Variable effects of spatial resolution on modeling of nitrogen oxides

. The lifetime and concentration of nitrogen oxides ( NO x ) are susceptible to non-linear production and loss, and consequently to the resolution of a chemical transport model (CTM). Here , (cid:58)(cid:58)(cid:58)(cid:58) due (cid:58)(cid:58) to (cid:58)(cid:58)(cid:58) the (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) strong (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) spatial (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) gradients (cid:58)(cid:58) of NO x (cid:58)(cid:58)(cid:58) and (cid:58)(cid:58)(cid:58) the (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) dependence (cid:58)(cid:58)(cid:58) of (cid:58)(cid:58) its (cid:58)(cid:58)(cid:58)(cid:58) own (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)


Introduction
Nitrogen oxides (NO x ≡ NO+NO 2 ) have major roles in tropospheric chemistry and air quality.During daytime, NO x interacts with hydrogen oxide radicals (HO x ≡ OH + HO 2 ) and volatile organic compounds (VOCs) via photochemical reactions to affect formation of ozone and nitrate aerosols (e.g., Sillman, 1999;Thornton et al., 2002;Pusede et al., 2015;Zhu et al., 2022).

Materials and methods
We use the GEOS-Chem model in its high performance implementation (GCHP, http://www.geos-chem.org,version 13.2.1,DOI: 10.5281/zenodo.5500718)to simulate NO x and its relevant components over the eastern US.
GCHP is a grid-independent implementation of GEOS-Chem operating in a distributed-memory framework for massive parallelization (Long et al., 2015;Eastham et al., 2018).Chemical transport is simulated using a finite volume advection code (FV3) on a cubed-sphere grid (Putman and Lin, 2007).GCHP uses identical chemistry and physics modules as the standard :::::::: traditional : GEOS-Chem code ::::::::::::: implementation : (GEOS-Chem Classic).A stretched-grid capability offers finer resolution over a user-specified domain of interest (Bindle et al., 2021).The model version used here (v13.2.1) features significant advances for performance and ease of use (Martin et al., 2022).The model is driven by the Goddard Earth Observation System Forward Processing (GEOS-FP) assimilated meteorological data with the native resolution of 0.25°×0.3125°,from the NASA Global Modeling and Assimilation Office (GMAO).The GEOS-FP data is currently the finest resolution meteorology available for GCHP simulations for the simulation year, and was regridded to each simulation resolution, including the resolution (of 13 km) that is finer than 0.25°×0.3125°.Although non-ideal, this capability as demonstrated by Bindle et al. (2021) will not significantly alter our interpretations focusing on discussing redistribution of NO x emissions and chemical feedbacks, rather than effects from meteorology.Yan et al. (2016) showed that sub-coarse-grid emission-chemical variability dominantly contributed to the differences of simulated tropospheric chemistry between resolutions, overwhelming the effects from resolution of non-chemical factors such as meteorological data.Consistent with GEOS-FP, the atmosphere is vertically distributed into 72 layers (from surface to 0.01 hpa) following the hybrid sigma-pressure grid definition during the simulation.Boundary layer mixing is simulated with a non-local scheme (Lin and McElroy, 2010).The lowest layer is roughly 120 m thick, with mixing ratios of NO x , HO x and ozone that we refer to as the "surface concentrations" :: or ::::::: "surface :::::: mixing :::::: ratios" ::::::::::::: interchangeably.
We use the standard full-chemistry scheme of the GEOS-Chem model which is widely used to study air quality (Koplitz et al., 2016;Li et al., 2017;Shah et al., 2020;Gu et al., 2021).The scheme includes detailed gas-phase mechanisms of HO x -NO x -VOC-ozone chemistry (Bey et al., 2001;Mao et al., 2013;Sherwen et al., 2016) including heterogeneous uptake of reactive gases (McDuffie et al., 2018;Holmes et al., 2019) by the simultaneously simulated aerosols.Anthropogenic NO x emissions are from EDGAR v5.0 at 0.1°resolution (Crippa et al., 2021), and speciated anthropogenic non-methane VOC emissions are from CEDS v2 (Hoesly et al., 2018).Open burning emissions are from GFED v4.1 (van der Werf et al., 2017).Although the latter two inventories have non-ideal (0.5°and 0.25°) resolutions due to availability, they are acceptable for our purpose of identifying the resolution dependence of NO x .One favorable capability of the simulation is the pre-calculated offline dust, lightning NO x , biogenic VOC (BVOC), soil NO x and sea salt aerosol emissions (Murray et al., 2012;Weng et al., 2020;Meng et al., 2021), which avoids possible regional emission biases due to online calculations using meteorological fields at different resolutions, and the consequent interference on the interpretation of the results.All the emissions are handled by the HEMCO 3.0 module (Keller et al., 2014;Lin et al., 2021).
3 Results 1c, : upper left), NO x exhibits notable local enhancements over cities and major industrial corridors due to its short lifetime (τ , several hours).Overall, the stronger emissions and agglomerate sources in the Great Lakes region (GL, green box) lead to higher NO x levels than in the Southern States (SS, magenta box) where NO x sources are relatively weaker and sparser.As the grid cell size increases to 22 km resolution, the NO x level shows overall decreases over emission centers and increases over nearby grids (by up to 1 ppb :::: ppbv) relative to 13 km, an expected consequence due to dilution of emissions.However, systematic biases in predicted NO x relative to 13 km resolution start to emerge especially further downwind :: of ::::: urban : NO x ::::::

Daytime resolution effects at surface in summer
sources and over the SS, reflecting the effects from the resolution-dependent τ .The biases relative to 13 km resolution become increasingly pronounced and regionally coherent as grid cells further enlarge.At the three coarse ::: two :::::: lowest resolutions (> 50 :: 90 : km), a clear dipole of negative biases over the GL and positive biases over the SS becomes observable ::::: visible.
The opposite resolution effects of simulated NO x over the GL and SS are summarized as regional mean biases in each panel reducing nitric oxide (NO) by the OH-promoted organic peroxy radicals (RO 2 ), an important NO x sink pathway under low-NO x and high-VOC environments (i.e. the SS) (Browne and Cohen, 2012;Perring et al., 2013;Romer et al., 2016;Romer Present et al., 2020).As NO x emissions continue to decrease, multiple lines of evidence suggest that NO x sources widely across the United States have recently entered or are approaching the NO x -limited regime (Laughner and Cohen, 2019;Jin et al., 2020;Koplitz et al., 2021;Jung et al., 2022;Zhu et al., 2022), especially over the SS since the 2010s (Jin et al., 2020;Koplitz et al., 2021;Zhu et al., 2022).Unlike over the GL where the regional biases of surface gradually increase in magnitude following increasing grid cell sizes (Figure 1c, green numbers), the five resolutions > 13 km indicate small changes in the regional concentration across the SS (i.e.biases of 6.4-8.7%);namely, the systematic increase occurs primarily between 13 and 22 km resolutions (Figure 1c, magenta numbers).This observation can be related with the variation of ::: The spatial extent of chemical regimes and their effects on the NO x biases :::: vary during the course of the day.-27.8%).These differences are consistent with the relative diurnal ::: diel : evolution of NO x (decreases since sunrise) and HO x (accumulates and peaks after noon) abundances and the consequence on the dominant HO x loss pathway (e.g., Ren et al., 2003;Ma et al., 2022).The inclusion of morning hours could therefore partially explain the relatively weaker resolution dependence in daytime over the SS.
Another potential cause of ::::::: relatively : weaker sensitivity of simulated NO x to resolution : in ::: the ::: SS is the impacts from BVOC in addition to NO x heterogeneity.Figure S3 :::: Fig. :::: A1b shows that changing VOC reactivity mainly affects OH concentration and τ : τ : over the NO x -limited regime while has little effects on the NO x -saturated regime, consistent with previous studies (Edwards et al., 2014;Laughner and Cohen, 2019;Zhu et al., 2022).Apart from increasing OH that decreases τ (Figure S3 ::: Fig. ::: A1b), decreasing VOC can also oppositely decrease the strength of the NO-RO 2 loss pathway and increase τ (Browne and Cohen, 2012).Nonetheless, both processes indicate increasing sensitivity of τ to VOC at low-NO x environments (Romer et al., 2016;Laughner and Cohen, 2019;Romer Present et al., 2020).The SS feature strong BVOC emissions as well as strong spatial segregation of NO x and VOC sources (Yu et al., 2016;Travis et al., 2016), as reflected by lower isoprene/NO x emission ratios in urban centers relative to its neighborhood in relative :: to :: in ::: the ::: GL.In summary, our simulations reveal that the predictability of actual resolution dependency of NO x in the NO x -limited regime is reduced due to the joint sensitivities to VOC. ).However, one characteristic phenomenon at nighttime that depends on resolution is the titration between NO and ozone (O 3 ), which is :: are : the main nighttime sink :::: sinks : to each other in urban environments (Brown et al., 2006;Wang et al., 2006;Brown and Stutz, 2012;Kenagy et al., 2018;Shah et al., 2020).(Jacob et al., 1995;Zhang et al., 2004;Jin et al., 2017;Yan et al., 2018;Sicard et al., 2020;Li et al., 2022) over strong NO x sources.This anti-correlation at fine resolution leads to inefficient NO-O 3 reaction, which is to first-order proportional to their products, shown in the third column in Figure S6.

Nighttime resolution effects at surface in winter
:::

Seasonal and diel variation of relevant processes
Figure ::: Fig. 3 summarizes the resolution effects of regional mean surface NO x , HO x and ozone, at different hours of the day.
Overall, the daytime resolution effects driven by the involvement of NO x in HO x and O 3 production (Section 3.1) compete with the nighttime effects driven by NO x -O 3 titration (Section 3.2).The changing dominance of each mechanism during summer vs. winter, as well as during daytime and nighttime, leads to the characteristic seasonal and diel variation in Figure     NO 2 columnar properties, using model simulations at these resolutions.

Implications for satellite remote sensing applications
Satellite retrievals of NO 2 vertical column density (Ω) have been widely used to quantify and characterize spatiotemporal variation of NO x abundances and sources.Here we evaluate the implications of the NO x resolution dependency on two major applications-estimating surface NO 2 concentration and deriving NO x emissions.
Figure ::: Fig. 6 shows the simulated fraction of NO 2 abundance within the surface layer of GEOS-Chem relative to the whole troposphere, during Low Earth orbit (LEO) afternoon satellite overpass time.This surface fraction (F s ) is lower in summer than in winter, driven by stronger convection, lightning NO x , and elevated boundary layer.F s is also lower over the SS than the GL in July, due to relatively less :::::: weaker : NO x emissions at :: the : surface and stronger lightning NO x emissions in the upper troposphere (Murray et al., 2012;Silvern et al., 2019;Zhu et al., 2019).The changes of F s following varying resolutions in general qualitatively resemble these of surface NO x (e.g., comparing Figure 6 with Figures :::  2a).Overall, F s has stronger biases in July than in January, lowered by 8 :: 10% over the GL and enhanced by 7 : 4% over the SS at 181 km, relative to 13 km resolution.As F s is a key parameter in estimating surface NO 2 concentration from satellite retrieved Ω (Lamsal et al., 2008;Cooper et al., 2020), directly applying the simulated NO 2 vertical profiles will propagate such resolution-dependent biases that also vary regionally and seasonally, as indicated in Figure :::   1c), the Ω and Ω s differences show stronger regional uniformity, revealing overall increasingly negative biases with increasing grid size over both seasons and regions.For July and over the SS, the daytime ::::::: afternoon : columnar biases are reversed to be negative compared to the positive surface biases (e.g., Figure
Attention to the NO x -limited regime and its corresponding resolution effects is timely given declining NO x emissions across the US with NO x emission regulations.At the same time, the joint sensitivity to NO x heterogeneity and concurrent VOC level (Section 3.1) in the NO x -limited regime will continue complicating its predictability, since NO x and VOC can have various spatial co-variabilities (e.g., positively correlated where transportation-relevant VOC and NO x both dominates) and regimedependent effects on τ .Therefore, accurately capturing such regime difference and transition from CTM requires not only accurate emission inventories of NO x and VOC, but also simulations at representative spatial scales :::: (e.g., :: 10 ::: km :: or ::::: finer) : that correctly distribute these emissions ::::::::::::::: (Valin et al., 2011).
We found systematic resolution effects of nighttime NO-O 3 titration efficiency that can drive the NO x biases over winter (Figure :::: Fig. 2 and Section 3.2), as the anti-correlation between NO and O 3 implies faster reaction rates at coarser resolutions.
In air quality modeling, many key reactions involve spatially correlated (e.g., co-emitted SO 2 and NO 2 to cause severe urban haze (Wang et al., 2020)) or segregated species (e.g., agricultural NH 3 and NO x -formed HNO 3 for nitrate aerosol partitioning (Gu et al., 2021)).Like in this study, the segregated species will consume precursors and produce products more efficiently at coarser resolutions, while collocated sources will experience opposite effects.Interpreting the evolution of relevant species and air pollution processes using : a : CTM is therefore also preferable at the spatial scales that are representative of these sources, or should take this effect into account if performed on coarser scales.
Our detailed simulation of resolution effects at different altitudes (Figures :::  retrieved Ω, namely estimation of surface NO 2 concentration and constraining NO x emissions, we found that regionally and seasonally varying biases at the level of ∼10% due to adopting coarse model simulations (∼200 km) are inevitable.
Overall, we conducted a comprehensive novel evaluation of NO x resolution dependence using a CTM across a wide range of resolutions (13-181 km) and scenarios (including nighttime, winter and higher altitudes).We found the strongest resolution effects in the summer and daytime (e.g., -18 :: -16% for surface NO x and -10 :: -8% for columnar NO 2 over the Great Lakes), where and when the NO x spatial heterogeneity is the strongest and its lifetime is the shortest (e.g., Figure S5).::: Although this study exploited state-of-science capabilities, biases with respect to resolutions finer than 13 km resolution likely exist considering the severely ::::: highly : localized NO x especially in summer (Valin et al., 2011;Larkin et al., 2017;Beirle et al., 2019).Following NO x regulations in the US, the magnitudes of resolution effects are expected to continue decreasing as the enhancements over sources reduced relative to the background NO x level (Russell et al., 2012;Jin et al., 2020;Qu et al., 2021), and the requirements on resolution may diminish (e.g., partially reflected by the smaller effects over the SS relative to over the GL).Nonetheless, over developing areas where current NO x emissions are stronger or are projected to increase, the resolution effects will be exacerbated, and applying finer-resolution simulations to accurately capture NO x lifetime and budgets will be increasingly critical for air quality modeling applications.Optimization of appropriate resolution that can capture the relevant processes accurately for specific applications given computational resource constraints is also of great interest.GCHP offers the unique ::: this global high resolution simulation capability, and also the opportunities to expand this analysis into a more comprehensive understanding of global resolution-dependence of NO x and its nonlinear chemistry.27 Table 1.Description of the simulations with six resolutions over the eastern US.

Figure
Figure ::: Fig. : 1a shows the study domain of interest (70-98°W and 26-48°N) and the emission ratio of isoprene to NO x .

Fig
Fig. :::: A4.By simply diluting their concentrations to larger grid cells (2rd-6th :::::: 2nd-6th rows), the products of NO-O 3 from less anti-correlated concentrations are enhanced systematically.Consequently, there would also be faster production of N 2 O 5 and nitrates, which were proposed by Zakoura and Pandis (2018) to explain the systematic overprediction of nitrate aerosols by CTMs at coarse resolution.As the GL region has greater NO concentrations ::::: mixing ::::: ratios : than the SS (Figure ::: Fig. : 2b), surface O 3 is more effectively titrated (Figure ::: Fig. 2c), leading to increased NO 2 and NO x concentrations (Figure ::: Fig. : 2d).Meanwhile over the SS, the NO 2 response is less pronounced due to the lower NO levels, and NO 2 exhibits reductions over certain locations at lower resolutions (Figure :::: Fig. 2d), indicating that the excess O 3 can consume more NO 2 after titrating NO over these grids.
Fig. :: S3) at resolutions > 13 km occur at nighttime in January (up to 5%), and at daytime in July (up to -30%), revealing a pronounced seasonality of dominant mechanisms driving the resolution effects.This seasonality is driven by the stronger intensity and duration of daytime oxidant production in July (i.e.magenta ::::: purple : lines for HO x and O 3 in Figure ::: Fig. : 3); meanwhile the greater nighttime O 3 titration at coarser resolution partially counteracts the daytime effects in July (i.e.reduces the percentage biases) and dominates in January.

Figure
Figure ::: Fig. 4 shows the resolution-dependent changes in regional mean daytime ::::::: afternoon : NO x vertical profile :::::: profiles in the lower troposphere (below 4 km).Uniform decreases in the simulated daytime ::::::: afternoon : NO x following larger grid cells are apparent at > 1km altitude in July, despite opposite changes over the two regions near surface (Figure ::: Fig. 1).These vertically dependent responses are caused by the different vertical profiles of NO x and HO x (i.e.magenta ::::: purple lines).As NO x mixing ratio decreases exponentially aloft while HO x increases (in the GL) or remains relatively uniform (in the SS), HO x becomes more abundant relative to NO x at higher altitudes, meaning that τ is less sensitive to NO x local concentrations :::::: mixing ::::: ratios even above strong NO x sources.The enhanced oxidants (ozone and HO x ) due to surface NO x emission heterogeneity (Section 3.1) then vertically mixed ::: mix : to systematically enhance :: the : HO x profile (Figure ::: Fig. : 4, right) and reduce τ and NO x in these aloft layers.Therefore, both regions exhibit negative NO x biases due to coarse resolution above 1 km, regardless of chemical regime.

Figure
Figure ::: Fig. : 5 shows the changes in nighttime vertical profile of NO x and O 3 in January.Again, there are opposite vertical distributions of NO x and its nighttime sink (ozone).Over the GL, although :: the : surface NO x lifetime can be possibly prolonged at coarse resolution due to the faster titration of O 3 by NO (Section 3.2), NO quickly becomes insufficient to titrate the increasing ozone at higher altitudes.Therefore, both NO x species ultimately become affected by the resolution-dependent titration efficiency above 1 km (similar to the surface responses over the SS), leading to the negative biases in simulated NO x , regardless of surface NO x emission strength.
Figs. : 4 and 5 reveal that the resolution effects of τ at ::: the : surface can differ from those at elevated altitudes, even over source regions.Such altitude-dependent responses will further affect interpretation of satellite-retrieved Fig. :: 6 :::: with ::::: Figs.1c and Figure
NO2 column within the surface layer at 13 km and biases at the other resolutions NO 2 column within the surface layer at 13 km and biases at the other resolutions

Figure 6 .
Figure 6.Coarse resolution simulations yield variable biases in satellite-based estimation of surface NO2 concentration.Panels (a) and (b) are both similar to Fig. 1c (for January and July, 2015, respectively) but for the fraction (%) of NO2 tropospheric column within the surface layer during afternoon satellite overpass time (UTC 19-21).The numbers for the other resolutions vs. 13 km are absolute differences in percentage number.
at 13 km and biases at the other resolutions

Figure 7 .
Figure 7. Coarse resolution simulations yield positive biases in spaceborne inverse modeling of NOx emissions.Panels (a) and (b) are both similar to Fig. 1c (for January and July, 2015, respectively) but for the mean GEOS-Chem tropospheric NO2 column density (in molecules/cm 2 ) during afternoon satellite overpass time (UTC 19-21).
-sphere grid contains a mosaic of six grids (faces).Each face is regularly spaced with N×N grid cells, and the notation of each resolution (CN) here identifies the size N. b Stretch factor (S) defines the strength of the grid-stretching.The resolution is about S times higher than the regular cubed-sphere over the refined region (eastern US), while is about 1/S of the original resolution over the antipode.