**4. Conclusions**

Machine learning (ML) has been used widely to infer ground-level PM2.5 using satellite-retrieved aerosol optical depth (AOD) to fill large gaps between PM2.5 stations without quantification of its contribution, which is the objective of this study. We rigorously and quantitatively assess the contribution of AOD to the ML-based estimation of PM2.5 by applying four common ML models (the Random Forest model, the Extratrees model, the XGBoost model, and the LightGBM model) to ample measurements from China's high-density PM2.5 observation network, the MODIS Multi-Angle Implementation of Atmospheric Correction satellite AOD retrieval product, and many other ancillary meteorological and environmental data from the eastern half of China. Two assessment methods are used, i.e., feature importance (FI) and permutation importance (PI). The contribution of AOD is also assessed by comparing the retrieval results obtained by including and not including AOD. All assessment tests are made for varying numbers of PM2.5 stations whose data are sampled by station-based and sample-based 10-CV.

The major findings are summarized as follows: (1) As the station density decreases, the FI and PI of AOD in the four ML models have clear upward trends. This trend indicates the importance and contribution of AOD to improving the accuracy of estimating PM2.5, becoming more pronounced in areas with sparse observation stations. (2) As the density of observation stations decreases, the ML models without AOD exhibit a more pronounced decline in overall accuracy compared to the models that incorporate AOD. Additionally, for every 10% reduction in the number of stations, the uncertainty in the estimated accuracy increases by approximately 0.7–1.2%. (3) As the station density decreases, the ML models without AOD exhibit a faster decline in predictive ability compared with these models with AOD. On average, for every 10% reduction in the number of stations, the uncertainty in the predicted accuracy increases by approximately 0.6–1.2%. These findings demonstrate the indispensable role of AOD in any ML model to effectively counteract the negative impact of no or sparse PM2.5 stations, resulting in improved accuracy for both estimating and predicting PM2.5 levels.

AOD represents the degree of light attenuation caused by the scattering and absorption of atmospheric aerosols in the vertical direction and has served as a crucial indicator in deriving surface particulate matter concentrations. The importance of AOD was confirmed through a sensitivity analysis showing that satellite AOD has the highest FI and PI values in PM2.5 modeling using various ML models. As the number of ground stations decreases, the AOD contribution is more apparent, as is the faster drop in ML model performance without AOD. This further underlines how using satellite AOD is essential, providing key background pollution information in areas without ground stations, thereby improving the prediction capability of ground-based PM2.5. On the contrary, in this case, relying solely on auxiliary factors such as meteorological fields is far from adequate.

Even though the chosen area in eastern China benefits from a dense and reasonably evenly distributed network of ground observation stations for PM2.5, enhancing its representativeness, there still exists the question of the uniformity of the spatial distribution of stations. Further analysis incorporating spatial-block cross-validation is needed to effectively reduce the impact of this issue. This will be undertaken in our future study. Additionally, this approach could be applied to PM10, considering its high similarities with PM2.5, i.e., AOD retains its significance as a crucial input variable in PM10 predictions [58]. However, additional sensitivity analyses are warranted to confirm this hypothesis. Regarding other pollutants, since they possess entirely different key input variables, further investigations are needed to accurately understand their behaviors [e.g., the importance of satellite tropospheric NO2 in surface NO2 modelling [59]].

**Author Contributions:** Conceptualization: Z.L. and J.W.; Methodology: J.W., Z.T. and Z.L.; Analysis: Z.T. and J.W.; Writing: Z.T., J.W. and Z.L.; Funding Acquisition: Z.L. All authors have read and agreed to the published version of the manuscript. Zhanqing Li's contribution to this publication was not part of his University of Maryland duties or responsibilities.

**Funding:** This research was funded by the National Natural Science Foundation (42030606).

**Data Availability Statement:** The PM2.5 observation station data used in this study are real-time ground-measured air quality data (including PM2.5) in China from the China National Environment Monitoring Center (http://www.cnemc.cn, accessed on 1 January 2023). The NASA data center (https://ladsweb.modaps.eosdis.nasa.gov/search/, accessed on 1 January 2023) provides MODIS MAIAC aerosol products. Meteorological reanalysis data are collected from the fifth-generation European Reanalysis Interim dataset (ERA5, https://www.ecmwf.int/, accessed on 1 January 2023) released by the European Centre for Medium-Range Weather Forecasts.

**Acknowledgments:** We thank M. Cribb from the University of Maryland for helping in editing the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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