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 . 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 . 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 ; constrain emissions across time, space, and sectors ; and evaluate real-world decisions . 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 .

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 , identify urban plumes, constrain emissions for the tracer of interest , and obtain observation-based ratios between tracers to infer structural changes in combustion activities . 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. ). Analogies to such local-scale systems in a global context include the AP-focused Tropospheric Chemistry Reanalysis version 2 TCR-2; and the GHG-focused Carbon Monitoring System Flux CMS-Flux;. Only a few recent multi-tracer modeling systems aim to bridge CO2 and NO2 column measurements , despite limits in their modeling tools (elaborated upon in the next paragraph). In addition, as emphasized in , most multi-tracer studies rely on emission ratio or conversion ratio from inventories, which can be problematic.

In efforts to interpret CO2 or NOx 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 CO2 and NOx (or a lifetime if for NOx) purely from observations in a computationally efficient manner without relying much on prior assumptions of emissions . These statistical approaches only provide a plume-integrated 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.,. 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 . 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 imperfections – i.e., to simplify the chemical transformation process that preserves the non-linear relationship between NOx emissions and the observed concentration field, together with a high-resolution 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; building upon HYSPLIT 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 source–receptor 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 . More importantly, the Lagrangian transport perspective is intuitively coupled with box models that handle chemical reactions. Noticeable examples include STOCHEM , ATLAS , CLaMS v2.0 , and HYSPLIT-based variations, including HYSPLIT CheM , ELMO-2 for ozone , and STILT-Chem . 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 under-appreciation 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 , predict the OH field with observational constraint , and calculate emissions . Other studies have assumed a constant first-order lifetime to estimate NOx emissions and emission ratios between NOx and CO2 . However, unlike chemically passive species such as CO2, the chemical tendency of NOx is not independent of atmospheric advection and turbulent mixing because of the chemically driven non-linearity between the NOx lifetime and the NO and NO2 concentrations . More specifically, during the day, NOx is lost through two more permanent pathways of (1) NO2 + OH to nitric acid and (2) NO + peroxy radicals (RO2), with a minor branch in producing alkyl nitrates or ANs (point 3 in Fig. ). The two pathways compete with one another and either may dominate, depending on the chemical conditions. Such non-linear dependence of the NOx lifetime or chemical tendency with the NOx concentration must be accounted for to estimate the NOx emissions from atmospheric NO2 concentrations. Such non-linearity will affect the interpretation of tracer-to-tracer emission ratios from observed enhancement ratios.

In this study, we present a non-linear modeling framework, STILT–NOx, to simulate tropospheric column-averaged NO2 mixing ratio (tNO2) as retrieved from the TROPOspheric Monitoring Instrument (TROPOMI). Note that initial NO2 vertical column density (VCD; molec.cm-2) is converted to tNO2 (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. , 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 CO2, CO, and NOx 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 NOx concentrations to its emission (point 3 in Fig. ). The proposed STILT–NOx framework is comprised of four components, outlined below, which correspond, respectively, to points 1 to 4 in Fig.  and will be coupled to an upcoming non-linear flux inversion module (point 6).

The HYSPLIT–STILT core resolves fine-scale atmospheric advection and turbulence and calculates the sensitivity of concentration anomalies to upwind fluxes (footprint) , with an additional simplified inter-parcel mixing scheme (Sect. ).

We illustrate the skill of this framework using comparisons of modeled tNO2 and those diagnosed from TROPOMI over three United States (US) power plants and two cities across seasons (Sect. ). Last, we discuss possible future advances in Sect.  and demonstrate the benefits of applying this framework, especially on the quantification of CO2 emissions, emission ratios between NOx and CO2, and near-field wind biases in Sects.  and .

Building upon the HYSPLIT–STILT atmospheric transport core, the STILT–NOx framework traces the origin of the atmospheric column observed by the satellite and calculates changes in the NOx concentrations due to emissions, inter-parcel mixing, and chemical transformations at the (sub-)minute scale. The STILT–NOx simulations are conducted in three steps (Fig. ).

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. ). 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 . As most anthropogenic and all soil sources of NOx 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 . 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 NOx mixing ratios from TCR-2 . TCR-2 is a global chemical reanalysis that includes full physical and chemical processes for various species and assimilates multiple satellite products of NO2, ozone, CO, and SO2. As a result, the monthly mean NOx 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 NO2 background from the total tropospheric columns to minimize the non-anthropogenic influences with a plume detection algorithm, following . The model–data comparisons with background subtracted are discussed in Sect. .

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 t0 in Fig. ). Step 1 also provides the STILT footprint (ppm(µmolm-2s-1)-1) per air parcel per timestamp . 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 . The footprint concept, by definition, relies on atmospheric transport and only accounts for concentration changes due to emissions but not chemical transformations.

Next, NOx 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. ). TM5-MP is an auxiliary dataset in which the NO2 vertical profiles serve as the prior knowledge facilitating the stratosphere–troposphere separation in Level 2 (L2) NO2 retrieval . Here, we simply assume that most NOx is presented as NO2 at nighttime, despite the apparent caveat for neglecting NO3 chemistry and heterogenous reactions involving N2O5.

Once NOx is initialized at the time t0 for the endpoint of every trajectory, we proceed with Step 3 (Fig. ) to estimate the changes in concentrations due to emissions, chemical transformation, and inter-particle mixing. Mathematically, the concentration per air parcel per timestamp (Cp,t) relies on that from the last timestamp, following Eq. (): 1Cp,t=Cp,t-Δt+ΔCemis,p,t(E,Fp,t)+ΔCchem,p,t(Cp,t,θp,t)+ΔCmix,p,t(Cp,t,Cpngb,t‾), where the time interval for updating concentrations, Δt, is defaulted to 1 min or reduced to a sub-minute value when Ct becomes nonphysically negative to ensure numerical stability. Concentration gains from emissions, ΔCemis, result from multiplying STILT-parcel-specific footprints (Fp,t) with prior emissions (E) from EDGARv6.1 and the U.S. Environmental Protection Agency (EPA; ) for power plant cases in this study. We neglect soil NOx emissions, given the relatively small contributions in cities. Unlike sophisticated CTMs which resolve the chemical reactions of an individual or lumped groups of species, concentration anomalies due to chemical reactions, ΔCchem, are solved in an explicit first-order fashion involving a net chemical tendency, with a unit of parts per billion per hour (ppbh-1). Such a chemical tendency (RNOx in Eq. ) is parameterized offline as functions of NOx concentrations and solar zenith angles, θ, which is explained in Sect. . The final term, ΔCmix,p,t, denotes the concentration exchange between a given air parcel and its volumetric neighborhood (pngb), which is explained in Sect. .

Following these steps, we obtain the modeled NOx mixing ratio for every trajectory released between the surface and 2 km, based on NOx curves described in Sect. . To compare against TROPOMI tropospheric NO2 columns, we account for the fraction of NOx that is present as NO2 (Sect. ) and properly weight the modeled NO2 from different altitudes, according to the pressure weighting function and averaging kernel profiles, following . Such an approach in applying averaging kernel (Fig. ) to the modeled profiles is equivalent to a more commonly used approach, which re-calculated the retrieved tNO2, as seen from the CTM, by re-calculating the air mass fraction based on modeled NOx profiles, as investigated in . In addition, we evaluate the modeled meteorology and chemistry using a separate set of STILT–NOx simulations with true NOx emissions from the EPA for three US power plants (Sect. ).

As atmospheric transport and chemical transformation are the two main components in any CTMs, we assess how uncertainties tied to the modeled wind field, NOx loss timescale, and NO2 : NOx ratio may contribute to uncertainties in tNO2 (in ppb). 5σsim2=σtrans2+σts2+σnn2. Here we briefly describe how various tNO2 uncertainties were approximated, based on our understanding of errors in respective model parameters or inputs (i.e., wind error, NOx chemical tendency, or Ox levels). To approximate the tNO2 uncertainties due to transport errors, we followed previous approaches to first assess the GFS- and HRRR-modeled 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, σtrans2 in Eq. () is derived from the difference in the variance of STILT–NOx air-parcel-specific NO2 concentrations between the original simulation and a second simulation with wind error . The derivations of modeled wind errors and contributions to tNO2 errors are elaborated in Appendix . To evaluate the impact due to errors associated with chemical parameters, we perturbed the NOx curves or the Ox level according to 20 perturbing factors. Perturbed curves or parameters are used to generate 20 new sets of tNO2 fields, of which their respective standard deviation among perturbations serves as the chemical uncertainty (ppb) due to NOx net loss timescale and NO2 : NOx ratio (σts and σnn in Eq. ). These 20 perturbing factors were randomly selected from a normal distribution N (μ=1;σparam). Here we tested out σparam of 40 % for NOx loss timescales, according to uncertainties in the chemical tendency (Fig. ) and a σparam of 40 % for the Ox level (Eqs. ).

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 NO2 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. a. Considering the non-linearity between the chemical tendency and NOx concentration, sounding-specific uncertainties for all six cases are presented against modeled tNO2 in Fig. b. 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 tNO2 at the sounding level (third column in Fig. a). Higher transport errors may occur more frequently if an intensive point source is in the area or over pixels on the border of the NO2 plumes, with moderate signals of about 0.2 to 0.5 ppb (e.g., dots in Fig. b). 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 hyper-near-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. b). 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 Ox levels or NOx chemical tendency, chemical uncertainties (in ppb) remain small when modeled signals are compared (Fig. a). Uncertainties from chemical tendency first increase with tNO2 signals and gradually plateau for tNO2 beyond 0.7 ppb, likely because NOx is lost slowly when the NOx concentration stays high, and further perturbations in the chemical tendency are less impactful. In contrast, the uncertainty from Ox 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 Ox level approaches zero, the amount of NO that can be oxidized as NO2 becomes minimal (second column in Fig. a). This case mimics the scenario where O3 can be titrated in proximity to an intense release of NO before the ozone-depleted plume air is mixed with the ambient ozone-rich air. Nevertheless, considering the entire sample, the percent of errors due to chemical parameters remains relatively low (13 % to 18 % for six cases in Fig. b).

Whether chemical or meteorological errors dominate the total model errors fundamentally depends on tropospheric NO2 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 NO2 retrieval version of v2 compared to v1 , v2 retrieval is associated with a fractional uncertainty (normalized over retrieved tNO2) of ∼ 30 % to 50 % for most soundings within the plume. Uncertainties in the NOx 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 NO2 plumes is proposed in Sect.  to quantify near-field wind biases.

The tropospheric NO2 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. ). Modeled tropospheric NO2 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.

Only model–data comparisons using TROPOMI v2 are shown. As the satellite averaging kernel (AK) and observed tNO2 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.

Our ultimate goal is to explore what can be learned about the emission characteristics from anthropogenic hotspots with the joint use of space-based NO2, CO, and CO2 plumes. As an intermediate step, this study is informed by previous efforts to extract and constrain urban CO2 emissions from satellites using a Lagrangian framework and extends it to the interpretation of tropospheric NO2 satellite data. To diagnose NOx emissions from NO2 column signals, we need to effectively account for how NOx 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.

In developing STILT–NOx, we aim to quantify anthropogenic NOx emission signals for power plants and cities using remote sensors with a novel Lagrangian chemical system that preserves the non-linear relationship between NOx 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. ). Although uncertainties exist in modeling atmospheric transport, mixing, and chemical processes, this study covers the key NOx chemical mechanisms, various error sources, model validation, and the benefit of using NOx to constrain CO2 emissions and tracer–tracer 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. ), we compared modeled tropospheric NO2 columns using EPA-reported emissions against observed columns from TROPOMI over three power plants in the US (Fig. ). 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 NOx 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 NOx 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 NO2 is necessary, especially over stagnant days and regions with strong non-anthropogenic emission influences. Based on our limited case studies, NO2 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 NO2 : NOx ratios).

Our comprehensive analyses on modeling tNO2 further shed light on the estimation of CO2 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 NO2 plumes to obtain a quantitative value of the directional biases associated with the modeled wind (Sect. ) and biases with the emission distribution in prior inventories like EDGARv6 (Sect. ). As growing interest arose from the joint use of GHG and air pollutants, we also investigated the differences between NO2 : CO2 enhancement ratios and the ENOx : ECO2 emission ratios (Fig. ). 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–NOx, in conjunction with the forthcoming local-scale multi-tracer non-linear modeling and inversion system (Fig. ), 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 has the potential to be scaled up to a large number of cities for estimating emissions of NOx, CO2, and possibly other tracers from space-based sensors.