Hourly averaged and quality-assured AOPs are binned by month, day of week, and hour of day to study their annual, weekly, and diurnal cycles, respectively (Sect. 4.1). Geometric means and 95 % confidence intervals of the geometric means are calculated for the binned σsp and σap, whose distributions are closer to log-normal than normal. Arithmetic means and 95 % confidence intervals of the means are calculated for the binned intensive AOPs, whose distributions are suitably approximated as normal. Atmospheric variability for each month, day of week, or hour of day is quantified by the 95 % confidence intervals of the mean value, which are represented as error bars on the plots. Differences in the mean AOPs are termed “significant” in this paper if they are larger than both (1) atmospheric variability (e.g., if the error bars do not overlap); and (2) twice the precision measurement uncertainty (Table 3). We define the magnitude of temporal variability on each of the timescales as the amplitude of the cycle of mean values (difference between maximum and minimum values). Cycle amplitudes are also expressed as percentages by dividing this difference by the midpoint between maximum and minimum values.

Aerosol optical properties at the four sites vary primarily on seasonal timescales. Day of week variability in AOPs can be used as a tool for distinguishing anthropogenic from natural aerosol sources, since natural sources would not be expected to have AOPs that vary on weekly scales (Murphy et al., 2008). Diurnal variability is used along with co-located meteorological data to infer the influence of local pollution sources and mixing layer height on measured AOPs. Due to the dependence of most AOPs on season, their weekly and diurnal cycles are reported for both full years and individual seasons.

Data from co-located surface meteorological stations at the four sites are used to develop proxies to help explain some features of the AOP cycles at each station. Pollution-rose diagrams showing the dependence of σsp, σap, and some calculated AOPs on wind direction are shown for individual seasons to examine the influences of wind sectors and known regional pollution sources on measured AOPs (Figs. 5–8 and S16–S22). We compare the temperature dependence of σsp (Figs. S5 and S7) with reported temperature dependence of biogenic secondary organic aerosol (SOA) (Leaitch et al., 2011; Goldstein et al., 2009) and ammonium nitrate partitioning (Parworth et al., 2015; Rupakheti et al., 2005). We also use temperature dependence of σsp along with monthly median temperatures at the sites (Fig. S23) and monthly averaged σsp (Fig. 2a) to hypothesize the role of photochemistry on the seasonality of σsp. Mixing layer height climatologies have been reported for locations at or within ∼ 170 km of the sites. We use the seasonal dependence of the reported mixing layer heights to assess the effect of convection (or lack thereof) on the annual and diurnal cycles of measured near-surface σsp and σap at the four sites.

Mean values of AOPs over the entire 2010–2013 period are calculated for each site and the differences in mean AOPs among the sites are used as a measure of regional variability (Sect. 4.2). Seasonal differences of most AOPs at individual sites are often much larger than the regional differences of annual-mean AOPs so the seasonality of regional AOP differences must also be taken into account. The differences in mean AOPs among the sites are termed “significant” if they satisfy the same two criteria stated in Sect. 2.5.1 for temporal differences. Of the four sites, only BND and SGP have long enough time series (> 10 years) to evaluate trends in AOPs (Sect. 4.3). Slopes and significance are obtained using the function “TheilSen” in the R package “openair” (Carslaw and Ropkins, 2012; Carslaw, 2015). Data are de-seasonalized and autocorrelation is accounted for using options supplied with the TheilSen function. Decadal slopes (%/10 year) are calculated by multiplying the yearly slope by 10. Trends are not reported for SGP AOPs requiring absorption due to PSAP data quality issues over most of the 1997–2009 period. Absorption Ångström exponent trends are not calculated for BND because the available time series is less than 10 years.

Systematic relationships among intensive AOPs and aerosol loading are explored on an annual basis at the four North American sites for the 2010–2013 (Sect. 4.4). Relationships involving αap vary with season at some sites, so these relationships are also presented for individual seasons. D&O2002 suggested systematic relationships would be useful for constraining model parameterization of AOPs and for reducing uncertainties in satellite-based retrievals of AOD, which make assumptions regarding aerosol size distributions and ω0 (e.g., Levy et al., 2010). Systematic relationships can also provide information regarding aerosol source types and processes. Relationships between mean intensive AOPs and aerosol loading, represented by σsp at 550 nm, are investigated for each season at each site by separating hourly averaged σsp values into bins of 10 Mm-1 width and then calculating the mean AOPs for each σsp bin. The x values for the data points on each plot correspond to the bin center. Only bins with a number of data points exceeding 0.1 % of all data points are plotted. The relatively high ω0 values at all sites justifies the use of σsp, rather than σep, as a proxy for loading. Relationships among a few select intensive AOPs are also included to provide more insight into aerosol sources and/or processes influencing the properties measured at the sites.

The annual AOP cycle amplitudes are larger than the weekly and diurnal AOP cycle amplitudes at all sites. Nearly all annual AOP cycles are significant, with cycle amplitudes larger than the 95 % confidence intervals of both the monthly mean AOPs (Fig. 2) and the measurement uncertainties (Table 3). July and/or August σsp maxima are observed at all sites (Fig. 2a), with steeper σsp decreases from summer to fall than from summer to spring. Summer-to-spring and summer-to-fall σsp decreases at EGB and APP are approximately twice the magnitude of those observed at BND and SGP. Scattering coefficient reaches a minimum during October at all sites except APP, where it is lowest in December. Absorption coefficient is highest in summer and lowest in winter at all sites (Fig. 2b), although the differences between summer σap maxima and the surrounding months are only significant at BND and EGB. Summer-to-autumn σsp decreases are larger than those of σap, leading to minimum ω0 in October at all sites (Fig. 2e). Hemispheric backscatter fraction is highest in October at all sites (Fig. 2d). The confluence of early autumn decreases in σsp and ω0 and increases in b is indicative of less production and/or more efficient removal of large, highly scattering particles during early autumn, relative to summer. This effect is most noticeable at EGB and APP (Fig. 2) and also is seen in the summer–spring differences at APP. October ω0 minima contribute to DRFE maxima (least negative) at EGB and BND, but no significant autumn DRFE changes are seen at APP and SGP (Fig. 2f). Photochemistry likely influences the summer σsp maxima and σsp that are larger in spring than in fall at all sites. The temperature dependence of σsp (Fig. S5) and differences in monthly median temperatures (Fig. S23) combine to yield predicted differences in σsp that are of similar magnitude to the large observed summer–spring (July–April) σsp differences at EGB and APP and to the observed summer–autumn (July–October) σsp differences at EGB, BND, and SGP (Fig. 2a). The summer–autumn σsp difference based on temperature considerations is less at APP than the observed σsp difference, leading us to hypothesize an additional contributor to the autumn σsp decrease. Cloud and fog scavenging of large, highly reflecting particles would be consistent with cooler September temperatures (Fig. S23a), higher RH (Fig. S23b), and cloud cover in September at APP. The inverse relationship between σsp and b seen in the annual cycles at all sites (Fig. 2a and d) is indicative of the influence of particle growth (and possibly cloud or fog scavenging) on σsp. Wet deposition likely impacts σsp most in summer and least in spring and fall, given the seasonality of precipitation at the sites. Secondary σsp maxima are observed during winter at all sites except APP (Fig. 2a). When combined with winter σap minima, the result is a winter ω0 maxima at these sites (Fig. 2e).

In contrast to b, the annual Rsp and PM10 αsp cycles (Fig. 2c and g) at APP, BND, and SGP (the sites where these AOPs are calculated) do not demonstrate an obvious relationship with the annual σsp cycles. Collaud Coen et al. (2007) conducted simulations based on Mie theory to show that b at 550 nm is most sensitive to particle size changes for diameters ∼ 100–300 nm (their Fig. 7 and accompanying discussion). Schuster et al. (2006) combined simulations based on Mie theory with volume size distributions and AOD from AERONET to show that extinction Ångström exponent is relatively insensitive to fine mode effective radius for bi-modal aerosol size distributions and that extinction Ångström exponent may serve as a better indicator of fine-mode aerosol volume fraction than mean particle size. The stronger relationship between the annual b and σsp cycles (relative to relationships between the cycles of σsp with either αsp or Rsp) suggests that the major seasonal changes in the aerosol size distributions at APP, BND, and SGP may lie at the smaller end of the range of optically relevant accumulation mode particles (100–300 nm), with shifts toward larger particles in summer and smaller particles in fall. Photochemistry likely plays a role in the observed seasonal cycle of b, especially at APP and EGB. Gas-to-particle conversion onto existing particles is most efficient for the 100–500 nm diameter range, since this is where most of the aerosol surface area typically lies (Seinfeld and Pandis, 1998). Reduced gas to particle conversion in fall (when photochemistry and precursor levels are lower) would impact b more than αsp and Rsp.

Absorption Ångström exponent is lowest during summer months and highest during winter months (Fig. 2h) at APP, BND and SGP (the three sites where αap can be calculated). The summer-to-winter difference in αap is clearly larger at APP (∼ 0.9) than at BND and SGP (∼ 0.5). Absorption Ångström exponent values near and below 1 during May–September suggest that black carbon (BC) contributes most to σap during these months (Gyawali et al., 2009; Cazorla et al., 2013). Gyawali et al. (2009) performed simulations using Mie theory to show that αap values much less than 1 are possible (their Figs. 8 and 9) when absorbing particles are coated with non-absorbing substances. Clarke et al. (2007) also reported a large number of αap (470/660 nm) values clustered between 0.7 and 1.1 for pollution plumes during extensive flights over North America as part the of the INTEX/ICARTT experiment in summer 2004.

Weekly and diurnal cycle amplitudes of σsp (Fig. 3) and nearly all intensive AOPs observed at the four sites are much smaller than the corresponding annual cycle amplitudes. Weekly and diurnal σap cycle amplitudes (Fig. 4) are larger than those of σsp at all sites and are largest in summer. Weekly σap cycles at all sites are marginally significant in fall with σap cycle amplitudes approximately twice the σap measurement precision uncertainty (Table 3). All sites demonstrate small and/or insignificant weekly σsp cycle amplitudes (∼ 20 % or less) and a lack of weekly σsp patterns across seasons (Fig. 3). This suggests that weekly σsp cycles are driven by regional-scale phenomena, where any weekend effects are smoothed out by mixing. The weekly cycles of intensive AOPs are nearly always minimal at all sites (Figs. S9–S15).

Similar to the weekly σap cycles, the diurnal σap cycles are also much larger than diurnal σsp cycles at all sites. However, the diurnal σap variability is only significant during summer and (at all sites except APP) fall. Diurnal cycles of nearly all intensive AOPs are minimal and/or insignificant. Notable exceptions are ω0 and DRFE during summer and fall. The amplitudes of the diurnal ω0 cycles are ∼ 0.03–0.04 during summer and fall at all sites (Fig. S12). In most of these cases, ω0 is lowest during late evening and/or early morning and highest during afternoon. At APP, the ω0 peak extends from around noon to the early morning hours. Diurnal DRFE cycles (Fig. S13) in turn follow the diurnal ω0 cycles, due to the lack of diurnal variability in b. Summer and fall DRFE is more negative by ∼ 3 W m-2 AOD-1 during the afternoon than during the surrounding hours (Fig. S13). The lack of diurnal and weekly variability in mean b, Rsp, and αsp indicates that particle size distributions at APP, BND, and SGP likely demonstrate little variability on weekly or daily timescales. D&O2002 reported similar or slightly smaller ω0 and b diurnal cycle amplitudes for BND and SGP, but they did not consider the diurnal cycles for individual seasons.

Aerosol light scattering and absorption coefficients at APP are dominated by PM1 for all seasons and the relative influence of PM1 varies little with season, as seen by Rsp values of 0.80–0.88 (Fig. 2c), αsp values of 1.9–2.2 (Fig. 2g), and Rap values of 0.90–0.95 (Fig. S8c). Both σsp and σap are moderately elevated for NE wind sectors, with 0–90∘ wind directions (Fig. 5). Median σap is ∼ 20–30 % higher for NE wind sectors than for the prevalent westerly wind sectors for all seasons except winter, when σap for the NE wind sectors is ∼ 2 times higher than σap for westerly wind sectors (not shown). Median σsp is less elevated for the NE wind sectors (typically ∼ 10–15 %). Wind sector does not strongly influence median or mean values of most intensive AOPs, although low ω0 (< 0.80) is more frequently associated with NE wind sectors (Fig. S17a). It should be noted that the prevalent westerly wind sectors represent the confluence of 3–4 (seasonally dependent) different average air mass back-trajectories, which all typically arrive at APP from the west. Link et al. (2015) reported that aerosol and gas phase chemistry measured at APP displayed a generally homogeneous distribution across source regions. One exception was elevated levels of urban, oil and natural gas, combustion tracers, and OA mass concentrations associated with air mass back-trajectories passing over the polluted Ohio River valley and Appalachian mountain region before arriving at APP with ∼ 0–90∘ wind directions (Link et al., 2015).

PM1 σsp at APP and its seasonality (Fig. 2a) are largely influenced by regional background SOA and sulfate. Biogenic SOA and sulfate both exhibit summer maxima and winter minima in the SE US (Goldstein et al., 2009; Hidy et al., 2014) and both summer and winter non-refractory PM1 aerosol mass at APP are dominated by SOA and sulfate (Supplement of Link et al., 2015). Summer σsp at APP is correlated with both OA and sulfate mass concentrations (r=0.60 and r=0.62, respectively). The temperature dependence of PM1 σsp at APP during April–October (Fig. S7) also agrees well with the expected temperature dependence of biogenic emissions (Guenther et al., 2006) and with the temperature dependence of AOD over the SE US (Goldstein et al., 2009). The summer σsp peak coincides with a distinct minima in b (30–40 % lower than all other seasons) and maxima in ω0 (∼ 0.07 higher than during winter). Aerosol number concentrations measured at APP are also lower in summer than during spring and fall (unpublished result). The confluence of lower concentrations of larger, highly reflective PM1 particles during months with high regional temperatures, solar irradiance, and RH is consistent with gas-to-particle conversion onto existing particles.

The annual σap cycle at APP (Fig. 2b) is out of phase with the annual cycle of EC concentrations reported for rural eastern US IMPROVE sites (Hand et al., 2012b). Hand et al. (2012b) cited sources such as residential heating for the fall and winter EC concentration maxima. Absorption coefficient at APP exhibits a summer maximum and a winter minimum, though the summer σap maximum is not significantly different from early fall and spring σap (to 95 % confidence). Absorption Ångström exponents of ∼ 1.3–1.4 (Fig. 2h) and αsp > 2 during colder months (Fig. 2h) suggest a mixture of EC and light-absorbing OC (Fig. 2 of Cazorla et al., 2013). A contribution to σap from OC is also consistent with a biomass-burning OA factor in the winter aerosol mass spectra measured at APP (Fig. S2 of Link et al., 2015) and may result from winter residential wood-burning (US Census Bureau, 2010; Zhang et al., 2010). However, the diurnal σap cycles (Fig. 4b) suggest an influence from local traffic during all seasons and αap values of 1 or less for non-winter months suggest that BC is the major contributor to σap during these months.

APP is the only site to demonstrate consistent weekly σsp and σap cycles across seasons, with the exception of winter. Local commuter traffic likely exerts the largest influence on the diurnal σap cycles (Fig. 4b) and possibly the weekly σap cycles (Fig. 4a). Diurnal σap cycles are only significant at 95 % confidence during summer, but a similar bi-modal structure is seen for all seasons (Fig. 4b), with morning and late afternoon/early evening commuter peaks. The only sign of weekend local traffic influence is an insignificant Saturday morning peak Δσap∼ 0.1–0.2 Mm-1 present during most seasons (unpublished result), confirming the primary influence of local commuter traffic. The absence of any influence of diurnal PBL height variation on the diurnal σap cycles at APP is consistent with the relatively small afternoon/morning PBL height differences measured at the heavily forested APP site (unpublished result). PBL height is often poorly defined at APP and may be related to the fact that the APP site is situated on a ridge. The PBL and free troposphere do not fully decouple during the evening. As a result, pronounced late-evening through early morning σsp and σap maxima that are characteristic of a PBL height influence are not a regular feature of the diurnal cycles at APP (Figs. 3b and 4b). Diurnal variability of σsp and intensive AOPs is insignificant and/or minimal for all seasons (Figs. S9–S15), with the exceptions of (1) morning ω0 decreases (by ∼ 0.02–0.03) DRFE increases (by 2–3 W m-2 AOD-1) during all seasons, coinciding with the commuter traffic; and (2) a small summer daytime decrease (0.6 to 0.4) in αap, possibly due to coating of absorbing particles (Gyawali et al., 2009) or an artifact associated with filter-based σap measurements (Lack et al., 2008, 2009).

The spring, summer, and fall weekly σsp and σap cycles at APP (Figs. 3a and 4a) are characterized by early week increases leading to broad Wednesday–Friday maxima. Both σsp and σap begin to increase near the time of the Monday morning traffic peak (unpublished result) and decrease over the weekend, coinciding with less weekend traffic. The weekly σsp and σap cycles are likely the result of a build-up of scattering and absorbing aerosols in the PBL during the first half of the week. Sunday σap minima and weekly cycle amplitudes of ∼ 25–35 % during spring and fall are consistent with the timing and amplitudes of weekly EC concentration cycles reported for the rural US (Murphy et al., 2008) and with weekday–weekend EC concentration differences in the urban US (Bae et al., 2004; Blanchard et al., 2008). Smaller but significant weekly σsp cycle amplitudes of ∼ 15–20 % during spring, summer, and fall are larger than weekly cycles in OC and sulfate reported by Murphy et al. (2008). Absorption coefficient exhibits a larger summer weekly cycle amplitude of ∼ 50 % (Fig. 4a) than σsp (Fig. 3a). Local traffic is less during summer, but construction activity and road repairs on the Appalachian State University campus and in town are higher so a larger influence from diesel emissions could be a source for the larger σap cycle during summer. Local traffic influences on the weekly and diurnal σap cycles during winter may be masked by other sources of EC, such as wood-burning. Small weekly cycles in several intensive AOPs are consistent with the above-discussed local traffic influence. Single-scattering albedo decreases by ∼ 0.02 from Sunday to Wednesday during fall/winter (Fig. S12) with smaller decreases during spring/summer. DRFE increases by ∼ 2 W m-2 AOD-1 from Sunday to Wednesday during fall/winter, with smaller insignificant increases in spring/summer (Fig. S13). Absorption Ångström exponent increases during the week by ∼ 0.2 (0.4 to 0.6) during summer, with smaller, insignificant increases (∼ 0.1) during fall and winter (Fig. S15).

PM1 particles contribute ∼ 76 % (72 %) to the summer (winter) PM10 σsp and 88 % (∼ 80 %) to the summer (winter) PM10 σap at BND (Figs. 2c and S8c). The annual PM1 and PM10 σap and σsp cycles are similar for all seasons (Figs. 2 and S8) so the PM1 AOP cycles at BND are representative of the PM10 aerosol. Many of the same general features of the σsp annual cycle at BND (Fig. 2a) have been reported by others (D&O2002; Koloutsou-Vakakis et al., 2001), including the July–August σsp maximum and early autumn σsp minimum. D&O2002 reported similar summer–autumn and summer–spring σsp differences, with median σsp values in July approximately 2 times larger than σsp in October–November and ∼ 1.5 times larger than σsp in April–May. The σap annual cycle reported by D&O2002 was also very similar to that shown in Fig. 2b, except for an October σap maxima in their study. Planetary boundary layer heights reported for nearby Joliet, IL by Holzworth (1964) were approximately 3 times higher in summer than in winter, suggesting that summer aerosol production must be much higher (and/or sinks be much lower) to maintain the observed higher summer aerosol loading in the mixed layer.

Regional aerosol transport associated with southerly wind sectors (SE to SW wind directions) exerts a large influence on σsp during all seasons (Fig. 6a). Northerly wind sectors (NW to NE wind directions) exert a comparable or larger influence on σsp during winter months. Much of the light-scattering aerosol arriving from the south is likely secondary sulfate associated with the high-density of coal-burning power plants in southern Illinois and the Ohio River valley region (Buzcu-Guven et al., 2007). Summer σsp may also be influenced by biogenic SOA. Median summer temperatures are ∼ 3 ∘C higher for SW winds at BND than for SE winds and the forests over SW Illinois and SE Missouri emit high amounts of isoprene during summer (Fig. 3 of Parworth et al., 2015). Scattering coefficient for SW wind directions exhibits a sharp July peak and the temperature dependence of σsp at BND during April–October demonstrates modest agreement (r=0.47, as shown in Fig. S7) with the exponential temperature dependence of biogenic volatile organic compound emissions (Guenther et al., 2006). The secondary PM1 σsp peak during winter months at BND (Fig. 2a) may be influenced by temperature dependent gas-to-particle partitioning of regional ammonia and nitric acid into ammonium nitrate. Rupakheti et al. (2005) reported that gas-phase ammonia correlated positively with particulate ammonium and nitrate mass concentrations for temperatures below 12 ∘C and that more ammonia remained in the gas phase for T > 12 ∘C. The temperature dependence of median PM1 σsp at BND changes sign (positive to negative) for temperatures less than ∼ 10 ∘C, nearly doubling as temperature decreases from ∼ 10 to ∼ -5 ∘C (Fig. S5). The σsp increase is accompanied by an increase in median ω0 from 0.89 to 0.96 (Fig. S6); and a decrease in median b from 0.15 to 0.13. Addition of large, highly scattering PM1 particles at low temperatures is consistent with high winter ammonium nitrate concentrations reported for BND (Buzcu-Guven et al., 2007). Much of the winter σsp increase is likely due to regional transport from the north. Winter σsp exhibits the largest increase for northerly wind sectors (Fig. 6a) with winter σsp a factor of ∼ 1.5–3 larger than spring and fall σsp. Winter ω0 and b are highest for the northerly wind directions, with ω0≥ 0.93 and b < 0.15 for a majority of the arriving air masses (Fig. S19). Northerly wind sectors are typically associated with colder air mass traveling over regions with high concentrations of ammonium and nitrate precursor gases (Hand et al., 2012b). Temperature-dependent ammonium nitrate production is also consistent with the highly variable timing and magnitude of the winter σsp peak for individual years (Fig. S2). Lower winter PBL heights during winter (Holzworth, 1964) likely also contribute to elevated winter σsp. Variability in winter PBL heights could conceivably contribute to winter σsp variability.

Diurnal σsp cycles are insignificant for all seasons except for a marginally significant fall amplitude of ∼ 25 % (Fig. 3d). Diurnal σap cycle amplitudes (Fig. 4d) are much larger than those of σsp during all seasons except winter. Differences between σap and σsp diurnal cycle amplitudes are largest in summer (∼ 60 vs. 10 %) and are also non-negligible in fall (∼ 50 vs. ∼ 25 %) and spring (∼ 40 vs. ∼ 20 %). Diurnal σap and σsp cycles are both smallest during winter, with cycle amplitudes of ∼ 10 %. The influence of diurnal PBL height cycle is clearly seen in the diurnal σap cycles (Fig. 4d) and a smaller PBL height influence is seen in the σsp cycles. The differences between σap and σsp cycle amplitudes during summer and (to a lesser degree) fall and spring suggests a large additional source of scattering aerosols during summer daytime hours. Photochemical aerosol processing is the only source of scattering particles whose diurnal and seasonal dependence can explain the seasonality of differences between the σap and σsp cycle amplitudes. It is also consistent with the seasonality of sulfate mass concentrations reported for BND (Buzcu-Guven et al., 2007). Weekly σsp cycles are statistically significant for all seasons, but the cycle amplitudes are less than 15 % for all seasons except fall. Our weekly σsp cycle amplitude for the entire year (Fig. 3c) is similar to that of Murphy et al. (2008).

Regional pollution transport associated with southerly wind sectors also influences the annual σap cycle at BND over all seasons (Fig. 6b). Highest σap for the southerly wind sectors occurs during summer and fall and southerly winds are most common in summer (Fig. 6a), leading to the summer σap maxima (Fig. 2b). Lowest σap for the southerly wind sectors occurs during winter and air masses from the less anthropogenically perturbed W/NW reach the site most frequently in winter (Fig. 6b), leading to the winter σap minima. The difference between the month of maximum σap (August) and that reported by D&O2002 (October) could be due to differences in the seasonality of wind directions between the two periods. It could also arise due to differences in the seasonality of removal mechanisms such as precipitation between the periods, but this would have likely also shifted the month of maximum σsp.

The weekly and diurnal σap cycles during summer and autumn (Fig. 4c, d) are consistent with a large influence from regional diesel emissions during these seasons and possibly during other seasons, although the weekly and diurnal σap cycles are only significant in summer and autumn. Maximum σap extends from sunset to sunrise for all seasons (Fig. 4d), with a broad minimum extending from just after sunrise to just before sunset. Large seasonality of PBL heights is obvious in the diurnal σap cycles (Fig. 4d), consistent with large (factor of 3) summer-to-winter PBL height differences reported for the region by Holzworth (1964). The absence of early morning and late afternoon local commuter peaks at BND is not surprising, since emissions from interstate highway traffic and agricultural activity represent the largest local sources of absorbing aerosols. Long-distance trucking comprises a large portion of interstate highway traffic in the region and both this and farming activities typically persist throughout the day. The diurnal σap cycles for individual days of the week show the same broad features as the corresponding weekly integrated diurnal σap cycles (Fig. 4d) for all seasons, with the exception of differences between post-dusk and pre-dawn σap for individual days of the week (unpublished result). During summer, post-dusk σap is slightly larger than pre-dawn σap for each day during Monday–Friday, leading to a gradual build-up of absorbing aerosols in the PBL. Post-dusk σap is less than pre-dawn σap on Saturday and Sunday. The resulting weekly σap cycle (Fig. 4c) and the σap cycles for individual days suggest a nearly constant source of absorbing aerosols from sunrise to sunset, with the largest emissions from Monday to Friday. Both interstate truck traffic and farming activities are consistent with the observed diurnal and weekly patterns during summer, but truck traffic is likely the source more capable of contributing to the large summer diurnal and weekly σap cycle amplitudes (60 and 40 %, respectively), given the higher summer PBL heights in the region. The fall weekly σap cycle (Fig. 4c) also exhibits a build-up of absorbing aerosols from Monday to Tuesday, followed by lower aerosol loading during the remainder of the week. This cycle is not consistent with known weekly cycles in truck traffic or agricultural practices near the site. Scattering coefficient exhibits a similar weekly cycle as σap during autumn (Fig. 3c) and the weekly σap and σsp cycle amplitudes are similar (∼ 25 %) during fall. Similarities in the autumn weekly σap and σsp cycles could simply be the result of a smaller compensating effect on σsp from daytime secondary aerosol production during autumn (e.g., less photochemistry) or it could be due to sources of scattering and absorbing aerosols that are more similar in autumn than in summer. Diesel emissions from agricultural activity would seem more capable of contributing to the weekly σap cycle during autumn, when PBL heights are lower. Biomass burning is a less likely source, even though Buzcu-Guven et al. (2007) reported a significant biomass-burning influence on OM mass (38 %) at BND. Absorption Ångström exponent demonstrates minimal day of week variability during autumn (Fig. S15) and αap values of 1.1–1.2 are not statistically different from the theoretical value of 1 for BC (Bergstrom et al., 2002).

Annual PM1 σsp and σap cycles at EGB (Fig. 2a and b) are influenced by more polluted southerly air masses (120–240∘ wind directions) during all seasons, along with comparable contributions from less anthropogenically perturbed W/NW wind sectors during summer months (Fig. 7). Liggio et al. (2010) reported that S/SE wind directions were generally associated with transport from the greater Toronto area and that SW wind directions were often associated with more aged aerosol transported from the Ohio River valley region or other urban areas. Wind speeds are lower in May–October and polluted air masses from the south are typically associated with stagnant air masses ahead of fronts (Yang et al., 2011).

Scattering coefficient is elevated for all wind sectors during summer (Fig. 7a). Warm-season aerosol chemistry at EGB is influenced by temperature-dependent biogenic SOA from forests to the north (Leaitch et al., 2011; Slowik et al., 2010) and by photo-oxidation of anthropogenic pollutants from the south (Chan et al., 2010; Liggio et al., 2010). Scattering coefficients exhibit larger summer increases for the less anthropogenically perturbed wind sectors (all except 120–240∘ wind directions) than for the southerly wind sectors (Fig. 7a). Monthly median σsp for the southerly wind sectors are ∼ 1.5 times higher in summer than in spring and autumn, with larger summer σsp increases (factor of 2–5) for the other wind sectors (unpublished result). The largest summer σsp increases are for NW wind sectors (Fig. 7a). In addition to biogenic SOA, the NW wind sectors are influenced in summer by regional tourist traffic and by episodic long-range transport of smoke during peak fire season in northwest Canada. However, it is not possible to distinguish the effects of aged smoke from biogenic SOA from forests, based on the available aerosol optical measurements during the 2010–2013 period at EGB. The secondary σsp peak in winter is influenced by higher σsp associated with air masses from the S/SW (Fig. 7a), relative to spring and autumn. Winter σsp for wind directions 150–240∘ is ∼ 2 times higher than σsp from other wind sectors (not shown). Single-scattering albedo is also highest for the 150–240∘ wind sectors in winter, with values often 0.95 or above (Fig. S20a). Rupakheti et al. (2007) reported episodic high nitrate concentrations associated with air masses transported from urban areas south of EGB, mostly occurring during cold, humid conditions. Scattering coefficient does not exhibit a noticeable increase with decreasing winter temperatures at EGB during the 2010–2013 period (Fig. S5). Meteorology likely plays a role in the elevated winter σsp, as PBL heights in the region are lowest in winter at EGB (Horzworth, 1964).

The annual σap cycle (Fig. 2b) is qualitatively similar to annual EC mass concentration cycles reported for EGB (Yang et al., 2011) and for rural IMPROVE sites in the Great Lakes region (Spak and Holloway, 2009). Yang et al. (2011) reported mean EC concentrations (in units of µg m-3) at EGB of 0.83 for summer, 0.71 for fall, 0.49 for winter, and 0.36 for spring. Spak and Holloway (2009) reported highest regional EC mass concentrations in summer and lowest in winter, with the June EC maxima ∼ 2.2 times higher than the February EC minima. Our reported summer σap maxima in August is 2–2.5 times larger than the broad November–April minima (Fig. 2b).

Urban-influenced SE/S wind sectors are associated with highest σap and lowest ω0 for all seasons (Figs. 7b and S20a). Chan et al. (2010) attributed higher σap, higher EC concentrations, and lower OC / EC ratios in air masses arriving at EGB from the south to diesel emissions. Absorption coefficients are lowest in winter for all wind sectors and are largest for southerly wind sectors during summer and autumn (Fig. 7b), with monthly median σap ∼ 1.5 times higher in summer/autumn than in spring for these wind sectors. Much larger summer σap increases (factors of ∼ 3–7) are seen for westerly and northwesterly wind sectors (wind directions ∼ 240–360∘). Episodic long-distance NW transport during the Canadian wildfire season may contribute to summer σap, but local/regional tourism traffic is more consistent with the observed summer weekly and diurnal σap cycles.

Weekly and diurnal σap cycles at EGB are significant in summer, marginally significant in autumn, and insignificant in winter and spring (Fig. 4e and f). Summer and autumn diurnal σap cycle amplitudes are ∼ 50 % and summer and autumn weakly σap cycle amplitudes are ∼ 40 %. The diurnal and weekly cycles in σap during summer and autumn at EGB are more complicated than those at the other sites and are likely influenced to varying degrees by several sources, including (1) high volume of regional traffic during summer, largest on weekends; (2) transport of urban-influenced aerosol from the south; (3) diurnal PBL height evolution; and (4) local commuter traffic. Diurnal σap cycles for individual days of the week reveal morning commuter peaks from Monday to Friday (unpublished result). Daytime σap decreases due to lifting of the PBL height are dampened on each of these days by a large source of absorbing aerosol. Larger summer increases in σap for westerly wind sectors suggests a source in addition to transport from the south. The large additional source is likely regional tourism traffic. Differences between post-dusk and pre-dawn σap are small on Monday–Thursday (not shown) but are much larger on Friday (∼ 1 Mm-1) and Saturday (∼ 2 Mm-1) due to high volumes of weekend traffic. Post-dusk σap on Sunday is ∼ 3 Mm-1 lower than pre-dawn σap. The composite effect of these sources is the weekend σap maxima and Monday minima during summer (Fig. 4e). The weekend σap increase gives rise to a small decrease (0.02 to 0.03) in ω0 and a small increase (∼ 2 W m-2 AOD-1) in DRFE (Figs. S12, S13) Diurnal σsp cycles for individual days of the week during summer reveal some of the same features as σap (unpublished result) but are further complicated by an additional large source of daytime scattering aerosol, likely photochemical production and transport of SOA.

The autumn diurnal σap cycle (Fig. 4e) appears to be more influenced by frequent transport from the south (Fig. 7b), along with less regional traffic than during summer. Monthly averaged σap during September–October (Fig. 2b) remains near summer levels (except for August), but σap is much lower for all wind sectors except the urban-influenced southerly wind sectors, for which σap was similar in value to summer (Fig. 7b). The diurnal σap and σsp cycles exhibit very little structure during fall so lower fall PBL heights may be partially offset by lower production of scattering and absorbing aerosol and/or more efficient removal mechanisms. Some additional source may be responsible for the early week increase in σap, similar to that observed during autumn at BND (Fig. 4c). The source of absorbing aerosol persists throughout the day and into the evening (not shown) and may be local agricultural activities.

PM1 particles contribute ∼ 66 % (78 %) to the summer (winter) PM10 σsp and ∼ 85 % to both summer and winter PM10 σap at SGP (Figs. 2c and S8c). The annual PM1 and PM10 σap and σsp cycles are similar (Figs. 2a and S8a) so the PM1 AOP cycles at SGP are representative of the PM10 aerosol. The annual PM1 σap cycle (Fig. 2b) demonstrates good overall agreement with the annual PM10 σap cycle reported by D&O2002 for 1997–2000, with the exception that their winter σap minima extends from November to February, while our σap minima extends from January to February. The annual PM1 σsp cycle during 2010–2013 (Fig. 2a) also agrees well with that reported by D&O2002 for most non-winter months. D&O2002 reported a broad summer maxima, with monthly median σsp values lying ∼ 30–40 % above spring and autumn months. Our σsp cycle during non-winter months differs only by a larger summer-to-autumn σsp decrease of close to factor of 2. Agreement is worse for winter months. Both D&O2002 and Sheridan et al. (2001) reported minimum σsp in December and maximum in February, with median February σsp a factor of ∼ 4 higher than December. Box plots of monthly binned σsp for individual 2010–2013 years (Fig. S4) show that median February σsp at SGP varies by up to a factor of 4 for different years, with somewhat smaller differences between individual January months (factor of ∼ 2) and between individual March months (factor of ∼ 2–3). Much of the inter-annual variability is smoothed out in the monthly binned σsp box plot for the entire period (Fig. S3), giving rise to relatively constant monthly mean σsp during winter for the current period (Fig. 2a). Lower December σsp and much higher February σsp occurred during the period reported by D&O2002 and Sheridan et al. (2001), compared to the period reported here.

Pollution transport from the S/SE impacts PM1 σap and σsp throughout the year (Fig. 8). Wind directions are primarily from the S/SE for non-winter months (especially summer). Air mass back-trajectories show that air masses arriving at SGP from the S/SE often travel over or near large regional populations centers, including Oklahoma City, Tulsa, and (in summer) Dallas/Fort Worth (Parworth et al., 2015). Single-scattering albedo is generally lower for S/SE wind sectors than for the less anthropogenically influenced westerly and northerly wind sectors, except during summer (Fig. S22a). A large fraction of non-refractory PM1 aerosol mass (∼ 70 %) is aged SOA during April–October (Parworth et al., 2015). Many SE trajectories pass over regions of high summer isoprene emissions (Parworth et al., 2015), but the temperature dependence of σsp (Figs. S5 and S7) is less than for the sites with known biogenic SOA influence (EGB and APP). Absorption Ångström exponent values close to 1 for all seasons (Fig. 2h) suggest that despite high organic composition, light-absorbing OC exerts a minimal influence on the annual σap cycle and that most of the absorbing aerosol is BC. Daily averages of αap can have values that extend to as high as 2.5 (unpublished result), which is consistent with observed plumes of biomass-burning aerosol reported by Parworth et al. (2015). Other than lower σsp during autumn, σsp and σap for the S/SE wind sectors do not demonstrate much seasonality (Fig. 8). The lack of seasonal variability in mean σap and σsp during non-winter months (relative to the other sites) may be due to a longer distance from the population centers (increased aerosol dispersion) and higher PBL heights at SGP during spring, summer, and autumn. Removal processes may also be more efficient in late spring and summer, when monthly averaged rainfall at SGP is highest.

The frequency of episodic transport of ammonium nitrate to SGP likely exerts some influence on winter σsp and its variability. Parworth et al. (2015) reported that ammonium nitrate comprised approximately half of the non-refractory PM1 mass at SGP during the 2010–2011 and 2011–2012 winters and early springs (e.g., March) (their Figs. 2 and 6). Ammonia and NOx concentrations near SGP are relatively small and high nitrate episodes (mass concentrations > 3 µg m-3) were nearly always associated with temperatures < 3 ∘C and long-distance transport from agricultural states in the central Great Plains region. Colder temperatures and more frequent long-distance transport passing over these states likely contributed to nearly a factor of 2 higher average ammonium nitrate concentrations during the 2010–2011 winter than the 2011–2012 winter (Parworth et al., 2015). Average OA concentrations were similar between the two winters so variability in ammonium nitrate likely exerted an influence on the ∼ 50 % higher average PM1 mass concentration during the 2010–2011 winter. Lower relative humidity during the 2010–2011 winter indicates that less wet deposition could also have contributed to higher PM1 aerosol mass during that winter (Parworth et al., 2015). The frequency of episodically transported biomass-burning aerosol also influences σsp and σsp at SGP. Biomass-burning aerosol is most prevalent in the spring, when prescribed crop burning in preparation of planting is more common. Parworth et.al. (2015) reported a much larger biomass-burning aerosol influence in spring 2011 than spring 2012, primarily in March–April. Differences are observed in the mean σsp and σap between the two springs, in addition to differences in the 50th, 75th, and 95th percentiles between the two springs (Fig. S4). Differences between the 2 years are more noticeable for σap than for σsp.

Diurnal σap cycle amplitudes (Fig. 4h) are near 40 % for all seasons except spring (25 %). Only the summer and autumn cycles are statistically significant. Diurnal PBL height effects are clearly visible in the diurnal σap cycles (Fig. 4h), as is a lack of commuter influence. Similar to BND, there is no local commuter traffic that would be expected to influence AOP cycles at SGP. No obvious features are seen in the individual day of week σap cycles (unpublished result) to indicate a possible role of interstate traffic or agricultural influences in the weekly or diurnal σap cycles (Fig. 4g, h). This is complicated by biased SGP σap observations during the weekends. The diurnal σsp cycle is insignificant for all seasons (Fig. 3h), which may reflect increased daytime photochemical processing that is somewhat less in the winter months. Larger mid-day decreases in σap than σsp lead to increases in ω0 of ∼ 0.03. The hemispheric backscatter fraction varies negligibly during the day. The midday increase in ω0 leads to more negative midday DRFE, by ∼ 3 W m-2 AOD-1 in all and 2 W m-2 AOD-1 in summer. The aerosol parameters related to size show contrasting trends. No visible diurnal or weekly trend is apparent in b while αsp shows a decline with larger aerosol in the early evening. The trend in declining afternoon αsp values starts earlier in the day during the winter and is weakest during the summer and spring.

Single scattering albedo increases and b decreases with increasing σsp at all sites (Fig. 10a, b). Hemispheric backscatter fraction demonstrates an inverse relationship with ω0 over the entire ω0 range at EGB and for ω0 > 0.85 at the other sites (Fig. 10c), a condition representative of all months (Fig. 2d, e). The co-variability of ω0 and b leads to a DRFE dependence on σsp that is statistically insignificant for all sites, with the exception of the lowest σsp conditions at APP (Fig. 10d). Greater influences by smaller, darker particles under low-loading conditions and by larger, brighter particles under high-loading conditions are seen in the annual σsp, b, and ω0 cycles for the four sites in this paper (Fig. 2a, d, and e) and have been reported for SGP and BND by D&O2002. The tendency toward lower ωo and higher b for low-loading conditions is consistent with preferential removal of large, less-absorbing particles by cloud scavenging and/or wet deposition. It can also be the result of new particle formation with growth by condensation and/or coagulation to optically active sizes (Andrews et al., 2011). Scattering Ångström exponent and Rsp are both relatively insensitive to changes in σsp at APP over the entire σsp range (Fig. 10e, f). Scattering Ångström exponent is insensitive to changes in σsp for all but the lowest aerosol loading levels at BND and SGP (Fig. 10e). PM1 scattering fraction shows a modest decrease with increasing σsp for σsp > 20 Mm-1 at BND and SGP (Fig. 10f). A similar lack of sensitivity of αsp to changes in σsp at SGP and BND was reported by D&O2002. PM1 scattering fraction increases proportionally with αsp at APP, BND, and SGP (Fig. 10g). D&O2002 reported similar Rsp vs. αsp relationships for SGP and BND. The fact that the Rsp vs αsp relationship is much stronger than either of their relationships with σsp suggests that αsp is a better indicator of the relative contributions of coarse and fine mode aerosol to PM10 σsp than an indicator of average particle size-at least for APP, BND, and SGP. Based on the range of Rsp values measured at SGP, BND, and APP (Fig. 2c), the aerosol size distributions are on average bi-modal (with higher coarse mode fractions at SGP and BND than at APP) and care must be exercised when using αsp to infer average particle size or aerosol type. The Rsp vs αsp relationship (Fig. 10g) is consistent with decreasing trends in both Rsp and αsp at SGP (Table 4) but seems inconsistent with the lack of change in αsp at BND, despite reductions in Rsp similar in magnitude to those at SGP.

AOPs at the rural continental sites reported here have similar relationships (Fig. 10) as those at a majority of mountain sites reported on by Andrews et al. (2011). Andrews et al. (2011) also reported relationships amongst AOPs based on long-term aircraft measurements made over BND and SGP, although their free tropospheric AOP relationships for BND and SGP only extended up to σsp ∼ 25 Mm-1. Most of the free troposphere AOP relationships reported for SGP (Andrews et al., 2011) are similar to the corresponding near-surface AOP relationships (Fig. 10), but there are some noticeable differences for BND. Andrews et al. (2011) reported the following AOP relationships as σsp increased from zero to 25 Mm-1 at BND: (1) b increased slightly (0.12 to 0.13); (2) ωo remained nearly constant (less than 0.01 increase); and (3) αsp increased by a larger amount (∼ 0.12 to 0.17) than in our study (Fig. 10e). The differences between these relationships and those in Fig. 10a, b, and e could be due to smaller particles that undergo less atmospheric processing (particle growth, cloud scavenging, and deposition) in the free troposphere above BND, relative to particles near the surface.

The relationships between αap and σsp for individual seasons and the annual relationship are most different at APP (Fig. 11a) and least different at BND (Fig. 11b). Absorption Ångström exponent at APP is statistically higher than 1 (αap≥ 1.2) for all σsp bins during winter and is statistically lower than 1 (αap≤ 0.8) for all σsp bins during summer and for higher-loading conditions (σsp≥ 50 Mm-1) during spring and autumn (Fig. 11a). Absorption Ångström exponent at BND (Fig. 11b) and SGP (Fig. 11c) is not statistically different from 1 for any σsp bins except for (1) summer loading σsp≥ 30 Mm-1; and (2) spring and autumn loading σsp≥ 80 Mm-1 (SGP only). Relationships among αap and intensive AOPs (αsp and ω0) can be used to identify contributions to σap by sources other than BC, such as dust, OC, and coated BC (Cazorla, et al., 2013; Costabile et al., 2013; Gyawali et al., 2009). Absorption Ångström exponent exhibits a systematic decrease with increasing αsp for all seasons at SGP (Fig. 11f) and αsp decreases in a step-wise manner for all seasons except summer at BND (Fig. 11e). The αap-αsp relationship is more complicated at APP (Fig. 11d), where αap demonstrates a similar decrease with increasing αsp during summer to that observed at BND but a marginally significant increase with increasing αsp during winter. Values of αap that are statistically higher than 1 (αsp≥ 1.2) tend to be associated with αsp≥ 1.5 at APP (Fig. 11d), suggesting a mix of EC and OC (Fig. 2 of Cazorla, et al., 2013). Values of αsp≥ 1.2 at BND and SGP are most often associated with αsp < 1 (Fig. 11e, f), suggesting a mix of EC and dust (Fig. 2 of Cazorla et al., 2013). Dust influences σap at SGP during all seasons and also influences BND σap during autumn, as seen by the number of data points with αsp≥ 1.2 and αsp < 1 in Fig. 11e, f. Episodic biomass burning that impacts SGP during spring (Parworth et al., 2015) also contributes to high αap values, which can reach ∼ 2.5 for individual days (unpublished result). Summer values of αap are lower than those of other seasons for all αsp bins at BND and APP and for all but the lowest αsp bins at SGP (where dust likely influenced absorption). The slopes of the αap vs αsp curves indicates that αap values significantly lower than 1 during summer coincide with higher fractions of fine-mode aerosol (higher αsp).

The annual αap–ω0 relationships for all individual seasons are also most similar at BND (Fig. 11h) and least similar at APP (Fig. 11g), where the summer and winter αap–ω0 relationships are noticeably different. Absorption Ångström exponent is lowest over the entire ω0 range during summer at all sites. All of the individual season αap–ω0 curves are similar in that αap remains constant or slightly increasing with increasing ω0 until ω0 approaches 0.90 (specifically the ω0 bin centered at 0.875). This is followed by sharp decreases in αap with further increases in ω0. Absorption Ångström exponents significantly less than 1 (αap≤ 0.8) during summer months coincide with ω0≥ 0.85 at APP, ω0≥ 0.90 at BND, and ω0≥ 0.95 at SGP. Absorption Ångström exponent at APP is also significantly less than 1 for ω0≥ 0.95 during autumn. From the b vs. ω0 relationships (Fig. 10c), the lower mean αap values at all sites during summer also coincide with lower mean b values. When combined, these relationships indicate that lower αap values are associated with larger, less-absorbing, fine-mode particles. Gyawali et al. (2009) reported a similar αap–ω0 relationship for summer months with no biomass-burning influence in Reno, NV. Single-scattering albedo was near constant (αap∼ 1.1–1.2) up to ω0∼ 0.90, followed by αap values mostly below one for higher ω0. Gyawali et al. (2009) attributed this wavelength dependence of absorption to EC particles coated with non-absorbing organic and inorganic matter. It should be noted that Gyawali et al. (2009) used a photo-acoustic spectrometer, as compared to the filter-based techniques that are employed at the sites in this study. Gyawali et al. (2009) also used different wavelengths (405 and 870 nm) so the results are not directly comparable. The summer values of αap at APP are also much lower for all ω0 than those reported by Gyawali et al. (2009). Possible biases in filter-based absorption measurements made in high-OA environments could in principle contribute to this result (e.g., Lack et al., 2008, 2009). A detailed analysis of the effects, both real and artifact, of absorbing and non-absorbing coatings on the wavelength dependence of light absorption by black carbon is beyond the scope of this paper.