We present a new method to infer emissions and lifetimes of nitrogen oxides (NOx) based on tropospheric nitrogen dioxide
(NO2) observations together with reanalysis wind fields for cities located in polluted backgrounds. Since the accuracy of the method is
difficult to assess due to lack of “true values” that can be used as a benchmark, we apply the method to synthetic NO2 observations
derived from the NASA-Unified Weather Research and Forecasting (NU-WRF) model at a high horizontal spatial resolution of
4 km× 4 km for cities over the continental United States. We compare the inferred emissions and lifetimes with the values given by
the NU-WRF model to evaluate the method. The method is applicable to 26 US cities. The derived results are generally in good agreement with the
values given by the model, with the relative differences of 2 % ± 17 % (mean ± standard deviation) and 15 % ± 25 %
for lifetimes and emissions, respectively. Our investigation suggests that the use of wind data prior to the satellite overpass time improves the
performance of the method. The correlation coefficients between inferred and NU-WRF lifetimes increase from 0.56 to 0.79 and for emissions increase
from 0.88 to 0.96 when comparing results based on wind fields sampled simultaneously with satellite observations and averaged over 9 h data prior
to satellite observations, respectively. We estimate that uncertainties in NOx lifetime and emissions arising from the method are
approximately 15 % and 20 %, respectively, for typical (US) cities. The total uncertainties reach up to 43 % (lifetimes) and 45 %
(emissions) by considering the additional uncertainties associated with satellite NO2 observations and wind data. We expect this new
method to be applicable to NO2 observations from the TROPOspheric Monitoring Instrument (TROPOMI) and geostationary satellites, such as
Geostationary Environment Monitoring Spectrometer (GEMS) or the Tropospheric Emissions: Monitoring Pollution (TEMPO) instrument, to estimate urban
NOx emissions and lifetimes globally.
Introduction
Nitrogen oxides (NOx), consisting of nitrogen dioxide (NO2) and nitric oxide (NO), are important atmospheric trace gases
that actively participate in the formation of tropospheric ozone and secondary aerosols and accordingly have a significant effect on human health and
climate (Seinfeld and Pandis, 2006). NOx emission sources include anthropogenic activities, biomass burning, soil emissions, and
lightning. Fossil-fuel burning from mobile and industrial emitters represents the largest source of anthropogenic NOx emissions;
these sources are usually clustered near densely populated urban areas (Crippa et al., 2018).
We traditionally rely on a bottom-up method to estimate anthropogenic NOx emissions for a country or a region based on their total
fuel use and averaged emission factors, which are subject to uncertainties due to incomplete understanding of real-world operating conditions and
spatial distributions (Butler et al., 2008). Some sources may be missing from bottom-up emission inventories (McLinden et al., 2016). Additionally,
estimates of NOx emissions may become outdated when fuel consumption and emission factors change dramatically. For instance,
NOx emissions from China decreased by 21 % from 2011 to 2015 due to wide deployment of denitration devices (Liu et al.,
2016a). Inferring emissions for individual cities is even more challenging, due to the difficulties in acquiring a complete and reliable database for
fuel consumptions and emission factors at city level. Proxies such as population density, industrial productivity, and road network maps are often
used to downscale national/regional emissions to finer scales, which may incorrectly allocate emission sources spatially (Butler et al., 2008).
Satellite observations of tropospheric NO2 have been widely used to infer the strength of NOx emissions. Satellite
instruments, e.g., the Ozone Monitoring Instrument (OMI; Levelt et al., 2006, 2018) and TROPOspheric Monitoring Instrument (TROPOMI; Veefkind et al.,
2012), are used to retrieve the column density of NO2 in a vertical column of air. These data can then be related to NOx
emissions by considering chemical conversion and transport. Chemical transport models (CTMs) were initially employed to use NO2 measured
from space as a constraint to improve NOx emission inventories based on mass balance (e.g., Martin et al., 2003; Kim et al., 2009;
Lamsal et al., 2011). Techniques such as the four-dimensional variational (4D-Var) method (e.g., Henze et al., 2007, 2009), extended Kalman filter
(e.g., Ding et al., 2017), ensemble Kalman filter (e.g., Miyazaki et al., 2017), and hybrid mass balance/4D-Var (e.g., Qu et al., 2019) have also been
used to improve emissions estimates within CTMs.
Several studies have inferred emissions independent of CTMs (e.g., Beirle et al., 2011; Liu et al., 2017; Laughner and Cohen, 2019). Such
investigations were inspired by a pioneering study that used the downwind decay of NO2 in continental outflow regions to estimate the global
NOx lifetime and total emissions (Leue et al., 2001). Beirle et al. (2011) first proposed an empirical function to describe the
plume distribution around an isolated city without inputs from CTMs. Follow-up studies have adopted this function to provide estimates of
NOx emissions from power plants and cities based on OMI (e.g., de Foy et al., 2015 and Lu et al., 2015) and TROPOMI (e.g., Goldberg
et al., 2019) observations. Additional methods, such as the plume rotation technique (Pommier et al., 2013; Valin et al., 2013) and the divergence
approach (Beirle et al., 2019), were developed to refine the approach of Beirle et al. (2011). More recent studies explored additional constraints for
the empirical function using simulated atmospheric composition from models (e.g., Lorente et al., 2019; Lange et al., 2021). For sources with a
polluted background, Liu et al. (2016b) proposed a different fitting function to consider the interferences from surrounding sources; this approach
has been used to estimate NOx emissions for European cities (Verstraeten et al., 2018).
The uncertainties in satellite-derived emissions inferred from CTM-independent approaches have rarely been investigated. Field campaigns, e.g.,
Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality (DISCOVER-AQ), Korea–United
States Air Quality Study (KORUS-AQ), and Cabauw Intercomparison of Nitrogen Dioxide Measuring Instruments 2 (CINDI-2), have been performed to better
quantify errors in the NO2 observations (e.g., Choi et al., 2020) and therefore improve knowledge about uncertainties in satellite-derived
emissions. Existing studies usually quantify the uncertainties based on results from sensitivity analyses (e.g., Beirle et al., 2011), since we
usually lack “true values” that can be used as a benchmark for validation. De Foy et al. (2014) tested CTM-independent approaches using simulated
NO2 column densities from a single-point source with a specified emission and chemical lifetime. The good consistency between the derived
values and the specified values given to drive the simulation suggests that the uncertainty of the Beirle et al. (2011) approach is small for an
ideal, isolated source. However, the performance of the approach in the real world with complex source distributions has not yet been evaluated.
Schematic of our evaluation system to assess the accuracy of the inferring NOx lifetimes and emissions derived from MISATEAM. The blue symbols represent the inputs (dashed line) and outputs (solid line) of MISATEAM. The orange symbols represent the information derived from NU-WRF.
Here, on the basis of previous approaches (Beirle et al., 2011; Liu et al., 2016b), we develop a new CTM-independent approach for inferring
NOx lifetimes and emissions for cities with polluted backgrounds and complex spatial distribution of interfering emissions. We use
synthetic NO2 observations derived from a model simulation to evaluate the performance of the new approach and to estimate its
uncertainties. An overview of the synthetic observations, the methodology and features of the new CTM-independent approach is provided in Sect. 2. We
evaluate results by comparing the inferred emissions and lifetimes with values from the model simulation in Sect. 3.1. Section 3.2 compares the
performance of the method developed in this work with previous approaches (Beirle et al., 2011; Liu et al., 2016b). Section 3.3 discusses the
uncertainties of NOx lifetimes and emissions derived from the new approach. Section 4 presents a summary of the performance of the
new method and future work plans for applying the method to satellite observations.
Data and method
In this section, we develop an evaluation system to assess the performance of our newly developed CTM-Independent SATellite-derived Emission
estimation Algorithm for Mixed-sources (MISATEAM). Figure 1 displays the schematic of the evaluation system. MISATEAM uses satellite retrievals of
tropospheric NO2 vertical column densities (VCDs), together with wind information from a meteorological reanalysis, to infer
NOx lifetimes and emissions for cities. Cities are usually non-isolated sources with polluted backgrounds (Fig. S1 in the
Supplement). Additionally, emissions from cities may spread out and make cities not (quasi) point
sources, even at the footprint of satellite observations (a few kilometers; Fig. 3). We refer to these cities as mixed sources.
To evaluate MISATEAM, we replace satellite observations with synthetic NO2 VCDs derived from the NASA-Unified Weather Research and
Forecasting (NU-WRF) model (Tao et al., 2013; Peters-Lidard et al., 2015) (Sect. 2.1). We then apply MISATEAM to the synthetic NO2 VCDs and
NU-WRF meteorological fields to infer urban NOx lifetimes and emissions (Sect. 2.2). We investigate the impact of temporal
variations in wind fields on derived NOx lifetimes and emissions (Sect. 2.3). In Sect. 2.4, we describe the benchmark
NOx emissions directly given by NU-WRF and NOx lifetimes deduced from known NOx emissions and
concentrations (hereafter referred to as “given emissions and NU-WRF lifetimes”) that we will compare with the MISATEAM-derived lifetimes and
emissions. Analysis of the uncertainties in these datasets, including satellite observations and wind fields, is outside the scope of the study. We
briefly discuss the potential impact of ignoring systematic errors in Sect. 3.3.2.
Domain used for simulation. (a) Mean NU-WRF tropospheric NO2 vertical column densities. (b) Mean NEI NOx emissions fluxes used to drive the NU-WRF simulation. Hourly mean data at 14:00 LT are averaged from April through September 2016. Locations of the 26 cities investigated in this study are shown by circles (see Sect. 3).
Synthetic NO2 VCDs: NU-WRF simulations
We use a regional modeling system, NU-WRF (Tao et al., 2013; Peters-Lidard et al., 2015), to simulate tropospheric NO2 VCDs over the
continental United States. NU-WRF was developed from the advanced research versions of WRF (Michalakes et al., 2001) and WRF-Chem (Grell et al., 2005) with the
addition of several NASA-developed components (e.g., Chou and Suarez, 1999; Chin et al., 2002, 2007; Kumar et al., 2006; Peters-Lidard et al., 2007;
Shi et al., 2010). The gas-phase chemical mechanism in NU-WRF is the second-generation regional acid deposition model (RADM2; Gross and Stockwell,
2003). The aerosol module is the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model (Chin et al., 2002). We use the anthropogenic
emissions based on the 2011 National Emissions Inventory (NEI) compiled by the US Environmental Protection Agency (US EPA, NEI 2011) but with a few
modifications, in which the measurements from OMI, the ground-based Air Quality System (AQS), the in situ continuous emissions monitoring in power
plants, and the Air Pollutant Emissions Trends Data compiled by the US EPA
(https://www.epa.gov/air-emissions-inventories/air-pollutant-emissions-trends-data, last access: 1 December 2021) have been
employed to adjust the baseline emissions to the simulation year of 2016 (Tong et al., 2015; Tao et al., 2020). As such, the total anthropogenic
NOx emissions in 2016 were approximately 72 % of those in 2011, the baseline NEI year. The simulation also includes the fire
emissions from the Global Fire Data version 4 with small fires (GFED v4s; van der Werf et al., 2017; Randerson et al., 2015); biogenic emissions from
the online calculation using the Model of Emissions of Gases and Aerosols from Nature version 2 (MEGAN2; Guenther et al., 2006); dust emissions from
the online estimation based on the surface wind speed, soil moisture, and soil erodibility (Ginoux et al., 2001; Kim et al., 2017); and sea salt
emissions from the online computation based on the method by Gong (2003).
We run NU-WRF for 2016 at a high horizontal spatial resolution of 4 km× 4 km and 40 vertical layers extending from the surface
to 50 hPa in this study. Figure 2 illustrates the domain of the simulation, which covers the continental United States. We integrate NO2
concentrations from the surface to the tropopause to calculate tropospheric NO2 VCDs. We assume a consistent tropopause height of
10 km over the model domain to accelerate the data process because NU-WRF outputs do not include tropopause height, and NO2 VCDs
integrated above 10 km increase slightly. We have performed a sensitivity analysis by integrating NO2 concentrations from the
surface to altitudes ranging from 8 to 16 km, where the seasonal mean tropopause heights may occur over the United States (Pan et al., 2011; Rieckh
et al., 2014). The derived NO2 VCDs over the fit domain of individual cities vary slightly above 10 km, with the relative difference
of 3 % ± 2 % when increasing the integration altitude from 10 to 12 km, since most NO2 stays near the surface over the
polluted urban areas. The meteorological initial and lateral boundary conditions are derived from the Modern Era Retrospective-Analysis for Research
and Applications version 2 (MERRA-2; Rienecker et al., 2011; Gelaro et al., 2017). The chemical initial and lateral boundary conditions are derived
from the results of the Community Atmosphere Model with chemistry (CAM-chem; Lamarque et al., 2012). A 7 d model spin-up following the
recommendation by Berge et al. (2001) is used.
Figure 2a illustrates the 6-month average of the simulated hourly mean tropospheric NO2 VCDs sampled at 14:00 LT, which approximately corresponds to the early afternoon overpass time of OMI and TROPOMI. The NOx emissions used to
drive NU-WRF over the model domain for the same time period are presented in Fig. 2b. We focus on cities with populations > 200 000, which have
been defined as medium-size urban areas in Organisation for Economic Co-operation and Development (OECD) countries. Nearby cities (located within
50 km of the largest city in a given urban area) are considered as one city cluster when applying MISATEAM to infer lifetimes and
emissions. Cities on the boundary of the model domain, e.g., Seattle and San Francisco, are excluded from the following analysis because the data for
their inflow/outflow plumes are partially missing from the model output and thus do not meet the requirements of MISATEAM (see details of the fit
interval in Sect. 2.2). This filtering results in a total of 60 cities and urban conglomerations (see Table S1 in the Supplement) as the candidates
for applying MISATEAM, of which 26 have valid results. The locations of the 26 cities are shown in Fig. 2. Cities without valid results either lack
observations under calm wind conditions or are associated with large fitting errors (see details in Sect. 3.1).
Emission estimation algorithm
We develop MISATEAM based on the methods of Beirle et al. (2011) and Liu et al. (2016b). We develop a new model function aiming for determining
emissions for mixed sources, instead of isolated sources, within a clean background considered by Beirle et al. (2011). It is also different from that
of Liu et al. (2016b), which was developed for complex sources but adapted an additional model function to fit emissions in a separate step. More
comparisons with those two previous methods will be discussed in Sect. 3.2.
We adapt the basic approach of Liu et al. (2016b) that estimates NO2 emission rates, E(x), using NO2 observations,
LDcalm(x), following
E(x)=RNOx:NO2⋅[LDcalm(x)-b]τ,
where E(x) is a function of distance from the city center (denoted by x) in a particular direction and integrated over a given distance in a
direction y (perpendicular to that of x). The mean emission maps (two-dimensional, 2D) are reduced to 1D along the respective direction x by
integration across the direction y. LDcalm(x) is the so-called NO2 line densities, defined as the observed
NO2 VCDs (units molec.cm-2) under calm wind conditions (wind speed < 2 ms-1), integrated in the same way as E(x)
to give units of molecules per centimeter (molec.cm-1) as in Beirle et al. (2011).
RNOx:NO2 is the ratio of NOx to NO2. We use RNOx:NO2
of 1.32 to represent “typical urban conditions and noontime sun” (Seinfeld and Pandis, 2006). We investigate the effect of using a constant value of
RNOx:NO2 on derived emissions in Sect. 3.1; it is found to be insignificant.
b represents the NO2 background for each city, which is derived by analyzing the distribution of NO2 VCDs. We first calculate
the mean NO2 VCD under calm wind conditions for grid cells within the lowest 5th percentile of NO2 VCDs for each city. This
produces a good approximation of the mean NO2 VCD for grid cells with low NOx emissions (i.e., the lowest 5th percentile
of NOx emissions). We then multiply this mean VCD value by the spatial width of the across-wind integration interval to derive b.
τ is the NOx lifetime. Note that τ is assumed to be an effective mean dispersion lifetime (i.e., the result of the effect
of deposition, chemical conversion, and wind advection) because we do not consider downwind changes in the fitting functions, such as due to
variations in wind speeds or RNOx:NO2 or lifetime itself.
Sketch of the definition of line densities. For each wind direction, mean NO2 VCDs are integrated in across-wind direction y over the interval i, resulting in line densities LD(x). The fit is performed over the entire upwind interval (fupwind) and downwind interval (fdownwind). The city center is the coordinate origin. The top panel shows the NU-WRF tropospheric NO2 VCDs around New York City under southwesterly wind; however the image is rotated by 45∘ in the clockwise direction to present NO2 VCDs in an upwind–downwind direction. The city of Philadelphia and Long Island are located in the upwind and downwind direction, respectively.
We then use the following model function, f(x), to describe NO2 line densities under windy conditions (wind
speed > 2 ms-1) LDwindy(x):
f(x)=E(x)RNOx:NO2⋅w∗e-xw⋅τ+b=[LDcalm(x)-b]τ⋅w∗e-xw⋅τ+b,
where w is the mean wind speed at the emission level in a given direction x, and ∗ denotes convolution. Figure 3 illustrates the
calculation of LDwindy(x). Additional technical details of the model function f(x) and its differences compared to those proposed
by Liu et al. (2016b) are given in Appendix A.
Finally, we use estimates of b and RNOx:NO2 in Eq. (), along with values of w,
LDcalm(x), and LDwindy(x) from the model simulation to infer τ and E(x). As displayed in Fig. 1, we use
the NU-WRF high-resolution tropospheric NO2 VCDs sampled at 14:00 LT as the synthetic NO2 VCD observations, together with the
NU-WRF meteorological wind information, to estimate urban NOx emissions. In other words, here we assume perfect knowledge of the
winds and do not further consider the impact of errors in w. As in previous studies, we only analyze data from April to September, in order to
exclude winter data that have larger uncertainties and longer NOx lifetimes. We also investigate the impact of the inclusion of
winter data in Sect. 3.3.1; it is found to be associated with a larger uncertainty. We further compute total emissions for each city,
EmisNOx, by summing E(x).
NO2 line densities around New York for different wind direction sectors. Circles: NO2 line densities for calm (blue circles) and (a) southeasterly, (b) southerly, (c) southwesterly, (d) northeasterly, and (e) northerly winds (red circles) as a function of the distance x to the center of New York. Red line: the fit result f(x). The numbers indicate the fitted NOx lifetime (τ), average days of data used for calculating NO2 line densities (days), derived emissions (EmisNOx), and given emissions (EmisNOx′). NO2 line densities are derived from NO2 VCDs averaged from April through September 2016. NO2 line densities for the remaining wind direction sectors are discarded due to the fitting results having insufficient quality.
We perform a nonlinear least-squares fit of f(x) to the observed line densities under windy conditions, LDwindy(x), with
τ as the single fitting parameter. We use the package of scipy.optimize.curve_fit from the Python software library to perform the fitting. We
set the fit interval to 150 km in the downwind direction, which corresponds to the e-folding distance for τ= 6 h and
w= 7 ms-1. The fit intervals in the upwind direction and the y direction are set to half the e-folding distance (75 km);
the resulting area is large enough to cover a highly populated and spread-out metropolitan region such as New York City. The definitions of the fit
interval in the upwind and downwind direction and the across-wind integration interval are illustrated in Fig. 3. Note that we use
LDcalm(x) over a larger horizontal interval of 450 km to calculate the convolution in Eq. (), in order to
eliminate the edge effect of convolution. Fitting results of insufficient quality (i.e., the correlation coefficient R between the fitted and
observed NO2 LD < 0.9 and 1 standard deviation error of τ> 10 %) are discarded. We infer emissions simultaneously by
summing E(x) in Eq. (). We perform the fit for all wind direction sectors and then average the fitted τ and corresponding total
emission EmisNOx with good quality, using the fit residuals as inverse weights, to yield a best estimate
of 〈τ〉 and 〈EmisNOx〉 for a given city. The standard deviation of the fit results for
different wind directions has been used to quantify uncertainties in Sect. 3.3.2.
We use the city of New York as a case study to demonstrate our approach. This city is well suited for illustrating the strength of MISATEAM to
estimate emissions for mixed sources because it is a large city with multiple point and areal sources and is surrounded by many other large
sources. Figure 3 displays the complex spatial distribution of sources around New York. Under southwesterly wind, the city of Philadelphia is located
in the upwind direction, and Long Island is located in the downwind direction, both of which are significant NOx sources. Note that
we do not exclude cloudy days from our analysis to make the most of the NU-WRF NO2 simulations and to avoid additional uncertainties arising
from the inconsistent definitions of cloud fractions in the NU-WRF and satellite NO2 products. The uncertainty of the presence of clouds is
discussed in Sect. 3.3.2.
We use wind fields averaged from the surface to 1000 m altitude for w in this study. The synthetic NO2 VCDs around New York are
sorted by wind direction (Fig. S1). Figure 4a displays the observed line densities for calm (blue circles) and southeasterly winds (red circles)
around New York and the fitted model function f(x) (red lines). Generally, f(x) describes the observed downwind patterns very well; the
coefficients of determination (R2) between observation and fit are 0.90–0.98 for different wind directions. The resulting lifetimes show a range
of 2.2–2.9 h, which result in emissions of 754–996 molh-1 for different wind directions, as shown in Fig. 4a–e. Results for
other wind direction sectors are discarded due to the fitting results being of insufficient quality (westerly and northwesterly winds; Fig. S2 in the
Supplement) or a lack of observations (easterly wind).
Impact of temporal variations in wind fields
CTM-independent emission estimation algorithms usually assume a steady wind field over the duration of NOx lifetime. In the
demonstration in Sect. 2.2, we use the wind fields sampled at the satellite overpass time to drive MISATEAM, consistent with previous studies (e.g.,
Beirle et al., 2011; Valin et al., 2013; Lu et al., 2015; Liu et al., 2017, 2020; Goldberg et al., 2019). This is expected to be reasonable for
species with a short lifetime of a few hours such as NOx near noon of non-winter seasons. In reality, wind fields are variable over
the NOx lifetime. Consequently, NOx emitted at a time prior to the satellite overpass may be transported under
different wind conditions than those at the overpass time.
Wind barbs around New York City for different times of the day. All northeasterly winds at 14:00 LT from April to September of 2016 are averaged and shown in (i). Wind barbs for the northeasterly winds backward trajectories from 8 to 1 h prior to 14:00 LT are displayed in (a–h). Wind speed is given in units of knots, which is equivalent to nautical miles per hour (1.9 kmh-1). Each short and long barb represents 5 knots (9.3 kmh-1) and 10 knots (18.5 kmh-1), respectively. The average wind speed is displayed in the grey box.
Figure 5 illustrates the temporal variations in wind fields around New York. We use the northeasterly wind direction (with a good fitting result) for
demonstration. We select northeasterly winds observed at 14:00 LT as the baseline and find their backward trajectories for up to 8 h. The backward
trajectories are given at a time step of 1 h. Not surprisingly, winds are not constant during the 9 h from 8 h before the baseline to the exact
hour of the baseline. However, the temporal variations in wind directions are rather small for the northeasterly wind; wind directions are almost
constant over time. For wind directions without good fit results, we observe larger variations. For instance, for the westerly wind with a poor
correlation coefficient R of 0.76, the wind directions deviate from the west direction gradually for the time prior to the baseline (Fig. S3 in the
Supplement). These results shed light on the robustness of MISATEAM's steady-wind assumption. It is most likely that the fit fails when the assumption
of steady wind is not satisfied. In other words, the inherent fitting assumption is robust when the fit results have sufficient quality as defined in
Sect. 2.2.
We perform sensitivity analyses to investigate the potential impact of temporal variations in winds on the fit results. We extend the time windows
used for calculating averaged wind fields from 1 h (i.e., at the overpass time of 14:00 LT) to 3 h (i.e., starting from the overpass
time and extending into the past 2 h), 6, 9, and 12 h. We weight the winds based on their temporal proximity; i.e., the wind closer to
the overpass time is given larger weight, following Eq. ().
wi,d‾=∑h=0Nwh,i,d⋅e-h/t0∑h=0Ne-h/t0,
where h represents the number of hours prior to the overpass time. i and d denote an individual grid cell and day, respectively. wh,i,d is
the wind for a specific grid cell i on day d at the time of h hours prior to the overpass time. N is the length of the time window used (units
of hour). The weighted average winds wi,d‾ are further applied with MISATEAM to infer NOx lifetimes and emissions for
investigated cities. We set t0 to a constant value of 3 derived from rounding the average NU-WRF lifetimes for all investigated cities (see
details in Sect. 2.4). The fitting results are found to be relatively insensitive to the choice of t0. The differences of the fitted lifetimes
and emissions are -2 ± 15 % and 3 ± 16 %, respectively, when we increase t0 by a factor of 2. This is significantly smaller
than the difference between the fit results based on weighted average winds and the winds at the overpass time (shown in Sect. 3.1).
Scatterplots of (a) the fitted NOx lifetime τ as compared to the NU-WRF lifetime τ′ and (b) the fitted NOx emissions EmisNOx as compared to the given emissions EmisNOx′. Error bars show the standard error of the fitted results for all available wind directions. Standard error is defined as standard deviation divided by n, with n being the number of available wind directions. The results deriving from the wind fields sampled at 14:00 LT (“1 h”) and the weighted average of 9 h wind fields (“9 h”) are displayed by red and blue dots, respectively. The dashed line represents the 1:1 line.
Performance evaluation
In order to evaluate the fitting results, we infer given emissions and NU-WRF lifetimes from the NU-WRF inputs/outputs. The given emission
EmisNOx′ is derived by summing NU-WRF NOx emissions from all grid cells within the fit
interval. The NU-WRF lifetime τ′ can be computed by solving Eq. (); i.e.,
τ′=∑RNOx:NO2⋅[LDcalm(x)-b]∑E′(x),
where E′(x) is the given NOx emission line densities under calm wind conditions, as a function of distance x from the
city center. For evaluation, we compute the correlation coefficient (R), the normalized mean bias (NMB), and the root mean squared error (RMSE) of
the fitted emissions and the given emissions for all investigated cities. The model performance metrics of NMB and RMSE for the emission
(EmisNOx) evaluation are defined as
NMB=∑i=1n(EmisNOx,i-EmisNOx,i′)∑i=1nEmisNOx,i′
and
RMSE=∑i=1n(EmisNOx,i-EmisNOx,i′)2n
respectively, where i represents the individual city, and n is the total number of cities used for evaluation. The metrics for lifetime evaluation
are consistent with Eqs. () and () when replacing EmisNOx with τ and
EmisNOx′ with τ′. A good method should have a large R, a near-zero NMB, and a small RMSE.
Results and discussionEvaluation
We apply MISATEAM to 60 large cities over the United States (see the selection criteria of cities in Sect. 2.1). For five cities, we are not able to initiate the
fitting procedure, due to a lack of observations under calm wind conditions to calculate LDcalm(x). We derive valid fitting results
for 26 cities. The locations of the 26 cities are shown in Fig. 2. The other 29 cities without valid results either had small correlation coefficients
(< 0.9) or large fitting errors (standard deviation error of τ> 10 %); those cities tend to have larger temporal variations in winds
(similar to Fig. S3), which do not satisfy MISATEAM's requirement for steady winds prior to the satellite overpass.
Scatterplot of the fitted total NOx emissions EmisNOx as compared to the given total emissions EmisNOx′ under different scenarios. The blue, grey, and red dots represent the scenarios based on the fitted lifetime τ and a constant NOx to NO2 ratio of 1.32 (“this study”), the fitted lifetime τ and the NOx to NO2 ratio given by the NU-WRF model (“NU-WRF NOx/NO2”), and a constant lifetime of 2.5 h and a constant NOx to NO2 ratio of 1.32 (“constant lifetime”), respectively. The dashed line represents the 1:1 line. Statistics are provided in the inset table.
Figure 6 compares MISATEAM estimated lifetimes and emissions with the NU-WRF lifetimes and given emissions for the 26 cities. The comparison shows
good consistency in general. For results derived from the wind data sampled at the overpass time (hereafter referred to as “1 h wind”; red
dots), values of R are 0.56 and 0.88 for lifetimes and emissions, respectively. The bias is rather small for the lifetime comparison with NMB of
-0.04 and RMSE of 0.54. The bias is larger for emissions, primarily caused by the assumption of a constant NOx to NO2
ratio (RNOx:NO2). The errors arising from the differences between RNOx:NO2 for
individual cities and a constant value of 1.32 will be propagated into the resulting emissions. The impact of the prescribed
RNOx:NO2 on inferring emissions will be discussed in more detail in this section (Fig. 7).
The use of wind data over 9 h prior to the overpass time improves the performance of MISATEAM. Figure 6 compares the inferred lifetimes and emissions
based on the 9 h weighted average of wind data (hereafter referred to as “9 h wind”; blue dots). The results derived from the
weighted average wind data show larger correlations with R increasing from 0.56 to 0.79 for lifetimes and from 0.88 to 0.96 for emissions and a smaller bias with NMB decreasing from -0.04 to 0.02 for lifetimes and from 0.23 to 0.13 for emissions, when comparing with results derived from the
1 h wind. We have performed the comparison using results based on the weighted averages of 3, 6, and 12 h wind data as well. The use
of wind information prior to the satellite overpass time succeeds in improving the performance of MISATEAM in all these cases (Fig. S4 in the
Supplement). Note that the correlation between the inferred and the NU-WRF lifetimes based on 12 h wind (R= 0.64) is not as good as that
based on 3 h (R= 0.74), 6 h (R= 0.78), and 9 h (R= 0.79) wind, which is most likely caused by the inclusion of
overnight wind information.
The importance of applying wind information prior to the satellite overpass time should not be overinterpreted. The fitting function Eq. ()
by definition is not capable of describing the NO2 plumes under significantly varying wind directions because such temporal variations are
not considered in the fitting function. In this way, wind directions and the results inferred from different wind scenarios are not expected to vary
significantly, as far as fits with sufficient quality are yielded. Only 6 out of 26 cities show relative differences larger than 20 % when
comparing results derived from 1 h wind to those derived from 9 h wind.
We examine a scenario, namely “NU-WRF NOx/NO2”, to investigate possible errors from the assumption of a constant
RNOx:NO2. We replace RNOx:NO2 with the ratio of NOx and
NO2 calculated directly from NO2 and NO VCDs per grid cell by NU-WRF outputs and then use MISATEAM for inferring
NOx emissions. Any difference in the inferred emissions compared to the emissions based on the prescribed ratio of 1.32 (“this
study”) can then be assumed to originate from errors in the assumption of RNOx:NO2. Figure 7 compares the results
using a prescribed ratio (blue dots) with those using NU-WRF NOx/NO2 (grey dots). The comparison shows nearly the same
correlations to the given emissions but a smaller bias for results based on NU-WRF NOx/NO2, with NMB dropping from 0.13
to almost zero (0.03). The comparison suggests that the influence of changing ratio on derived emissions is limited because its spatial variation is
significantly smaller than that of NOx lifetime and NO2 columns (τ and LDcalm(x) in
Eq. ). Considering the investigated cities are located all over the country and have a wide range of geographic features, we conclude that a
constant ratio is a reasonable assumption without resulting in significant bias to the derived emissions for typical US cities. The error associated
with the assumption is estimated to be 10 %, consistent with our previous estimates based on literature reviews (Beirle et al., 2011; Liu et al.,
2016b). However, for applications based on geostationary satellites with changing local observation time, the approach using a constant value for
RNOx:NO2 is subject to larger uncertainties arising from the diurnal cycle of
RNOx:NO2(Han et al., 2011).
We examine an additional scenario, namely “constant lifetime”, to show the necessity of deriving lifetimes for individual cities. Instead of
individually fitted lifetimes for each city, we use the mean NU-WRF lifetime of all cities (2.5 h) for the calculation of emissions in the
constant lifetime scenario. The emissions correlation drops to -0.03 (Fig. 7), showing that individually fitted lifetimes are critical for this
method. The bias is also larger, with RMSE increasing by a factor of 3 compared to results based on the individually fitted lifetimes. This further
improves our confidence that the derived variation of the fitted lifetimes carries important information on local variability of the oxidizing
capacity of urban plumes. The individual lifetimes are well suited for the determination of emissions, suggested by the significantly improved
consistency with given emissions.
Scatterplots of (a) the fitted NOx lifetime τ as compared to the NU-WRF lifetime τ′ and (b) the fitted NOx emissions EmisNOx as compared to the given emissions EmisNOx′. Error bars show the standard error of the fitted results for all available wind directions. Standard error is defined as standard deviation divided by n, with n being the number of available wind directions. The results derived from MISATEAM, the approach of Beirle et al. (2011), and the approach of Liu et al. (2016b) are displayed by blue, grey, and red dots, respectively. The dashed line represents the 1:1 line. Note that (b) is plotted on a logarithmic scale.
Comparison with previous methods
We further evaluate MISATEAM by comparing the results with those derived from two previous approaches, including Beirle et al. (2011) and Liu
et al. (2016b). The comparison of the technical details between MISATEAM and these two previous approaches is given by Fig. S5 in the Supplement. We
apply all three approaches to fit lifetimes and emissions for all 26 cities investigated by this study. Note that we use the 9 h wind for all
approaches for best performance and consistency.
Figure 8a illustrates the comparison for inferring lifetimes. The approach of Beirle et al. (2011) does not predict lifetimes well, with a poor
correlation (R= 0.01). The correlation improves (R= 0.36) when eliminating the data for seven cities with large (> 5 h) or small
(< 1 h) fitted lifetimes, assuming the NOx emission distributions around these cities do not meet the requirements of
the Beirle et al. method. The poor correlation is not surprising because by definition the method can only represent a single-point source convolved
with a Gaussian function and was not intended to be applied to mixed sources with interfering emissions from nearby cities or industrial areas. For
instance, it is capable of giving an accurate estimate for the isolated city of St. Louis in Missouri, with a relative difference of less than 10 %
compared to the NU-WRF lifetime. However, for most cities with a polluted background, the fitted lifetimes are biased significantly due to the
interference from surroundings. This is consistent with the previous findings for this approach: an additional source at 100 km with only
10 % of the emissions of the source under investigation causes a lifetime bias of 20 %; for an interfering source of the same order as the
source of interest, the method fails completely (Liu et al., 2016b). Several studies adopted a plume rotation technique (Pommier et al., 2013; Valin
et al., 2013) to advance the approach of Beirle et al. (2011), which is not applicable to mixed sources as well. These techniques rotate NO2
measurements centered over the city center so that NO2 columns under different wind directions are aligned in a common upwind-to-downwind
direction. This increases the number of observations used for analysis without introducing additional errors for (quasi) point sources, compared with
individually analyzing observations by wind directions as done in this study. However, for mixed sources investigated in this study, the use of such
rotation techniques may result in significant bias by allocating the NO2 from interfering sources into a ring of elevated NO2
values around the source of the interest and thus amplifying the NO2 signal of the source. An illustration of this amplification can be
found in Fig. S2 of Fioletov et al. (2015).
We note that the performance of MISATEAM is also better than that of the approach reported in Liu et al. (2016b), although they share the same concept
of using the NO2 patterns observed under calm wind conditions as a proxy for emission patterns instead of assuming a single-point source as in
Beirle et al. (2011). It is most likely that Liu et al. (2016b) overfit the model by introducing too many degrees of freedom. As suggested by
Fig. 8a, the model function of Liu et al. (2016b) occasionally tries to “explain” changes of scaling factors by a shorter lifetime, resulting in a
small R of 0.21. In MISATEAM, we decrease the number of fitting parameters from three in Liu et al. (2016b) to only one (see details in Eq. A4 of
Appendix A), which improves the robustness of the fit results.
The mean relative change of lifetimes and emissions for different choices of fit and integration intervals and wind fields.
a Intervaldownwind= 150 km. Intervalupwind= 75 km. Intervalintegrate= 150 km. b The wind fields are averaged from the surface up to this height.
Emission comparisons in Fig. 8b show better agreement than lifetime comparisons in Fig. 8a for all approaches. MISATEAM-derived emissions show the
best consistency with the given emissions. According to mass balance, the magnitude of emissions equals the total mass of NOx
divided by lifetime. In the evaluation for MISATEAM, the given emissions range from 57 to 717 molh-1 for all investigated cities, the
variation in which is significantly larger than that in lifetimes ranging from 1.5 to 3.7 h. This finding also holds for the other two
approaches. The other two approaches can achieve a good correlation with the given emissions by providing reasonable estimates for the magnitude of
the total NOx mass, even though they fail to predict variations in lifetimes between cities. For instance, the results derived from
the approach of Liu et al. (2016b) show a small R of 0.21 to the NU-WRF lifetimes but a significantly stronger correlation to the given emissions
of 0.94, which is comparable to that of MISATEAM-derived emissions. But Liu et al. (2016b)-derived emissions are still associated with larger biases
arising from the estimates for lifetimes. The values of NMB are 0.13 and -0.21 for emissions derived from MISATEAM and the approach of Liu
et al. (2016b), respectively, when comparing against the given emissions. Note that the derived and given emissions from the approach of Liu
et al. (2016b) are smaller than the two other approaches but do not indicate a smaller bias. Liu et al. (2016b) only aim to estimate emissions from
the city center, considered as a (quasi) point source, instead of all sources in the urban area. In this way, EmisNOx
and EmisNOx′, and thus RMSE, are smaller than those for MISATEAM.
Uncertainty analysis
The good consistency in Sect. 3.1 increases our confidence that the fitted lifetimes and emissions represent the real-world characteristics well. We
investigate their uncertainties in this section.
Sensitivity analysis
Analogous to Beirle et al. (2011) and Liu et al. (2016b), we investigate the impact of the a priori choice of fit and integration intervals and wind
layer height. The dependency of the fit results for τ and EmisNOx on these three choices is tabulated in Table 1.
The fitted lifetimes are generally robust with respect to changes of the fit and integration intervals because the NO2 distribution under
calm wind conditions, LDcalm(x), is a good representation of the emission pattern in any case. An increase of the fit interval in
the downwind direction by 50 km affects the resulting lifetimes by about -2 ± 11 %. The changes of derived lifetimes are also small
when increasing the fit interval in the upwind direction (4 ± 12 %) or the integration interval (interval i+ 25 km in Fig. 3;
4 ± 18 %) by 50 km. MISATEAM succeeds in avoiding choosing intervals city by city manually, which has been done in previous studies
in order to minimize the influence of other nearby sources.
We use the change of the ratio of fitted emissions EmisNOx to given emissions
EmisNOx′, Δ(EmisNOx/EmisNOx′), to show
the impact of the enlarged fit and integration intervals on emissions. We do not focus on the change of emissions,
ΔEmisNOx/EmisNOx because the fitted emissions are expected to be sensitive to the
enlarged intervals, which include additional sources and thus more emissions. The fitted emissions show an average growth of 48 % associated with
extending the integration interval by 50 km to increase the given emissions by 36 %. The rise in emissions is similar to increasing the
fit interval in the upwind direction by 50 km with 33 % for the given emissions and 42 % for the fitted emissions. However, for the
scenario of a larger downwind-direction, upwind-direction, and integration interval, the change of the ratio of EmisNOx
to EmisNOx′ is rather small, which is 3 %, 9 %, and 9 % on
average, respectively; the fitted emissions show good consistency with the given emissions, reporting correlation coefficients of 0.95, 0.92, and
0.86, respectively. It is interesting to note that the fitted emissions are rather insensitive to the extension of the fit interval in downwind
direction. Neither the given nor the fitted emissions are significantly changed by increasing the downwind-direction interval from 150 to
200 km. It suggests that we succeed in capturing the complete downwind plume and reaching the background areas by the default setting of
150 km for the investigated cities in this study.
Uncertainties associated with the choice of top wind layer height (e.g., 500, 1000, or 2000 m) are relatively small. The resulting lifetimes
and emissions change about 16 % and -9 % on average when averaging the wind fields from the surface to up to 500 m. The average changes
are -11 % and 13 % for inferring lifetimes and emissions, respectively, when adopting the wind layer height of 2000 m. This is
consistent with the findings in the previous studies (e.g., Beirle et al., 2011 and Liu et al., 2016b).
We also apply MISATEAM to year-round NO2 data to investigate the impact of including winter data on the performance of the method. We keep
default settings of MISATEAM as described in Sect. 2.2 for the fit. As expected, the fitted results differ more significantly from given values
compared with results based on using only non-winter data. The bias is larger with NMB changing from 0.02 to -0.14 for lifetimes and from 0.13 to
0.27 for emissions. This indicates that MISATEAM, most likely its inherent steady-wind assumption, is less accurate during the winter season with
longer NOx lifetimes.
Uncertainty quantification
We calculate the uncertainties of inferred results based on the fitting metrics (Figs. 6 and 7) and the dependencies on the a priori settings as
investigated in the above sensitivity studies. We attribute uncertainties of 15 % and 20 % to the derived lifetimes and emissions,
respectively, based on the mean of relative differences for all 26 cities (14 % for lifetimes and 21 % for emissions). The derived emissions
have higher uncertainties arising from uncertainty in the NOx to NO2 scaling factor. The derived emissions in terms of
NO2 are upscaled to NOx based on a constant NOx/NO2 ratio of 1.32, representing typical
urban conditions at noon (Seinfeld and Pandis, 2006). Since MISATEAM aims to provide estimates for cloud-free satellite observations at the overpass
time close to noon of non-winter seasons, and it focuses on polluted regions with generally high tropospheric ozone, this value is reasonably
accurate. However, the NOx/NO2 ratio might vary locally. NU-WRF reports 1.4 ± 0.1 with a range of 1.2–1.6. The
overall impact of variations in this ratio is shown to be relatively small (see Sect. 3.1).
We can identify additional uncertainties that would be present when applying MISATEAM to “real” data instead of synthetic data. The uncertainty of
satellite NO2 observations propagates into the uncertainty of emissions. The uncertainty of satellite NO2 observations has less
impact on the lifetime estimation and only results in errors for lifetimes when satellite observations have systematic errors depending on the
distance from the source. The total uncertainty of NO2 VCDs results from uncertainties in the spectral fit in the retrieval, the
stratospheric and tropospheric separation, and the tropospheric air mass factor (AMF). In the model function of MISATEAM, a possible bias associated
with the stratospheric and tropospheric separation is eliminated by use of the background term b. The uncertainty in the spectral fit in the
retrieval is rather small compared to that associated with AMF (Boersma et al., 2007). We estimated the overall uncertainty primarily arising from the
uncertainty in the tropospheric AMF is about 25 % based on validation of TROPOMI NO2 products with ground-based measurements (e.g.,
Griffin et al., 2019; Ialongo et al., 2020; Zhao et al., 2020). Since the random uncertainty of the tropospheric NO2 observations could be
suppressed due to the consideration of long-term means, this estimate may be conservative.
The presence of clouds is an additional source of uncertainties. We are required to exclude satellite observations with significant cloud fractions in
the instrument's field of view. For TROPOMI NO2 products, we usually remove data with cloud radiance fraction ≥ 0.5. A bias is observed
in NO2 VCD averages as a result of removing the data during cloudy conditions (Geddes et al., 2012). The bias is associated with changing
photochemistry, meteorology, and pollutant transport, which may also have impacts on the NOx/NO2 ratio and
NOx lifetime. NOx lifetime on a sunny day with valid satellite observations will likely be shorter than that on
a cloudy day since faster photolysis rates are expected for NOx reactions on sunny days. The magnitude of a bias is expected to
vary from city to city. We calculate the fraction of cloudy scenes to total scenes over the fit domain of individual cities based on TROPOMI
NO2 products from April through September, 2020. The fractions range from 16 %–56 % for the considered cities. For cities with
heavy cloud cover, like New York, Philadelphia, and Washington D.C., with a fraction > 50 %, the impact associated with cloud selection criteria
is expected to be larger than cities with more clear sky. We estimated an uncertainty of 10 % arising from cloud selection criteria based on the
evaluation performed at urban sites (Geddes et al., 2012).
Additionally, the accuracy of wind fields contributes to the uncertainties of both lifetimes and emissions. It can affect the sorting of the
NO2 VCDs according to wind direction as well as the conversion of the downwind decay from a function of distance into a function of time in
Eq. (). We estimate the uncertainties associated with the wind data to be approximately 30 % based on the comparison of wind information
between the reanalysis product and sounding measurements (see Table S3 in Liu et al., 2016b).
We define total uncertainties of the resulting lifetimes and emissions as the root of the quadratic sum of the above-mentioned error contributions
that are assumed to be independent. We estimated that total uncertainties of NOx lifetime and emissions for a US city are 43 %
and 45 %, respectively.
Conclusions and future work
In this work we developed a CTM-independent approach, MISATEAM, to infer NOx lifetimes and emissions from satellite NO2
observations. As in Liu et al. (2016b), MISATEAM is developed for sources with polluted backgrounds. It adopts the approach of using NO2
spatial patterns under calm wind conditions as a proxy for the spatial patterns of emission sources to account for interferences from neighboring
strong sources. MISATEAM improves upon Liu et al. (2016b) by advancing the fitting function to reduce the number of parameters and to provide
estimations of NOx lifetimes and emissions simultaneously.
We applied MISATEAM to synthetic tropospheric NO2 VCDs over the continental United States provided by a NU-WRF high-resolution model simulation. We
found that our new method for determining NOx lifetimes and emissions was applicable to 26 cities. The derived results were
generally in good agreement with the NU-WRF given values. In existing studies, wind fields sampled simultaneously with satellite observations were
used to drive the CTM-independent approach. We investigated the impact of temporal variations in winds on fitted results and found the use of wind
data prior to the satellite overpass time improves performance of our approach. R between inferred and NU-WRF lifetimes increased from 0.56 to 0.79 and
for emissions increased from 0.88 to 0.96 when comparing results based on 1 and 9 h winds, respectively. The comparison between MISATEAM and
the approaches of Beirle et al. (2011) and Liu et al. (2016b) suggests that MISATEAM is more suitable for non-isolated sources, particularly for
lifetime estimation. Lifetimes inferred from the previous approaches showed rather weak correlations with respect to NU-WRF lifetimes (0.01 for Beirle
et al., 2011 and 0.21 for Liu et al., 2016b) as compared with those from MISATEAM (0.79).
We plan to apply MISATEAM to observations from TROPOMI and geostationary satellite instruments including the Korean Geostationary Environmental
Monitoring Spectrometer (GEMS; Kim et al., 2012), NASA Tropospheric Emissions: Monitoring of Pollution (TEMPO; Chance et al., 2012), and ESA
Sentinel-4 (Ingmann et al., 2012). These instruments have spatial resolutions similar to the NU-WRF simulation (4 km) used in this study. For
applications based on geostationary satellites with local observation time outside of the early afternoon time frame, additional investigation about
the impact of the diurnal cycle of NO2 lifetime is required, since MISATEAM is expected to have a larger uncertainty when the lifetime is
longer. We estimate that uncertainties in NOx lifetime and emissions arising from MISATEAM are approximately 15 % and 20 %,
respectively, for typical (US) cities. Additional uncertainties are associated with wind errors in the reanalysis dataset as well as errors in the
satellite NO2 retrievals, increasing the total uncertainties of NOx lifetime and emissions to 43 % and 45 %,
respectively. The general low bias of NO2 tropospheric VCDs from TROPOMI for polluted sites (Verhoelst et al. 2021) is directly transferred
into the inferred NOx emissions if no correction is performed. We will attempt to reconcile bottom-up and satellite-derived urban
emissions to generate a merged inventory (e.g., Liu et al., 2018) to provide timely NOx emissions estimation for air quality and
climate modeling communities.
Derivation of the model function f(x)
We derive Eq. () based on the continuity equation for a steady state, following Eqs. (A1) and (A2) given by
A1E(x)=S(x)+D(x),A2S(x)=RNOx:NO2⋅LD(x)τ,
where E(s), S(x), and D(x) represent the line densities of NOx emission, sink, and divergence, respectively. As the
NOx sinks are dominated by the chemical loss due to reaction of NO2 with OH at the local overpass time of TROPOMI
(13:30 LT), sink S(x) can be described by a first-order time constant τ and thus is proportional to the NO2 line density
LD(x) itself as shown in Eq. (A2). Beirle et al. (2019) provided further details.
We use NO2 line densities under calm wind conditions, LDcalm(x), to simplify Eqs. (A1) and (A2). In principle, there is
no NOx transport under perfect calm wind conditions (i.e., divergence D(x) is zero), and thus the emission E(x) equals the
sink S(x) given by RNOx:NO2⋅LDcalm(x)τ. However, we use the threshold of
2 ms-1, instead of 0 ms-1, as the criterion for calm wind to get a good compromise between sufficient sample sizes for
the calculation of line densities under both calm conditions and windy conditions. In order to account for the error associated with this
criterion and possible systemic differences between windy and calm wind conditions (e.g., cloud conditions, vertical profiles, or lifetimes), and to
account for the upper tropospheric background column which is not driven by local emissions, we introduce a constant background b in the fitting
function, as given by Eq. (A3).
E(x)=S(x)=RNOx:NO2⋅[LDcalm(x)-b]τ
We derive Eq. () following the concept proposed by Liu et al. (2016b). We use LDcalm(x) as a proxy for emissions instead of assuming a
single-point source as in previous studies (e.g., Beirle et al., 2011; Laughner et al., 2019). The NO2 line density without considering the
chemical decay is given by E(x)RNOx:NO2⋅w based on a Gaussian plume model. This formulation is
different from the model functionf(x)' originally proposed by Liu et al. (2016b), which was given by
f(x)′=a⋅LDcalm(x)∗e-xw⋅τ+b.
We replaced one fitting parameter, the scaling factor a in f(x)′, with variables that have physical meanings in the new model
function f(x). The new formulation was shown to improve the model performance in Sect. 3.2. We then convolved
E(x)RNOx:NO2⋅w with an exponential function e-xw⋅τ describing the chemical
decay to form the new model function f(x)), implicitly assuming a constant effective lifetime τ.
Data availability
The NU-WRF model outputs are available upon request from Zhining Tao (zhining.tao@nasa.gov). Additional data related to this paper may be requested from the corresponding author.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-22-1333-2022-supplement.
Author contributions
FL, JJ, and SB provided conceptualization and methodology, ZT performed model simulation, FL and YY performed formal analysis, FL prepared the original draft, and all authors reviewed and edited the finalized draft. FL prepared visualization, and FL and JJ provided supervision, project administration, and funding acquisition.
Competing interests
At least one of the (co-)authors is a member of the editorial board of Atmospheric Chemistry and Physics. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at the Goddard Space Flight Center. We thank two anonymous reviewers for helpful comments.
Financial support
This research has been supported by NASA through the Aura project data analysis program and through the Atmospheric Composition Modeling and Analysis Program (ACMAP) (grant no. 80NSSC19K0980).
Review statement
This paper was edited by Aijun Ding and reviewed by two anonymous referees.
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