The impact of atmospheric motions on source-speciﬁc black carbon and the induced direct radiative effects over a river-valley region

. Black carbon (BC) is one of the most important short-lived climate forcers, and atmospheric motions play an important role in determining its mass concentrations of pollutants. Here an intensive observation was launched in a typical river-valley city to investigate relationships between atmospheric motions and BC aerosols. Equivalent BC ( e BC) source apportionment was based on an aethalometer model with the site-dependent absorption Ångström exponents (AAEs) and the mass absorption cross sections (MACs) retrieved using a positive matrix factorization (PMF) model based on observed chemical components (i.e., EC, POC, K + , Mg, Al, Si, S, Cl, Ca, V, Mn, Fe, Ni, Cu, As, Se, Br, Sr, Pb, Ga, and Zn) and primary absorption coefﬁcients at selected wavelengths from λ = 370 to 880 nm. The derived AAEs from 370 to 880 nm were 1.07 for diesel vehicular emissions, 2.13 for biomass burning, 1.74 for coal combustion, and 1.78 for mineral dust. The mean values for e BC fossil and e BC biomass were 2.46 and 1.17 µg m − 3 , respectively. Wind run distances and the vector displacements of the wind in 24 h were used to construct a self-organizing map, from which four atmospheric motion categories were identiﬁed (local-scale dominant, local-scale strong and regional-scale weak, local-scale weak and regional-scale strong, and regional-scale dominant). BC pollution was found to be more likely when the inﬂuence of local-scale motions outweighed that of regional-scale motions. Cluster analysis for the back-trajectories of air mass calculated by the Hybrid Single-Particle Lagrangian Integrated Trajectory model at the study site indicated that the directions of air ﬂow can have different impacts for different scales of motion. The direct radiative effects (DREs) of source-speciﬁc e BC were lower when the inﬂuence of regional-scale motions outweighed that of the local ones. However, due to chemical aging of the particles during transport – the DRE efﬁciencies under regional-scale motions were ∼ 1.5 times higher than those under more local inﬂuences. The ﬁnding that the DRE efﬁciency of BC increased during the regional transport suggested signiﬁcant consequences in regions downwind of pollution sources and emphasizes the importance of regionally transported BC for potential climatic effects.


Text S1. Minimum R-squared method
The minimum R squared method developed by Wu et al., (2016) was used to separate secondary organic carbon (SOC) from the primary organic carbon (POC).The assumption behind this method is the organic carbon (OC) from non-combustion source is negligible.As explained by Wang et al., (2019), the major non-combustion source is biogenic which is mainly exists in coarse mode.Thus, the non-combustion organic carbon is considered negligible in this study.Therefore, SOC and POC can be separated by using following equations.For each date set, the ratios of OC to eBC and SOC and the R 2 between eBC and SOC can be calculated.SOC and eBC are considered independent, so the (OC/eBC)pri should be the value obtained when the R 2 between eBC and SOC is minimum.
where EC in this study is eBC.The (OC/EC)pri is the ratio in freshly emitted OC and EC from combustion sources.
The light absorption at shorter wavelengths (<660nm) is not only from primary light absorbing substances but also from the secondary organic carbon (Wang et al., 2019).The assumption for this method is that the light absorption caused by non-combustion sources is negligible.As mentioned above, most of the biogenic BrC is in coarse mode.Another common light absorbing substance is the Fe2O3 in the dust, but the impact of that should be limited because the absorption from Fe2O3 in the dust has been reported to be much smaller than that from BC (Ramachandran and Kedia, 2010).Thus, to separate the secondary light absorption (babs(λ)secondary) from the primary light absorption (babs(λ)primary), a BC-tracer method coupled with a minimum R-squared method was used.The equations used for the calculation are follows:

Text S2. Cluster analysis of air-mass trajectories
Back trajectories were calculated by using Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model (Draxler and Hess, 1998) developed by the Air Resource Lab (ARL) of the National Oceanic and Atmospheric Administration (NOAA).The model can predict the position of air mass by using mean wind.The back-in-time positions are calculated by reversing the advection equation (Draxler and Hess, 1997).The calculation requires the mean wind, for calculating trajectories, only advection is considered (Stein et al., 2015).The basic equations for trajectory calculation in HYSPLIT are as follows: Where () is the initial position,  ′ ( + ∆) is the first guess position,  is the average velocity,  is the time, ∆ is the time step.
A large number of 24 h trajectories (793) that were retrieved for the study period showed diverse pathways, so in order to find out the representative pathways for those trajectories, a cluster analysis based on an angle-based distance statistics method was conducted.Compared with Euclidean distance, angle-based distance statistics method focuses on the direction of air mass instead of the speed.The angle-based distance statistics method is defined by following equations (Sirois and Bottenheim, 1995): (S7) Where  67 is the average angle between the two backward trajectories, varying between 0 and π;  A and  A are the position of the receptor site; and  6 ( 6 ) and  7 ( 7 ) are the backward trajectories 1 and 2, respectively.In this study, three clusters were chosen as representative of the backward trajectory clusters based on the total spatial variance (TSV) value.The simulation was conducted using the GIS-based TrajStat software (Wang et al., 2009).

Figure S1 .
Figure S1.A map of the research site; (a) map of China-the red shape is the location of Baoji, (b) a map of the Guanzhong Plain, the black star represents the location of Baoji; (c) a map of Baoji City, the black dots and the black triangle represent 12 stations and the triangle is the location of sampling site, (d) a map of the sampling site from © Google (https://www.google.com/maps).

Figure S2 .Figure S3 .
Figure S2.Map of fire occurrences.The yellow star represents the study site, the red dots represent the fire.The image from © NASA (National Aeronautics and Space Administration) (https://firms.modaps.eosdis.nasa.gov/map)

Figure S5 .Figure S6 .
Figure S5.Ratio Qtrue/Qexpected for two to seven factors.The red triangles are the Qtrue/Qexpected values for each run for different factor solutions.

Figure S7 .
Figure S7.Linear regression of the daily averaged NOx versus the daily averaged elemental carbon (EC) emitted from diesel vehicular emissions.The red line is the linear fit.

Figure S12 .
Figure S12.Non-parametric wind regression plots for eBCbiomass (a) and eBCfossil (b) at night.The radial and tangential axes represent the wind direction (°) and speed (m s −1 ), respectively, nws100m represents the night wind speed 100m above the ground level.

Figure S13 .
Figure S13.Diel variations of planetary boundary layer height (PBLH, m) under the dominance of regional scale of motion (RD), the blue dots represent the hourly-averaged PBLH and the black lines represent the standard deviations for each point.
Figure S14.24h-backward in time air mass trajectories (grey lines) and 72h-back trajectories (blue lines), and trajectory clusters at the sampling site 100 m above the ground.The green line represents Cluster No. 1, the yellow line represents Cluster No. 2, and the red line represents Cluster No. 3.

Table S1 .
The seasonal meteorological data of Baoji

Table S2 .
Data and parameters used in HYSPLIT model

Table S3 .
The results of Bootstrap (BS) and displacement (DISP)

Table S4 .
Mass absorption cross sections (MAC) and absorption Ångström exponents (AAE) derived from the positive matrix factorization model

Table S5 .
Mean (range) BC mass concentration in river valley sites worldwide a asl stands for "above sea level."