A Comparison of Regression Methods for Inferring Near-Surface NO₂ With Satellite Data

Abstract

Nitrogen dioxide (NO₂) is an atmospheric pollutant emitted from anthropogenic and natural sources. Human exposure to high NO₂ concentrations causes cardiovascular and respiratory illnesses. The Environmental Protection Agency operates ground monitors across the U.S. which take hourly measurements of NO₂ concentrations, providing precise measurements for assessing human pollution exposure but with sparse spatial distribution. Satellite-based instruments capture NO₂ amounts through the atmospheric column with global coverage at regular spatial resolution, but do not directly measure surface NO₂. This study compares regression methods using satellite NO₂ data from the TROPospheric Ozone Monitoring Instrument (TROPOMI) to estimate annual surface NO₂ concentrations in varying geographic and land use settings across the continental U.S. We then apply the best-performing regression models to estimate surface NO₂ at 0.01° by 0.01° resolution, and we term this estimate as quasi-NO₂ (qNO2). qNO2 agrees best with measurements at suburban sites (cross-validation (CV) R² = 0.72) and away from major roads (CV R² = 0.75). Among U.S. regions, qNO2 agrees best with measurements in the Midwest (CV R² = 0.89) and agrees least in the Southwest (CV R² = 0.65). To account for the non-Gaussian distribution of TROPOMI NO₂, we apply data transforms, with the Anscombe transform yielding highest agreement across the continental U.S. (CV R² = 0.77). The interpretability, minimal computational cost, and health relevance of qNO2 facilitates use of satellite data in a wide range of air quality applications.

Key Points

• We compare regression methods to estimate surface nitrogen dioxide concentrations at 0.01° resolution using satellite and land use data

• Multivariate linear regression with Anscombe-transformed inputs has strongest agreement with surface nitrogen dioxide measurements

• Regression methods provide accurate, low-bias concentration estimates with minimal computational and data requirements

Plain Language Summary

Nitrogen dioxide (NO₂) is an air pollutant which causes cardiovascular and respiratory illnesses and reacts in the atmosphere to form other harmful pollutants. This necessitates accurate and reliable quantification of NO₂ concentrations in the air. Ground monitors directly observe NO₂ concentrations near the Earth's surface. However, monitors do not have sufficient spatial coverage to quantify NO₂ at large scales. Satellite-based instruments capture NO₂ amounts across the Earth at increasingly high spatial resolution. However, satellite instruments cannot directly observe surface NO₂ concentrations. In this study, we compare regression methods for estimating surface NO₂ over the continental U.S. using satellite data and auxiliary land-use variables. We find that NO₂ estimated using multivariate regression models with transforms applied to inputs result in the highest agreement with surface NO₂ among the regression methods we investigated. We then use the regression models to quantify surface NO₂ concentration across the U.S. at 0.01° by 0.01° spatial resolution. Our work leverages the precision of ground observations and the high resolution of satellite data to accurately quantify surface NO₂. The interpretable, generalizable, and easily applicable methods used in our study will facilitate the use of satellite data for air quality and human health assessments.

1 Introduction

1.1 Background

Nitrogen dioxide (NO₂) is an air pollutant with harmful impacts on human health. Exposure to high concentrations of NO₂ is closely associated with hospital admissions and mortality for a range of respiratory and cardiovascular diseases (Mills et al., 2015). NO₂ pollution accounts for a significant portion of asthma cases among children worldwide (Anenberg et al., 2022; Chowdhury et al., 2021). Given these health effects, NO₂ is regulated by the United States Environmental Protection Agency (EPA) under the National Ambient Air Quality Standards (NAAQS), which requires the annual mean concentration of NO₂ to remain below 53 parts per billion (ppb) in inhabited areas.

In addition to directly harming human health, NO₂ acts as a reactant in the troposphere to form other harmful air pollutants. In the presence of volatile organic compounds and sunlight, NO₂ reacts to form tropospheric ozone (O₃) which in turn damages human health, increases mortality, and harms ecosystems (Ashmore, 2005; Jerrett et al., 2009; Sillman, 1999). NO₂ also contributes to the formation of particulate nitrate (NO₃⁻), a component of fine particulate matter (PM_2.5) which causes cardiovascular, respiratory, and birth-related illnesses and impairments (Behera & Sharma, 2012; Feng et al., 2016).

NO₂ is emitted from both anthropogenic and natural sources, mainly through high temperature combustion from biomass burning and fossil fuels (M. Lee et al., 1997). Thus, NO₂ serves as a tracer for air pollution from traffic, industrial sites, and other point sources. NO₂ is therefore important for estimating emissions of greenhouse gases that are co-emitted during combustion, such as CO₂ (Goldberg et al., 2019; Konovalov et al., 2016; Levy et al., 2014). Anthropogenic activity is the dominant source of NO₂ in industrialized North America, Europe, and Asia (van der A et al., 2008). Natural sources of NO₂ include soils and lightning (Olivier et al., 1998). Because NO₂ has a relatively short lifetime of several hours, it remains concentrated near its source, resulting in distinct spatial gradients in concentration that are strongly correlated to emissions (L. N. Lamsal et al., 2011; Pommier, 2023). Thus, reliable quantification of NO₂ concentration is critical for characterizing emissions from human activity and for measuring human air pollutant exposure in urban, roadside, and industrial areas with high NO₂ concentrations.

The EPA maintains a national network of ground-based monitors that provide ambient air pollution data known as the Air Quality System (AQS). Although AQS monitors provide hourly measurements of NO₂ concentrations, their sparse and irregular spatial distribution renders them insufficient for capturing the spatiotemporal variability of NO₂ at regional and national scales. Ground monitors have limited usefulness for comprehensive assessments of human exposure to air pollution (Guay et al., 2011). Satellite data products provide global coverage of column NO₂ on a high-resolution spatial grid, but generally have daily frequency as opposed to hourly ground measurements, and are limited to daylight hours. Satellite data offer the potential to bridge the spatial gaps in ground-based monitor data for capturing surface NO₂ concentrations (Holloway et al., 2021). However, satellites do not directly measure NO₂ at the surface and instead detect NO₂ amounts through the atmospheric column with greater sensitivity to mid-tropospheric background NO₂ (Dang et al., 2023). Since NO₂ sources are concentrated at the surface, NO₂ vertical column densities (VCD) measured by satellites have varying strengths of correlation with surface NO₂ depending on spatiotemporal scale, season, region, and the characteristics of the surface and satellite data (Bechle et al., 2013; Goldberg et al., 2021; Griffin et al., 2019, 2021; Ialongo et al., 2020; Judd et al., 2020; Lamsal et al., 2008, 2015; H. J. Lee et al., 2023; Penn & Holloway, 2020; Pommier, 2023; Yu & Li, 2022; van der A et al., 2008).

The highest resolution global satellite NO₂ data currently available comes from the TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor satellite, launched by the European Space Agency (ESA) in October 2017 (van Geffen et al., 2020; Veefkind et al., 2012). TROPOMI follows a lineage of remote sensing spectrometers including the Global Ozone Monitoring Experiment, the Scanning Image Spectrometer for Atmospheric Chartography (SCIAMACHY), and the Ozone Monitoring Instrument (OMI). TROPOMI provides column NO₂ data at a peak resolution of 3.5 km by 5.5 km at nadir, a significant improvement over the 13.0 km by 24.0 km peak resolution of the OMI NO₂ data product (Veefkind et al., 2012). The smaller pixel size of TROPOMI enables an unprecedented scale of observation, such as distinguishing signals from individual sources at the scale of individual cities (Ialongo et al., 2020). By capturing the spatial heterogeneities in NO₂ at a finer scale, TROPOMI provides opportunities for significant improvements in satellite-based quantification of surface NO₂.

1.2 Literature Review

To best leverage the global coverage and high spatial resolution of satellite NO₂ data, it is critical to investigate the agreement between column NO₂ amounts and surface NO₂ concentrations across varying spatiotemporal scales. Prior studies evaluating satellite-surface NO₂ agreement have used four main methods: (a) chemical transport models (CTM), (b) machine learning, (c) spatial interpolation models, and (d) regression. The advantages and disadvantages of each method are detailed in Table 1.

Table 1. Comparison of Common Methods for Investigating Agreement Between Satellite-Derived and Surface Measurements of NO₂

Model type	Advantages	Disadvantages	Examples in literature
Chemical transport	Provides vertical profiles of chemical concentrations	Requires extensive data and computational resources to run chemical transport models	Bechle et al. (2013); Cooper et al. (2020); Gu et al. (2017); Lamsal et al. (2015)
	Enables direct computation of ground-level concentration estimates	CTM outputs have lower resolution
Machine learning	Learns complex non-linear patterns from high dimensional data sets with minimal human supervision	Difficult to interpret	Chan et al. (2021); Chi et al. (2022); Ghahremanloo et al. (2021); Grzybowski et al. (2023); Kim et al. (2021); Li et al. (2022); Qin et al. (2020); Yeganeh et al. (2018)
		Requires significant computational resources and expertise
Spatial interpolation models	Direct encoding of spatial and/or temporal information	May struggle to generalize to spatial and/or temporal contexts beyond the training domain	Qin et al. (2017); Young et al. (2016)
Regression	Minimal data and computational requirements	Cannot capture complex nonlinear relationships	Goldberg et al. (2021); Griffin et al. (2019); Henderson et al.(2007, p. 200); Hoek et al. (2008); H. J. Lee et al. (2023); Novotny et al. (2011); Yu and Li (2022)
	Easy to interpret

Vertical profiles of mixing ratios from CTM have been used to derive surface NO₂ concentrations from satellite data. Commonly used CTMs include the global three-dimensional Goddard Earth Observing System-Chemistry (GEOS-Chem) model and the regional-scale Community Multi-Scale Air Quality (CMAQ) model and Comprehensive Air Quality Model with extensions (CAMx) (Bechle et al., 2013; Lamsal et al., 2015). Cooper et al. (2020) applied GEOS-Chem vertical profiles to both OMI and TROPOMI column NO₂ to correct for inaccuracies in vertical mixing assumptions in satellite products. Their work showed that TROPOMI-derived surface NO₂ had lower variance and greater ability to capture emissions sources at high resolution than OMI-derived surface NO₂. Gu et al. (2017) compared ground monitor NO₂ in China with both unadjusted OMI NO₂ and OMI surface NO₂ derived using CMAQ NO₂ profiles. Using the CMAQ-adjusted OMI NO₂, they found 0.03 greater correlation coefficients (R) for January 2014 and 0.05 greater R-values for July 2014. However, the use of CTM in near-real-time requires meteorological reanalysis data and emissions inventories, significant computational resources, and additional re-gridding steps to accommodate for the lower spatial resolution of models. In this study, we use TROPOMI column NO₂ without CTM-based adjustments, to provide surface NO₂ estimates with minimal computational burden.

Machine learning methods are well-suited for estimation and prediction problems with complex input data sets, as is the case for air quality estimation and forecasting. Several recent studies implement machine learning methods using TROPOMI column NO₂ as well as meteorological and land use data inputs to estimate surface NO₂ concentrations (Chi et al., 2021; Grzybowski et al., 2023; Li et al., 2022; Qin et al., 2020; Yeganeh et al., 2018). Ghahremanloo et al. (2021) trained convolutional neural networks to predict surface NO₂ concentrations over Texas using TROPOMI column NO₂, vegetation, land-use, and meteorological data as inputs. Their machine learning method improved (R = 0.91) had stronger agreement with surface NO₂ than multiple linear regression (R = 0.77). Kim et al. (2021) used tree-based ensemble machine learning methods with TROPOMI NO₂, land-use, meteorological, and topographic variables to predict hourly surface NO₂ over Switzerland and northern Italy. Their model achieved R² of 0.54 for monitors held-out from model training and R² of 0.84 for all monitors. Chan et al. (2021) estimated surface NO₂ concentrations over Germany for 2018 through 2020 at weekly to seasonal time-scales using artificial neural networks and TROPOMI NO₂ reprojected to 0.5 by 0.5 km resolution, resulting in R² of 0.64. These studies demonstrate that machine learning models can accurately estimate surface NO₂ from large, multi-dimensional input data sets. However, the usability of machine learning models is limited by their significant computational demands and their inherent lack of interpretability. Here, we investigate the ability of regression models with column NO₂ input to estimate surface NO₂. Regression models have minimal computational demands and are straightforward to interpret, enabling a broad range of applications.

Spatial interpolation models including kriging and geographically and temporally weighted regression (GTWR) have been used to estimate ground-level NO₂ concentrations. Kriging applied to NO₂ ground monitors provides adequate performance in areas with clustered monitors, and incorporating satellite NO₂ data improves prediction at locations far from monitors (Young et al., 2016, p. 201). GTWR improved on ordinary least squares (OLS) regression for predicting ground-level NO₂, with a cross-validation (CV) R² of 0.60 for GTWR compared to 0.44 for OLS at a daily scale over central and eastern China (Qin et al., 2017). These spatial interpolation models provide accurate predictions of surface NO₂ but require the inclusion of chemical transport model profiles, meteorological data, and other spatial information which are not readily available in a real-time prediction context.

Previous regression-based studies have shown strong agreement between surface measurements and TROPOMI column NO₂. Griffin et al. (2019) compared TROPOMI NO₂ and surface measurements in the Canadian Oil Sands and found an R² of 0.67, demonstrating the improved capability of TROPOMI in capturing fine-scale surface NO₂ variations compared to OMI. Yu and Li (2022) explored the agreement of TROPOMI NO₂ with surface monitors in China's Xinjiang Province, finding a province-wide R² of 0.78. Their work also explored meteorological and economic factors, using annual GDP of industry as a proxy for industrial activity. Goldberg et al. (2021) investigated the weekly and diurnal variability of TROPOMI NO₂ as well as the impact of temperature. Their study found an R² of 0.66 between annual-average EPA surface NO₂ and TROPOMI column NO₂ across the continental U.S.

Land use regression (LUR) studies incorporate land use and road data to estimate surface NO₂. Early literature conducted seasonal to annual-scale measurement campaigns of surface NO₂ to generate data for LUR. These studies improved on spatial interpolation methods while achieving particularly strong performance in urban areas with fine-scale gradients in NO₂ concentrations (Beelen et al., 2013; Henderson et al., 2007; Hoek et al., 2008). Novotny et al. included OMI-derived surface NO₂ as input to LUR models, resulting in a median R² of 0.76 on the hold-out set of monitors over the continental U.S. (Novotny et al., 2011). Lee et al. (2023) used multivariate regression, land use data, and TROPOMI column NO₂ to estimate NO₂ across 89 monitor sites in California, attaining an R² of 0.76. Further, Lee et al. estimated surface NO₂ on a 500 m-resolution grid across California.

Here, we investigate TROPOMI NO₂ to capture spatial heterogeneities in the distribution of ambient NO₂ at the surface across the continental U.S. We compare regression methods for estimating surface NO₂ concentrations in varied land use settings (urban/suburban/rural and highway proximity) and geographies (seven distinct U.S. regions). We then apply the regression models to provide a reliable metric of surface NO₂ across CONUS. This metric provides an easily interpretable, high-resolution estimate of surface NO₂ with minimal data and computational requirements. Recognizing the limitations of an annual average metric, we term this quantity “quasi-NO2” (qNO2 for short). We assess the performance of this metric on regional and national scales, investigate spatial patterns and potential causes of biases, and evaluate the applicability of qNO2 across different use cases. We anticipate qNO2, with its high spatial resolution and ease-of-use, will facilitate air quality and health impact assessments.

2 Methods

2.1 Surface Monitor Data

Hourly NO₂ measurements over the U.S. were obtained from the EPA Air Quality Service (AQS) for 2019 (US EPA, 2013). AQS monitors use a chemiluminescence method which measures the amount of NO that is converted from NO₂ by a molybdenum oxide converter (Fontijn et al., 1970). Other oxidized nitrogen compounds such as nitric acid (HNO₃) and peroxyacetyl nitrate (PAN) are also converted to NO by these converters, causing an overestimation of NO₂ when there are high concentrations of HNO₃ or PAN (Steinbacher et al., 2007). Interference is observed to be highest during afternoon hours for urban areas and in the summer season for rural areas (Dunlea et al., 2007; Steinbacher et al., 2007). This positive monitor bias is often corrected when used in comparison with satellite data (Cooper et al., 2020; Lamsal et al., 2015). Following the reasoning previously described in Penn and Holloway, and given the annual scale of our analysis, we do not apply a bias correction factor to the monitor data (Penn & Holloway, 2020). EPA NO₂ is used without bias corrections for many health impact studies and regulatory purposes, such as determining attainment of the NAAQS across the U.S. Several prior studies use EPA AQS NO₂ data without bias correction (Goldberg et al., 2021; Jiang et al., 2018; Lu et al., 2015; Novotny et al., 2011; Qu et al., 2021). Further, obtaining HNO₃ and PAN concentrations for each monitor location at daily or hourly time scales requires output from a chemical transport model, as done by Cooper et al. (2020), which is a computationally expensive task that limits the accessibility of our methods. To remain consistent with the US air quality management community and to minimize the computational burden of our methods, we use the monitor data without bias correction.

EPA NO₂ data were filtered to only include monitors for which at least 75% of 2019 hourly measurements were considered “valid” by EPA quality control checks. Then, for each of the remaining 402 monitors, all valid 2019 hourly measurements were averaged to obtain the final “ground-truth” data set. Our filtering method aligns with the criterion implemented in prior annual average NO₂ studies (Novotny et al., 2011; Penn & Holloway, 2020).

We use two monitor classifications provided by the EPA as input variables for regression modeling: “location setting,” which consists of urban (n = 152), suburban (n = 146), and rural (n = 104) classes, and “road proximity,” which has non-near-road (n = 333) and near-road (n = 69) classes. We use the term “location setting” rather than “land use” because our classification scheme is more general than traditional land use data sets. Near-road monitors are located near highways in metropolitan areas. 57% of these monitors are within 20 m of a highway and 89% are within 30 m (Watkins, 2016). Our data set includes 49 near-road monitors in urban areas, 20 near-road monitors in suburban areas, and no near-road monitors in rural areas.

2.2 Satellite Data

We use 2019 annual average TROPOMI (version 2.3.1) column NO₂ as an input variable for regression models. Our primary motivation for conducting analysis at the annual-average scale is to align with the metrics used by the air quality management community. Further, the annual-average scale mitigates the impact of missing pixels in satellite data and enables re-gridding to a higher spatial resolution. However, the annual-average scale smooths over significant diurnal and seasonal NO₂ variability. We further discuss the applicability of annual-average results in Section 4. TROPOMI measures the slant column density using a differential optical absorption spectroscopy technique, separating the column into stratospheric and tropospheric components. Air mass factors (AMFs) are then used to convert the SCDs into VCD (VCDs) (van Geffen et al., 2020). Current AMFs are subject to uncertainty and may be a partial cause of low bias in column NO₂ observations in urban areas (Judd et al., 2020). The highest resolution of TROPOMI is 3.5 km by 5.5 km at nadir (resolution increased from 3.5 km by 7.0 km on 6 August 2019).

TROPOMI has an approximate overpass time of 1:30 p.m. local time (Veefkind et al., 2012). We compared satellite-surface agreement using surface measurements averaged across the full 24 hr and averaged only for 1–2 p.m. to align with TROPOMI overpass time. Prior studies investigating annual-average satellite-surface NO₂ agreement have used both 24-hr surface averages (Lee et al., 2023; Young et al., 2016) and overpass time averages (Chi et al., 2022). We found surface measurements averaged for 1–2 p.m. and for the full 24 hr are strongly correlated (R = 0.93). We also found that simple linear regression fit on TROPOMI NO₂ (methods detailed in Section 2.4) better estimates daily average surface NO₂ (R² = 0.55) than 1–2 p.m. average surface NO₂ (R² = 0.45). Further, as NO₂ concentrations tend to be lower during the mid-day satellite overpass times and greater during nighttime (Penn & Holloway, 2020), 24-hr average concentrations are a more relevant metric for NO₂ exposure. Thus, we use 24-hr average surface measurements in our work, with the aim of providing the most relevant metric for exposure assessments and regulatory work. We use the method used in Goldberg et al. (2021) to re-grid TROPOMI NO₂ to a 0.01° by 0.01° grid (approximately 1 km by 1 km). Figure 1 shows the re-gridded TROPOMI NO₂ data used in this study.

Figure 1

2019 annual average TROPOMI NO₂ gridded at 0.01° by 0.01° resolution across the continental United States.

2.3 Road and Location Setting Data

To characterize surface NO₂ concentration across the full domain, we applied our regression models to each TROPOMI NO₂ CONUS grid cell. To apply the regression models, we classified each grid cell by road proximity and location setting, as defined in Section 2.1.

We use road data from the U.S. Census Bureau TIGER/Line Primary Roads data set. All EPA NO₂ monitors classified as “near-road” are within the same TROPOMI grid cell as a Census Bureau “primary road.” Thus, to create the near-road data set for the full 0.01° by 0.01° CONUS grid, TROPOMI NO₂ grid cells overlapping with any segment of a TIGER/Line “primary road” were classified as “near-road.” All remaining grid cells were classified as “non-near-road.” We used ArcGIS Pro 3.0 to re-grid the TIGER/Line data onto the TROPOMI NO₂ grid. Figure S1 in Supporting Information S1 shows primary roads on the 0.01° by 0.01° CONUS grid along with near-road EPA monitors.

We determined the location setting classification of each TROPOMI grid cell based on the National Center for Education Statistics (NCES) Education Demographic and Geographic Estimates locale classification. The NCES data set provides boundaries for four categories of locales across the U.S.: City, Suburban, Town, and Rural. We used ArcGIS Pro 3.0 to determine the locale class with the most area covered in each TROPOMI grid cell. To align NCES and EPA classifications when applying our regression models across the full CONUS grid, we classified NCES “City” grid cells as EPA “Urban,” NCES “Suburban” as EPA “Suburban,” and NCES “Rural” and “Town” as EPA “Rural.” Figure S2 in Supporting Information S1 shows the location setting classifications for each grid cell. Text S1 in Supporting Information S1 details the agreement between NCES and EPA location setting classifications, which are displayed in Figure S3 in Supporting Information S1.

We use the three-class land use classification instead of a more complex land use data set to maximize reproducibility of our methods to other regions and time periods. Using a more detailed land use data set would result in a small number of monitors for each land use category in the data set, which would limit the generalizability of the regression models. Further, we opt to use land use categories in lieu of comprehensive emission inventory data for two main reasons. First, emissions data would have a strong correlation with the TROPOMI data and thus prevent direct evaluation of satellite column data for quantifying surface emissions. Second, as with complex land use data sets, obtaining and processing comprehensive emissions inventory data necessitates significant computational resources, which may inhibit straightforward application of satellite data. Thus, we choose the NCES classifications as a sufficiently simple yet informative input variable to distinguish the impact of land use on column-surface agreement.

2.4 Regression Methods

We fit simple (SLR) and multivariate linear regression (MLR) models to evaluate the relationship between surface monitor NO₂ and TROPOMI column NO₂. SLR has one input parameter (TROPOMI NO₂) and MLR has three input parameters in our work (TROPOMI NO₂, location setting, and road proximity). The main difference lies in the number of input parameters — both SLR and MLR are fitted by minimizing the sum of squares of the residuals (linear least squares). The output of SLR is termed qNO2 SLR and the output of MLR is termed qNO2 MLR. Through this analysis, we aim to (a) understand under which conditions NO₂ satellite data best represents surface NO₂ concentrations and (b) compare the performance of different satellite NO₂-based regression methods for estimating surface NO₂. The TROPOMI NO₂ measurements have a Poisson-like distribution (Figure S4 in Supporting Information S1). Thus, to satisfy the normality and constant variance assumptions of linear regression, we fit additional regression models with the log transform and Anscombe transform applied to TROPOMI NO₂ inputs. Equation 1 gives the Anscombe transform for positive real number x.

$$$\begin{array}{c}a(x)=2\sqrt{x+\frac{3}{8}}\end{array}$$$ (1)

The distribution for the log and Anscombe transformed-TROPOMI NO₂ has greater symmetry than the non-transformed distribution (Figure S4 in Supporting Information S1). The Anscombe transform ensures transformed values remain positive, whereas log-transformed values may be negative and thus result in negative regression outputs (Anscombe, 1948). The outputs of MLR with log transform of TROPOMI NO₂ are termed qNO2 logMLR, and the outputs of MLR with Anscombe transform of TROPOMI NO₂ are termed qNO2 anscMLR.

While the resolution of TROPOMI NO₂ is much finer than previous NO₂ satellite data products, we still expect the kilometer-scale data to be insufficient to capture emissions near individual major roads, which can have sharp decay gradients over hundreds of meters (Kimbrough et al., 2017). Thus, we separately conduct simple linear regression on near-road and non-near road monitors. To further compare TROPOMI NO₂ performance over different location settings, we also conduct simple linear regressions on each location setting class: urban, suburban, and rural.

We fit multivariate regression models with three input variables: TROPOMI column NO₂ concentration (no transform, log transform, Anscombe transform), road proximity, and location setting. Road proximity is a binary variable representing EPA monitor “near-road” and “non-near-road” classification. Location setting is a categorical variable with three levels corresponding to EPA monitor classification: urban, suburban, and rural. Multivariate regression provides a single interpretable model for calculating qNO2 across the U.S., facilitating interpretation and application by stakeholders.

2.5 Evaluation Methods

We evaluate regression model performance using four metrics: coefficient of determination (R²), root mean squared error (RMSE), mean fractional error (MFE), and mean fractional bias (MFB).

$$$\begin{array}{c}\text{RMSE}=\sqrt{\frac{\sum\limits _{i=1}^{N}{\left(qNO2[i]-{EPA\,NO}_{2}[i]\right)}^{2}}{N}}\end{array}$$$ (2)

$$$\begin{array}{c}\text{MFB}=\frac{1}{N}\left(\frac{\sum \nolimits_{i=1}^{N}\left({qNO2[i]-EPA\,NO}_{2}[i]\right)}{\sum\limits _{i=1}^{N}\frac{\left({qNO2[i]+EPA\,NO}_{2}[i]\right)}{2}}\right)\end{array}$$$ (3)

$$$\begin{array}{c}\text{MFE}=\frac{1}{N}\left(\frac{\sum \nolimits_{i=1}^{N}{\vert qNO2[i]-EPA\,NO}_{2}[i]\vert }{\sum\limits _{i=1}^{N}\frac{\left(qNO2[i]+{EPA\,NO}_{2}[i]\right)}{2}}\right)\end{array}$$$ (4)

R² is the proportion of variance in the output that is captured by the model. RMSE is a metric of absolute error with the same units as the model output (ppb), calculated using Equation 1. MFB is a unitless metric of relative bias. For instance, MFB = 0.67 indicates that the model output is an overestimate of observed values by a factor of 2. MFB = 0.4 indicates that the model output is an overestimate by a factor of 1.5. MFE is a unitless metric of relative error. MFB and MFE are used to measure the relative performance of qNO2, enabling comparison between models fit on different classes and regions.

The multivariate regression models were evaluated for seven distinct regions of the continental U.S.: Northeast, Southeast, Midwest, Rockies, Southwest, Northwest, and Southern California. These regions were selected due to their distinct topographical and meteorological conditions, and to ensure a similar number of EPA monitors (n = 51 ∼ 63) in each region. Figure S5 in Supporting Information S1 shows region divisions and monitor locations.

We implement random and spatial CV methods to assess the generalization ability of the multivariate regression models. Generalizability is an important factor for the utilization of qNO2 as a metric for surface NO₂ in spatial and temporal domains beyond those evaluated in this work. We conduct random CV using k-fold and Monte Carlo. We also use each of the seven regions as CV “folds” to conduct spatial CV. Cross-validation experiments are described in greater detail in Text S2 in Supporting Information S1.

After model training and evaluation, we compute qNO2 MLR, logMLR, and anscMLR for the full CONUS TROPOMI NO₂ grid and discuss the spatial variation of qNO2 values and qNO2 performance metrics across road proximity and location setting classes as well as U.S. regions. Additional analyses are presented for three metropolitan areas with some of the highest TROPOMI NO₂ levels in the United States: Los Angeles, Dallas-Fort Worth, and New York City.

3 Results and Discussion

3.1 Regression Results

We present SLR and MLR results for surface NO₂ estimation, their relative performance across U.S. regions, and the impact of transforms applied to TROPOMI NO₂. Figures 2a–2c show the relationship between TROPOMI NO₂ and EPA NO₂, separated by road proximity and location setting classes. Table S1 in Supporting Information S1 displays performance metrics for SLR and MLR models. SLR with TROPOMI NO₂ as the sole input resulted in an R² of 0.55 when evaluated over all monitors. We fit separate SLR models for near-road and non-near-road monitors (Figure 2a). SLR with TROPOMI NO₂ captures the majority of variance in surface NO₂ concentrations at non-near-road monitors (R² = 0.66) but does not fully capture near-road variation (R² = 0.41). Surface monitors better detect NO₂ near major roads compared to TROPOMI NO₂ because the kilometer-scale resolution of TROPOMI cannot fully capture fine-scale NO₂ concentration gradients. However, while SLR at near-road sites has higher absolute error than non-near-road sites, fractional error and bias is lower at near-road sites than non-near-road sites. Thus, SLR with TROPOMI NO₂ can be useful as a nearly unbiased estimate in data-sparse settings near major roads. To account for the difference in performance between near-road and non-near-road sites, we include road proximity as a binary variable in the MLR models, aligning with several prior studies which include road proximity information in satellite NO₂-based statistical models to estimate surface NO₂ (Grzybowski et al., 2023; Henderson et al., 2007; Kim et al., 2021; H. J. Lee et al., 2023; Novotny et al., 2011; Yeganeh et al., 2018; Young et al., 2016).

Figure 2

Simple and multiple linear regression results for TROPOMI NO₂ with no transform, log transform, and Anscombe transform. (a) Simple regression models fit separately on near-road (black line-of-best-fit) and non-near-road (gray line-of-best-fit) Environmental Protection Agency (EPA) NO₂ monitors. Dashed lines indicate mean near-road and non-near-road TROPOMI and EPA NO₂ values. (b) Simple regression models fit separately on urban (pink line-of-best-fit), suburban (blue line-of-best-fit), and rural (green line-of-best-fit) EPA NO₂ monitors. Dashed lines indicate mean urban, rural, and suburban TROPOMI and EPA NO₂ values. (c) qNO2 MLR fit on all monitors. y = x line in red. (d) Simple regression models with log transform of TROPOMI NO₂ input fit separately on near-road and non-near-road EPA NO₂ monitors. (e) Simple regression models with log transform of TROPOMI NO₂ input trained fit on urban, suburban, and rural EPA NO₂ monitors. (f) qNO2 logMLR fit on all monitors. y = x line in red. (g) Simple regression models with Anscombe transform of TROPOMI NO₂ input fit separately on near-road and non-near-road EPA NO₂ monitors. (h) Simple regression models with Anscombe transform of TROPOMI NO₂ input trained fit on urban, suburban, and rural EPA NO₂ monitors. (i) qNO2 anscMLR fit on all monitors. y = x line in red.

In addition to classification by proximity to major roads, we separated monitor sites by their location setting (urban, suburban, rural) and fit SLR models to each class (Figure 2b). We found TROPOMI NO₂ best captures surface concentrations at suburban sites (R² = 0.60, RMSE = 2.77 ppb), captures around half of concentration variance at rural sites (R² = 0.53, RMSE = 1.80 ppb), and has the poorest performance at urban sites (R² = 0.33, RMSE = 3.95 ppb). Column NO₂ does not fully capture surface NO₂ concentration peaks in urban areas but has stronger performance in suburban and rural areas, which have lower and more uniform NO₂ concentrations. However, urban and suburban sites have lower relative error and bias than rural sites (Table S1 in Supporting Information S1). SLR with TROPOMI NO₂ is useful as a low bias estimate of urban and suburban surface NO₂. In rural areas, SLR-based estimates have moderate positive bias. To account for the differing performance of column NO₂ in capturing surface concentrations across location settings, our MLR models include location setting as a categorical variable.

We then fit a multiple linear regression (MLR) model with TROPOMI NO₂, road proximity, and location setting variables as inputs and surface NO₂ concentration estimates as the output (Figure 2c). MLR evaluated across all monitor sites results in an R² of 0.76, greater than the full-domain SLR R² of 0.55. Thus, incorporating road proximity and location setting information aids in surface NO₂ estimation. MLR also has lower absolute (RMSE = 2.58 ppb) and fractional error (MFE = 0.29) than SLR (RMSE = 3.59 ppb, MFE = 0.40) and results in a lower positive bias (MFB = 0.09) than SLR (0.15). Thus, in locations with readily available data on major roads and basic land use classifications, we recommend the use of the MLR model for surface NO₂ estimation. Table S2 in Supporting Information S1 shows coefficients for the SLR models of each site classification and for the MLR model. Text S3 in Supporting Information S1 includes additional analysis of regression coefficients. As noted in Section 2.4, we term the surface NO₂ estimates of the MLR model as qNO2 MLR.

2019 annual average TROPOMI NO₂ amounts over CONUS have a log-normal distribution. Figure S4 in Supporting Information S1 shows distributions of TROPOMI NO₂ values without transforms and with log-transform and Anscombe transform. To better satisfy the assumption of normality in regression and to improve regression performance, we applied a log-transform and Anscombe transform to TROPOMI NO₂ and compared performance with the corresponding no-transform models. Figures 2d–2f show the relationship between TROPOMI NO₂ with log-transform and EPA NO₂. Figures 2g–2i show the relationship between TROPOMI NO₂ with Anscombe transform and EPA NO₂. For SLR, both log (R² = 0.63) and Anscombe (R² = 0.61) transformed-TROPOMI NO₂ have greater R² than no-transform SLR (R² = 0.55) when fit on all sites. For MLR, both log (R² = 0.77) and Anscombe (R² = 0.78) transforms resulted in marginal improvements in performance. Performance metrics and regression coefficients for log-transform models are presented in Tables S3 and S4 in Supporting Information S1, respectively. Performance metrics and regression coefficients for Anscombe-transform models are presented in Tables S5 and S6 in Supporting Information S1, respectively. Following the naming convention defined in Section 2.4, we term the output of the MLR with log transform as qNO2 logMLR and the output of MLR with Anscombe transform qNO2 as anscMLR.

We specify the model configuration with the best surface NO₂ estimation performance for each site classification. For rural sites, SLR with no transform has the highest R² and lowest RMSE, but SLR with log-transform of TROPOMI NO₂ has the lowest fractional bias. For near-road sites, SLR with log transform has the highest R², lowest RMSE, and lowest fractional bias. For urban sites, MLR with log transform has the highest R². The difference in performance between MLR and SLR is greatest at urban sites, which indicates the value of road proximity information for estimating urban surface NO₂. For non-near-road and suburban sites, MLR with Anscombe transform has the best performance. MLR with Anscombe transform has the best performance across all monitors, with an overall R² of 0.78.

3.2 qNO2 Computation

To analyze spatial patterns of surface NO₂ estimates, we computed qNO2 MLR for all TROPOMI 0.01° by 0.01° grid cells over CONUS (Figure 3a). qNO2 MLR is highest in major cities and along major highways across the U.S. The Great Lakes and much of the eastern half of the U.S. have high overall qNO2 MLR concentrations, while the Mountain West and Northern New England have lower overall concentrations. Western North Dakota and the Permian Basin in western Texas have elevated qNO2 MLR levels compared to the surrounding rural areas, coinciding with the high oil industry activity in both regions.

Figure 3

(a) 2019 qNO2 gridded across the continental United States, computed using multiple linear regression (qNO2 MLR). (b) 2019 qNO2 gridded across the continental United States, computed using multiple linear regression with log transform of the TROPOMI NO₂ input (qNO2 logMLR). (c) The difference between qNO2 logMLR and qNO2 MLR. Red indicates areas where qNO2 logMLR is greater than qNO2 MLR, and blue indicates areas where qNO2 logMLR is less than qNO2 MLR. (d) 2019 qNO2 gridded across the continental United States, computed using multiple linear regression with Anscombe transform of TROPOMI NO₂ input (qNO2 anscMLR). (e) The difference between qNO2 anscMLR and qNO2 MLR. Red indicates areas where qNO2 logMLR is greater than qNO2 MLR, and blue indicates areas where qNO2 logMLR is less than qNO2 MLR.

We also computed qNO2 logMLR (Figure 3b) and anscMLR (Figure 3d) at 0.01° by 0.01° resolution across CONUS. Figure 3c displays the difference between qNO2 logMLR and qNO2 MLR for each grid cell. qNO2 logMLR is greater than qNO2 MLR across the eastern half of the United States, particularly around the Great Lakes, Texas, and the Mid-Atlantic. qNO2 logMLR is also greater than qNO2 MLR in the California Central Valley and in areas around Seattle, Portland, Salt Lake City, Phoenix, and Denver, as well as the Bakken oil fields in North Dakota and Permian Basin in Texas. qNO2 logMLR and qNO2 MLR are close in value in most urban areas and throughout most of the rural western U.S. qNO2 logMLR and MLR have the greatest difference in the Los Angeles and New York City areas, where qNO2 logMLR concentrations are more than 4 ppb lower than qNO2 MLR. Figure 3e shows the difference between qNO2 anscMLR and qNO2 MLR for each grid cell. qNO2 anscMLR follows a similar spatial pattern of differences to qNO2 MLR as qNO2 logMLR, but with a lower magnitude of difference. Overall, qNO2 logMLR and anscMLR have greater spatial spread of NO₂ from urban areas and greater background concentrations in the eastern U.S. as well as lower maximum concentrations compared to qNO2 MLR.

3.3 Regional Evaluation

We evaluated qNO2 in seven U.S. regions to investigate the variability of satellite-surface agreement between large spatial domains with similar topographic and meteorological conditions. qNO2 MLR best aligns with surface NO₂ in the Midwest states (R² = 0.88). Northeast, Southeast, Rockies, and Southern California regions have comparable qNO2 MLR performance with R² values ranging from 0.72 to 0.76. The Southwest (R² = 0.65) and Northwest (R² = 0.66) regions have the lowest qNO2 MLR performance (Table S7 in Supporting Information S1). The strong performance in the Midwest and relatively weak performance in the Western U.S. suggests that elevation gradient may be an additional variable that could be included to further improve MLR performance.

All regions have positive MFB except the Northwest, which has an MFB of −0.06 indicating that qNO2 is a slight underestimate of surface NO₂. Rockies region has the greatest MFE (0.46) and MFB (0.15). This may be due to the larger proportion of rural sites in the Rockies region with very low NO₂ concentrations, which inflates relative error metrics. For rural and remote areas with low background NO₂ concentrations, absolute error metrics are more relevant for assessing model performance.

qNO2 logMLR exhibits similar regional variability as qNO2 MLR. R² in the Northeast, Midwest, Northwest, and Southern California is slightly higher compared to qNO2 MLR, while R² in the Southeast is slightly lower (Table S8 in Supporting Information S1). qNO2 anscMLR has slightly higher R² than qNO2 MLR and logMLR in all regions (Table S9 in Supporting Information S1).

qNO2 performance varies within regions as well as between regions. Figure 4 displays the fractional bias of qNO2 at each EPA monitor. qNO2 MLR (Figure 4a) overestimates surface NO₂ relative to the measured value along the California coast, Wyoming, Montana, the Dakotas, and Texas. qNO2 MLR underestimates surface NO₂ in the California Central Valley and the Southwest. Sites in the Midwest and Southeast have low overall bias. qNO2 anscMLR (Figure 4c) and qNO2 MLR have similar spatial variation in fractional bias across EPA monitor sites, but qNO2 anscMLR has lower fractional bias in Wyoming and Montana. qNO2 logMLR (Figure 4b) also has similar spatial fractional bias variation as MLR and anscMLR but has a much greater degree of bias in Wyoming and Montana.

Figure 4

(a) Fractional bias between Environmental Protection Agency (EPA) NO₂ and qNO2 MLR at EPA monitor locations (n = 402) across the continental United States. Red indicates monitor locations where qNO2 is relatively high compared to the measured NO₂ concentration. Blue indicates monitor locations where qNO2 is relatively low compared to the measured NO₂ concentration. (b) Fractional bias between EPA NO₂ and qNO2 logMLR at EPA monitor locations. (c) Fractional bias between EPA NO₂ and qNO2 anscMLR at EPA monitor locations.

3.4 Urban Case Studies

Figure 5 shows qNO2 MLR, logMLR, and anscMLR over three large U.S. metropolitan areas: Los Angeles, CA; Dallas-Fort Worth, TX; and New York City, NY-NJ-CT-PA. qNO2 MLR in Los Angeles (Figures 5a, 5d, and 5g) is greater than 20 ppb in the city center. qNO2 MLR decreases sharply between the metropolitan area and the surrounding rural areas. qNO2 logMLR has a lower maximum level in the city center and a more gradual decrease toward the surrounding rural areas than qNO2 MLR. The urban-rural concentration gradient for qNO2 anscMLR is steeper than qNO2 logMLR but less steep than qNO2 MLR. All qNO2 models indicate concentrations greater than 18 ppb along the major highways extending south and east from central LA. Among the qNO2 models, qNO2 MLR (RMSE = 3.65 ppb) and anscMLR (3.52 ppb) have the lowest error in Los Angeles, while logMLR (RMSE = 7.78 ppb) has the highest error.

Figure 5

qNO2 MLR, qNO2 logMLR, and qNO2 anscMLR over three selected large U.S. metropolitan areas. (a) qNO2 MLR over Los Angeles, CA. (b) qNO2 MLR over Dallas-Fort Worth, TX. (c) qNO2 MLR over New York-Newark-Jersey City, NY-NJ-CT-PA. (d) qNO2 logMLR over LA. (e) qNO2 logMLR over Dallas. (f) qNO2 logMLR over NYC. (g) qNO2 anscMLR over LA. (h) qNO2 anscMLR over Dallas. (i) qNO2 anscMLR over NYC.

Dallas-Fort Worth (Figures 5b, 5e, and 5h) has lower overall qNO2 than Los Angeles, with maximum qNO2 of 16–18 ppb along major highways. The qNO2 models estimate similar concentration levels in the metropolitan area, but logMLR and anscMLR have a broader radius of high concentrations than qNO2 MLR. In Dallas, qNO2 has high accuracy, with logMLR having the lowest error (RMSE = 1.56 ppb).

New York City (Figures 5c, 5f, and 5i) has comparable peak qNO2 levels to Los Angeles, as the urban core and adjacent highways have qNO2 concentrations greater than 20 ppb. As in Los Angeles and Dallas-Fort Worth, qNO2 logMLR and anscMLR over New York City have smoother gradients toward the edges of the metropolitan area than qNO2 MLR. The spatial patterns of qNO2 anscMLR are a combination of the sharp gradients and high peak concentrations of qNO2 MLR and the smoother gradients of qNO2 logMLR. Among the qNO2 models, anscMLR results in the lowest error (RMSE = 3.49 ppb) while logMLR has the highest error (RMSE = 7.04 ppb).

3.5 Cross-Validation

We implemented k-fold and Monte Carlo CV to investigate the generalizability of qNO2 on data sets held out from model fitting. Table S10 in Supporting Information S1 displays k-fold CV results and Table S11 in Supporting Information S1 displays Monte Carlo CV results.

Both CV methods indicate that qNO2 anscMLR performs well on unseen data. k-fold CV resulted in similar mean holdout set performance for k = 5 and k = 10 with R² of 0.74. However, using k = 20 resulted in a mean holdout set performance of R² = 0.71. Smaller holdout sets are more likely to be unrepresentative of the population distribution, thus resulting in poor evaluation performance. Monte Carlo CV using holdout set sizes of 25% and 50% indicated strong evaluation performance on the holdout data, with anscMLR R² of 0.77. When evaluated over a sufficiently large set of unseen data points, qNO2 anscMLR exhibits strong generalization ability. Further, the difference between holdout set and training set performance is small, indicating that the anscMLR model is not overfit to the training data. This finding supports the use of qNO2 anscMLR as a reliable metric for future surface NO₂ estimation beyond the domain of our analysis.

We also conduct CV using the seven CONUS regions by leaving one region out for evaluation and fitting anscMLR models on the remaining six regions. As with non-cross-validated regional evaluation detailed in Section 3.3, qNO2 anscMLR generalizes well to Midwest monitors with an R² of 0.89 and has the lowest generalization performance for Southwest (R² = 0.65), Pacific Northwest (R² = 0.66), and Northeast sites (R² = 0.69) (Table S12 in Supporting Information S1). The similar results between cross-validated and non-cross-validated region-wise evaluation indicate that qNO2 is generalizable to new geographic contexts.

4 Conclusions

We fit regression models with TROPOMI NO₂, location setting, and road proximity inputs to estimate 2019 annual average surface NO₂ concentrations at 0.01° by 0.01° resolution across the continental U.S. Among the regression models studied, qNO2 anscMLR has the strongest overall performance. qNO2 anscMLR is the best estimate for surface NO₂ at non-near-road sites (anscMLR R² = 0.76) and suburban sites (anscMLR R² = 0.74). We also investigate qNO2 spatial patterns over large U.S. urban areas, compare qNO2 performance across U.S. regions, and assess the generalizability of qNO2. We find that qNO2 performs best in the Midwest, with CV anscMLR R² of 0.89.

Using easily accessible data and interpretable methods, we demonstrate comparable or improved performance over prior regression-based studies which use satellite NO₂ to estimate surface NO₂. Table 2 presents R² values of satellite-surface NO₂ agreement for prior studies which cover four main methods, both OMI and TROPOMI NO₂ data, and a wide range of spatiotemporal scales. Novotny et al. (2011) used GEOS-Chem to derive surface NO₂ concentrations from OMI, which was then used as regression input along with land use to estimate annual-average surface NO₂ at 30-m resolution. Their work resulted in a CV R² of 0.77 and an MAE of 2.40 ppb evaluated at EPA NO₂ monitors across CONUS. The slightly stronger performance of qNO2 anscMLR using a three-variable regression model without GEOS-Chem-based column NO₂ adjustments highlights the improved ability of the higher resolution TROPOMI to capture surface NO₂ compared to prior satellite products. Goldberg et al. (2021) found an R² of 0.66 between annual-average TROPOMI NO₂ and EPA NO₂ at non-near-road sites. Using the same 0.01° by 0.01° TROPOMI data set, we apply the Anscombe transform to TROPOMI NO₂ which results in 0.06 greater R² at non-near-road sites. Lee et al. (2023) used multivariate regression to analyze TROPOMI NO₂ agreement with 2018–2019 annual-average surface NO₂ over California at 0.5 by 0.5 km resolution. Their final regression models included land use and road proximity inputs. Meteorological inputs were initially considered but were removed because they did not contribute to model performance. Their work achieved a CV R² of 0.76 and RMSE of 2.51 ppb. These metrics are comparable to qNO2 anscMLR metrics computed using the same CV method as Lee et al., for all CONUS monitor sites (CV R² = 0.75 and RMSE = 2.64 ppb). We further find that qNO2 anscMLR has CV R² of 0.76 and RMSE of 2.63 ppb in California, in close agreement with the Lee et al. results while using simpler input variables.

Table 2. Comparison of R² Values With Other Studies Investigating Agreement Between Satellite-Derived and Surface Measurements of NO₂

Model type	Study	Satellite product	Spatial domain	Temporal domain	R^2
Chemical transport	Bechle et al. (2013)	OMI (Ozone Monitoring Instrument)	S. Cali.	Annual	0.86
	Gu et al. (2017)	OMI	China	Monthly	0.61–0.64
	Cooper et al. (2020)	TROPOMI (TROPOspheric Monitoring Instrument)	U.S., Canada	Annual	0.53
Machine learning	Qin et al. (2020)	POMINO	E. China	Monthly	0.72^a
	Chan et al. (2021)	TROPOMI	Germany	Daily	0.64^a
	Ghahremanloo et al. (2021)	TROPOMI	Texas	Daily	0.71^b
	Chi et al. (2022)	TROPOMI	China	Daily	0.73^a
	Li et al. (2022)	TROPOMI	China	Daily	0.78^a
	Grzybowski et al. (2023)	TROPOMI	Poland	Weekly	0.60^a
Spatial interpolation	Young et al. (2016)	OMI	U.S.	Annual	0.65–0.80^b
Regression	Henderson et al. (2007)	–	Vancouver, Canada	Annual	0.69
	Novotny et al. (2011)	OMI	U.S	Annual	0.77^a
	Ghahremanloo et al. (2021)	TROPOMI	Texas	Daily	0.59^b
	Goldberg et al. (2021)	TROPOMI	U.S.	Annual	0.66
	Yu and Li (2022)	TROPOMI	Xinjiang Province	Monthly	0.78
	Grzybowski et al. (2023)	TROPOMI	Poland	Weekly	0.49^a
	Lee et al. (2023)	TROPOMI	California	Annual	0.76^a
	Present Study	TROPOMI	CONUS	Annual	0.78 ^b

• ^a Holdout set or k-fold CV R² values.
• ^b Spatial CV R² values.

Our results compare favorably to prior studies using CTM, machine learning, and spatial interpolation models to investigate satellite-surface NO₂ agreement (Table 2). Cooper et al. (2020), who used GEOS-Chem simulated vertical profiles to infer surface NO₂ from TROPOMI columns over CONUS and Canada, attained an annual-average R² of 0.53 against surface observations, comparable to the R² of 0.55 we obtain with SLR for all monitors. Chi et al. (2022) used XGBoost, a popular machine learning method, to estimate 2018–2020 annual-average surface NO₂ over China using TROPOMI, meteorological, and land use data. They obtained a CV R² of 0.73. Ghahremanloo et al. (2021) used convolutional neural networks, a deep learning method specialized for image-based inputs, to estimate surface NO₂ over Texas. They attained a spatial CV R² of 0.71 averaged over 2019. We found a spatial CV R² of 0.65 for monitors in the Southwest region, of which a majority are in Texas. Lastly, Young et al. (2016) use kriging to estimate annual-average surface NO₂ over CONUS from 1990 through 2012 using OMI NO₂, obtaining spatial CV R² values between 0.65 and 0.80, depending on the year. Although our results are not directly comparable to the above studies due to differing spatiotemporal domains and data sets, our anscMLR R² of 0.78 indicates favorable performance compared to studies using machine learning and spatial interpolation models. Despite the relative simplicity of regression methods, they provide comparable performance for estimating surface NO₂ using satellite and auxiliary data.

Although the analyses in this work are conducted over the continental United States, the strong region-wise CV performance of the MLR models indicate that qNO2 can be applied to other regions with relatively similar climates, geographies, and chemical regimes to CONUS, such as Northern Europe and East Asia. Given the multitude of studies which have investigated satellite-surface NO₂ agreement over China (e.g., Chi et al., 2022; Li et al., 2022) and Europe (e.g., Chan et al., 2021; Grzybowski et al., 2023), we anticipate the data sources and methods used in our work can be reproduced over these regions. Additionally, since both road density and location setting are relatively static over time, surface NO₂ concentrations of additional years in the TROPOMI record can be estimated using qNO2, thus enabling NO₂ exposure assessments in areas or time periods with sparse or no monitor coverage. However, qNO2 may not generalize well to regions with characteristics not represented in CONUS, such as tropical and polar regions. In addition to characterizing surface NO₂, our analysis of satellite-surface agreement across spatial scales, contexts, and regression model configurations informs the application of satellite NO₂ products in different domains.

The annual-average scale of our analysis is suitable for characterizing long-term spatial characteristics of surface NO₂. However, as NO₂ exhibits significant daily and seasonal variability, our results are less applicable for studies of short-term pollution events and trends. For example, our methodology is less applicable for inferring NO₂ from biomass burning events because of their short time scale (less than 1 week) and tendency to be obscured from satellite measurements since they produce high-density smoke which is often indistinguishable from clouds (Griffin et al., 2021). We expect our results to support long-term, high-spatial resolution NO₂ exposure assessments, such as those used to determine compliance with the EPA annual-average NO₂ NAAQS.

The spatial distribution of EPA monitors presents a potential source of bias for qNO2. In the eastern half of the U.S., clusters of monitors are evenly distributed, mainly near urban areas. In the western U.S., monitors are concentrated in rural Wyoming, western North Dakota, and throughout California but are sparse in Washington and Oregon. Thus, monitor measurements may not be fully representative of NO₂ spatial patterns over the U.S., impacting the generalizability of qNO2 to less-represented location settings and regions. Spatial interpolation models which account for error correlations between monitors in proximity may help to account for the inconsistent distribution of surface monitors.

We anticipate that the results presented here will inform analysis of data from TEMPO (Tropospheric Emissions: Monitoring of Pollution), a new NASA geostationary satellite instrument launched in April 2023 which captures hourly column NO₂ during all daylight hours at 2.1 km by 4.4 km resolution over the entire continental United States (Zoogman et al., 2017). The greater spatial and temporal resolution from TEMPO will expand the scope of air quality analyses. For example, the methods in this work can be extended to compare hourly TEMPO observations with hourly ground monitor measurements of NO₂. Further, greater spatial resolution will enable investigation of satellite-surface agreement over finer-scale emissions sources such as industrial sites in addition to major roads.

Acknowledgments

EK, TH, MH, CH, and SE were supported by NASA Grant 80NSSC21K0427 for the NASA Health and Air Quality Applied Sciences Team (HAQAST). DG was supported by NASA Grant 80NSSC21K0511 for the NASA Health and Air Quality Applied Sciences Team (HAQAST). EK was also supported by the Hilldale Undergraduate Research Fellowship at the University of Wisconsin-Madison.

Open Research

Data Availability Statement

TROPOMI NO₂ data can be obtained here: https://doi.org/10.5270/S5P-9bnp8q8 (Copernicus Sentinel-5P (processed by ESA), 2021). TROPOMI NO₂ data re-gridded by DG to 0.01° resolution over CONUS for 2019 through 2023 can be found here: https://disc.gsfc.nasa.gov/datasets/HAQ_TROPOMI_NO2_CONUS_A_L3_2.4/summary. The road data used in our work was derived from shape files accessible at https://www2.census.gov/geo/tiger/TIGER2021/PRIMARYROADS/. Location setting data was obtained from https://nces.ed.gov/programs/edge/Geographic/LocaleBoundaries. The above data re-gridded to the custom 0.01° by 0.01° grid used in this work is available at https://doi.org/10.5281/zenodo.10601063. EPA AQS data is accessible at https://aqs.epa.gov/aqsweb/airdata/download_files.html. All code for the analysis and visualizations presented in this study are available at https://doi.org/10.5281/zenodo.10582277.