We use surface observations of hourly PM2.5 abundances (µg m-3) provided by India's Central Pollution Control Board (CPCB; http://www.cpcb.gov.in/CAAQM/mapPage/frmindiamap.aspx). We consider the time period 1 October 2015–31 March 2016 as the highest PM2.5 abundances in Northern India typically occur during late fall to early spring (Moorthy et al., 2013) and very few observations are available for years prior to this period. A total of 22 sites across Northern India provide data for this time period; however, many of these sites span areas of only a few tens of kilometers (e.g., 9 are located in a single area of about 25 × 25 km in and around New Delhi). Table 1 provides a summary of the sites used. The data contains obvious repetitive “fill” values when presumably the monitor obtains a null value or the measurement is outside of the detectable range (e.g., 985, 1985 µg m-3). However, these values are not flagged and are also considered in the daily averages that CPCB provides. Most of these fill values are well over 1000 µg m-3 and so we exclude any PM2.5 abundance ≥ 985 µg m-3, although such high levels have occasionally been observed in similarly polluted environments (e.g., Liu et al., 2017). This process filters 812 observations, or ∼ 1 % of the total hourly data. Daily averages are calculated from each site's hourly abundances as long as there is at least one valid value.

We also use surface observations of total PM2.5 and its chemical composition collected at Kanpur (26.5∘ N, 80.3∘ E, 142 m a.s.l.) over the period 25 October 2008–30 January 2009. The chemical composition data includes organic carbon (OC) converted to organic matter (OM) using a factor of 1.6, elemental carbon (EC), ammonium (NH4+), sulfate (SO42-), nitrate (NO3-), Na+, K+, Mg2+, Ca2+, Cl-, and HCO3-. A thorough description of the sampling details and measurements is provided by Ram and Sarin (2011) and Ram et al. (2012a, b, 2014).

We use reanalysis fields (2.5∘ × 2.5∘ linearly interpolated to 1∘ × 1∘) from the National Centers for Environmental Prediction (NCEP/NCAR) (version 1; http://www.esrl.noaa.gov/psd/) of several variables known to influence PM2.5 abundances including relative humidity (RH), surface (2 m) temperature, precipitation, and wind speed and direction at the surface (10 m), 850, and 500 mb, each of which are provided at 6-hourly intervals. We also use boundary layer height (BLH) reanalysis from ECMWF ERA-Interim (Dee et al., 2011) as NCEP/NCAR does not provide this variable; we note that there is uncertainty in BLH from reanalysis data. We calculate an inversion strength (INV) as the difference between the 850 mb and surface (2 m) temperature (Gutiérrez et al., 2013).

We additionally derive metrics from the reanalysis data that relate to air stagnation, as stagnation describes the basic meteorological conditions that are thought to exacerbate the worst pollution levels (e.g., Jacob and Winner, 2009; Fiore et al., 2012, 2015; and references therein). Stagnation has also been used as a proxy for air quality under future climate change (e.g., Horton et al., 2014). The first metric we consider is the modified air stagnation index (ASI) (Wang and Angel, 1999; Horton et al., 2012), which is a Boolean index that is true (i.e., the air mass is considered stagnant) when (i) daily average 10 m wind speed < 3.2 m s-1, (ii) daily average 500 mb wind speed < 13.0 m s-1, and (iii) daily total precipitation is less than < 1.0 mm. We also calculate the wind run and recirculation factor, which characterize stagnation and recirculation of surface level flow, respectively, as described in detail by Allwine and Whiteman (1994). While the wind run and recirculation factor do not utilize upper level wind data like the ASI, their advantage is that they provide a measure of the magnitude of stagnation. The recirculation factor takes values between 0 and 1, with 1 meaning total recirculation of an air parcel and 0 meaning complete ventilation. The wind run is a measure of cumulative wind with a value of 276.5 km, equivalent to the daily 3.2 m s-1 cutoff for the 10 m wind speed.

We use a developmental version of the new-generation NOAA Geophysical Fluid Dynamics Laboratory Atmospheric Model, version 4 (GFDL AM4) for our analysis (Zhao et al., 2018a, b). The standard model setup as described by Zhao et al. (2017a, b) consists of a cubed sphere finite-volume dynamical core with a horizontal resolution of ∼ 100 km on a cubed sphere grid (96 × 96 grid boxes per cube face) with 33 levels extending from the surface up to about 50 km (1 hPa).

The physical atmospheric model (AM4) differs from the previous version (AM3) as described by Zhao et al. (2018b). AM4 contains increased resolution compared to AM3 (∼ 200 km). AM4 has significantly updated the GFDL radiative transfer code, with refitting to line-by-line calculations using the latest spectroscopy and adding 10 micron CO2 bands, among other changes. The shortwave radiation time-step is reduced from 3 h (AM3) to 1 h. In addition AM4 uses a new topographic gravity wave drag parameterization described by Garner (2005) and a new double plume moist convection scheme developed based on the University of Washington shallow cumulus scheme (Bretherton et al., 2004). The new scheme represents shallow and deep convection, with stronger (weaker) lateral mixing into the shallow (deep plume), with convective inhibition closure for the shallow plume mass flux and cloud work function relaxation closure for the deep plume. The deep plume lateral mixing is also prescribed to vary with the environmental relative humidity.

The base version of AM4 described by Zhao et al. (2017a, b) includes interactive aerosols, but only “simple” chemistry needed to drive aerosol formation by oxidation of precursors. We modify this configuration by adding detailed tropospheric and stratospheric chemistry, and expand the vertical extent of the model to 49 levels (extending up to ∼ 80 km or 1 Pa). This vertical resolution is similar to that in AM3, except an extra layer is placed near the surface so that the model's lowermost layer is thinner.

The chemistry and aerosol physics module in our “full chemistry” version of AM4 are similar in structure to AM3, but with significant modifications. In particular, the efficiency of removal of tracers by convective precipitation is significantly increased (Paulot et al., 2016) compared to the unrealistic weak removal in AM3 (Fang et al., 2011), while the wet removal by frozen precipitation produced by the Bergeron process is strongly reduced (Liu et al., 2011; Paulot et al., 2017). As a result, the spatial distribution of aerosol climatology and seasonal cycle simulated by AM4 has been significantly improved relative to AM3.

The base chemical mechanism used is from AM3, as described by Naik et al. (2013), with gas-phase and heterogeneous chemistry updates from Mao et al. (2013a, b), and updates to the treatment of sulfate and nitrate chemistry and revised treatment of wet deposition (Paulot et al., 2016, 2017). Here we do not take into account the uptake of SO2 and HNO3 on dust. The heterogeneous uptake coefficients used here are provided in Table S1 in the Supplement (Mao et al., 2013a). The model includes the FAST-JX version 7.1 (Li et al., 2016) photolysis code and interactive biogenic isoprene emissions, following Guenther et al. (2006), as implemented by Li et al. (2016).

Modeled aerosol species include black carbon (BC), primary OM, anthropogenic secondary organic aerosol (SOA), NH4+, SO42-, NO3-, sea salt, and mineral dust. Hydrophobic BC and OM are converted to hydrophilic with a 1.44 days e-folding time. Sea salt and mineral dust are partitioned into five size bins (e.g., dust1, dust2, ssalt1, ssalt2; see Eq. 1) with constant volume size bin distributions. The thermodynamic equilibrium of the SO42-–NO3-–NH4+ system is simulated using ISORROPIA (Fountoukis and Nenes, 2007) with the equilibrium between gas and aerosol assumed to be reached at each model time step (30 min). Modeled dry PM2.5 abundances are defined using Eq. (1). We consider 100  % of each aerosol species to be included in PM2.5, except for sea salt and mineral dust where only the bin or fraction of the bin with diameter < 2.5 µm is used. We calculate the dry mass of PM2.5 as follows: PM2.5(dry)=SOA+dust1+0.25dust2+ssalt1+ssalt2+0.167ssalt3+BC+OM+NH4++NO3-+SO42-. This formulation (Eq. 1) does not consider the mass of aerosol water (i.e., hygroscopic growth). Due to diagnostic limitations, assumptions of the SO42-–NO3-–NH4+ system must be made in terms of partitioning NH4+ between NO3- and SO42-, in order to retrieve hourly abundances of PM2.5 that includes hygroscopic growth, as the growth factors are described for NH4NO3 and (NH4)2SO4. At each hourly time step, we calculate the fraction (α) of NH4+ present as (NH4)2SO4 using the following equation: ∝=2SO42-/NO3-+2SO42-. The remaining NH4+ forms NH4NO3. We partition NH4+ this way as (NH4)2SO4 is more stable. The (NH4)2SO4 hygroscopic growth factor is then applied to SO42-+∝NH4+ and thus the NH4NO3 growth factor is applied to NO3- + (1-∝)NH4+. We recognize using this method (as opposed to online calculation using ISORROPIA) introduces some uncertainty into the modeled aerosol mass. However, we use this method as we want to apply constant hygroscopic growth factors at 50 % RH in order to realistically compare modeled results to the observations, as this RH value is operationally defined by CPCB. In addition, there are variations in how different models represent hygroscopic growth. For example, the GEOS-CHEM chemical transport model (Martin et al., 2003) applies the same hygroscopic mass growth factor at 50 % RH of 1.51 to NH4+, NO3-, and SO42-, which is slightly higher than our growth factors for NH4NO3 (1.32) and (NH4)2SO4 (1.46). In addition, GEOS-CHEM includes a growth factor of 1.24 for hydrophilic OM and SOA, whereas our parameterization has no hygroscopic growth of organics at 50 % RH (Ming and Russel, 2004). Sea salt has the largest growth factor (2.32). In any case, we present both dry and wet aerosol mass whenever possible in order to highlight the uncertainty involved with aerosol water content. Equation (3) shows the calculation of PM2.5 mass including water (hence wet PM2.5). PM2.5wet@50%RH=SOA+dust1+0.25dust2+2.32(ssalt1+ssalt2+0.167ssalt3)+BC+OM+1.32NO3-+(1-∝)NH4++1.46(SO42-+∝NH4+) The model is nudged with NCEP-NCAR reanalysis winds (Lin et al., 2012) using a pressure-dependent nudging technique and a relaxation time scale of 6 h at the surface and weakening to ∼ 60 h by 100 ha; this facilitates a consistent comparison of modeled and observed daily PM2.5 abundances.

We perform two simulations, each of 36 years and 3 months duration (1 January 1980–31 March 2016), with the first year used as model spin-up. The first simulation, denoted as AM4-CMIP5, is driven by emissions developed in support of the CMIP5 (Lamarque et al., 2010) and is extended from 2000 to 2016 following the Representative Concentration Pathway 8.5 (RCP8.5; van Vuuren et al., 2011). The second simulation, referred to as AM4-CMIP6, is driven by emissions developed for the upcoming CMIP6 (Hoesly et al., 2018; van Marle et al., 2017) wherein the period from 2000 to 2014 represents historical emissions rather than projections. Years 2015–2016 emissions were set to year 2014 values.

The spatial patterns (1∘ × 1∘) of the CMIP6 total anthropogenic extended wintertime (October–March 2015–2016) emissions (Gg) of BC, OM, NO, SO2, and NH3 used over India in the AM4-CMIP6 simulation are shown in Fig. 1a–e, respectively. Emissions are largest for all species over the IGP and lowest over the oceans and the Himalayan Plateau. The patterns of BC, OM, NO, and NH3 are fairly uniform over the IGP while SO2 emissions (Fig. 1d) are highly localized due to large emissions from coal-fired power plants.

Figure 1f–i show the percent difference between CMIP6 and CMIP5 emissions for the same time period and for the five species in Fig. 1a–e. For BC, OM, NO, and NH3 emissions, most grid cells within the IGP show differences of 50–100 %. Differences in SO2 emissions are more variable, with some grid cells showing moderate differences while others greater than 100 %. Figures S1–S5 in the Supplement compare the evolution of these emissions over the full time period of the model simulation for ten sub-regions in India. For almost every region and every species, the difference between CMIP5 and CMIP6 emissions is largest over 2000–2016 period (i.e., when CMIP5 is extended using RCP8.5); however, some large differences are also seen in earlier years. Overall, anthropogenic emissions in the CMIP6 dataset are much higher than those in the CMIP5 dataset.

Figure 2a, b show the 6-month time series of daily average PM2.5 for two grid cells with multiple observation sites. Nine observations sites are located in the grid cell over New Delhi (Fig. 2a), and they show extreme variability between them despite being within ∼ 25 km of one another. The average difference among the maximum and minimum abundance of the sites on a given day is 160 µg m-3, sometimes reaching over 400 µg m-3. The AM4-CMIP5 abundances are a factor of ∼ 2–4 less than the observations, but the actual magnitude of the bias clearly depends on which observation is being compared against. The AM4-CMIP6 abundances are also generally biased low, mainly in December–January, but often fall within the range of the observations for other months. The correlation coefficient (r) between the two simulations is 0.96 and 0.94 for New Delhi and Kanpur/Lucknow, respectively, highlighting the strong control of meteorology on daily variability. The correlation of the AM4-CMIP6 dry and wet PM2.5 with the average of the observations is 0.57 and 0.56, respectively. The four sites located in the grid cell over the cities of Kanpur and Lucknow (∼ 75 km apart) (Fig. 2b) show less variability between them than those over New Delhi, with an average min-to-max difference of 94 µg m-3. The correlation of AM4-CMIP6 with the average of the observations is slightly better for this grid cell, 0.65 (dry) and 0.63 (wet). In both grid cells, the inclusion of aerosol water slightly decreases the correlation between models and average observations; however, it reduces the normalized mean bias (NMB) from -41 to -28 % and -26 to -10 % over New Delhi and Lucknow/Kanpur, respectively. This is true for most of the individual sites as well: only four sites show an improvement in correlation and all but two sites show a reduction in the NMB (Table S2 in the Supplement). Noteworthy is the model bias for both locations during the 5-day festival of Diwali (shown by the vertical dashed lines in Fig. 2), which is a period marked with extensive fireworks celebrations and thus high aerosol loading (Tiwari et al., 2012) that the model obviously would not reproduce as the emission inventories used here have monthly resolution. These plots show that PM2.5 abundances can vary substantially over regions smaller than a model grid cell (i.e., ∼ 100 km), especially in megacities such as New Delhi (∼ 22 million people) and Lucknow/Kanpur (∼ 6 million people). The model abundances represent an average over the grid cell while the observations represent a point measurement, and thus this incommensurability necessitates caution when comparing the two (e.g., Schnell et al., 2014).

Figure S6a–d show the same time series for the observations and both simulations but separates modeled total PM2.5 into its individual components. For both grid cells and simulations, NO3- is the dominant driver of modeled PM2.5 variability, accounting on average around one-third of PM2.5, largest on days with the highest total PM2.5. Thus, the model's ability to match the time series of PM2.5 observations is largely dependent on NO3- variability. OM is the second largest contributor to total PM2.5 (∼ 25 %), but is less variable than NO3-. Table S2 also shows the correlation of each site's observed PM2.5 time series with each of the modeled components of PM2.5. For most sites, the correlation with either OM or BC is highest (shown by the bolded numbers).

We next compare the fractional contribution of each PM2.5 component to the speciation measurements in Kanpur during October 2008–January 2009. The observations include an “unidentified” component so we separately show the observed fractions excluding the unidentified fraction (Fig. 3a) and including it (Fig. 3b). The results for AM4-CMIP5 and AM4-CMIP6 are shown in Fig. 3c and d, respectively. The average total PM2.5 abundance is shown below each pie chart. The largest model-measurement discrepancy is for the OM and NO3- component fractions. The model underestimates the OM contribution by 12–27 % for AM4-CMIP5 and 19–34 % for AM4-CMIP6, depending on whether the unidentified fraction is included. The model overestimates the NO3- contribution by 19–21 % for AM4-CMIP5 and 30–32 % for AM4-CMIP6, again depending on whether the unidentified fraction is included. In absolute terms, the AM4-CMIP5 and AM4-CMIP6 is overestimating NO3- by 17 µg m-3 (217 %) and 53 µg m-3 (680 %), respectively. For OM, AM4-CMIP5 underestimates it by 6 µg m-3 (-15 %) while AM4-CMIP6 overestimates it by 7 µg m-3 (18 %). The unidentified fraction is quite large (42 % of total PM2.5, Fig. 3b), which Ram and Sarin (2011) hypothesize to be mineral dust; while the AM4 may underestimate wintertime dust like previous versions of the model (Ganguly et al., 2009), it is unlikely the underestimate is this large.

Figure 4a–c respectively show the 5th, 50th, and 95th percentile of the AM4-CMIP6 (wet) daily average PM2.5 abundances for 1 October 2015–31 March 2016 overlain with the observed site values over the same time period. As expected from the emission patterns in Fig. 1, the highest PM2.5 abundances in Northern India are found throughout the IGP for all percentiles. Within the IGP, the eastern edge shows the highest abundances in both observations and AM4 simulations. This feature is most evident at the 95th percentile, where the observed values in the east exceed those in the north and central IGP by up to 50 %, with the 95th percentile value at one site reaching ∼ 400 µg m-3–16 times the WHO-recommended health standard for a 24 h average abundance (WHO, 2005). The AM4-CMIP6 simulation is biased slightly low at the 50th (normalized mean bias (NMB) = -19 %) and 95th percentiles (NMB = -22 %) for most sites, while slightly high for some sites at the 5th percentile (NMB = +4 %). This is a major improvement compared to the AM4-CMIP5 (wet) simulation (Fig. S7 in the Supplement), which has NMBs at the 5th, 50th, and 95th percentile of -35, -53, and -57 %, respectively. The changes from CMIP5 to CMIP6 are almost entirely in terms of magnitude as the spatial correlations between the AM4-CMIP5 and AM4-CMIP6 percentile maps are all around r=0.99.

Figure 5 shows modeled (AM4-CMIP6) and observed RH, BLH, INV, and 10 m, 850 mb, and 500 mb wind speed and direction averaged over the 1 October 2015–31 March 2016 time period. Note that the reference wind vectors in Fig. 5d and f are the ASI cutoffs for 10 m and 500 mb wind speeds, respectively. Overall, the AM4 simulates these meteorological quantities reasonably well, as should be expected as the wind fields in AM4 are nudged to reanalysis data. Ideally, these comparisons should be made with surface observations and soundings; however, data limitations hinder a complete evaluation of modeled meteorology.

The general northwesterly direction of the 10 m and 850 mb winds (generally biased high for 850 mb) along the IGP (Fig. 5d, e) allows for accumulation of aerosols as air masses flow to the southeast across the high-emission IGP region (e.g., Nair et al., 2007; Kumar et al., 2015; Sen et al., 2017). Nair et al. (2007) highlights the role of this transport mechanism by showing PM2.5 levels in the IGP increased with the distance the air mass had traveled from the west. Nair et al. (2007) note that this also applies to the transport of weather phenomena conducive to aerosol buildup such as a cold air mass. The surface winds are light and variable at the eastern edge of the IGP, a recirculation pattern that inhibits outflow into the Bay of Bengal. The winds at 500 mb are strong westerlies with the largest values (∼ 18 m s-1) in the central and eastern IGP.

The modeled and observed correlations of daily average PM2.5 with the meteorological variables in Fig.5a–f is shown in Fig. 5g–l, respectively. Only model correlations significant at the 95 % confidence level based on a Student's t test are shown, and significant observed correlations are denoted with an “x”. Overall, AM4 reproduces most of the observed PM2.5–meteorology correlation patterns well, especially in the eastern IGP, which consistently shows the strongest magnitude correlations for most variables. As for the meteorological variables, INV and BLH generally show the strongest correlations (r > 0.6 in the eastern IGP). RH is positively correlated with PM2.5 over all of Northern India except for the western edge bordering the coast. Small negative correlations are found for 850 mb winds while, unexpectedly, positive correlations are found between PM2.5 and 500 mb wind speed. NO3- is the dominant driver of this positive correlation with 500 mb winds (see below; Fig. S8 in the Supplement), but all anthropogenic aerosol components show high positive correlation over the far eastern edge. The negative correlation of PM2.5 with surface and 850 mb winds and positive correlation with 500 mb winds suggest that the surface and upper-level airflow are independent. This finding is explored further in Sect. 3.3 in the context of the ASI.

The correlations of the meteorological variables with the components of PM2.5 are not always comparable to those with total PM2.5. Figure S8 shows the correlations with each of the main components of PM2.5 (i.e., dust, sea salt, BC, OM, SOA, NH4+, SO42-, and NO3-) with the same meteorological variables as in Fig. 5. The correlations in Fig. S8 are computed over 2011–2015 to reduce the influence of interannual variability. For most variables and regions, particularly in the IGP, the individual PM2.5 components have the same sign and similar magnitude correlations as those for total PM2.5. Because NO3- is the dominant component of PM2.5 in most regions (Fig. S9 in the Supplement), the correlations for NO3- are very similar to those for total PM2.5. But, in some cases, differences reflect the source of the component (e.g., dust vs. BC) and aerosol chemistry. At some locations, dust and sea salt have several correlations that are opposite in sign than the rest of the components. The positive correlations with surface wind are expected given that emissions of dust and sea salt are simulated as a function of wind speed (Ginoux et al., 2001), which is especially evident near strong source regions such as the western coast (sea salt) and the Thar Desert (dust).

As both the modeled and observed PM2.5 reflect constant 50 % RH conditions, the correlation of RH and PM2.5 is not due to hygroscopic growth. In Fig. S8 the correlation with RH is positive for all PM2.5 components except dust. As NO3- and OM are the dominant components of total PM2.5 over most locations (Fig.  S9), their correlations with RH (and thus the other meteorological variables) are what is predominantly reflected in terms of total PM2.5. We also examine the correlation of RH with the other meteorological variables to determine the underlying driver of the correlations of RH and PM2.5 and its components. RH has large negative correlations with surface wind speeds and is positively correlated with INV and low cloud cover (not shown), which all are indicative of a stable boundary layer (e.g., Chen et al., 2017) and would cause PM2.5 to accumulate (e.g., high RH ∼ low wind speeds, low ventilation → high PM2.5). Essentially, the positive correlation of PM2.5 with RH likely reflects that high RH is indicative of other meteorological conditions that allow PM2.5 to accumulate. For SO42-, the positive RH relationship may also reflect in-cloud SO2 oxidation (e.g., Ram et al., 2012a).

The seasonal cycle of total PM2.5 over the IGP is driven by a combination of meteorology and emissions. For example, the relatively cold winters in the IGP (∼ 7 ∘C average daily December–January minimum over Kanpur/Lucknow) increases overall energy demand and leads to additional burning of fuel for indoor heating. The colder temperatures also play a role in the chemistry of PM2.5 (e.g., nitrate is more stable at colder temperatures). The strong radiative cooling at the surface during the winter nights often result in foggy conditions and a shallow inversion layer that traps aerosols near the surface.

Figure 6a shows the monthly average PM2.5 abundances for the min-to-max range of the individual stations (gray shading) and their median (black line) over the 6-month period. Also shown is the median of modeled PM2.5 for AM4-CMIP5 dry (blue), AM4-CMIP6 dry (red), and AM4-CMIP6 wet (green). The maximum PM2.5 abundances in the observations occur over a broad peak from November–January, with a mean of ∼ 200 µg m-3 and individual sites ranging from ∼ 125–300 µg m-3. Both AM4 simulations reproduce month-to-month variations well, but the AM4-CMIP5, although biased very low, matches the January peak that the AM4-CMIP6 misses.

Figure 6b–e show the 6-month cycle for RH, BLH, INV, and 10 m wind speeds, respectively. As expected from the correlations shown in Fig. 5g–l, the cycles of these variables align, such that meteorology is most conducive to formation and accumulation during the months with maximum PM2.5: e.g., low BLH and strong INV trap pollution near the surface and low wind speeds decrease ventilation. High RH also increases ambient observed PM2.5 due to hygroscopic growth, but the connection here is probably due to the relationship between RH and a stable boundary layer. The model reproduces the shape of these cycles well, but is biased slightly low in RH (∼ 5 % from November to January), low in BLH (∼ 200 m for all months), high in INV (∼ 2∘ for most months), and low in surface wind speed (0.5 to 1 m s-1). There is some evidence for aerosol feedback onto meteorology seen by comparing the curves of AM4-CMIP5 (blue) to AM4-CMIP6 (green), namely a stabilization effect on the boundary layer. The much higher aerosol abundances in AM4-CMIP6 seem to have caused higher relative humidity, decreases in boundary layer height and surface wind speeds, as well as a stronger inversion.

The skill of the model in reproducing the seasonal cycle of PM2.5 and related meteorology provides confidence in the seasonality of emissions and the ability of the model to simulate the large-scale PM2.5-meteorology relationships. A more stringent test is to compare the diurnal cycles from observations and the model. Like the seasonal cycle, the diurnal cycle of PM2.5 is controlled by a combination of emissions and meteorology. However, as the model lacks a diurnal cycle of emissions, it may not be capable of accurately reproducing the observed diurnal cycle of PM2.5. If the model were to simulate the observed diurnal cycle well, even without a diurnal cycle of emissions, this would provide confidence in the model's ability to simulate high-frequency PM2.5–meteorological relationships.

Figure 6f shows the diurnal cycle of PM2.5 for the min-to-max range of the individual stations (gray) and their average (black) over the 6-month period. The AM4-CMIP5 (dry), AM4-CMIP6 (dry), and AM4-CMIP6 (wet) values are also shown in blue, red, and green, respectively. We also show the diurnal cycle of each major PM2.5 component for AM4-CMIP6 (dry) (in addition to a sensitivity experiment, see below) in Fig. S10 of the Supplement. The minimum PM2.5 abundance in the observations occurs at ∼ 15:00 LT, aligning with the lowest RH, deepest boundary layer, and highest wind speeds. As evening approaches, wind speeds decrease and the boundary layer collapses, trapping the PM2.5 emitted and produced over the day at the surface. These features, together with an evening pulse in traffic and biofuel emissions for heating and cooking (Rehman et al., 2011), cause PM2.5 abundances to reach their maximum at around 21:00 LT. PM2.5 abundances decrease through the night, likely due to a drop off in emissions as all other meteorological variables would suggest further PM2.5 increases. Abundances begin to increase about an hour before the ∼ 07:00 sunrise and a short-lived secondary maximum occurs at around 09:00 LT. Part of this increase may be driven by emissions (e.g., cold engine starts and morning traffic); however, Nair et al. (2007) attribute the rise mostly to fumigation (Stull, 1988; Fochesatto et al., 2001), i.e., thermals that break up the nighttime inversion layer and mix aerosols trapped in the residual layer down to the surface.

The PM2.5 concentrations simulated by AM4 are biased low during all hours of the day, with the largest bias at the time of the evening maximum. AM4 reproduces a slightly delayed morning maximum, closely following the rise in BC and OM/SOA (Fig. S10b, c). AM4 largely misses the evening rise in PM2.5 abundances despite simulating the changes in meteorology, which would otherwise increase PM2.5 abundances. Thus, the lack of a diurnal emission cycle in the AM4 likely explains why it misses the evening peak in PM2.5. Indeed, Ram and Sarin (2011) find that, for a site in Kanpur, boundary layer dynamics are not the only cause for the evening rise PM2.5 but rather an increase in source emissions and enhanced secondary aerosol formation. Additionally, Ram and Sarin (2011) find that particulate NO3- was a factor of four higher during nighttime, attributable to secondary formation via the hydrolysis of N2O5 under high humidity conditions. However, AM4 shows the reverse, with a peak in NO3- during midday. Overall, NH4+, NO3-, and SO42- in AM4 (Fig. S10d–f) act to increase midday PM2.5 and cause a relative decrease in morning and early evening PM2.5, thereby decreasing the overall amplitude of the PM2.5 diurnal cycle.

We test if the seemingly aberrant NO3- diurnal cycle is a result of our choice of the value for the N2O5 heterogenous uptake coefficient (0.1), which is significantly higher than those reported by previous studies (e.g., Davis et al., 2008; Chang et al., 2016), by performing an additional simulation with a N2O5 uptake coefficient of 0.01 over period of the Ram et al. (2012a) observations. The effect of the updated value is to reduce NO3- by ∼ 15 µg m3, NH4+ by ∼ 5 µg m-3, and SO42- by ∼ 1 µg m-3, all with the largest changes at night (Fig. S10d–f in the Supplement). However, the diurnal cycle of NO3- (as with NH4+ and SO42-) is qualitatively unchanged from the base simulation, with a relative maximum still occurring at midday. So, while we have reduced nitrate abundances (and total PM2.5), the midday NO3- peak is still evident even with the updated gamma. One possible explanation is that the model prescribes monthly average deposition rates for NH4NO3 (i.e., no diurnal cycle); however, determining the cause of this midday peak will require additional experimentation beyond the scope of this paper.

The Air Stagnation Index (ASI) is a metric commonly used to identify days when meteorology is conducive to the buildup of pollutants, viz. light winds at the surface and upper levels and no precipitation (Wang and Angell, 1999). Meteorologically, light winds at the surface hinder dilution of pollutants, no precipitation prevents pollutant washout and implies no convection and thus less dilution, and light upper level winds are related to slow moving synoptic systems. The index was developed over the United States, but it has been used in relation to air quality in other regions (e.g., Horton et al., 2012, 2014; Huang et al., 2017). Figure S11 in the Supplement shows the frequency of each of the stagnation criteria over the 6-month period. Stagnation with respect to 10 m wind speeds and precipitation occurs on nearly 100 % of the days over large portions of Northern India. The 500 mb wind speed criteria is the limiting factor for total ASI, both occurring on ∼ 35 % of the days. These patterns of stagnation frequency are nearly identical from year to year over the period of the simulations, with only a few grid cells (most over the ocean and the Himalayas) showing significant trends in any of the stagnation criteria (not shown).

The large negative correlations between PM2.5 and 10 m wind speed shown in Fig. 5j clearly imply that days with low surface wind speeds have higher PM2.5 abundances. Precipitation is weakly correlated with PM2.5 (not shown), but it is relatively rare during winter months. However, the positive correlation of PM2.5 with 500 mb wind speeds – the third component of the ASI – suggests that the ASI may not accurately describe conditions susceptible to pollution buildup over India.

We test the ability of the ASI to predict extreme pollution days by comparing the composite average PM2.5 on days when any individual or all stagnation criteria are met with the average on days that they are not met. We calculate the composite using anomalies relative to the monthly mean to remove the influence of seasonality. Notably, as nearly 100 % of the days are considered stagnant with respect to 10 m wind speeds and precipitation, the composites are not a completely fair comparison. However, the 500 mb and total ASI criteria are achieved as often (Fig. S11 in the Supplement). Figure 7a–d show the results for observations and AM4-CMIP6 over the October 2015–March 2016 time frame. The gray regions in Fig. 7a and d are grid cells where a composite cannot be constructed as 100 % of the days are considered stagnant for the respective criterion. Both the observations and AM4-CMIP6 have large positive composites (∼ 30 µg m-3 ASI minus non-ASI, relative to the monthly mean) in the IGP on days when the 10-m wind ASI criterion is met. The results for the precipitation criterion are mixed, with the observations showing positive composite anomalies for most sites, but the model only showing positive composites for areas in the far eastern edge of the IGP. The composites for the 500 mb component and total ASI agree very well, but are also mixed between the observations and model. For the observations, most composites are slightly positive (0–10 µg m-3) with the model showing similar magnitudes but opposite in sign. Examining the composites on a monthly basis shows that the positive composites for 500 mb and total ASI in the observations occur mostly outside of December–January, the months when the highest PM2.5 abundances typically occur. Indeed, plots of the composites using the raw data (i.e., not relative to the monthly mean) (Fig. S12 in the Supplement) shows that nearly all observations and all model grid cells have large negative composites for the 500 mb wind speed and total ASI.

We test if these composites are representative of a broader time period by calculating the composites for seven 5-year intervals over the 1981–2015 period in AM4-CMIP6 (Fig. S13). The spatial patterns of the 10 m wind and precipitation composites are extremely similar across the 5-year intervals, although the magnitude increases with time. Interestingly, the results for the 500 mb and total ASI composites in the earlier decades are different from those in the last decade. In the first two decades the composites are near zero or slightly positive for most of northern India except in the far eastern edge. However, the last decade shows negative composites over most of the domain. Unfortunately there are no observations to confirm these results, but it nevertheless suggests a regime change in the relationship between wintertime PM2.5 and synoptic meteorology, possibly resulting from a combination of changing climate and emissions.

These results suggest that atmospheric conditions at the surface are decoupled with those in the upper atmosphere over Northern India. This disconnect is frequently observed in mountainous topography, such as the western US (e.g., Wolyn and Mckee, 1989; Holmes et al., 2015; Chachere and Pu, 2016) where cold air pools form at the surface, such that a temperature inversion and/or deep stable boundary layer traps pollution close to the surface (Whiteman et al., 2001), leaving light surface winds despite relatively strong winds aloft (Wolyn and Mckee, 1989). A complete decoupling between the lower and upper atmosphere would presumably yield a near zero or insignificant correlation between surface PM2.5 and 500 mb wind speeds; however, significant correlations greater than +0.35 are found over the entirety of the IGP – and greater than +0.60 over the far eastern edge bordering Bangladesh. It remains unclear what – if any – mechanism is responsible for the positive relationship between PM2.5 and 500 mb wind speeds.

The future of air quality over Northern India will largely be determined by emission changes. However, even with drastic emission reductions, pollutant levels may still exceed recommended levels due to the size of the population and the socioeconomics in the region. Meteorological changes due to a warming climate will also play a role, especially for the days with the highest pollution levels. It is thus important to identify meteorological conditions that have consistent effects on air quality, at least from a model standpoint, in order to provide confidence in how air quality may respond to changes in those variables.

In Fig. 8, we show PM2.5 and meteorological composites for the 10 days with the highest PM2.5 abundance for each observations site and each grid cell in AM4-CMIP6-wet (∼ 95th percentile over October 2015–March 2016) minus the 10 days with the lowest abundances (i.e., the ∼ 5th percentile). For PM2.5 (Fig. 8a), abundances are up to 200 µg m-3 higher on the most polluted days compared to the cleanest days in both the model and observations. The pattern is matched extremely well by the model despite being biased low for PM2.5 at most locations and times. Compared to the cleanest days, the most polluted days in most locations have higher RH (Fig. 8b, +5 to +15 %), lower BLH (Fig. 8c, -50 to -200 m), and stronger temperature inversions (Fig. 8d, +1 to +3 K). We also perform the composites for two other stagnation metrics, the wind run and recirculation factor (Allwine and Whiteman, 1994). The wind run (i.e., a similar measure to daily average wind speed) is much lower over the IGP (about -100 km), but over the western side of Northern India it is higher in the model (about +50 km) and lower in the observations (about –50 km). As this area has higher dust and sea salt fractions (Fig. S9 in the Supplement), which are both parameterized as function of wind speed, and the model does not seem to be biased high in wind speed (Fig. 5d), this may indicate the dust emission source is too large or too sensitive to wind speed. For wind recirculation, most sites have positive composite values (i.e., increased recirculation), with the model showing positive composites along the length of the IGP and largest near the far eastern edge of the IGP bordering Bangladesh where the surface winds are variable (Fig. 5d).

We extend this analysis for seven 5-year intervals to test if these relationships have changed over the recent decades and plot the results in Fig. S14 in the Supplement. Here we use the 50 most polluted and cleanest days over 5 years (still ∼ 95th percentile minus the ∼ 5th percentile). Notably, the composite values for PM2.5 have increased substantially (∼ 40 to > 200 µg m-3) over the period due to massive increase in emissions. However, overall the results are extremely similar to Fig. 8, but the patterns are more pronounced than those using only one winter and 10 days. Based on the consistent results over the time period, we suggest using these variables (or possibly others unexplored here) to gauge potential future changes in poor air quality days due to changing meteorology.