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Since the launch of MODerate resolution Imaging Spectroradiometer (MODIS) on Aqua (1999) and Terra (2002) satellites by the National Aeronautics and Space Administration (NASA), satellite-based aerosol data have been increasingly used to infer ground-level PM_2.5 concentrations (Hoff and Christopher, 2009). Satellite instruments and algorithms retrieve data on aerosol optical depth (AOD; unitless), which is a measure of light extinction (i.e., scattering and absorption) by aerosols. Therefore, AOD reflects the abundance of PM_2.5 in the atmosphere, enabling AOD to be a reasonable proxy or predictor of PM_2.5. In general, AOD values reported at visible wavelengths (e.g., 550 nm) are used to derive PM_2.5 concentrations.

There are several key properties of satellite-retrieved AOD to determine the applicability of the aerosol data for ambient PM_2.5. First, the vertical profile of aerosols is unknown from most of satellite AOD products except for NASA’s Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO). When aerosols are well-mixed within a planetary boundary layer height (i.e., near-surface level), satellite AOD tends to be closely related to ambient PM_2.5. On the contrary, satellite AOD may not well reflect ambient PM_2.5 with a large fraction of aerosols aloft above the mixing layer. Second, AOD and PM_2.5 are not the measures of indicating exactly same aerosol properties. PM_2.5 concentration measures dry mass per unit volume of air, while AOD represents aerosols that are affected by the level of relative humidity (i.e., hygroscopic property). With the same PM_2.5 level, AOD is likely to be higher in more humid atmospheric condition. Third, AOD does not represent specific size distribution of aerosols unlike PM_2.5 characterizing aerosols or PM with the aerodynamic diameter of 2.5 μm or less. Despite the potentially non-overlapping fraction of size distributions between AOD and PM_2.5, AOD is known to be sensitive to small-sized aerosols roughly with the diameters of 0.05-2.5 μm, which is similar to the size distribution of PM_2.5 (Liu et al., 2007; Kahn et al., 1998). Towards the end, the applicability of satellite AOD for ambient PM_2.5 concentrations depends on how well these factors, among others, are accounted for in the identification of PM_2.5-AOD relationships.

Table 1 shows a list of AOD products from multiple satellite instruments that are currently available. One of the most popular satellite AOD products is MODIS AOD data retrieved from NASA’s Aqua and Terra satellites (Levy et al., 2013). These two satellites were launched around the year 2000 (i.e., Terra in 1999 and Aqua in 2002), and MODIS instruments onboard Terra and Aqua have provided aerosol data for the last two decades. Under cloud-free conditions, these polar-orbiting satellites retrieve AOD data almost daily at a global scale at the spatial resolution of 3 km (‘Dark Target’ algorithm) and 10 km (both ‘Dark Target’ and ‘Deep Blue’ algorithms) (nominal resolution at nadir), crossing the equator approximately at 10:30 am (Terra) and 1:30 pm (Aqua) local sun time. Most recently in 2018, a new AOD data product, called Multi-Angle Implementation of Atmospheric Correction (MAIAC), was released to the public by NASA (Lyapustin et al., 2018). The MAIAC AOD retrieval algorithm also utilizes observations from MODIS and provides AOD data at 1 km resolution, which enables the investigation of local-scale aerosol distributions to be viable. In addition to AOD retrievals from MODIS, Visible Infrared Imaging Radiometer Suite (VIIRS) onboard Suomi National Polar-orbiting Partnership (Suomi NPP), operated by the U.S. National Oceanic and Atmospheric Administration (NOAA), also generates spatiotemporal AOD data daily at the spatial resolution of 6 km (Environmental Data Record; EDR) and 750 m (Intermediate Product; IP) (Jackson et al., 2013). The EDR AOD data are aggregated by 8×8 boxes of the IP AOD data.

Multi-angle Imaging SpectroRadiometer (MISR) onboard the Terra satellite has also retrieved AOD data by NASA’s Jet Propulsion Laboratory (JPL) (Garay et al., 2017; Diner et al., 1998). The key advantage of MISR AOD over other AOD products is that the multi-angle feature of MISR enables aerosols to be monitored from 9 different cameras or angles, generating a range of quantitative aerosol properties such as fractional AOD components, representing the size, shape, and refractive index of aerosols, as well as total AOD. The spatial resolution of MISR AOD was originally 17.6 km and improved to 4.4 km in 2017. Due to MISR’s rather coarse temporal resolution (every 9 days), day-to-day variability of PM_2.5 concentrations is not plausible to obtain from MISR AOD.

In addition to polar-orbiting satellites mentioned above, there are geostationary satellites that monitor aerosols at a high temporal resolution, such as Advanced Baseline Imager (ABI; Geostationary Operational Environmental Satellite (GOES-16 (East) and 17 (West); U.S. NOAA)) (Kondragunta et al., 2020), Geostationary Ocean Color Imager (GOCI; Korea Institute of Ocean Science and Technology (KIOST)) (Choi et al., 2018), and Advanced Himawari Imager (AHI; Japan Meteorological Agency (JMA)) (Yoshida et al., 2018). The geostationary feature enables these satellites to provide AOD data hourly or sub-hourly during the daylight time and thus observe the diurnal variation of aerosols. However, the feature prevents them from covering the entire globe because they are only capable of looking down at a specific region of interest.

The selection of a specific AOD data product depends largely on the spatial and temporal resolutions and accuracy of AOD data to reasonably address the objectives of PM_2.5 exposure studies. In this regard, the pros and cons of the AOD products listed in Table 1 are relative and thus determined by these properties that meet specific research needs. When local or subject-specific PM_2.5 exposures are needed, AOD data at a finer spatial resolution (e.g., <10 km) would be more preferable. In case of examining PM_2.5 exposures at a global scale (e.g., global burden of disease (GBD)) (Brauer et al., 2016), AOD data at a coarser resolution (e.g., ≥10 km) are still useful to estimate PM_2.5 exposures and correspond them to health outcomes at a country level. Because AOD data are not retrieved on days with cloud and snow cover, the satellite overpass frequency in combination with the proportion of cloud-free days determines the overall frequency of AOD retrievals. Hence, the AOD products with shorter retrieval frequency lead to PM_2.5 concentration estimates at a higher temporal resolution, which is more applicable to acute health effect studies. On the other hand, the accuracy of satellite-retrieved AOD data can be evaluated by comparing the data to AOD values obtained from the AErosol RObotic NETwork (AERONET) monitoring networks as ground-truth, which is a global network of ground-based remote sensing instruments (i.e., sun photometers) to retrieve the optical, microphysical, and radiative properties of aerosols (Holben et al., 1998). A satellite AOD product that shows a better agreement with AERONET AOD (i.e., higher correlation, slope closer to 1, and intercept closer to 0 in a simple linear regression) demonstrates higher accuracy (Xiao et al., 2016).

The simplest approach of estimating AOD-derived PM_2.5 concentrations is to employ a simple linear regression model (i.e., 1 independent variable or predictor in a model) and identify the relationship between AOD and PM_2.5 at the locations where both AOD values and measured PM_2.5 concentrations are available (Schaap et al., 2009; Engel-Cox et al., 2004; Wang and Christopher, 2003). This relationship (i.e., fitted model with an intercept and a slope estimated) is then used to estimate PM_2.5 from AOD at the locations where AOD data are available but ground PM_2.5 monitoring is not available. This initial methodology demonstrated space-dependent predictive power of AOD for PM_2.5, which was generally higher in areas with vegetation and homogeneous land and meteorology types (e.g., eastern U.S.) than in semi-arid and barren areas or areas with diverse terrains and meteorology (e.g., western U.S.) (Li et al., 2015; Engel-Cox et al., 2004). When satellite AOD values are corresponded to ground PM_2.5 measurements, two temporal scales of PM_2.5, i.e., PM_2.5 measured at a satellite overpass time and 24-hour average PM_2.5, are used in the objectives of performing the synoptic evaluation of AOD-to-PM_2.5 predictability and applying AOD-derived PM_2.5 for policy assessment and health effect studies, respectively.

Multiple linear regression models are employed to account for additional spatial and/or temporal factors (e.g., local meteorology and land use information) that influence PM_2.5 concentrations and thus PM_2.5-AOD relationships (also for PM₁₀ depending on ground PM data availability) (Marsha and Larkin, 2019; Seo et al., 2015; Gupta and Christopher, 2009b). The importance of adding the meteorological parameters into the model is attributed to atmospheric conditions that may affect PM_2.5 and AOD differently. For example, when planetary boundary layer height is lower (assuming the same area and amount of aerosols), the reduced air volume results in higher PM_2.5 concentrations but the column integrated AOD levels are likely to be the same. Adding data on planetary boundary layer height into the model would mitigate its disproportionate impacts on PM_2.5 and AOD to some extent. The meteorological parameters (e.g., relative humidity, temperature, wind speed, and planetary boundary layer height) can be obtained from ground weather stations (except for planetary boundary layer height) and global and regional meteorological modeling such as ERA5 (31 km resolution; European Centre for Medium-range Weather Forecasts (ECMWF)), Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2, 0.5×0.625 degree; NASA), and North American Regional Reanalysis (NARR, 32 km resolution; NOAA) among others.

Land use parameters are incorporated with the model in order to explain the fine-scale PM_2.5 variability around ground PM_2.5 monitors as emission proxies. The ‘land use’ parameters are rather loosely defined and thus inclusive and generally used to represent any temporally invariant parameters, such as distance to roads, road density, population density, impervious areas, elevation, and distance to industrial complex. Some of the parameters vary by time in reality, but lack of frequent updates on the data leads them to be considered time-invariant in the model. On the other hand, the term ‘fine-scale’ is intended to represent smaller spatial scales than the spatial resolution of satellite AOD. For example, when a PM_2.5 monitor is located in close proximity to highways (i.e., traffic as a PM_2.5 emission source), measured PM_2.5 concentrations tend to be high, but satellite-based AOD may not well account for such near-source impacts depending on the relative scales of the spatial resolution of AOD data and the spatial heterogeneity of PM_2.5 around the highways. Consequently, the land use parameters are likely to be more beneficial with AOD data at a coarser spatial resolution.

In addition to the linear regression models described above, a statistical model called a generalized additive model (GAM) is utilized to allow non-linear relationships between PM_2.5 and independent variables (e.g., AOD, meteorology, and land use) (Strawa et al., 2013; Liu et al., 2009). When the non-linear or smooth function follows the actual relationships more closely than the linear function, replacing the linear function with the non-linear one would improve the PM_2.5 predictive power. However, the model predictability may also increase even when the non-linear function only follows pseudo relationships (i.e., data-driven wiggling patterns, causing model overfitting) regardless of the actual ones. To prevent the latter, those non-linear relationships need to be supported by scientific knowledge on atmospheric chemistry and physics. For instance, if the GAM displays a quadratic pattern between PM_2.5 and AOD, including both positive and inverse correlations, it is not likely to be an actual relationship that would be appropriate only with positive correlations.

Once linear or non-linear models are fitted, estimated PM_2.5 concentrations are validated by comparing them to measured PM_2.5 concentrations generally with the metrics of coefficient of determination (R²), root mean squared error (RMSE), and mean absolute error (MAE). When the estimated and measured PM_2.5 concentrations are in a better agreement (i.e., higher R² and lower RMSE and MAE), the model estimates are considered to be more accurate. However, in this comparison, model overfitting may be caused because the same data are used for both model fitting and validation, likely overstating the model performance. To prevent the model performance from being overestimated, cross-validation (CV) techniques have been widely implemented by randomly splitting data into the subsets of the data (e.g., 10 equal sized subsets; 10-fold CV), fitting the model with all the subsets except for one, estimating PM_2.5 for the hold-out subset using the fitted model, and repeating the same process for each of the subsets (Liu et al., 2009; Yanosky et al., 2008). The equal sized subsets can be based on observations (i.e., same number of observations in each subset) and monitoring sites (e.g., all observations from the same number of sites in each subset). The observation-based CV is more advantageous than the site-based CV because the overall model performance is not influenced by the subset-specific number of observations, while the site-based CV is more appropriate in that PM_2.5 concentrations at a given site are estimated independently from those at other sites by non-overlapping predictors (e.g., land use parameters) (Lee, 2019). All the PM_2.5 concentration estimates from the CV analysis are compared to measured PM_2.5 concentrations to evaluate the overall model performance. In addition, the CV analysis can be performed separately by spatial and temporal portions of the model estimates (i.e., spatial and temporal CV R²) (Kloog et al., 2011). Instead of the CV analysis, the model estimates have been also validated by comparing them to measured PM_2.5 concentrations obtained from a monitoring network that is independent from the network used in the modeling processes (Knibbs et al., 2018). This validation approach may be advantageous due to potential residual overfitting from the CV approach, but it is often not feasible to have an independent PM_2.5 monitoring network.

The approach of using a mixed effects model to estimate AOD-derived PM_2.5 substantially improved the predictive power of AOD for PM_2.5 (CV R² between daily measured and estimated PM_2.5=0.92) (Lee et al., 2011). Lee et al. (2011) showed that the mixed effects model outperformed the simple linear regression model (both models only with AOD), i.e., CV R² of 0.95 versus 0.51 (average of site-specific R²), in the New England region of the U.S. (including Massachusetts, Connecticut, and Rhode Island). Since then, this modeling approach has been widely adopted by many researchers in the world, many of which incorporated additional spatiotemporal predictors into the model (Shtein et al., 2020; de Hoogh et al., 2018; Pereira et al., 2017; Ma et al., 2016; Just et al., 2015; Xie et al., 2015; Hu et al., 2014; Kloog et al., 2011).

The key feature of the mixed effects model is to allow day-to-day variability in the relationships between measured PM_2.5 concentrations and AOD values. The term ‘mixed’ represents a combination of ‘fixed’ and ‘random’ effects, which identifies an average relationship of PM_2.5 and AOD that is applied to the entire study period and the daily variations of the relationships (i.e., daily deviations from the average relationship; day-specific slopes and intercepts), respectively. On the contrary, the simple and multiple linear regression models and GAM only generate an average relationship between PM_2.5 and AOD for the entire period. As discussed above, the impacts of local meteorology and large-scale weather systems on the PM_2.5-AOD relationships tend to be diverse by day in a region. The mixed effects model implicitly accounts for such temporal parameters by allowing the PM_2.5-AOD relationships to vary on a daily basis, regardless of the feasibility of parameterizing and including each temporal parameter in the model. Moreover, the daily relationships of PM_2.5 and AOD, generated by the mixed effects model, are more robust than those derived from day-specific simple linear regression models, because the mixed effects model produces daily PM_2.5-AOD relationships by identifying the overall average relationship and then quantifying daily deviations from this average relationship. This is an important feature of the mixed effects model particularly due to the number of PM_2.5 and AOD pairs that varies by day. Furthermore, spatial variations in PM_2.5-AOD relationships were accounted for by adding region-specific relationships into the mixed effects model (Chudnovsky et al., 2014) or by combining the model with a geographically weighted regression (GWR) model, which generates a continuous spatial surface of each parameter and subsequently identifies the local slopes of AOD for PM_2.5 with geographical weighting (Hu et al., 2014).

The mixed effects modeling approach motivated the use of satellite-based PM_2.5 exposure estimates in acute and chronic health effect studies with low PM_2.5 modeling errors and subsequent gap-filling techniques exploiting those AOD-derived PM_2.5 (Son et al., 2017; McGuinn et al., 2016; Shi et al., 2016; Hyder et al., 2014). Previous studies developed statistical approaches to estimate PM_2.5 exposure levels for days without AOD data (largely due to cloud cover) by clustering days with similar PM_2.5 spatial patterns (Lee et al., 2012) and by assuming season-specific PM_2.5 spatial patterns (Kloog et al., 2011). These statistical approaches relied on AOD-derived PM_2.5 concentrations (i.e., days with AOD data) as a first step of estimating all the missing PM_2.5 concentrations, leading to no spatial and temporal gaps of PM_2.5 exposure estimates. These gap-filling approaches contributed to epidemiological studies that require both short-term and long-term PM_2.5 exposures such as subject-specific trimester PM_2.5 exposures and their birth outcomes (e.g., lower birth weight) (Hyder et al., 2014) and hospital admissions (Kloog et al., 2012). Finally, such modeling approaches facilitated health effect studies associated with PM_2.5 levels below current PM_2.5 standards (i.e., ‘low-level’ PM_2.5 and health) (Shi et al., 2016). In the U.S., most of ground PM_2.5 monitors are located in highly populated urban or non-populated remote (i.e., forest; Interagency Monitoring of Protected Visual Environments (IMPROVE) network) areas, and satellite-based PM_2.5 exposure approaches enable epidemiological studies to include suburban and rural populations generally with ‘low-level’ PM_2.5 exposures.

A combination of chemical transport models (CTM) (e.g., GEOS-Chem, global 3-D simulations) and satellite AOD data has been also employed to estimate PM_2.5 exposures. Previous research simulated relationships between column AOD at a satellite overpass time and ground-level 24-hour average PM_2.5, which relied on the size, composition, and vertical and diurnal profiles of aerosols and relative humidity, and these relationships were used to calculate PM_2.5 as follows: [simulated (ground PM_2.5/column AOD)×satellite column AOD=estimated PM_2.5] (Liu et al., 2004). This approach is different from statistical calibrations because the simulated conversion factors are not derived from empirical relationships between the observations of ground PM_2.5 and satellite AOD. Instead, the CTM simulations tracked the atmospheric processes of emissions and meteorology and thus quantified model-driven daily relationships of 24-hour average PM_2.5 and column AOD at a given satellite overpass time (van Donkelaar et al., 2010). With respect to GEOS-Chem, daily conversion factors were calculated originally at the spatial resolution of 2°×2.5° (global), and nested simulations at the resolution of 0.5°×0.67° were conducted in selected regions such as North America, Europe, and East Asia (Hammer et al., 2020). Despite the spatial resolution of estimated PM_2.5 generally following that of satellite AOD, the spatial resolution of the simulations for the conversion factors may limit the ability of capturing local PM_2.5 gradients. As a recent improvement, the GWR modeling was further adopted to calibrate annual average PM_2.5 concentrations estimated from the conversion factors and satellite AOD for measured annual average PM_2.5 concentrations, while incorporating spatial parameters such as elevation and proximity to urban land surface, leading to CV R² of 0.81 (van Donkelaar et al., 2016).

Due to the nature of global scale modeling, the approach of utilizing GEOS-Chem and satellite AOD (recently also with statistical calibration) has contributed to global burden of disease (GBD) studies, providing global long-term PM_2.5 exposure estimates (Brauer et al., 2016). In addition, this modeling has been used to generate PM_2.5 exposure estimates for multi-country and nationwide health effect studies (Pinault et al., 2016; Fleischer et al., 2014). The approach of adopting GEOS-Chem and satellite AOD is useful particularly in developing countries where no ground monitoring exists and thus empirical models are not plausible. Nonetheless, ground PM_2.5 data are still necessary to further increase model predictability through statistical calibration (e.g., GWR) and validate model estimates.

As artificial intelligence (AI) has infiltrated into a wide range of industries, machine learning techniques can be also applied to the estimation of satellite-based PM_2.5 exposures and environmental health research in general (National Academies of Sciences, Engineering, and Medicine, 2019). Machine learning seeks to find the most accurate relationships between PM_2.5 and a number of predictors (i.e., ‘training’ similar to model fitting), while considering interactions between those predictors, and thus reach the best predictive power without explicitly specifying modeling assumptions (i.e., linear or non-linear) and structures (e.g., interactions between predictors). The training process tends to be more robust as more high-quality data are added into the dataset. Though the concept to apply machine learning for PM_2.5 or PM₁₀ is nearly two decades old (Chaloulakou et al., 2003; Perez et al., 2000), incorporating satellite AOD data with the machine learning frameworks is comparatively recent (Gupta and Christopher, 2009a). For the last few years, machine learning techniques have been implemented into numerous statistical and programming software packages (e.g., R packages), making the machine learning techniques more accessible to researchers.

A number of machine learning techniques such as neural network, random forest, and gradient boosting (or extreme gradient boosting) have been applied for PM_2.5 exposure estimates, taking advantage of simultaneous advancement of satellite remote sensing, machine learning tools, and computational infrastructure (Just et al., 2020; Park et al., 2019; Hu et al., 2017; Di et al., 2016; Reid et al., 2015). These studies resulted in high predictive power for PM_2.5 in a range of CV R² roughly between 0.70 and 0.90. However, it is noted that the model performance is not directly comparable to each other due to different study periods and regions and selected predictors among others, and therefore it is challenging to conclude one machine learning approach performs better than the others. An ensemble modeling was further employed in an effort to generate more refined PM_2.5 estimations collectively from multiple CTMs, statistical (i.e., mixed effects model), and machine learning approaches and enhance the overall predictive power compared to each individual one (Shtein et al., 2020). Furthermore, the machine learning approaches have imputed missing AOD or combined CTM-calibrated AOD to fill the spatial and temporal gaps of satellite-based PM_2.5 (Li et al., 2020; Di et al., 2016). Due to high accuracy of ambient PM_2.5 exposure estimates attributed to machine learning, those estimates have been employed in health effect studies (Wei et al., 2020; Di et al., 2017). A summary of the early development and recent advancement for AOD-derived PM_2.5 estimation approaches (i.e., simple linear regression through machine learning) is presented in Table 2.

Despite the capability of machine learning to process complex multi-dimensional data and thus enhance the predictive power, it is worthwhile to address scientific aspects of machine learning in the context of predictive accuracy versus ‘black box’-like predictions. As discussed in the National Academies of Sciences, Engineering, and Medicine (NASEM) of the U.S., data quality, transparency, and reproducibility of machine learning need to be emphasized to further promote the use of machine learning for environmental health research (National Academies of Sciences, Engineering, and Medicine, 2019). Unlike statistical models, the processes of machine learning techniques do not yield the coefficients of each model predictor and their corresponding uncertainties. Hence, it is challenging to understand and evaluate scientific mechanisms and pathways that lead to the enhanced predictive power from machine learning. In this regard, statistical approaches described above are still crucial to delve into the relationships between each predictor and PM_2.5 exposure levels and prioritize input data resources for future improvement of PM_2.5 exposure models. Moreover, during the processes of machine learning, there are a number of details to be disclosed to reproduce outputs because they may cause substantial differences in the outputs (Peng, 2020).