A simpliﬁed non-linear chemistry transport model for analyzing NO 2 column observations: STILT–NO x

. Satellites monitoring air pollutants (e.g., nitrogen oxides; NO x = NO + NO 2 ) or greenhouse gases (GHGs) are widely utilized to understand the spatiotemporal variability in and evolution of emission characteristics, chemical transformations, and atmospheric transport over anthropogenic hotspots. Recently, the joint use of space-based long-lived GHGs (e.g., carbon dioxide; CO 2 ) and short-lived pollutants has made it possible to improve our understanding of emission characteristics. Some previous studies, however, lack consideration of the non-linear NO x chemistry or complex atmospheric transport. Considering the increase in satellite data volume and the demand for emission monitoring at higher spatiotemporal

Abstract.Satellites monitoring air pollutants (e.g., nitrogen oxides; NO x = NO + NO 2 ) or greenhouse gases (GHGs) are widely utilized to understand the spatiotemporal variability in and evolution of emission characteristics, chemical transformations, and atmospheric transport over anthropogenic hotspots.Recently, the joint use of space-based longlived GHGs (e.g., carbon dioxide; CO 2 ) and short-lived pollutants has made it possible to improve our understanding of emission characteristics.Some previous studies, however, lack consideration of the non-linear NO x chemistry or complex atmospheric transport.Considering the increase in satellite data volume and the demand for emission monitoring at higher spatiotemporal scales, it is crucial to construct a local-scale emission optimization system that can handle both long-lived GHGs and short-lived pollutants in a coupled and effective manner.This need motivates us to develop a Lagrangian chemical transport model that accounts for NO x chemistry and fine-scale atmospheric transport (STILT-NO x ) and to investigate how physical and chemical processes, anthropogenic emissions, and background may affect the interpretation of tropospheric NO 2 columns (tNO 2 ).
Interpreting emission signals from tNO 2 commonly involves either an efficient statistical model or a sophisticated chemical transport model.To balance computational expenses and chemical complexity, we describe a simplified representation of the NO x chemistry that bypasses an explicit solution of individual chemical reactions while preserving the essential non-linearity that links NO x emissions to its concentrations.This NO x chemical parameterization is then incorporated into an existing Lagrangian modeling framework that is widely applied in the GHG community.We further quantify uncertainties associated with the wind field and chemical parameterization and evaluate modeled columns against retrieved columns from the TROPOspheric Monitoring Instrument (TROPOMI v2.1).Specifically, simulations with alternative model configurations of emissions, meteorology, chemistry, and inter-parcel mixing are carried out over three United States (US) power plants and two urban areas across seasons.Using the U.S. Environmental Protection Agency (EPA)-reported emissions for power plants with non-linear NO x chemistry improves the model-data alignment in tNO 2 (a high bias of ≤ 10 % on an annual basis), compared to simulations using either the Emissions Database for Global Atmospheric Research (EDGAR) model or without chemistry (bias approaching 100 %).The largest modeldata mismatches are associated with substantial biases in wind directions or conditions of slower atmospheric mixing and photochemistry.More importantly, our model development illustrates (1) how NO x chemistry affects the relationship between NO x and CO 2 in terms of the spatial and seasonal variability and (2) how assimilating tNO 2 can quantify systematic biases in modeled wind directions and emission distribution in prior inventories of NO x and CO 2 , which laid a foundation for a local-scale multi-tracer emission optimization system.

Introduction
Emissions of air pollutants (APs) and greenhouse gases (GHGs) adversely impact urban ecosystems and environments, human health, and the climate via the moderation of energy budgets (Myhre et al., 2013;Watts et al., 2021).APs and GHGs are directly inter-connected, considering that they are co-emitted from many combustion sources, suggesting that reductions in GHGs may bring co-benefits in mitigating APs (Cifuentes et al., 2001;West et al., 2013;Lin et al., 2018).Although quantifying emissions in GHGs and APs and understanding their underlying drivers at all scales are equally important, emission estimates beyond a county or city become more relevant in addressing policy-relevant topics such as emission mitigation.
Space-based remote sensors offer an objective perspective to monitoring global air quality and GHGs.These new data enable us to uncover the spatial variability along with the temporal trend and perturbation of anthropogenic emissions.Air-quality-related observations have been among the first to demonstrate the capability of satellite remote sensing to globally diagnose air quality (Duncan et al., 2016;Laughner and Cohen, 2019;Jin et al., 2020); constrain emissions across time, space, and sectors (Jiang et al., 2018;Goldberg et al., 2019;Tang et al., 2019;Qu et al., 2022); and evaluate real-world decisions (Lamsal et al., 2011;Demetillo et al., 2020).Leveraging satellite observations in understanding the spatiotemporal distribution of emissions within cities is still limited compared to those city total estimates.Data and analysis uncertainty further present the main challenge in extracting robust combustion signals from remotely sensed measurements, and these uncertainties are amplified in attempt to resolve dynamic flows and heterogeneous combustion activities within cities (Valin et al., 2013;Goldberg et al., 2022;Souri et al., 2022).
Making full use of the existing and upcoming satellites that retrieve concentrations of APs and GHGs offers an informative way to target urban emissions from different sources at a policy-relevant scale of a few kilometers.Combining satellite observations of species with different atmospheric lifetimes has enabled studies to diagnose chemical conditions and meteorological processes (Jin et al., 2017;Lama et al., 2022), identify urban plumes, constrain emissions for the tracer of interest (Wunch et al., 2009;Yang et al., 2023), and obtain observation-based ratios between tracers (Silva and Arellano, 2017;Wu et al., 2022;MacDonald et al., 2022) to infer structural changes in combustion activities (Reuter et al., 2014;Miyazaki and Bowman, 2023).In light of the rapid rise in satellite data volume, it is beneficial to have an analysis system that adequately accounts for the important local-scale processes in interpreting the abundance of GHGs and APs in a coupled manner (Fig. 1).Analogies to such local-scale systems in a global context include the APfocused Tropospheric Chemistry Reanalysis version 2 (TCR-2; Miyazaki et al., 2020) and the GHG-focused Carbon Mon-itoring System Flux (CMS-Flux; Hurtt et al., 2022).Only a few recent multi-tracer modeling systems aim to bridge CO 2 and NO 2 column measurements (Reuter et al., 2014;Kaminski et al., 2022;Hakkarainen et al., 2023), despite limits in their modeling tools (elaborated upon in the next paragraph).In addition, as emphasized in Reuter et al. (2014), most multi-tracer studies rely on emission ratio or conversion ratio from inventories, which can be problematic.
In efforts to interpret CO 2 or NO x emission signatures from satellite observations, most prior studies used either statistical or inversion approaches.The former approach involves the use of a Gaussian plume or exponentially modified Gaussian distribution (EMG) models with input from simple wind information to derive emissions of CO 2 and NO x (or a lifetime if for NO x ) purely from observations in a computationally efficient manner without relying much on prior assumptions of emissions (Nassar et al., 2022;Beirle et al., 2011).These statistical approaches only provide a plumeintegrated emission estimate that can be sensitive to the input wind speed and chemical lifetime.Multiple satellite overpasses need to be aggregated with wind direction aligned for a robust fit in the EMG model to obtain the emission and lifetimes.It is challenging to infer and evaluate sub-grid-cell variations in emissions.The more sophisticated inverse approach involves the use of a chemical transport model (CTM) that comprehensively accounts for atmospheric transport and chemical transformation and a coupled inversion or data assimilation system (e.g., Liu et al., 2022;Qu et al., 2022).CTMs are, however, computationally expensive and often involve hundreds of species and their coupling reactions.Most CTMs used in AP-related studies are Eulerian models, which may suffer from complications caused by rigid model grids (Wohltmann and Rex, 2009;Valin et al., 2011).Motivated by these approaches that rely on a constant lifetime or solve for individual chemical reactions, we have built a modeling framework to balance the advantages and imperfectionsi.e., to simplify the chemical transformation process that preserves the non-linear relationship between NO x emissions and the observed concentration field, together with a highresolution atmospheric transport using a Lagrangian particle dispersion model (LPDM).
LPDMs have been increasingly utilized for emission estimates over the past few decades.For instance, the Stochastic Time-Inverted Lagrangian Transport model (STILT; Lin et al., 2003) building upon HYSPLIT (Stein et al., 2015) has been well adapted to analyze emission signals from all sorts of measurement platforms.STILT was designed to better describe the movement of air parcels only relevant to an observation site and explicitly provide the sourcereceptor relationship (i.e., the Jacobian matrix) to facilitate efficient atmospheric inversions for optimizing emissions.Besides, LPDMs themselves possess inherent numerical and computational advantages, such as avoiding artificial smoothing of concentration fields by spurious numerical diffusion in confined model boxes (Wohltmann and Rex,Figure 1.A conceptual diagram of our proposed local-scale multi-tracer modeling framework in interpreting column observations.It contains a road map for this study (points 1 through 5).The diagram highlights the key biogenic, physical, and/or chemical processes for quantifying NO x , CO, and CO 2 around cities, based on space-based measurements (pixels from red to blue).These include details on the atmospheric conditions (wind speed and planetary boundary layer height for vertical mixing, horizontal mixing, and diffusion lengths); chemical conditions (photolysis rate and NO x regimes and regional versus local oxidant conditions); the spatial distribution of emissions (urban vs. power plant); and sensitivities of the column abundance to individual vertical levels (averaging kernel).
2009; Lin et al., 2013).More importantly, the Lagrangian transport perspective is intuitively coupled with box models that handle chemical reactions.Noticeable examples include STOCHEM (Collins et al., 1997), ATLAS (Wohltmann and Rex, 2009), CLaMS v2.0 (Konopka et al., 2019), and HYSPLIT-based variations, including HYSPLIT CheM (Stein et al., 2000), ELMO-2 for ozone (Strong et al., 2010), andSTILT-Chem (Wen et al., 2012).These Lagrangian chemical models describe the chemical reactions of each species or lumped group with similar functional groups to calculate chemical transformation along trajectories but vary in the complexity of implemented chemistry and parameterization for turbulent mixing and numerical diffusion.Despite these prior modeling efforts, Lagrangian chemical models are more often adopted to inform the origins of APs but are less commonly used to constrain emissions.Such underappreciation is in part a result of the heavy computational expenses in solving chemical changes at a high frequency via ordinary differential equations (similar to most Eulerian CTMs) and the reliance on external meteorological fields.
To reduce computational costs in dealing with complex chemistry, studies have proposed machine learning techniques or defaulted to a constant-lifetime assumption as a shortcut.Machine learning techniques have been applied to approximate the chemical mechanisms (Keller and Evans, 2019;Huang and Seinfeld, 2022), predict the OH field with observational constraint (Zhu et al., 2022), and calculate emissions (He et al., 2022).Other studies have assumed a constant first-order lifetime to estimate NO x emissions and emission ratios between NO x and CO 2 (Lee et al., 2014;Hakkarainen et al., 2023).However, unlike chemically passive species such as CO 2 , the chemical tendency of NO x is not independent of atmospheric advection and turbulent mixing because of the chemically driven non-linearity between the NO x lifetime and the NO and NO 2 concentrations (Laughner and Cohen, 2019).More specifically, during the day, NO x is lost through two more permanent pathways of (1) NO 2 + OH to nitric acid and (2) NO + peroxy radicals (RO 2 ), with a minor branch in producing alkyl nitrates or ANs (point 3 in Fig. 1).The two pathways compete with one another and either may dominate, depending on the chemical conditions.Such non-linear dependence of the NO x lifetime or chemical tendency with the NO x concentration must be accounted for to estimate the NO x emissions from atmospheric NO 2 concentrations.Such non-linearity will affect the interpretation of tracer-to-tracer emission ratios from observed enhancement ratios. https://doi.org/10.5194/gmd-16-6161-2023 Geosci.Model Dev., 16,2023 In this study, we present a non-linear modeling framework, STILT-NO x , to simulate tropospheric column-averaged NO 2 mixing ratio (tNO 2 ) as retrieved from the TROPOspheric Monitoring Instrument (TROPOMI).Note that initial NO 2 vertical column density (VCD; molec.cm −2 ) is converted to tNO 2 (ppb) by dividing by a dry air VCD.The dry air VCD is calculated by integrating a profile of the ideal gas number density of air minus a modeled water vapor profile.As illustrated in Fig. 1, the overarching goal of this framework is to facilitate emission optimizations over global anthropogenic hotspots by simulations of the concentrations of key trace gases of CO 2 , CO, and NO x at the local scale.To do so, the current work aims to equip the STILT model with simplified chemistry that avoids explicit calculations of chemical reactions, while preserving the non-linearity that ties the NO x concentrations to its emission (point 3 in Fig. 1).The proposed STILT-NO x framework is comprised of four components, outlined below, which correspond, respectively, to points 1 to 4 in Fig. 1 and will be coupled to an upcoming non-linear flux inversion module (point 6).
2. A column-weighting module to simulate atmospheric columns (and uncertainties) that incorporates pressure weighting functions and retrieval-specific averaging kernel profiles (X-STILT; Wu et al., 2018).
3. A simplified chemistry module that describes the NO x chemical tendency (Sect.2.1) and how much NO x is presented as NO 2 (i.e., NO 2 : NO x ratio; Sect.2.2).
4. An error analysis module that quantifies errors and biases in wind fields and chemical parameters (Sect.3), following the methods initially proposed in Lin and Gerbig (2005) and Wu et al. (2018), which can be used for future flux inversions.
We illustrate the skill of this framework using comparisons of modeled tNO 2 and those diagnosed from TROPOMI over three United States (US) power plants and two cities across seasons (Sect.4).Last, we discuss possible future advances in Sect.5.3 and demonstrate the benefits of applying this framework, especially on the quantification of CO 2 emissions, emission ratios between NO x and CO 2 , and near-field wind biases in Sects.5.1 and 5.2.

STILT-NO x model descriptions
Building upon the HYSPLIT-STILT atmospheric transport core, the STILT-NO x framework traces the origin of the atmospheric column observed by the satellite and calculates changes in the NO x concentrations due to emissions, interparcel mixing, and chemical transformations at the (sub-)minute scale.The STILT-NO x simulations are conducted in three steps (Fig. 2).
First, the backward-trajectory mode records the latitude, longitude, and pressure coordinates of air parcels originating from the same atmospheric column sampled by satellites and being driven by the Eulerian meteorological fields (Step 1 in Fig. 2).In this work, we test two meteorological fields when they are available for each examined region, namely from the Global Forecast System (GFS0p25) and the High-Resolution Rapid Refresh (HRRR), with a respective horizontal grid spacing of 0.25 • and 3 km (Rolph et al., 2017).As most anthropogenic and all soil sources of NO x are from the surface, air parcels are evenly distributed and released from the surface to 2 km, which is slightly above the typical planetary boundary layer (PBL) height (Wu et al., 2018).To evaluate how representative enhancements between 0 and 2 km are compared to the total tropospheric column enhancements (which can include sources from lightning and aviation), we analyzed vertical distributions of NO x mixing ratios from TCR-2 (Miyazaki et al., 2020).TCR-2 is a global chemical reanalysis that includes full physical and chemical processes for various species and assimilates multiple satellite products of NO 2 , ozone, CO, and SO 2 .As a result, the monthly mean NO x concentrations over the 2 • × 2 • area around the top 1000 cities is quite insignificant for pressure ≤ 700 hPa when compared to huge signals within the PBL (Fig. S1 in the Supplement).Although 0 to 2 km columns include most anthropogenic enhancements over urban areas, we subtracted a local NO 2 background from the total tropospheric columns to minimize the non-anthropogenic influences with a plume detection algorithm, following Kuhlmann et al. (2019).The model-data comparisons with background subtracted are discussed in Sect.4.1.
After being released from a given TROPOMI sounding at the overpass time (∼ 13:00 local time for nadir soundings), air parcels are dispersed backward in time for 12 h (time at t 0 in Fig. 2).
Step 1 also provides the STILT footprint (ppm (µmol m −2 s −1 ) −1 ) per air parcel per timestamp (Lin et al., 2003).The STILT footprint of a given air parcel is proportional to the time this parcel spends in a small area (of ∼ 100 m) and describes how the downwind concentration may be altered if this air parcel is influenced by emissions.A much more complete description of STILT can be found in Lin et al. (2003); Fasoli et al. (2018).The footprint concept, by definition, relies on atmospheric transport and only accounts for concentration changes due to emissions but not chemical transformations.
Next, NO x concentrations at the endpoints of the model trajectory are extracted from the Tracer Model version 5, massively parallel version (TM5-MP) to serve as the initial conditions (Step 2 in Fig. 2).TM5-MP is an auxiliary dataset in which the NO 2 vertical profiles serve as the prior knowledge facilitating the stratosphere-troposphere separa- Step 1 is a routine backward-time calculation that records the locations of air parcels at each timestamp ( t) of 1 min or shorter and their influence from potential fluxes (footprint).
Step 2 is to calculate the initial condition for which the trajectory endpoint at time t 0 is given a concentration from 4D fields (e.g., TM5 in the case of NO x ).
Step 3 is a forward-time concentration calculation that updates change in concentrations due to emissions, net chemical losses, and inter-parcel mixing along each trajectory at a timescale of ≤ 1 min.To clarify, Step 3 makes use of trajectories originating from a column receptor stretching from the surface to 2 km, as generated from Step 1. tion in Level 2 (L2) NO 2 retrieval (Van Geffen et al., 2022).Here, we simply assume that most NO x is presented as NO 2 at nighttime, despite the apparent caveat for neglecting NO 3 chemistry and heterogenous reactions involving N 2 O 5 .
Once NO x is initialized at the time t 0 for the endpoint of every trajectory, we proceed with Step 3 (Fig. 2) to estimate the changes in concentrations due to emissions, chemical transformation, and inter-particle mixing.Mathematically, the concentration per air parcel per timestamp (C p,t ) relies on that from the last timestamp, following Eq.(1): where the time interval for updating concentrations, t, is defaulted to 1 min or reduced to a sub-minute value when C t becomes nonphysically negative to ensure numerical stability.Concentration gains from emissions, C emis , result from multiplying STILT-parcel-specific footprints (F p,t ) with prior emissions (E) from EDGARv6.1 (Monforti Ferrario et al., 2022) and the U.S. Environmental Protection Agency (EPA; United States Environmental Protection Agency, 2022) for power plant cases in this study.We neglect soil NO x emissions, given the relatively small contributions in cities. Un-like sophisticated CTMs which resolve the chemical reactions of an individual or lumped groups of species, concentration anomalies due to chemical reactions, C chem , are solved in an explicit first-order fashion involving a net chemical tendency, with a unit of parts per billion per hour (ppb h −1 ).Such a chemical tendency (R NO x in Eq. 2b) is parameterized offline as functions of NO x concentrations and solar zenith angles, θ , which is explained in Sect.2.1.The final term, C mix,p,t , denotes the concentration exchange between a given air parcel and its volumetric neighborhood (p ngb ), which is explained in Sect.2.3.
Following these steps, we obtain the modeled NO x mixing ratio for every trajectory released between the surface and 2 km, based on NO x curves described in Sect.2.1.To compare against TROPOMI tropospheric NO 2 columns, we account for the fraction of NO x that is present as NO 2 (Sect.2.2) and properly weight the modeled NO 2 from different altitudes, according to the pressure weighting function and averaging kernel profiles, following Wu et al. (2018).Such an approach in applying averaging kernel (Fig. 1) to the modeled profiles is equivalent to a more commonly used approach, which re-calculated the retrieved tNO 2 , as seen from the CTM, by re-calculating the air mass fraction based https://doi.org/10.(2022).In addition, we evaluate the modeled meteorology and chemistry using a separate set of STILT-NO x simulations with true NO x emissions from the EPA for three US power plants (Sect.4.1).
2.1 NO x net chemical tendency, R NO x , and uncertainty Inspired by the theoretical non-linear curves of NO x lifetimes as functions of NO 2 vertical column density and volatile organic compound reactivity (VOC R ) and based on a box model in Laughner and Cohen (2019), we extract similar non-linear parameterizations using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem v4.0.2;Grell et al., 2005).Focusing primarily on polluted environments, we carried out WRF-Chem simulations for three mid-latitude cities and extracted model outputs from a 2 • × 2 • region centered around each city.Three cities, namely Los Angeles in the USA, Shanghai in China, and Madrid in Spain, represent typical megacities in North America, Asia, and Europe.Their varied climatic conditions and sectoral emissions of NO x , VOC, and GHGs provide a holistic view of the variability in the NO x chemical tendency.While our analyses extended to power plants and cities beyond these three training sites when compared to TROPOMI data (Sect.4), it helps assess the broader applicability of our chemical parameterizations.
Appendix A describes our specific WRF-Chem settings used to generate lookup tables of NO x chemical loss tendencies, which we will refer to as NO x curves (Fig. 3).Of the WRF-Chem settings, the chosen chemical mechanism (Regional Acid Deposition Model or RADM2; Stockwell et al., 1990) is the most relevant to the accuracy of these NO x curves.Despite uncertainties in these WRF-Chem simulations, what matters the most for reproducing the NO x tendency is how NO x varies with, for example, the solar zenith angle (SZA) and ozone, rather than the exact accuracy of NO x concentrations themselves (from WRF-Chem).Thus, non-chemical components (prior emissions, boundary conditions, and physical processes) in this specific WRF-Chem configuration do not necessarily need to be perfect or optimized against observations.We clarify that WRF-Chem simulations had been performed to facilitate the parameterization of the NO x tendency within STILT-NO x but are not required when running STILT-NO x .
By leveraging WRF-Chem's chemical diagnostic capability, we derive the net chemical tendency of NO x within each hour (R NO x , ppb h −1 ) for every model grid within the lower 12 vertical levels (x, y, z).R NO x is calculated specifically from the cumulative changes in NO and NO 2 concentrations, solely due to chemical reactions (i.e., chem_no2 and chem_no in WRF-Chem registry), following Eq.( 2): where the model hour h denotes the start time of each hour interval in the WRF-Chem outputs, and z denotes the index of model vertical levels (i.e., from 1 to 12).h h 0 C NO x describes the cumulative net changes to the NO x concentration, given the chemical reactions from the initial model hour h 0 .
WRF-Chem pixel-specific hourly NO x rate changes, R NO x , are then grouped by both SZA (θ ) bins, with a spacing of 2 • , and C NO x bins, with equal spacing, in log10 scale (Fig. 3a).θ is chosen, given the close relation to solar radiation under clear-sky conditions, and controls the photolysis frequency of ozone and OH production (Rohrer and Berresheim, 2006) when the ozone and water vapor abundance remain unchanged.Because the intention in using STILT-NO x is to inform the relationship between emission sources and satellite NO 2 columns, which are almost always filtered to remove cloudy scenes (i.e., quality assurance of ≥ 0.7), the choice of θ without considering cloud coverage is reasonable.Specifically, these net chemical changes explicitly contain all NO x -relevant reactions within the WRF-Chem and RADM2 scheme, such as the recycling of NO x from oxidized odd-nitrogen species like peroxyacetyl nitrate.
The above grouping procedure of R NO x is based on a finite number of bins of C NO x , and θ unavoidably reduces the variability in the R NO x that were directly derived from WRF-Chem.To assess the extent to which the R NO x variability can be explained by the selected binning feature variables, we performed a sensitivity test to quantify the deviation of bin-averaged R NO x from the initial R NO x .Generally, the R NO x variability is better preserved over polluted regimes with a higher-NO x level > 1 ppb than over low-NO x regimes (Fig. S2a and b in the Supplement).Choosing C NO x alone better explains the R NO x variability than choosing SZA or air temperature alone.Including additional variables (e.g., air temperature, NO 2 : NO x ratio, and VOC R ) on top of our default choice of SZA and C NO x marginally improves the prediction of R NO x , except for the inclusion of ozone.However, estimating ozone remains a challenging problem; thereby, ozone is not included as a feature variable in this study.
As a net result, R NO x is mostly negative during the day, meaning that NO x is removed from the system.R NO x is large, with small spread at low θ of ≤ 20 • and gradually decreases during the day.R NO x becomes positive as it approaches the nighttime hours (Fig. S2c), and its vari- ], with a fractional uncertainty of over 100 % (blue error bars in Fig. 3a) when considering the transition to nighttime chemistry.When focusing on the daytime portion with θ < 70 • and C NO x ≥ 1 ppb, the spread in R NO x among the WRF-Chem urban pixels ranges from 12.2 % to 67.9 %, according to varied θ and C NO x (red to yellow error bars in Fig. 3a), with an average uncertainty of 41.2 %.When focusing on the nighttime portion with θ ≥ 70 • and C NO x ≥ 1 ppb, the spread in R NO x spans from 27.9 % to over 100 %, with an average uncertainty of 96.3 % that is largely skewed by the high uncertainty around the dusk hours.Last, the average daytime uncertainty in the NO x tendency at medium to high NO x concentrations (i.e., 41.2 %) will be propagated into chemical uncertainties in tNO 2 for cases of power plants and urban areas, which is further described in Sect.3.
Given the further fluctuation in R NO x with C NO x , we define a net loss timescale (h) as ts NO x = −C NO x /R NO x and distinguish it from the conventional chemical lifetime that only accounts for chemical losses.For reference, a positive (or negative) timescale corresponds to a net loss (or production) of NO x (Fig. 3b).The contribution from NO x production is minor during noon hours.The non-linear dependence of ts NO x with C NO x is largely driven by several NO x loss pathways (predominately by the loss processes of NO 2 + OH and the formation of alkyl nitrates during the daytime and by the NO 3 chemistry and heterogeneous chemistry at nighttime; Fig. S2).Here, we do not differentiate between the NO x curves by VOC R , despite its critical role in determining the turning point when NO x is mainly lost to either nitric acid or alkyl nitrates (Laughner and Cohen, 2019).We instead perform a sensitivity study of the impact on NO x curves for three VOC R intervals in Sect.5.3.Note that these NO x curves should be considered to be a first-order approximation and can certainly be improved upon to evaluate more complex parameterization (Sect.5.3).When it comes to calculating chemical changes within STILT-NO x per air parcel per timestamp (i.e., C chem,p,t in Eq. 1), such a loss timescale is looked up according to parcel-specific θ and C NO x to enable the non-linearity core (Fig. 2; bottom panel).

NO 2 : NO x ratio
As only the vertical column density of NO 2 is retrieved, the fraction of NO x present as NO 2 as TROPOMI passed over is an important component of our analysis.Prior studies estimated such ratios using a constant value (e.g., 0.75) at noon hours across seasons, with a 10 % uncertainty (Beirle et al., 2011(Beirle et al., , 2019;;Goldberg et al., 2022), monthly mean climatology of ozone from reanalysis (Beirle et al., 2021), and CTMs.NO x is primarily emitted as NO but converted to NO 2 via the reaction with ozone.During the daytime, NO 2 is photolyzed back to NO with a photolysis frequency, J NO 2 .Thus, the NO 2 : NO x ratio scales with the ratio of ozone and J NO 2 (Eq.3a).
Considering the close coupling between NO 2 and O 3 , their sum O x in Eq. ( 3b) is a key indicator of the atmospheric oxidant capability for understanding the urban air chemistry (Clapp and Jenkin, 2001;Fujita et al., 2016) and informing chemical dynamics (e.g., during the COVID-19 pandemic; Parker et al., 2020;Lee et al., 2020).O x levels within the PBL can be regarded as a NO x -independent component related to regional ozone inflow plus a NO x -dependent component that varies non-linearly with local NO x and VOC R conditions (Clapp and Jenkin, 2001;Jenkin, 2004) For simplification, we prescribed a typical O x level of 50 ppb in the first version of STILT-NO x and calculated the NO 2 : NO x ratio via Eq.( 3), assuming a steady state.
where J NO 2 relies on θ for daytime, and the reaction rate coefficient of NO with O 3 (k NO+O 3 ) is a function of the air temperature T A and pressure P (Fig. 2; bottom panel).The inclusion of O x in calculating the NO 2 : NO x ratio is to avoid a non-physical infinite conversion of NO to NO 2 at high-emitting sources, following the titration of the ambient ozone.Sensitivity tests were performed to reveal how biases in the prescribed O x level may modify the modeled tNO 2 (Sect.3).Typical NO 2 : NO x ratios over the examined midlatitude targets across seasons are summarized in Sect.5.2.In the future, satellite observations of tropospheric ozone could be used to add the additional complexity of variable O x .

Inter-parcel mixing
Eulerian chemical models often suffer from mixing or numerical diffusion that is too strong within their model grid, while Lagrangian models (equivalent to those possessing extremely high spatial resolution) may lack any mixing between air parcels that are normally assumed to be independent of one another (Lin et al., 2013;Brunner, 2012).Such a lack of mixing has a negligible impact on the passive tracers, as mixing alters only the spatial distribution of concentration among air parcels but not the resultant concentration averaged across parcels at the receptor.However, nonlinear processes alter both the spatial distribution of parcelspecific concentrations and the average resultant concentration.As a result, the calculation of the total NO x tendency will be sensitive to how inter-parcel mixing is parameterized.Common ways to realize turbulence mixing are through (1) stochastic processes followed by the exchanging or averaging properties of air parcels found within a certain mixing length (e.g., STILT-Chem; Wen et al., 2012), (2) implemented deformation-driven and instability-driven schemes that rely on atmospheric stability and wind shear or stress characteristics (e.g., CLaMS; McKenna et al., 2002;Konopka et al., 2019), and (3) diffusion approaches that require the vertical gradient of concentrations (e.g., CiTTyCAT and ELMO-2; Pugh et al., 2012;Strong et al., 2010).
Here we follow the STILT-Chem approach to enable a process of exchanging concentrations per timestamp among the air parcels in close proximity to each other ( C mix term back in Eq. 1), which smooth the horizontal gradient of concentrations among those air parcels.Specifically, at the timestamp of t, the concentration for a given air parcel p is updated, based on the concentration gradient between p and its neighborhood according to a mixing timescale (τ mix ) within a grid volume, with a mixing length scale of a horizontal area and the mixed layer height for the height as follows: where exp(− t τ mix ) implies the degree of horizontal mixing, and C(t) represents the average concentration among air parcels within the mixing volume.The update of C p,t from C p,t responds to C mix in Eq. (1).A relatively fast mixing timescale of 3 h and a horizontal mixing length of 1 km is used for testing the mixing impact on modeling tNO 2 .Although we neglect the mixing in the free troposphere and the mixing between the mixed layer and the free troposphere in this first model version, we tested a spectrum of the horizontal mixing scales and include possible future improvements (Sect.5.3.2).
3 Model uncertainty in tNO 2 due to wind and chemistry As atmospheric transport and chemical transformation are the two main components in any CTMs, we assess how uncertainties tied to the modeled wind field, NO x loss timescale, and NO 2 : NO x ratio may contribute to uncertainties in tNO 2 (in ppb).
σ 2 sim = σ 2 trans + σ 2 ts + σ 2 nn . (5) Here we briefly describe how various tNO 2 uncertainties were approximated, based on our understanding of errors in respective model parameters or inputs (i.e., wind error, NO x chemical tendency, or O x levels).To approximate the tNO 2 uncertainties due to transport errors, we followed previous approaches to first assess the GFS-and HRRRmodeled wind profiles against radiosonde; calculate respective error statistics including wind error, correlation time, and length scales; and, last, propagate wind error statistics into errors in column concentrations.Mathematically, σ 2 trans in Eq. ( 5) is derived from the difference in the variance of STILT-NO x air-parcel-specific NO 2 concentrations between the original simulation and a second simulation with wind error (Lin and Gerbig, 2005;Wu et al., 2018).The derivations of modeled wind errors and contributions to tNO 2 errors are elaborated in Appendix B. To evaluate the impact due to errors associated with chemical parameters, we perturbed the NO x curves or the O x level according to 20 perturbing factors.Perturbed curves or parameters are used to generate 20 new sets of tNO 2 fields, of which their respective standard deviation among perturbations serves as the chemical uncertainty (ppb) due to NO x net loss timescale and NO 2 : NO x ratio (σ ts and σ nn in Eq. 5).These 20 perturbing factors were randomly selected from a normal distribution N (µ = 1; σ param ).Here we tested out σ param of 40 % for NO x loss timescales, according to uncertainties in the chemical tendency (Fig. 3) and a σ param of 40 % for the O x level (Eqs.3).Due to heavy computational expenses in conducting such wind and chemical perturbation analyses for all overpasses and locations, we only ran error analyses for a total of six overpasses over a power plant and a city.To cover the seasonal changes in the NO 2 signals and their uncertainties, overpasses in varied seasons are examined for the New Madrid (USA) power plant on 8 February, 15 June, and 8 December 2020 and Phoenix (USA) on 7 February, 27 May, and 23 December 2020.Two winter cases with relatively large signals are shown in Fig. 4a.Considering the nonlinearity between the chemical tendency and NO x concentration, sounding-specific uncertainties for all six cases are presented against modeled tNO 2 in Fig. 4b.When conducting those perturbations, other model parameters like the meteorological field and emissions remain unchanged.
As a result, the average percent error in u or v wind speed in the PBL is roughly 22 % for the New Madrid case (Fig. S3a in the Supplement), which contributes to 50 % uncertainty in tNO 2 at the sounding level (third column in Fig. 4a).Higher transport errors may occur more frequently if an intensive point source is in the area or over pixels on the border of the NO 2 plumes, with moderate signals of about 0.2 to 0.5 ppb (e.g., dots in Fig. 4b).This is because a small deviation in the modeled wind vectors causes air parcels to either hit or miss the intensive source.The transport uncertainty appears to first correlate positively with the signals and then decreases when signals are sufficiently high, e.g., > 0.7 ppb.Such a decline may be associated with hypernear-field soundings, where the deviation in wind fields may not alter modeled signals, as modeled air parcels will always experience a large influence from the emission source (dotted-dashed lines in Fig. 4b).Compared to power plants, cities may be associated with a more homogeneous transport uncertainty if emissions are more homogeneous and better mixed in the PBL.
Given a roughly 40 % uncertainty in the O x levels or NO x chemical tendency, chemical uncertainties (in ppb) remain small when modeled signals are compared (Fig. 4a).Uncertainties from chemical tendency first increase with tNO 2 signals and gradually plateau for tNO 2 beyond 0.7 ppb, likely because NO x is lost slowly when the NO x concentration stays high, and further perturbations in the chemical tendency are less impactful.In contrast, the uncertainty from O x levels appears to consistently scale against the signals, i.e., more apparent for soundings adjacent to the power plant, with reasons explained as follows.When the certain perturbed O x level approaches zero, the amount of NO that can be oxidized as NO 2 becomes minimal (second column in Fig. 4a).This case mimics the scenario where O 3 can be titrated in proximity to an intense release of NO before the ozone-depleted plume air is mixed with the ambient ozonerich air.Nevertheless, considering the entire sample, the per-cent of errors due to chemical parameters remains relatively low (13 % to 18 % for six cases in Fig. 4b).
Whether chemical or meteorological errors dominate the total model errors fundamentally depends on tropospheric NO 2 signals which further rely on factors like atmospheric stability with wind errors, chemical tendency, and emission distribution.Such a dependence leads to a spatial gradient and seasonal variations in estimated errors, as seen from the above examples.In brief, our limited perturbation experiments suggest that transport uncertainties dominate the total modeled uncertainties, except for a few hyper-near-field soundings, where chemical uncertainties become more substantial.
For future emission optimizations, uncertainties in the emissions, retrieval, and background should also be included.Despite the significant advance in the TROPOMI NO 2 retrieval version of v2 compared to v1 (Van Geffen et al., 2022), v2 retrieval is associated with a fractional uncertainty (normalized over retrieved tNO 2 ) of ∼ 30 % to 50 % for most soundings within the plume.Uncertainties in the NO x emissions between inventories can serve as the prior uncertainty, which is substantial at the pixel level (Figs.S4 and S5 in the Supplement).Besides the regional wind assessment, a novel plume rotation algorithm based on model-data NO 2 plumes is proposed in Sect.5.2 to quantify near-field wind biases.

Model-data evaluations and comparisons
The tropospheric NO 2 mixing ratio at a given sounding location is influenced by the regional inflow, atmospheric advection and turbulence mixing, underlying emission characteristics, and chemical changes en route to the sounding (Fig. 2).Modeled tropospheric NO 2 mixing ratios using a variety of model configurations are compared against retrieved values from TROPOMI.Such model-data comparisons help evaluate the overall model performance and the roles of individual physical and chemical processes with a naming convention of MET _ EMISS _ GAS _ PROC , which is explained as follows: -MET represent the meteorological fields of either 0.25 • GFS or 3 km HRRR that are used to drive STILT air parcels.
-EMISS represent two prior NO x emission inventories.
EDGARv6.1 is presented with monthly mean emissions, and the latest year available ( 2018) is the primary one for simulating all cases.Hourly mean emissions from EPA reports are only used to evaluate modeled chemistry and meteorology for several US power plants (Sect.4.1).
-GAS represent the simulated species, with a default string of TNO2  background subtracted is shown in multi-track comparisons (Fig. 6; Sect.4.1).
-PROC denotes the physical and chemical processes considered per run.Two main configurations include (1) DEF runs, with both inter-parcel mixing and chemical parameterization included, and (2) NOCHEM runs, with mixing but without considering the NO x chemical tendency.The NOCHEM runs do account for the NO 2 : NO x conversion but as a constant ratio of 0.74, according to EMG-based studies.
Only model-data comparisons using TROPOMI v2 are shown.As the satellite averaging kernel (AK) and observed tNO 2 differ substantially between v1 and v2, modeled concentrations are weighted by the version-specific AKs to yield apples-to-apples comparisons.Changes in AKs and the retrieved and modeled values between versions are summarized in Fig. S6 in the Supplement.

Model validation: US power plants
The New Madrid power plant along the Mississippi River is a 1300 MW coal-fired power station (GEM, 2021), which ranks first in 2020 among the US power plants regarding NO x emissions provided by EPA.The Thomas Hill and Martin Lake power plants ranked second and third in 2020, respectively.We also report results for an overpass over the Intermountain power plant in Utah, where the surrounding complex terrain is difficult to model properly.Let us start with two examples to illustrate plumes modeled by different model configurations (Sect.4.1.1)and then present modeldata comparisons over dozens of overpasses of the three power plants (Sect.4.1.2).

Single-track demonstration
The correction in NO x emissions greatly improves the model-data alignment.For example, EDGAR-based simulations substantially underestimate or overestimate the tropospheric columns (Fig. 5a1 and c1), as EDGAR emissions are almost one-third or twice of the reported hourly EPA emissions for the New Madrid or Intermountain power plants, respectively (Fig. S7 in the Supplement).EPA-based simulations align better with retrieved values from TROPOMI v2, despite deviations over the far-field region (Fig. 5a2 vs. Fig.5a6).Such improvements in the model-data alignment are also inferred from the linear regression slopes reported in Fig. 5b and d.Not accounting for NO x chemistry or lifetime elevates NO 2 concentrations both within the plume and over the background, even if EPA emissions are assumed to be correct (Fig. 5a3 and a5).The inter-parcel mixing with a 3 h mixing timescale redistributes the NO x concentrations among adjacent air parcels but leads to a minimal impact of ≤ 5 % of the modeled tNO 2 at individual column receptors (thereby not shown).
The choice of meteorological fields with different spatial resolutions insignificantly affects the modeled signals, except for cases surrounded by complex topography and flows.For example, the HRRR-based plumes resemble the GFSbased plumes for the New Madrid power plant (Fig. 5a2 vs. Fig.5a4), which is also revealed by their similar wind error statistics (Fig. S3a).However, the complex terrain and stable PBL during wintertime complicate and usually worsen the model performance as a result of increased meteorological errors.On 14 February 2020, EPA-based plumes over the Intermountain power plant in Utah using two meteoro-  logical fields differ substantially from each other, and they both deviate from the observed plume regarding the plume shape.GFS delineates the mean wind direction within its coarser 0.25 • grid box, while 3 km HRRR offers more spatial variability in wind directions (Fig. 5c2 vs. Fig.5c4).Yet, precisely capturing the curvature in the wind vector is extremely challenging, even when using 3 km meteorological fields (Fig. 5c6) and is more difficult when using Gaussian plume approaches that rely on only one effective wind vector.Such a model-data mismatch in plume shapes can further help to quantify the wind biases, which are discussed in Sect.5.2.1.Besides modeling challenges, the retrieval uncertainty cannot be neglected, as it ranges from 22 % to 31 % of the retrieved signal for the New Madrid case (Fig. 5a7) and up to 100 % for the Intermountain case (Fig. 5c7) at the sounding level.When using retrieved data and the averaging kernel from TROPOMI v1, the regression slope becomes 1.18 and 1.25 (Fig. S8 in the Supplement), indicating that modeled plumes using both meteorological fields are larger than observed plumes.While using TROPOMI v2, the respective slopes are 0.88 and 1.2 (Fig. 5b and d).This again emphasizes the substantial uncertainty in the retrieved signals, which is large enough to even alter the conclusion of whether emissions are underestimated or overestimated for a single overpass, and the need for analyzing multiple overpasses for evaluations (Sect.4.1.2).

Multi-track evaluation
To provide a broad impression of the model performance, we expand the model-data comparisons to a total of 50 TROPOMI overpasses across all seasons in 2020, including 34 overpasses for the New Madrid power plant and 9 and 7 summertime overpasses for the Thomas Hill and Martin Lake power plants, respectively.These overpasses are selected based on their relatively intense signals compared to the surroundings.Model-data comparisons for all overpasses are shown in the maps in Figs.S9-S12 in the Supplement, with the linear regression slopes reported and summarized in Fig. 6 and Table S1 in the Supplement.
Cases with slopes deviating significantly from 1 are usually associated with substantial near-field wind directional biases.For instance, modeled wind vectors on 11 March, 28 April, and 9 September 2020 have directional biases of > 30 • (Figs.S9b and S10b), which explain the respective abnormal linear regression slopes of −1.75, 0.49, and 3.2 (Fig. 6).EDGAR-based simulations are biased too high or too low by a factor of 2 or more when compared to observed values from TROPOMI v2.3 (green dots in Fig. 6) that are driven by the biases in the EDGAR emissions (Fig. S7).The NOCHEM simulations without accounting for NO x losses overestimate tNO 2 by a factor of 2 across all seasons and three power plants, regardless of the meteorological or emission fields adopted (empty circles in Fig. 6).Upgrading meteorological fields to a higher resolution seems to contribute less to the improvement of model-data agreements than correcting the emissions or chemistry.In the end, modeled values with NO x chemistry and correct EPA emissions using either GFS or HRRR yield the best agreement with retrieved values from TROPOMI v2 (orange dots and lines in Fig. 6).When aggregating the results of all overpasses, simulations using the best knowledge of the emissions, the simplified chemistry, two different meteorological fields, and inter-parcel mixing are biased slightly high (regression slope up to 1.2; Table S1).RMSE values between the observed and modeled tNO 2 with NO x chemistry-enabled range from 0.11 to 0.15 ppb (Table S1), which is comparable to the random uncertainty in the NO 2 retrieval of 0.09 ppb.
The statistics discussed above compared the total tropospheric NO 2 columns from the model and TROPOMI for soundings around each power plant.It is noticeable that modeled tNO 2 uncontaminated by emissions (i.e., background tNO 2 ) are sometimes slightly lower than observed background tNO 2 (Figs.S9a and S10a), possibly because higher chemical uncertainties are related to low-NO x regimes, and non-anthropogenic NO x sources from soil and lightning are excluded from current simulations but can play a significant role on tNO 2 over rural regions (Goldberg et al., 2022;Shah et al., 2023).In particular, column contributions from lightning NO x emissions aloft may be amplified, since the TROPOMI NO 2 retrieval has a higher sensitivity towards the free troposphere than PBL.Since our current model setup only accounts for anthropogenic NO x sources below 2 km, we conducted an additional test by subtracting the background tNO 2 from total tNO 2 to arrive at observed anthropogenic enhancements (the second paragraph in Sect.2), assuming that the soundings within or outside the plumes have equal contributions from the nearby non-anthropogenic NO x sources.After subtracting the tNO 2 background, the model-data comparison based on observed tNO 2 enhancements does not change dramatically (e.g., orange crosses vs. orange solid dots in Fig. 6).
In summary, using more accurate NO x emissions with chemistry considerably improves the model-data comparison.Increasing the spatial resolution of meteorological fields has less impact on cases with relatively flat terrain.Larger model-data mismatches generally are associated with larger wind directional biases.Modeled values in tNO 2 may be biased to be slightly low in summer months from April to June and high in winter months from November to February, with minimal annual biases, assuming that the EPA emissions and observed tNO 2 are unbiased.

Model application: two cities
We now move to city cases that include an industrial Chinese city, Baotou, and one of the fastest growing megacities in the US, Phoenix.As CO 2 and NO x are commonly coemitted into the atmosphere, observed XCO 2 enhancements derived from the Orbiting Carbon Observatory 3 (OCO-3) Snapshot Area Mapping (SAM) mode are displayed with observed tNO 2 (Fig. 7).Background XCO 2 is defined as the mean values over the background region that is determined by NO 2 plumes (modified from the background approach in Wu et al., 2018).Both cities possess relatively richer OCO-3 SAM observations co-located with TROPOMI data.Since no true NO x emissions are available for cities, EDGAR is utilized as the prior emission inventory for simulating tNO 2 and optimizing NO x emissions.
We simulated 18 and 12 TROPOMI overpasses, respectively, for Baotou and Phoenix (Figs.S14 and S15 in the Supplement) and first presented one example per city in Fig. 7. Baotou is surrounded by four point sources, as suggested by EDGARv6, but one large source in the city cen-ter, as informed by both the observed tNO 2 and XCO 2 enhancements on 3 October 2020 (Fig. 7a).Such a mismatch is confirmed by the comparison of normalized tNO 2 across all 18 TROPOMI overpasses with various wind speeds and directions (Fig. S14b), suggesting that EDGAR very likely misallocated anthropogenic NO x sources.Similarly, the largest emission source to the east of the city center of Phoenix, according to EDGAR, seems suspicious and may again be misplaced when more overpasses are simulated (Fig. S15b).The observed plume is concentrated near the city center, compared to the HRRR-derived plume that dispersed farther away from the city center on 23 December 2020 (Fig. 7b).Such a spatial offset of the tNO 2 plumes is likely due to an overestimation in the modeled wind speed, https://doi.org/10.5194/gmd-16-6161-2023 Geosci.Model Dev., 16, 6161-6185, 2023 which pushes the plumes to the southern edge while diluting tNO 2 values over the urban core.When more overpasses are examined, the model captures the seasonal variation in tNO 2 well (i.e., higher or lower values in winter or summer months; Figs.S14a and S15a).Other than emission biases that affect all cases, a few overpasses stand out for Baotou, with poorer agreements with TROPOMI likely owing to (1) clear biases in wind direction on 31 May, 9 August, 15 December 2020, and19 February 2021; (2) a likely overestimation in STILT footprint that may trigger several effects on 29 September, 29 March 2020, and 16 October 2021 (Fig. S14a).Although STILT can characterize the sub-grid-cell turbulent mixing by its stochastic nature, the 0.25 • GFS may be insufficient to resolve the complex terrain and air flows, contributing to biases in wind directions and planetary boundary layer heights (PBLHs) over mountainous locations (Lin et al., 2017) such as over Baotou.Deviations in the PBLH may cause a cascade of effects, such as deciding up to what height the emissions are diluted, whether such height is above or below the emission or plume height, and chemical changes along the way.Such effects may be magnified under low-mixing and low-wind conditions where the model particularly struggles with the accuracy of PBLH.Without much mixing between the plume and background air, the prescribed available O x level may be overestimated adjacent to intensive NO x sources.Overestimation in the NO 2 concentration may further be amplified when considering the dependence of NO x rate changes on its concentration.Hence, concentrations of chemically reactive species under low-mixing scenarios are extremely challenging to model properly with an extreme during the nighttime.

Discussion
Our ultimate goal is to explore what can be learned about the emission characteristics from anthropogenic hotspots with the joint use of space-based NO 2 , CO, and CO 2 plumes.As an intermediate step, this study is informed by previous efforts to extract and constrain urban CO 2 emissions from satellites using a Lagrangian framework (Wu et al., 2018;Roten et al., 2022) and extends it to the interpretation of tropospheric NO 2 satellite data.To diagnose NO x emissions from NO 2 column signals, we need to effectively account for how NO x evolves in air parcels from its initial source to locations sampled by TROPOMI, making the Lagrangian perspective an ideal candidate.Now we discuss when and how such a framework can be of most use and also the possible future improvements.

Model advantages and flexibility
Our framework accounts for atmospheric transport and chemical transformation in a more rigorous way than typical statistical approaches such as the EMG method and in a more efficient way than full-chemistry models that explicitly resolve individual chemical reactions.
Another advantage of the STILT-NO x design is that each of the three main components (trajectory calculations representing air transport, chemical production or loss of the target species, and optimization of emission) are independent and each can reuse the previously saved output from the others.For example, if one wanted to test how sensitive model concentrations were to the chosen chemical scheme, then the simulations of atmospheric transport can be reused via the storage of trajectory-based modeling, thereby reducing the computational cost.Our prototype demonstrates a global solution of the NO x chemical tendency parameterized by the one set of NO x curves in Fig. 3.Although this simplification may be thought of as a limitation, one can easily replace those default curves with alternatives that are tailored toward a specific region or regime of interest.Such flexibility can inform us of the influence on modeled columns from NO x curves derived from different chemical mechanisms.Similarly, one can investigate the sole meteorological influence by diversifying the meteorological and mixing parameters.Moreover, because air parcels in LPDMs are not tied to a certain atmospheric tracer, we can estimate the concentrations of various species along model trajectories.It allows us to constrain emissions for multiple atmospheric constituents in a consistent framework, which may shed light on tracertracer analyses (Sect.5.2).
The Lagrangian modeling approach has its inherent benefits.First, the generation and recording of trajectories can easily reveal the source regions that are only relevant to a specific satellite sounding and the sub-city-scale variations in emission characteristics (Wu et al., 2022).In addition to storing latitudinal and longitudinal coordinates and extrapolated meteorological quantities along every trajectory at each timestamp, STILT-NO x outputs and records NO x concentration changes due to every process, including emission, net chemical changes, and inter-parcel mixing at minute scales.Those trajectory-level concentration changes are further driven by several model configurations listed in Sect.4, which facilitates model debugging and comprehends modeled results.See Sect.5.2 for one of the applications.Second, the spatial resolution of concentration calculations is not bounded by the rigid boundary of model grid cells, which is particularly important for dealing with non-linear processes for chemically active species.As demonstrated in several studies (e.g., Valin et al., 2011), the grid-averaged concentration may undergo excessive mixing in Eulerian models, and the concentration-driven chemical tendency varies with the adopted spatial resolution.While the Lagrangian perspective solves for concentration changes at extremely high spatiotemporal resolutions, inter-parcel mixing schemes can be implemented to smooth the concentration gradients, whereas it may be challenging to recover the sub-grid-cell concentration gradients in the Eulerian framework unless also increasing the spatial resolution.
More broadly, the proposed simplified parameterization of the non-linear NO x tendency or NO x curves is not limited to the STILT framework and can potentially be incorporated into other Lagrangian modeling frameworks or even Eulerian frameworks with a fine spatial resolution to resolve the local variability in chemistry.

Implications for constraining urban CO 2 emission and emission ratios
The knowledge learned from analyzing NO 2 plumes can be transferrable to constraining bottom-up CO 2 emissions.Two main sources of biases influencing the urban CO 2 emission constraint include biases in wind direction and emission locations.Model-data mismatches in NO 2 columns have shown great value in easily identifying the biases with emission locations, even without deploying atmospheric inverse analyses (Sect.4.2), especially for point sources in urban areas, when plumes from multiple sources overlap less with one another.Additionally, diagnosing the NO x emissions can facilitate CO 2 emission estimates in two ways.It can reveal systematic biases in near-field wind directions (Sect.5.2.1) and quantify the NO x : CO 2 emission ratios for point and/or area sources to assist in sector-based attribution (Sect.5.2.2).

Quantifying wind bias
In addition to leveraging limited radiosonde measurements, the obtained modeled and retrieved NO 2 plumes can be used to quantify wind biases to improve the accuracy of top-down CO 2 emission constraints, whether or not conventional atmospheric inversions are employed.To do so, we conducted a second wind assessment involving a plume rotation algorithm.In brief, a NO 2 plume from either model or retrieval is rotated clockwise (α from −180 to −5 • , with a spacing of 5 • ) or counter-clockwise (from 5 to 180 • ) around the emission source and then resampled onto the original TROPOMI pixels (Fig. S16 in the Supplement).tNO 2 from an original and a rotated plume are multiplied to arrive at a cross-product of tNO 2 (in ppb 2 ), which is analogous to the concept of crosscorrelation.The original or rotated plume can be chosen from either the model or observations, and their normalized crossproduct can be expressed as a function of rotating angles (colors in Fig. 8a).More details on intermediate steps to calculate such a function are described in Appendix C. As a result, the width of the Gaussian-shaped curve of the cross-product (as measured by the σ parameter of a Gaussian fit) reflects the bias in the plume shape resulting from horizontal dispersion.A larger area under the Gaussian curve indicates a greater overlap between the initial plume and the rotated plume.More importantly, deviations in the central line of the Gaussian fit away from zero (as measured by the µ parameter) imply possible biases in the near-field wind direction for each TROPOMI overpass (Fig. 8b).Specifically, wind directional biases of both GFS and HRRR appear to be smaller from May to early September than in the remaining months (Fig. 8b).A few outliers stand out due to large wind biases on 11 March, 28 April, 20 September, 5 October, 16 October, and 16 November 2020.
By identifying those outliers with strong wind directional biases, one can consider either removing those cases or assigning a larger observational uncertainty when attempting to constrain emissions of NO x , CO, and CO 2 , assuming that their emissions are mostly co-located.Alternatively, we can use this rotating algorithm to create a model plume with minimized wind directional bias before being fed into atmospheric inversions or data assimilation systems (which usually deal with random uncertainties).A more sophisticated approach would be to optimize the emission and wind field simultaneously (Liu et al., 2017).More investigations may be needed to examine the degree of freedom of such a windemission optimization framework.

Quantifying emission ratios between NO x and GHGs
Our modeling development offers additional insights into the discrepancy between emission ratios at the sources and directly observed enhancement ratios between two species with different chemical lifetimes.The joint use of NO 2 and CO 2 has enabled the calculation of emission ratios by adopting a spatial constant NO x lifetime (MacDonald et al., 2022;Hakkarainen et al., 2023) and the constraint of CO 2 emissions using NO 2 plumes by adopting inventory-based emission ratios (Zheng et al., 2020;Zhang et al., 2023).However, inventory-based emission ratios might not be well constrained, and the impact of how NO x decays over time and space on observed ENO x : ECO 2 emission ratios has not been comprehensively assessed, which may impair the ability to accurately quantify such observed emission ratios (Kuhlmann et al., 2021).Thanks to the ability of our model to track NO x and NO 2 concentrations along trajectories with different model configurations, we can provide an assessment of the influence of atmospheric chemistry on estimating emission ratios.Specifically, the impact from NO x net losses from each satellite sounding(s) is specified as the ratio of modeled tropospheric NO x with chemistry over that without chemistry in the following: γ ts,s = NO x,CHEM,s /NO x,NOCHEM,s .Because NO x is simply treated as a passive tracer like CO 2 in the NOCHEM simulations, γ ts are naturally smaller than 1.Lower γ ts corresponds to faster NO x chemical frequency and more chemical losses en route to the sounding location, suggesting that NO 2 : CO 2 enhancement ratios derived directly from satellites need to be scaled up to render the ENO x : ECO 2 emission ratios at source locations.
We calculated γ ts for every sounding and present their distribution as histograms in Fig. 9a or as a function of the distance from the emission source (Fig. 9b).γ ts ranges from 0.24 to 0.61 for three power plants and from 0.42 https://doi.org/10.5194/gmd-16-6161-2023 Geosci.Model Dev., 16, 6161-6185, 2023 to 0.84 for three cities, where lower values correspond to summer months (green bars in Fig. 9a).That is to say, the directly observed NO 2 : CO 2 enhancement ratios may have to be scaled up by 1.2 to even 4 times across seasons to properly recover the NO x being lost en route from emission sources to the sounding locations.Not properly accounting for such an effect leads to an underestimation of the derived emission ratios from satellites.More importantly, discrepancies between enhancement ratios and emission ratios, reflected by γ ts , are not spatially uniform.γ ts gradually decline as soundings move away from the emission sources (Fig. 9b).Soundings located farther downwind of emission sources tend to undergo more chemical transformations, likely because NO x losses become more rapid as NO x concentrations become lower by atmospheric dispersion (triggering positive feedback).We clarify that only downwind soundings affected by major NO x emissions are included in Fig. 9b, and simulations with or without chemistry have included the effect of atmospheric dispersion as distance increases.Furthermore, how quickly γ ts declines with distance depends on the wind speed and heterogeneity in emissions.For example, the faster the wind may be, or the more isolated emissions there are, the steeper γ ts decline with distance.γ ts at the distance of 0 are much lower than 1 in summer, which suggests that the chemical transformation can affect the NO x inflow.We further observe slight differences in the distribution of γ ts for cities versus power plants.Histograms of both tropospheric NO x (Fig. S17 in the Supplement) and γ ts over cities are associated with a wider spread than power plants because cities contain a wider spectrum of emission types and intensities.
Last, enhancement ratios need to be adjusted considering the NO 2 : NO x ratio and differences in averaging kernels among two retrievals.The medians of our estimated NO x : NO 2 ratio over power plants and cities range from 1.33 to 1.66, which generally aligns with previous studies of around 1.32 (Beirle et al., 2011;Goldberg et al., 2022).Our estimates are lower in winter than in summer and can be as large as 2 or 3 for a few soundings experiencing intense NO x sources (Fig. 9c).

Limitations and room for improvement
The diversity of VOC emissions, the vertical profiles of emissions, and the extent of inter-parcel mixing may impact the modeled results.Perhaps one of the biggest limitations of the current NO x chemical representation lies in not directly accounting for VOCs, which may affect (a) the sweet spot on NO x curves, where two NO x loss pathways reach their maximum, and (b) the O x -based NO 2 : NO x ratios (Sect.5.3.1).Moreover, the influence of representations of the emission profile on modeled tNO 2 can be magnified when further when considering the TROPOMI NO 2 averaging kernel (Sect.5.3.2).Simulations of point sources like power plants may be more sensitive to these factors compared to simulations of areal sources.

The impact from VOC R
To investigate the impact of VOCs on NO x curves, we calculated the VOC reactivity against OH from existing WRF-Chem results, based on the following formula: Figure 9.A quantitative metric of the impact from NO x chemistry on tropospheric NO x and NO 2 columns.Ratios in tNO x between simulations with and without chemistry are calculated as γ ts,s = tNO x,CHEM,s /tNO x,NOCHEM,s , which is displayed as a histogram (a) and as a function of the distance of the satellite sounding from the site center (b).Soundings in summertime overpasses are colored in dark green, whereas brown is used for soundings in the dormant months.Soundings of all overpasses for all city and power plant cases are included in histograms.Only downwind soundings in the NO 2 plumes are included in the distance panel (b), with a smooth spline fitted per overpass to reveal the anti-correlation.The ratio between the modeled tropospheric NO x column versus the tropospheric NO 2 column is derived from each sounding to reveal the NO 2 : NO x ratio influence (c).As a reference, most previous studies adopted a constant NO x : NO 2 ratio (reciprocal of NO 2 : NO x ratio) of 1.32 and can reach 2 in a hyper-near-field area of a major NO x source.VOC R = i = 1 n k OH+VOC i [VOC i ] and generated separate sets of NO x curves for four respective VOC R intervals of [0.1, 1), [1, 3), [3, 10), and [10, 50) s −1 , with a coarse SZA bin spacing of 10 • .Curves become much noisier at night and in pristine environments with extremely low NO x (≤ 0.1 ppb), where WRF-Chem and RADM2 may be less suitable (thereby not shown in Fig. 10).
When considering lower SZAs (consistent with the TROPOMI overpass time of 13:00 local time), the general non-linear characteristic of these NO x curves holds as VOC R increases (Fig. 10).Higher VOC R relative to lower NO x concentration favors the oxidation of VOCs by OH and the associated minor loss pathway of NO + RO 2 to form alkyl nitrates with a minor branching ratio over the competing major https://doi.org/10.5194/gmd-16-6161-2023 Geosci.Model Dev., 16, 6161-6185, 2023 NO x loss pathway of NO 2 + OH (Fig. 1).With rising VOC R , the NO x chemical tendency becomes more positive (P -L; Fig. S18a in the Supplement), and the net loss timescale elongates (e.g., ts_min from 2 to 4 h in Fig. 10).Moreover, NO x is required to reach a higher level to compete with the reactions involving VOCs, evident by the shift in the trough of the NO x curves (e.g., NOx_min from 1.4 to 3.7 ppb in Fig. 10).
To put it in context, the NO x curves shown in Fig. 3 represent typical patterns, as long as VOC R remains below 10 s −1 .VOC R may also affect the x level and the NO 2 : NO x ratio.The prescribed O x level of 50 ppb (Sect.2.2) overlooks the non-linear O x variability related to VOC R (Murphy et al., 2007;Li et al., 2022).In NO x -limited scenarios, OH favors the oxidation of VOCs, and local-scale O x is predominately produced by NO + RO 2 or HO 2 , suggesting higher O x levels with increased NO x concentrations.The omission of NO + RO 2 or HO 2 in Eqs.(3) could lead to an underestimation of the NO 2 : NO x ratio, which likely explains the modeled tNO 2 being consistently lower than observations over background regions.Conversely, under NO x -saturated conditions, the consumption of OH by NO x may limit the VOC oxidation and O x production, leading to a decline in O x level as the NO x concentration rises.Consequently, the NO 2 : NO x ratio might be overestimated when the true O x levels fall below 50 ppb (particularly under stagnant atmospheric mixing) or underestimated due to the absence of NO + RO 2 reactions.Nevertheless, our predetermined O x level of 50 ppb acts as a first-order limit to prevent unrealistic conversion from NO to NO 2 at extremely high NO x levels when O 3 is being titrated.
To address these limitations, one potential approach is to leverage formaldehyde concentrations retrieved from TROPOMI.Recent studies revisited the use of the formaldehyde : NO 2 ratios (i.e., FNR) from satellites as a means of inferring O 3 production rates (Goldberg et al., 2022;Souri et al., 2022).Our WRF-Chem simulations, which were used to parameterize the NO x chemical tendency, show that modeled formaldehyde generally increases with VOC R with varying slopes influenced by SZA and NO x concentrations (Fig. S18c), and O 3 concentrations scale non-linearly with FNRs with O 3 concentration, approaching a background value at a high FNR > 10 (Fig. S18d).Even though satellitebased FNRs may theoretically help probe the O 3 or O x concentration to better parameterize NO 2 : NO x ratios, Souri et al. (2022) stressed that retrieval errors, especially from formaldehyde (40 % to 90 % with ≤ 50 % over cities) and inherent chemical errors in the predictive power of FNRs, may hinder the broad application of space-based FNRs at the current stage.Nonetheless, sensitivity analyses in Sect. 3 indicate an overall chemical uncertainty in tNO 2 of about 10 % to 20 % with respect to NO 2 signals, even if the perturbed O x level is much lower than 50 ppb (Fig. 4).

Uncertainties in non-chemical processes
Besides the simplification of chemical reactions, modeled tNO 2 values can be subject to a few physical processes and parameters, including emission profiles, inter-parcel mixing scales, and dry deposition.
The underlying STILT v2 (Fasoli et al., 2018) accounted for a gradual growth of the mixed layer height over the hypernear-field area around emissions.Yet, by convolving the STILT footprint with NO x emissions, we assumed that emissions originate from the surface and are uniformly mixed over the mixed layer without considering the possible uneven distribution of emissions from different vertical levels.In reality, under stable atmospheric conditions, the stack heights or plume heights of emission sources can sometimes extend above the shallow PBL.Our current assumption may thus lead to an overestimation in modeled concentrations, and such biases can in turn affect the estimate of the NO x tendency.More importantly, changes in the vertical profile of emissions can lead to changes in concentration per model level, which affect the tropospheric columns, as the typical averaging kernel profile is far from uniform within the PBL.Recall that TROPOMI NO 2 AKs decrease rapidly towards the surface (Fig. 1).Hence, placing an emission plume at the surface or an elevated altitude (e.g., 400 m) can cause a discrepancy in modeled column concentrations.In addition, if the wind shear is strong over an intensive point source (likely the Intermountain example in Fig. 5c), assumptions about the injection height and vertical profile of emission plumes may affect the modeled plume shape and possibly deviate the estimated near-field wind bias, following Sect.5.2.1.Noticeably, Maier et al. (2022) investigated the influence of the inaccurate representation of emission profiles on the flask-like modeled concentrations by implementing a time-varying, sectorspecific emission profile into STILT.Such an impact on column concentrations may be minimized but requires future in-depth investigations, particularly over point sources.
Accounting for inter-parcel mixing was an important aspect when developing Lagrangian chemical models.Omitting inter-parcel mixing makes solving for non-linear processes (such as chemical NO x loss) problematic.On the contrary, Eulerian models suffer from excessive numerical diffusion.Mixing that is too strong smooths the spatial gradient of concentration and can lower the concentration within the fixed model grids, which may cause slight shifts in the NO x regimes.Valin et al. (2011) suggested that a spatial resolution of 4 to 12 km is sufficient to capture the non-linearity in the NO x loss rate.As for Lagrangian models, efforts can be made to enable the flux exchange between air parcels via deformations (Konopka et al., 2019;McKenna et al., 2002).In addition to the inter-parcel mixing within the mixed layer (ML), several other turbulent mixing processes require future investigation, including (1) horizontal mixing in the free troposphere (FT), (2) vertical mixing between the ML and FT, and (3) mixing between tracked air parcels with the un-tracked surrounding background.For example, Real et al. ( 2008) utilized a linear relaxation, with an exponential decay of the plume concentrations towards the background based on a timescale of 2 d to address the third mixing process.The second mixing process requires future modifications involving the determination of entrainment zones and mixing hyperparameters for such ML-FT exchange.
The original STILT model realized vertical mixing by diluting the surface emissions across the ML height (Lin et al., 2003), and we further enabled an exchange in pollutants' concentrations with prescribed mixing length scales and timescales representing typical horizontal mixing rates (Sect.2.3).As part of the final sensitivity tests, we simulated tNO 2 based on a spectrum of mixing hyperparameters for the New Madrid power plant.Uncertainties in the mixing parameters result in minimal uncertainties in the soundingspecific modeled tNO 2 values (Fig. S19 in the Supplement).For example, differences in modeled tNO 2 between the mixing and non-mixing simulations become larger as mixing becomes faster and for receptors or soundings located on the edge of the plume (i.e., only a small fraction of the trajectories encountered power plant emission in Fig. S20 in the Supplement).Uncertainties in the prescribed mixing hyperparameters contribute even less to the modeled values over urban areas (i.e., < 10 % for Phoenix cases), where emissions are generally better mixed than at power plants.In addition, such a mixing influence can vary with the spatial resolution of the emission inventory used in the simulations.
The dry deposition of NO 2 was not factored into this study, which could lead to an overestimation of modeled NO 2 .For future model implementations, it is possible to track the loss of NO 2 concentrations due to dry deposition by calculating the dry deposition velocities (e.g., Wesely, 1988) when air parcels descend close to the surface, e.g., 50 m above the surface (Wen et al., 2012).

Summary
In developing STILT-NO x , we aim to quantify anthropogenic NO x emission signals for power plants and cities using remote sensors with a novel Lagrangian chemical system that preserves the non-linear relationship between NO x concentrations and emissions.This development is motivated by the desire to reduce computational costs by replacing the conventional kinetics-based approach to solve for concentration changes with a simplified parameterization relying on as few variables as possible.Such a simplified parameterization can be improved and adopted by other Lagrangian models.This work expands the capability of (X-)STILT in tracing the origins of chemically reactive species to simulate their concentrations at satellite soundings (Fig. 1).Although uncertainties exist in modeling atmospheric transport, mixing, and chemical processes, this study covers the key NO x chemical mechanisms, various error sources, model validation, and the benefit of using NO x to constrain CO 2 emissions and tracertracer emission ratios.
To evaluate our modeling system, which consists of the HYSPLIT-STILT core and modules of column weighting, simplified chemistry, and error analyses (Fig. 1), we compared modeled tropospheric NO 2 columns using EPA-reported emissions against observed columns from TROPOMI over three power plants in the US (Fig. 6).The largest model-data discrepancies are found for overpasses with substantial wind directional biases.Across three power plants and seasons, the systematic bias informed by the model-data regression slope appears to be small when using EPA emissions.Switching NO x emissions from prior emissions to EPA (usually with a scaling factor of 2 to 3) greatly improves the model-data agreement, followed by the impact of whether to turn on the NO x chemistry.Upgrading to a higher-resolution meteorological field minimally alleviated the model-data mismatches but should be considered for regions with complex terrain.Subtracting the background NO 2 is necessary, especially over stagnant days and regions with strong non-anthropogenic emission influences.Based on our limited case studies, NO 2 simulations of power plants are usually more challenging compared to urban areas with more of the areal source for several reasons (from atmospheric mixing, spatial heterogeneity, and vertical profiles of emissions to the exposure of ambient ozone-rich air when estimating the NO 2 : NO x ratios).
Our comprehensive analyses on modeling tNO 2 further shed light on the estimation of CO 2 emissions at the local scale.Modeling two species in a consistent modeling framework makes the quantification of two key bias terms easier, namely from wind directions and emission locations.For example, we demonstrate the use of model-data NO 2 plumes to obtain a quantitative value of the directional biases associated with the modeled wind (Sect.5.2.1) and biases with the emission distribution in prior inventories like EDGARv6 (Sect.4.2).As growing interest arose from the joint use of GHG and air pollutants, we also investigated the differences between NO 2 : CO 2 enhancement ratios and the ENO x : ECO 2 emission ratios (Fig. 9).Such differences between the two tracer-tracer ratios vary across seasons and space and are again driven by the non-linearity between the emissions and concentrations.For instance, to be consistent with emission ratios at the sources, observation-based enhancement ratios need to be scaled up by 2 to 3 times in the summer months due to faster photochemistry.Soundings with a separation of 60 km from the site center need to be scaled up further by roughly 1.3 times more than near-field soundings when concerning changes in chemical tendency.
STILT-NO x , in conjunction with the forthcoming localscale multi-tracer non-linear modeling and inversion system (Fig. 1), can be employed to simultaneously constrain emissions from multiple species of both GHGs and key air pollutants, along with their respective emission ratios, allowing for improvements in sectoral attributions.Such a framework https://doi.org/10.5194/gmd-16-6161-2023 Geosci.Model Dev., 16, 6161-6185, 2023 has the potential to be scaled up to a large number of cities for estimating emissions of NO x , CO 2 , and possibly other tracers from space-based sensors.
Appendix A: WRF-Chem setups We used meteorological fields from the Global Forecast System (0.25 • × 0.25 • GFS-FNL; NCEP, 2015) to generate hourly outputs at a grid spacing of 12 km for 5 consecutive days in each month of 2020.The first day is regarded as the spin-up time to stabilize the model whose concentration fields are excluded from the following analyses.Anthropogenic emissions of air pollutants and VOCs are adopted, respectively, from EDGARv6.1 (Monforti Ferrario et al., 2022) andEDGARv4.3.2 (Huang et al., 2017), with biogenic VOC emissions derived from the Model of Emissions of Gases and Aerosols from Nature (MEGANv2; Guenther et al., 2012).No lightning or soil NO x source is included in WRF-Chem simulations.The boundary condition of chemicals relies on the CAM-CHEM model (Buchholz et al., 2019).The most important part is the gas-phase photochemistry scheme, which is driven by the second generation of the Regional Acid Deposition Model (RADM2; Stockwell et al., 1990), with dry and wet depositions included.RADM2 is well suited under polluted environments but may miss several key aromatic components for pristine environments dominated by biogenic volatile organic compounds (BVOCs; Stockwell et al., 1997).can be accessed from https://data.jrc.ec.europa.eu/dataset/df521e05-6a3b-461c-965a-b703fb62313e (Monforti Ferrario et al., 2022) and have been preprocessed.The STILT-NO x v1 model is built on previous efforts of the X-STILT model in modeling NO 2 .The exact version used in the paper is archived on Zenodo at https://doi.org/10.5281/zenodo.8057850(Wu, 2023).The GFS and HRRR meteorological files are available from the READY website (https://www.ready.noaa.gov/archives.php,Rolph et al., 2017).

Figure 2 .
Figure 2. A schematic of STILT-NO x for simulating concentrations in three steps.Step 1 is a routine backward-time calculation that records the locations of air parcels at each timestamp ( t) of 1 min or shorter and their influence from potential fluxes (footprint).Step 2 is to calculate the initial condition for which the trajectory endpoint at time t 0 is given a concentration from 4D fields (e.g., TM5 in the case of NO x ).Step 3 is a forward-time concentration calculation that updates change in concentrations due to emissions, net chemical losses, and inter-parcel mixing along each trajectory at a timescale of ≤ 1 min.To clarify, Step 3 makes use of trajectories originating from a column receptor stretching from the surface to 2 km, as generated from Step 1.

Figure 3 .
Figure 3.A diagram of NO x net chemical loss tendency (R NO x ; ppb h −1 ) as functions of the NO x concentration (C NO x ) and solar zenith angle (θ ).The net loss timescale was first calculated for each 12 km grid cell of all WRF-Chem simulations for three cities (with specific model setups summarized in Appendix A) and then aggregated into multiple bins of NO x concentration (ppb).The NO x bins are equally divided in the logarithmic space.The solid dots and error bars denote the average and standard deviation of R NO x within each combined θ and C NO x bin.For the net loss timescale, only positive values are displayed, given the logarithmic scale of the y axis in panel (b), and data points with values > 72 h are simply treated as infinite.

Figure 4 .
Figure 4. (a) Demonstrations of best-estimated tNO 2 (TNO2) and their uncertainties (ppb) due to random u or v wind errors (Trans_Error), NO x chemical tendency (Tendency_Error), and O x levels (Ox_Error) on 8 December 2020, over the New Madrid power plant (USA), and 23 December 2020, over Phoenix (USA).(b) Scaling between uncertainties and mean tNO 2 signals over six overpasses for the two targets with smooth splines fitted (crosses with solid lines for tendency errors, stars with dashed lines for O x errors, and circles with dotted-dashed lines for transport errors).Colors differentiate the sites and TROPOMI overpass times.

Figure 5 .
Figure 5. Maps (a) and scatterplots (b) of the modeled plumes, based on several model configurations (first five columns) versus retrieved plumes and uncertainties from TROPOMI v2.3 (last two columns) for the New Madrid power plant on 15 June 2020 and Intermountain, a Utah power plant, on 14 February 2020.Varied model configurations are labeled at the top of each panel, following the naming convention of MET _ EMISS _ GAS _ PROC , as explained in the list of Sect.4.In particular, _DEF and _NOCHEM denote the modeled columns using the default (with mixing and chemistry) and non-chemistry configurations.Grid cells with intensive NO emissions from EDGARv6 are labeled as white circles, with the sizes denoting the relative emission magnitude.The type-II linear regression slope is fitted for each configuration (dotted-dashed line), and modeled and retrieval uncertainties are added (dashed error bars).The underlying road maps were created using the ggmap library in R (map data © 2023).

Figure 6 .
Figure 6.A summary figure of the linear slope between the observed tNO 2 and simulated tNO 2 , using a variety of model configurations over all three US power plants.Model configurations include simulations (1) with or without NO x chemistry parameterization (empty vs. solid dots); (2) using default EDGAR or scaled emissions from EPA (green vs. orange dots); (3) using 0.25 • GFS or 3 km HRRR (dark green or orange vs. light green or orange dots); and (4) using total tNO 2 or background-removed local enhancements (e.g., CHEM-FF as crosses).Annual mean slopes are displayed as horizontal solid or dashed lines.The model evaluation here uses TROPOMI v2.3 and emissions from EDGARv6.1.Evaluations that are based on TROPOMI v1.3 and annual mean EDGARv5 emissions are shown in Fig. S13a in the Supplement.

Figure 7 .
Figure 7.An example of GFS-based tNO 2 plumes over Baotou (China) on 3 October 2020 (a) and the HRRR-based tNO 2 plumes over Phoenix (USA) on 23 December 2020 (b).Modeled plumes are generated using annual mean ENO x from EDGAR, with the top emitters highlighted in light-gray circles.Both observed tNO 2 and the anthropogenic XCO 2 enhancements from OCO-3 are plotted.XCO 2 enhancements calculated from a local background have been averaged based on the TROPOMI sounding size.Overpass time differences between TROPOMI and OCO-3 for the two cases are < 1 h.TROPOMI observations are cropped to match the boundary of the available OCO-3 soundings.The underlying road maps over Baotou and Phoenix were created using the ggmap library in R (map data © 2023).

Figure 8 .
Figure 8.(a) An example of the normalized spatial mean of the sounding-wise product (ppb 2 ppb −2 ) between an unrotated observed tNO 2 and a rotated plume for the New Madrid power plant on 15 June 2020.Gaussian-like curves are fitted to each set, with the mean and standard deviation indicating modeled wind biases.Five sets of rotated plumes include observed tNO 2 (purple) and simulated tNO 2 driven by GFS (dark green) or HRRR (dark orange), with or without the account of the NO x lifetime (light green or light orange).The horizontal dashed lines denote the µ parameter that can translate into wind bias in degrees or radians.(b) Near-field wind directional bias quantified by the modeled tNO 2 plumes, using 3 km HRRR (orange bars) or 0.25 • GFS (green bars), and retrieved tNO 2 plumes for every examined TROPOMI overpass (y axis; in degrees), following the rotation algorithm in panel (a).

Figure 10 .
Figure 10.(a) Similar to Fig. 3b but differentiated by four intervals of VOC R and SZA bins smaller than 70 • , with a spacing of 10 • .All panels here utilized model results from the same WRF-Chem simulations described in Sect. 2 and Appendix A.