) and PM_2.5 monthly averages (R2=0.72, RMSE = 3.7 µg m⁻³) show good agreement between NOODLESALAD PM_2.5 and OpenAQ ground stations data . Given the better spatial coverage compared to ground stations and the high spatial resolution at satellite overpass, we utilize NOODLESALAD PM_2.5 to inform the model about PM_2.5 fine spatial distribution. In this work, we consider NOODLESALAD PM_2.5 retrievals in Paris, France, in 2019, and utilize them as part of the target data to train our model.

OpenAQ (https://openaq.org/, last access: 13 April 2023) is an open-access database for ground stations air quality data. In this study, we utilize OpenAQ as our source for surface in-situ PM_2.5 observations. OpenAQ offers pointwise air quality measurement data from thousands of stations. The temporal resolution of the data varies by station, with 1 h and daily observations commonly available. Figure  shows a map of OpenAQ stations that provide hourly data within our region of interest. We discard PM_2.5 observations when they are greater than the calculated upper fence Q3+6×(Q3-Q1) (where Q3 and Q1 are respectively the third and first quartiles of the PM_2.5 distribution), regarding them as outliers. This step was carried out to filter extreme outliers, which can be caused by exceptional events or ground station malfunctions.

The Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), is NASA's reanalysis model . MERRA-2 provides model data for various variables in meteorology, aerosols and air quality. MERRA-2 has a spatial resolution of 0.5° × 0.625°, which is approximately 50 km in the Central Europe region. The time-varying variables from MERRA-2 that we use have a temporal resolution of 1 h, with both instantaneous and time-averaged values available depending on the variable and data product. Appendix  contains a list of all MERRA-2 variables that are used as inputs in the proposed approach.

In addition to the variables contained in the MERRA-2 data, we calculate certain input variables from the MERRA-2 meteorological and aerosol data. These data are defined as:

Relative humidity (RH) at the surface. Equation based on the Clausius-Clapeyron equation see e.g.:1RH=0.263⋅PS⋅QLML/exp⁡((17.67⋅(T2M-273.15))/(T2M-29.65))

All geographic variables with the original resolution larger than 100 m were regridded to a common spatial grid with a resolution of 100 m using the Universal Transverse Mercator (UTM) projection. Linear interpolation method was used for continuous features and nearest neighbor interpolation for categorical variables. This preprocessing ensured that all features were spatially collocated prior to input into the deep learning model.

We use the Mean Square Error (MSE) as the loss function in the supervised regression problem of fitting the 3D U-Net model to the training data. Ideally in clear sky conditions for a satellite overpass, we would have a full PM_2.5 map. In ideal conditions for a single ground station, we would have a full time series without missing data. However, in reality satellite overpass data can lack information at some pixels, e.g. cloud covering can hinder AOD retrievals, therefore hindering PM_2.5 estimates, and a ground station can malfunction, leading to missing data in the time-series of the station. Furthermore, on a single day we usually have significantly more PM_2.5 pixel values coming from the satellite overpasses than measured values from the ground stations. The ground stations PM_2.5 data are usually more accurate than satellite estimate data and they are our only data source available hourly. On the other hand, NOODLESALAD PM_2.5 is our data source providing information far from the ground stations at the time of satellite overpasses. Therefore, to take the missing data and highly different number of satellite versus ground station data available into account, we consider masking and weighting the data in the MSE loss function.

Let the batch size be denoted by B (with B=4 for this particular case) and define N={1,…,960×960} as the set of all pixel indices. For each sample b in the batch, define Hst,b⊆{1,…,24} as the set of hours during which ground stations measurements are available, and Hop,b⊆{1,…,24} as the corresponding set of hours for satellite overpasses. Let yb,h,i represent the target measurement at sample b, hour h, and pixel index i, with y^b,h,i denoting the corresponding predicted value by the deep learning model. When a measurement is not available (due to lacking data from a ground monitoring station or failed satellite retrieval due to cloud covering) yb,h,i is encoded as 0, since this value does not naturally occur in the dataset (PM_2.5 is not zero in a realistic setting). On the other hand, y^b,h,i is always a positive real value by choice, since SoftPlus was chosen as activation function for our model output.

For each sample b and hour h, define: 6Sst,b,h={i∈N∣yb,h,i≠0 and h∈Hst,b},7S̃op,b,h={i∈N∣yb,h,i≠0 and h∈Hop,b}, representing pixel indices where ground station measurements (Sst,b,h) and satellite overpass measurements (S̃op,b,h) are available. The sets Sst,b,h and Sop,b,h are defined separately for the ground stations and satellite overpass data. From the satellite overpass data, we create a subset Sop,b,h⊂S̃op,b,h of data with 25 % of size of S̃op,b,h by uniform random sampling of the pixels to be used in the minimization. The random sampling is performed at each training step (for every update of the network parameters) and can be seen as an optimization technique analogue to batch shuffling. This undersampling is beneficial for training on overpass estimates, especially given the substantial pixel count (nearly 1 million when all pixels provide valid measurements at overpass times).

The average losses for the ground stations and overpass contributions are defined by summing over the respective sets of valid hours: 8Lst,b=Cst,b∑h∈Hst,b1|Sst,b,h|∑i∈Sst,b,h(yb,h,i-y^b,h,i)29Lop,b=Cop,b∑h∈Hop,b1|Sop,b,h|∑i∈Sop,b,h(yb,h,i-y^b,h,i)2 where Cst,b and Cop,b are factors depending on the sizes of the sets Hst,b and Hop,b (defined respectively as |Hst,b| and |Hop,b|). If these sets are empty, Cst,b and Cop,b are equal to 0, otherwise they correspond to 1|Hst,b| and 1|Hop,b| respectively. Analogously, |Sst,b,h| and |Sop,b,h| represent the sizes of the sets Sst,b,h and Sop,b,h.

We then define the sample-specific loss Lb as: 10Lb=Lst,b+Lop,b2,if Lst,b≠0 and Lop,b≠0Lst,b,if Lop,b=0Lop,b,if Lst,b=0

Finally, the overall loss for the batch is defined as: 11L=1B∑b=1BLb

This formalization provides the necessary structure to include both ground station and satellite overpass target data within each batch. A schematic representation of the loss function is presented in Fig. .

For each data sample, one or two target maps correspond to the available satellite overpasses data (i.e. NOODLESALAD PM_2.5) while the others contain only ground stations data (therefore 11 pixels for each map when data is available from all the stations). In order to test the results from the network training, we used leave-one-out cross-validation (CV) (i.e. we removed one different station from each training and used the data left out of training for testing purposes). Therefore, we trained 11 different networks (one for each ground station in the region of interest). Furthermore, the dataset has been split into training set (approximately 80 % of the data samples) used for the optimization of the network weights and validation set (approximately 20 % of the data samples) used for early stopping of the optimization. The early stopping is a form of regularization useful to avoid overfitting of the network . It consists in keeping track of both the training error and validation error with the objective of stopping the training when the validation error starts to increase (i.e. when the network stops to learn useful patterns and noise in the training set starts to play a significant role). While early stopping is not the only regularization technique applicable to train deep learning models, it offers a good trade-off between model performance and training time. We consider a patience parameter equal to 30, meaning that the training stops when no improvement on the validation loss is recorded over 30 epochs. Since using a small batch size introduces fluctuations in the loss during training, this choice of the patience parameter is reasonable, as a lower patience value could prematurely stop training and lead to underfitting.

We utilized the Adam algorithm (with learning rate equal to 0.0001) and the custom loss function described in Sect.  to optimize the network model parameters.

We considered a leave-one-out CV approach, training 11 models, each time leaving one station out of the training as test station. The results of predicted PM_2.5 at the locations of the 11 AQ stations in Paris are shown in Fig. .

Different fidelity metrics (per each trained model) were calculated to compare MERRA-2 estimates (orange bars) and our model predictions (blue bars) to OpenAQ measurements (ground truth). Correlation R2, Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values are shown on the left, middle and right columns. These metrics are evaluated for hourly averages, daily averages and monthly averages (estimated using the hourly averages) on the top, middle and bottom row. The fidelity metrics averages show that our model clearly outperforms MERRA-2. R2 CV averages for our model are 0.51 (hourly averages), 0.65 (daily averages) and 0.87 (monthly averages). R2 CV averages for MERRA-2 are respectively 0.10, 0.18, and 0.42. RMSE CV averages for our model are 6.58 µg m⁻³ (hourly averages), 4.92 µg m⁻³ (daily averages) and 2.87 µg m⁻³ (monthly averages). The same metrics averages for MERRA-2 are respectively 9.05, 7.04 and 4.08 µg m⁻³. MAE CV averages for our model are 4.61 µg m⁻³ (hourly averages), 3.59 µg m⁻³ (daily averages) and 2.51 µg m⁻³ (monthly averages). MAE CV averages for MERRA-2 are respectively 6.39, 5.14 and 3.30 µg m⁻³. We can notice from Fig.  that our model outperforms MERRA-2 on all hourly and daily value metrics, and in most monthly averaged with the exceptions that MERRA-2 has better monthly MAE for stations 5 and 11, better RMSE for station 11. The R2 values still show a clear improvement of our model. For what regards station 5, the better RMSE and worse MAE are due to the fact that RMSE highlights outliers (i.e. MERRA-2 commits less but bigger mistakes). Anyway, the important R2 values for both station 5 and station 11 show that our model correctly predicts the AQ trends better but is off mainly by a scaling factor. From Fig. , one would expect some differences in the performances at different ground stations, since the more isolated is the station, the less information from surrounding stations is present in the training data (we have ideally full PM_2.5 maps only once per day). Stations 1, 2, 10, and 11 are clearly positioned outside the city center of Paris. Looking at the metrics for these stations, only the location of station 11 seems to have somewhat different prediction accuracy by our model than the stations located in the city center. Although we considered a relatively small dataset to train and test our model, these results suggest it is not overfitting the training data.

Figure  presents an example of model performance at hourly resolution at Station 1 between 4 and 13 December 2019, compared against MERRA-2 and OpenAQ observations. The comparison illustrates that our model captures the observed variability more accurately than MERRA-2. Figure  shows hourly PM_2.5 concentration maps for the Paris region on 6 December 2019, with spatial patterns that agree well with OpenAQ station data. Zooming on these hourly maps we can notice slight block artifacts arising from MERRA-2 input low resolution. This effect could potentially be mitigated via spatial continuity constraints (i.e. adding a regularizer to the loss function) and will be considered in future work.

Figure  shows daily cycle averages on the different seasons (top and middle rows) and monthly averages (bottom row) of 2019 at the test station 1. Black lines represent the ground station measurements, while orange lines and blue lines represent respectively MERRA-2 estimates and our model predictions. Focusing on the daily cycle averages, qualitatively our model and MERRA-2 seem comparable for the spring seasons (March, April, May). The difference is evident on the winter (December, January, February), autumn (September, October, November) and summer (June, July, August) seasons. Especially on the summer season, our model improves notably the accuracy and correlation over MERRA-2. The improvement can be seen quantitatively looking at the metrics on the bottom-right of Fig.  (here the estimates for all the seasons have been taken into account in the calculation of the evaluation metrics). Notice how the metrics values for MERRA-2 and our model have been encoded with the same colors of the legend. On the bottom-left of Fig.  we compare monthly averages estimates. Again, the difference between MERRA-2 and our model is evident. While MERRA-2 could seem to give a good approximation to the PM_2.5 annual average at the station, it is not able to capture the time series trend. Our model improves notably from this point of view, showing also improvements in accuracy. This is clear from the metrics for monthly averages, where the R2 is more than 3 times higher for our model, while the RMSE and MAE are about half of the respective errors in the MERRA-2 estimates.

Figure  shows PM_2.5 seasonal averages maps by hour for the 2019 winter season (December, January, February) predicted by our model on the city of Paris. The dots represent ground stations measurements. The general time series trend reflects the PM_2.5 variations seen in Fig.  on the top-left panel. The PM_2.5 levels seem to decrease at day time, and raise again at night time. This behaviour can be expected and physically explained through boundary layer height variations. Spatial variations of PM_2.5 are reasonable and in agreement with what found predicting PM_2.5 levels at satellite overpass : the city center and areas surrounding main highways are predicted as the most polluted areas. The maps shown in Fig.  are obtained considering station 1 as test station.

The maps shown in Fig.  represent PM_2.5 monthly averages for the year 2019 predicted by our model on the city of Paris. Dots represent ground stations measurementes. The general time series trend reflects the content of the bottom-left panel in Fig.  as expected: PM_2.5 levels are higher in colder months, while lower in warmer months. Again, this temporal variation of PM_2.5 could be explained through boundary layer height variations and also residential heating plays an important role in winter. Spatial variations of PM_2.5 present the same structure already discussed before for Fig. . Again, the maps shown in Fig.  are obtained considering station 1 as test station. The agreement with the test station and training stations is generally good.

We employed the SHAP DeepExplainer to compute SHAP values and assess feature importance for the model predictions at station 1 . Due to computational constraints, the SHAP values were calculated using a smaller background dataset, with analysis conducted on a subset of 90 randomly selected days. Feature importances were determined by summing the normalized absolute SHAP values, and are shown in Fig. . As expected, T2M (2 m air temperature) emerged as one of the most significant predictors, consistent with prior findings. For instance, T2M influences the temporal variability of PM_2.5 through boundary layer dynamics and contains information about seasonal emission changes. Specific aerosol variables such as BCCMASS (Black Carbon Column Mass Density), could give the model an idea of how much important black carbon concentration is for the final PM_2.5 estimate, but at the same time act as proxy for other species related to black carbon emission sources. Among the most important high resolution input features, ASTERDEM (ASTER Digital Elevation Model) and BlackMarble (NASA Black Marble Night Lights) offer information about terrain topology and human activities location. While the former could provide useful information about aerosol transport, the latter could act as a proxy for aerosol sources spatial distribution. More generally, aggregating the feature importances in Fig. , one can estimate the importance of athmosperic variables (35 %), aerosol variables (25 %) and high resolution indicators (40 %).