Parameterization of size of organic and secondary inorganic aerosol for efficient representation of global aerosol optical properties

Accurate representation of aerosol optical properties is essential for the modeling and remote sensing of atmospheric aerosols. Although aerosol optical properties are strongly dependent upon the aerosol size distribution, the use of detailed aerosol microphysics schemes in global atmospheric models is inhibited by associated computational demands. Computationally efficient parameterizations for aerosol size are needed. In this study, airborne measurements over the United States (DISCOVER-AQ) and South Korea (KORUS-AQ) are interpreted with a global chemical transport model (GEOS-Chem) to investigate the variation in aerosol size when organic matter (OM) and sulfate–nitrate–ammonium (SNA) are the dominant aerosol components. The airborne measurements exhibit a strong correlation (r=0.83) between dry aerosol size and the sum of OM and SNA mass concentration (M_SNAOM). A global microphysical simulation (GEOS-Chem-TOMAS) indicates that M_SNAOM and the ratio between the two components ($\mathrm{OM}/\mathrm{SNA}$) are the major indicators for SNA and OM dry aerosol size. A parameterization of the dry effective radius (R_eff) for SNA and OM aerosol is designed to represent the airborne measurements (R²=0.74; slope = 1.00) and the GEOS-Chem-TOMAS simulation (R²=0.72; slope = 0.81). When applied in the GEOS-Chem high-performance model, this parameterization improves the agreement between the simulated aerosol optical depth (AOD) and the ground-measured AOD from the Aerosol Robotic Network (AERONET; R² from 0.68 to 0.73 and slope from 0.75 to 0.96). Thus, this parameterization offers a computationally efficient method to represent aerosol size dynamically.

1 Introduction

Aerosol size has numerous effects on aerosol physical and chemical properties and further on atmospheric chemistry. Aerosol-size-dependent heterogeneous chemistry affects gaseous oxidants that in turn affect the production rates of aerosol components such as sulfate and secondary organic aerosol (Ervens et al., 2011; Estillore et al., 2016). Aerosol size also affects loss rates due to dry and wet deposition (Seinfeld and Pandis, 2016). Both direct and indirect aerosol radiative forcing are sensitive to aerosol size, as aerosol size affects the interaction between particles and radiation, and the water supersaturation ratio needed for a particle to be activated into a cloud droplet (Adams and Seinfeld, 2002; Faxvog and Roessler, 1978; Mishchenko et al., 2002; Emerson et al., 2020). The size dependence of aerosol extinction and scattering-phase function also affects the retrieval of aerosol properties from satellites (Levy et al., 2013; Kahn et al., 2005; Jin et al., 2023). Aerosol size affects the fraction of particles that deposit in the body when breathing in addition to the location within the body where they deposit (Hinds and Zhu, 1999). An appropriate representation of aerosol size is essential for modeling aerosol composition and optical properties (Kodros and Pierce, 2017), interpreting satellite data (Levy et al., 2013; Kahn et al., 2005), studying climate processes (Twomey, 2007; Kellogg, 1980), and moving from aerosol exposure towards health studies (Kodros et al., 2018).

The evolution of the aerosol size distribution is affected by various processes, such as nucleation, condensation, coagulation, and deposition. Nucleation events contribute to the number of particles in the nucleation mode (diameters less than about 10 nm) and thus tend to decrease the mean aerosol size for a population (Aalto et al., 2001). In polluted areas with high emission rates of aerosol precursors, the mean aerosol size tends to increase by condensation and coagulation (Sakamoto et al., 2016; Sun et al., 2011). Dry and wet aerosol deposition have strong size dependencies due to competing physical processes (Emerson et al., 2020; Ruijrok et al., 1995; Reutter et al., 2009). The aerosol size distribution can be simulated using aerosol microphysical schemes, such as the TwO-Moment Aerosol Sectional (TOMAS; Adams and Seinfeld, 2002) microphysics model, the advanced particle microphysics (APM; Yu and Luo, 2009) model, the Global Model of Aerosol Processes (GLOMAP; Mann et al., 2010), and the four-mode version of the Modal Aerosol Module (MAM4; Liu et al., 2016). These schemes have valuable prognostic capabilities; however, their computational cost has limited their use in chemistry climate models (CCMs) or chemical transport models (CTMs). For example, the wall clock time increases by about 2.5 times when APM is enabled in GEOS-Chem CTM relative to the bulk model (GCST et al., 2023). Only 3 of the 10 models that included aerosols, studied by the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP), include online size-resolved aerosol microphysics, reflecting its computational cost and complexity (Lamarque et al., 2013; Liu et al., 2012; Szopa et al., 2013; Kodros and Pierce, 2017).

Methods are needed to better represent aerosol size in CCMs or CTMs without a microphysics scheme (referred to as bulk models). These bulk models usually use prescribed relationships to obtain size-resolved aerosol properties (Croft et al., 2005; Karydis et al., 2011; Zhai et al., 2021), which may insufficiently represent the temporal and spatial variation (Kodros and Pierce, 2017). For example, in the GEOS-Chem (Goddard Earth Observing System coupled with chemistry) CTM, a fixed dry aerosol geometric mean radius (R_g) is assumed for organic matter (OM) and sulfate–nitrate–ammonium (SNA), which is based on analysis of long-term aerosol composition and scattering measurements provided by the IMPROVE network across the continental USA (Latimer and Martin, 2019). However, subsequent analysis by Zhai et al. (2021) found that this aerosol size underestimated the aerosol mass scattering efficiency and the aerosol extinction coefficients during an aircraft campaign over South Korea (KORUS-AQ). Thus, neglecting the aerosol microphysical processes that shape aerosol size distributions can be a significant source of uncertainty in aerosol optical properties in a CTM. A balance between computational cost and representativeness of aerosol size is needed. One option is to use models with size-resolved aerosol microphysics models to inform bulk models, such as was done for the parameterization of biomass burning aerosol size by Sakamoto et al. (2016).

Recent airborne measurements offer information to evaluate and improve the simulation of aerosol size. DISCOVER-AQ (Deriving Information on Surface conditions from Column and Vertically Resolved Observations Relevant to Air Quality) was a multi-year campaign over four USA cities that provides 3-D-resolved measurements of atmospheric gas composition, aerosol composition, size distribution, and optical properties (Choi et al., 2020; Sawamura et al., 2017; Chu et al., 2015). KORUS-AQ (the Korea–United States Air Quality Study) offers similar measurements in a different environment with higher aerosol mass loadings (Choi et al., 2020; Zhai et al., 2021; Nault et al., 2018; Jordan et al., 2020).

To study the global variation in aerosol size, we explore airborne measurements from DISCOVER-AQ and KORUS-AQ, in addition to output from the GEOS-Chem-TOMAS microphysics model. We focus on OM and SNA, which dominate fine aerosol composition in populated areas (Weagle et al., 2018; Geng et al., 2017; Meng et al., 2019; Van Donkelaar et al., 2019; Li et al., 2017). The driving factors for the variation in aerosol size are examined. A parameterization of aerosol size using these driving factors is proposed. This parameterization is then applied to a GEOS-Chem high-performance model bulk simulation for global aerosol optical depth (AOD), which is evaluated by ground-measured AOD from the Aerosol Robotic Network (AERONET).

2 Observations and models

2.1 Observations

2.1.1 Aircraft measurements

We examine airborne measurements from two NASA campaigns, DISCOVER-AQ and KORUS-AQ. DISCOVER-AQ includes four deployments in Maryland (MD), California (CA), Texas (TX), and Colorado (CO). KORUS-AQ is an international cooperative field study program conducted in South Korea (KO), sponsored by NASA and the South Korean government through the National Institute of Environmental Research. The year, date range, and altitude range of each deployment are given in Table 1.

Measurements used in this study include aerosol composition, ambient aerosol extinction, aerosol number size distribution, gas tracer species, and meteorological data. Measurement methods are listed in Table 2. Measured aerosol mass is converted from a standard to an ambient condition before analysis using ambient temperature and pressure. We use OM directly measured during KORUS-AQ. We use water-soluble organic carbon (OC) and a parameterized ratio between OM and OC (Philip et al., 2014) to calculate OM for DISCOVER-AQ. The parameterized OM is evaluated with KORUS-AQ data, and consistency is found overall (Fig. A1; Appendix A). For both campaigns, dust concentration is derived from Ca²⁺ and Na⁺, assuming that non-sea-salt Ca²⁺ accounts for 7.1 % of dust mass, as follows (Shah et al., 2020):

$$\begin{array}{}\text{(1)}& \mathrm{Dust}={\displaystyle \frac{\left(\left[{\mathrm{Ca}}^{\mathrm{2}+}\right]-\mathrm{0.0439}\frac{\left[{\mathrm{Na}}^{+}\right]}{\mathrm{2}}\right)}{\mathrm{0.071}}}.\end{array}$$

Sea salt is calculated from measured Na⁺, following previous studies (Remoundaki et al., 2013; Malm et al., 1994; Snider et al., 2016). The crustal component is removed by subtracting 10 % of the [Al³⁺] (Remoundaki et al., 2013). A 2.54 scalar is applied to [Na⁺]_ss to account for [Cl⁻], as follows (Malm et al., 1994):

$$\begin{array}{}\text{(2)}& \mathrm{Sea}\mathrm{salt}=\mathrm{2.54}\left(\right[{\mathrm{Na}}^{+}]-\mathrm{0.1}[{\mathrm{Al}}^{\mathrm{3}+}\left]\right).\end{array}$$

The effective radius (R_eff; Hansen and Travis, 1974), defined as the area-weighted mean radius of a particle population, is used as a surrogate for aerosol size, as follows:

$$\begin{array}{}\text{(3)}& R_{\mathrm{eff}}={\displaystyle \frac{\int r\mathit{\pi }{r}^{\mathrm{2}}n\left(r\right)\mathrm{d}r}{\int \mathit{\pi }{r}^{\mathrm{2}}n\left(r\right)\mathrm{d}r}}.\end{array}$$

Measurement data are screened for dust influence by excluding data with the sum of SNA and OM (M_SNAOM) < 4 × dust mass.

Table 1 Temporal and spatial coverage of each aircraft deployment.

Table 2 Aircraft observations used in this study^∗.

^∗ Adapted from Zhai et al. (2021). ^a Ion chromatography particle-into-liquid sampler (PILS), with a 1.3 µm inlet cutoff aerodynamic diameter (Lee et al., 2003; Hayes et al., 2013). ^b Soluble Acidic Gases and Aerosol (SAGA) instrument (Dibb et al., 2003). The cutoff aerodynamic diameter of the inlet is around 4 µm (McNaughton et al., 2007). ^c Water-soluble organic carbon particle-into-liquid sampler, with a 1 µm inlet cutoff diameter at 1013.25 hPa (Sullivan et al., 2019; Timonen et al., 2010). ^d University of Colorado, Boulder, high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) with a 1 µm inlet cutoff diameter (Nault et al., 2018; Guo et al., 2021; Canagaratna et al., 2007). ^e Single-particle soot photometer (SP2), measuring refractory black carbon with a volume equivalent diameter of 100–500 nm (Lamb et al., 2018; Schwarz et al., 2006). ^f Particles with mobility diameters between 60 to 1000 nm can be measured by ultra-high-sensitivity aerosol spectrometer (UHSAS), which illuminates particles with a laser and relates the single-particle light scattering intensity and count rate measured over a wide range of angles to the size-dependent particle concentration (Moore et al., 2021). Particles in the sample are dried to less than 20 % relative humidity (RH). ^g Particles between 100 to 5000 nm. measured by a laser aerosol spectrometer (LAS; TSI, model 3340). The principle of LAS is the same as that of UHSAS but with a different laser wavelength (1054 nm for the UHSAS and 633 nm for the LAS) and intensity (about 100 times higher for the UHSAS). These differences affect how the instrument sizes non-spherical or absorbing aerosols (Moore et al., 2021). Particles in the sample are dried to less than 20 % RH. ^h NASA Langley airborne High Spectral Resolution Lidar (HSRL; Hair et al., 2008). ⁱ National Center for Atmospheric Research (NCAR) four-channel chemiluminescence instrument (Weinheimer et al., 1993). ^j NASA Diode Laser Hygrometer (DLH; Podolske et al., 2003).

2.1.2 AERONET AOD

We use ground-based AOD observations to evaluate our parameterization and simulated AOD. The Aerosol Robotic Network (AERONET) is a worldwide network that provides long-term sun-photometer-measured AOD and is conventionally considered to be the ground truth for evaluating model-simulated (Zhai et al., 2021; Meng et al., 2021; Jin et al., 2023) or satellite-retrieved AOD (Levy et al., 2013; Wang et al., 2014a; Kahn et al., 2005; Lyapustin et al., 2018). We use the Version 3 Level 2 database, which includes an improved cloud-screening algorithm (Giles et al., 2019). AOD at 550 nm wavelength, interpolated based on the local Ångström exponent at 440 and 670 nm channels, is used in this study. For each site, we use data for the year 2017, excluding months with fewer than 20 d of measurements and excluding sites with fewer than 4 months of observations.

2.2 GEOS-Chem simulation

We interpret the aircraft observations with the GEOS-Chem chemical transport model (http://www.geos-chem.org, last access: 30 October 2022). GEOS-Chem is driven by offline meteorological data from the Goddard Earth Observing System (GEOS) of the NASA Global Modeling and Assimilation Office (Schubert et al., 1993). We use the high-performance implementation of GEOS-Chem (GCHP; Eastham et al., 2018; Bindle et al., 2021) to examine the effect of the variation in aerosol size on AOD. We also use the TOMAS microphysical scheme, coupled with the standard GEOS-Chem implementation (GEOS-Chem Classic), to explicitly resolve aerosol microphysics. The bulk and microphysics simulations share common emissions and chemical mechanisms. They are both conducted for the year 2017 and driven by the meteorological fields of the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2).

The GEOS-Chem aerosol simulation includes the sulfate–nitrate–ammonium system (Fountoukis and Nenes, 2007; Park, 2004), primary and secondary carbonaceous aerosols (Park et al., 2003; Wang et al., 2014b; Marais et al., 2016; Pye et al., 2010), sea salt (Jaeglé et al., 2011), and mineral dust (Fairlie et al., 2007). The primary emission data are from the Community Emissions Data System (CEDS_GBD-MAPS; McDuffie et al., 2020). Dust emission inventories include updated natural dust emission (Meng et al., 2021), and anthropogenic fugitive, combustion, and industrial dust (AFCID; Philip et al., 2017). Resolution-dependent soil NO_x, sea salt, biogenic volatile organic compounds (VOCs), and natural dust emissions are calculated offline at native meteorological resolution to produce consistent emissions across resolution (Weng et al., 2020; Meng et al., 2021). Biomass burning emissions use the Global Fire Emissions Database, version 4 (GFED4; van der Werf et al., 2017). We estimate organic matter (OM) from primary organic carbon using the same $\mathrm{OM}/\mathrm{OC}$ parameterizations as applied for DISCOVER-AQ (Philip et al., 2014; Canagaratna et al., 2015). Dry and wet deposition follows Amos et al. (2012), with a standard resistance-in-series dry deposition scheme (Wang et al., 1998). Wet deposition includes scavenging processes from convection and large-scale precipitation (Liu et al., 2001).

Global relative-humidity-dependent aerosol optical properties are based on the Global Aerosol Data Set (GADS; Köpke et al., 1997; Martin et al., 2003), with updates for SNA and OM (Latimer and Martin, 2019), mineral dust (Zhang et al., 2013), and absorbing brown carbon (Hammer et al., 2016). In the current GEOS-Chem model, the SNA and OM R_eff, of particular interest here, are based on co-located measurements of aerosol scatter and mass from the IMPROVE network at USA national parks over the period 2000–2010, together with a κ-Kohler framework for aerosol hygroscopicity (Kreidenweis et al., 2008), as implemented by Latimer and Martin (2019). Aerosol extinction is calculated as the sum of extinction from each aerosol component, with aerosol optical properties listed in Table A1 (as described in Appendix A2).

A global GCHP simulation (Eastham et al., 2018) version 13.0.0 (https://doi.org/10.5281/zenodo.4618180) that includes advances in performance and usability (Martin et al., 2022), is conducted on a C90 cubed-sphere grid corresponding to a horizontal resolution of about 100 km, with a spin-up time of 1 month.

The TOMAS microphysics scheme, coupled with the GEOS-Chem simulation, conserves aerosol mass and tracks particles with diameters from approximately 1 nm to 10 µm (Adams and Seinfeld, 2002). Microphysical processes in TOMAS include nucleation, condensation, evaporation, coagulation, and wet and dry deposition (Adams and Seinfeld, 2002). Nucleation in TOMAS follows a ternary scheme (sulfuric acid, ammonia, and water) when ammonia mixing ratios are greater than 0.1 ppt (parts per trillion); otherwise, a binary nucleation scheme is used (Napari et al., 2002). The nucleation rate is scaled by 10⁻⁵ to better match the observations (Westervelt et al., 2013). The condensation and evaporation algorithm is based on a study from Tzivion et al. (1989), including the interaction with secondary organic aerosol (D'Andrea et al., 2013). Interstitial coagulation in clouds is also included (Pierce et al., 2015).

For each size bin, TOMAS tracks the mass and number of sulfate, sea salt, black carbon, OC, dust, and water. Primary sulfate emissions have two lognormal modes, namely 15 % of the mass with a number median diameter (NMD) of 10 nm and geometric standard deviation (σ) of 1.6 and the remainder with a NMD of 70 nm and σ of 2 (Adams and Seinfeld, 2003). The size of the emitted carbonaceous particles varies, depending on the source; those produced by fossil fuels have a NMD of 30 nm and σ of 2, while biofuel and biomass burning particles are emitted with a NMD of 100 nm and σ of 2 (Pierce et al., 2007). Meteorology and most of the emissions in GEOS-Chem-TOMAS follow the bulk simulation, except that online schemes are used for dust (Zender et al., 2003) and sea salt (Jaeglé et al., 2011).

The GEOS-Chem-TOMAS (version 13.2.1; https://doi.org/10.5281/zenodo.5500717) is used to provide insights into global-scale aerosol size variation and the driving factors. For computational feasibility, a 1-year global simulation is conducted with a horizontal resolution of 4^∘ × 5^∘ and 47 vertical layers from surface to 0.01 hPa. The spin-up time is 1 month. Aerosols are tracked in 15 size bins, with particle diameters ranging from about 3 nm to 10 µm. We also conducted a 2^∘ × 2.5^∘ simulation for October to evaluate the sensitivity of our conclusions to the resolution of the aerosol microphysics simulation.

3 Development of a parameterization of aerosol size

We first examine the aircraft measurements for insight into the observed variation in aerosol size. Then we apply the size-resolved GEOS-Chem-TOMAS model to extend our analysis to the global scale and identify the driving factors of the aerosol size. We subsequently develop and test a parameterization of the aerosol size for use in bulk models.

3.1 Observed variation in aerosol size

Figure 1 shows the daily mean dry effective radius from DISCOVER-AQ and KORUS-AQ as a function of aerosol mass. Aerosol size, in terms of dry R_eff, ranges from 90 to 179 nm for DISCOVER-AQ, which is generally smaller than for KORUS-AQ (ranging from 135 to 174 nm). M_SNAOM from DISCOVER-AQ (1.4 to 27.4 µg m⁻³) is also generally less than that from KORUS-AQ (5.5 to 33.2 µg m⁻³). A strong correlation (r=0.83) between aerosol size and M_SNAOM is evident. R_eff from KORUS-AQ is less sensitive to M_SNAOM (slope = 1.23) compared to DISCOVER-AQ (slope = 3.57). The relatively large particle size at low mass concentration during KORUS-AQ might reflect the influence of aged aerosol transported from upwind (Jordan et al., 2020; Zhai et al., 2021; Nault et al., 2018).

Figure 1 Airborne measurements of dry effective radius (R_eff) versus the sum of SNA and OM mass (M_SNAOM) for DISCOVER-AQ (Maryland is abbreviated as MD, California as CA, Texas as TX, and Colorado as CO) and for KORUS-AQ (KO) campaigns. Each point represents a daily average for the entire flight profile. Only data with M_SNAOM > 4 × dust mass are used.

The positive relationship between dry aerosol size and mass of SNA and OM reflects the roles of emission, condensation, and coagulation in simultaneously increasing aerosol size and mass. This general tendency is also observed by many other studies (e.g., Sakamoto et al., 2016; Rodríguez et al., 2007; Sun et al., 2012; Bahreini et al., 2003), despite variable aerosol sources and growth mechanisms. In cities, the joint increases in aerosol size and mass are usually attributable to anthropogenic emissions and condensation (Tian et al., 2019; Sun et al., 2011; Huang et al., 2013). In remote areas, biomass burning shifts the particle size distribution toward larger radii due to high emission rates and coagulation in plumes (Rissler et al., 2006; Ramnarine et al., 2019) that, for example, increase both aerosol size and mass from the wet season to the dry season in Amazonia (Rissler et al., 2006; Andreae et al., 2015). The positive relationship between aerosol size and mass suggests the possibility of using aerosol mass as a predictor of R_eff.

We examine the ability of the GEOS-Chem bulk model to reproduce the observed extinction. The top panel of Fig. 2 compares the measured aerosol extinction profiles to calculated aerosol extinction profiles using default R_eff. Details about the calculation are described in Appendix A2. Both measured and calculated extinction profiles exhibit increasing extinction toward the surface associated with increasing aerosol mass concentrations. However, biases are apparent for both DISCOVER-AQ and KORUS-AQ. The R_eff values from KORUS-AQ shown in Fig. 1 have a mean value of 164 nm, larger than the value of 101 nm inferred by Latimer and Martin (2019), which was based on measurements of aerosol scatter and mass by the U.S. IMPROVE network. This bias was previously noted by Zhai et al. (2021). The mean R_eff from DISCOVER-AQ of 138 nm is also larger than the inferred value. This likely reflects representativeness differences, since the DISCOVER-AQ deployments focused on major urban areas during months of high aerosol loadings, while the IMPROVE measurements were at national parks throughout the year. The middle panel shows the calculated extinction using the measured aerosol size distribution. Applying the measured aerosol size distribution addresses most discrepancies between the calculated and measured aerosol extinction profile for both KORUS-AQ and DISCOVER-AQ. The corresponding discrepancies in AOD estimation also significantly decreased (from 0.09 to 0.03 for DISCOVER-AQ and from 0.17 to 0.02 for KORUS-AQ). The reduced discrepancies support the conclusions from Zhai et al. (2021) that the GEOS-Chem aerosol size is underestimated for KORUS-AQ and motivates the parameterization of R_eff for an efficient representation of the aerosol size for global-scale aerosol modeling.

Figure 2 Aerosol extinction profile for the DISCOVER-AQ and KORUS-AQ aircraft campaigns. Blue lines are the measured extinction profiles. Horizontal bars are calculated extinction using (a, b) default GEOS-Chem R_eff, (c, d) measured R_eff, and (e, f) parameterized R_eff (described in Sect. 3.3), together with measured aerosol composition and relative humidity (RH). The aerosol extinction calculation is described in Appendix A.

3.2 Driving factors

Given the strong positive correlation of aerosol mass with aerosol size, we further examine this relationship globally using GEOS-Chem coupled with the TOMAS aerosol microphysics scheme. To focus on areas that are dominated by SNA and OM, we only include grid boxes with M_SNAOM > 90 % of the aerosol mass. Inspection of the GEOS-Chem-TOMAS size distribution across continental regimes reveals a general tendency for the distribution to shift toward smaller sizes as R_eff decreases and toward larger sizes as R_eff increases, thus supporting the use of the single-summary statistic of R_eff for aerosol size. The top panel of Fig. 3 shows the geographic distribution of annual mean surface layer dry R_eff for grid boxes that meet the criterion. Among the areas of interest, biomass burning regions of central Africa, South America, and boreal forests of North America exhibit the highest surface R_eff of about 180 nm. Industrial areas such as East Asia and South Asia also exhibit high R_eff of about 130 nm, given an abundance of particle emissions and gaseous precursors. The lowest surface R_eff of about 80 nm is found in North America, where aerosol mass concentrations are low.

The middle panel of Fig. 3 shows the simulated M_SNAOM from GEOS-Chem-TOMAS. Enhanced M_SNAOM concentrations of over 40 µg m⁻³ are apparent over East Asia and South Asia, reflecting intense anthropogenic emissions. Another M_SNAOM hotspot can be seen in central Africa, driven by biomass burning during the dry season (van der Werf et al., 2017; McDuffie et al., 2021) and sometimes exacerbated by anthropogenic emissions (Ngo et al., 2019). Moving from North America to Europe and then to Asia (defined by boxes in the middle panel), M_SNAOM concentrations exhibit a generally increasing tendency (mean values of 11, 17, and 25 µg m⁻³, respectively), consistent with the R_eff tendency (mean values of 124, 133, and 136 nm, respectively) in the top panel and aligning with the relationship between aircraft measurements over the USA and South Korea.

However, in South America, where R_eff is among the highest recorded level, M_SNAOM is relatively low. This discrepancy motivates the search for other factors (such as aerosol composition) that are associated with aerosol size. In South America, aerosol mass is mostly from natural sources, particularly biomass burning during the dry seasons. R_g for a particle population from biomass burning ranges from 60 to 170 nm (Rissler et al., 2006; Reid et al., 2005; Janhäll et al., 2010), which is usually larger than that of primary sulfate aerosol (5 to 35 nm; Whitey, 1978; Plaza et al., 2011). Therefore, the relative abundance of OM in the total M_SNAOM can serve as another predictor of R_eff. The bottom panel of Fig. 3 shows the ratio between OM and SNA mass. In addition to the Amazon basin, the biomass burning regions of central Africa and boreal forests in Asia and North America all represent areas with high OM mass fractions, which contribute to their high R_eff.

Figure 3 Geographic distribution of GEOS-Chem-TOMAS-simulated annual mean surface layer aerosol properties. (a) R_eff, when M_SNAOM > 90 % of aerosol mass. (b) The sum of SNA and OM mass (M_SNAOM). (c) $\mathrm{OM}/\mathrm{SNA}$.

3.3 Parameterization and evaluation

We use multiple linear regression (MLR) to derive a parameterization of dry R_eff for SNA and OM as a function of M_SNAOM and $\mathrm{OM}/\mathrm{SNA}$. We sample the GEOS-Chem-TOMAS simulation for locations dominated by M_SNAOM (>90 %). We include all qualified data (8569 grid boxes) from the planetary boundary layer (PBL) to focus on this region, while randomly sampling 0.5 % of simulations in the free troposphere (217 772 grid boxes) to allow the influence of remote regions in the training set. The reason for focusing on the PBL is two-fold. First, the PBL generally has the highest aerosol loading that largely determines the columnar mass and AOD (Koffi et al., 2016; Zhai et al., 2021; Tian et al., 2019). Second, the PBL is the domain where most model–measurement differences exist (Fig. 2, top panel).

Taking the logarithm of R_eff and the logarithm of the two predictors facilitates linear relationships for regression, which yields the initial parameterization, as follows:

$$\begin{array}{}\text{(4)}& R_{\mathrm{eff}}=\mathrm{78.3}{M}_{\mathrm{SNAOM}}^{\mathrm{0.20}}{\left({\displaystyle \frac{\mathrm{OM}}{\mathrm{SNA}}}\right)}^{\mathrm{0.065}},\end{array}$$

where the units of R_eff (units of nm), M_SNAOM (units of µg m⁻³), and $\mathrm{OM}/\mathrm{SNA}$ (unitless) are indicated here in parentheses. The R_eff parameterization is driven primarily by the mass of SNA and OM, modulated by the ratio of OM to SNA. This equation represents the variation in R_eff well during the aircraft campaigns, with an R² of 0.74 (Fig. B1, top left; Appendix B). The slope below unity (0.90) likely reflects the effect of the coarse model resolution, which dilutes the particle or precursor concentration and in turn reduces the condensation and coagulation growth (AboEl-Fetouh et al., 2022; Ramnarine et al., 2019; Sakamoto et al., 2016). An adjustment to this parameterization to account for these effects and align the slope with the airborne measurements rather than the model results in a final parameterization, as follows:

$$\begin{array}{}\text{(5)}& R_{\mathrm{eff}}=\mathrm{87.0}{M}_{\mathrm{SNAOM}}^{\mathrm{0.20}}{\left({\displaystyle \frac{\mathrm{OM}}{\mathrm{SNA}}}\right)}^{\mathrm{0.065}}.\end{array}$$

Figure 4 shows the distribution of dry R_eff based on GEOS-Chem-TOMAS and Eq. (5). Circles in Fig. 4 show the mean values of the sampled GEOS-Chem-TOMAS-simulated R_eff as a function of simulated M_SNAOM concentrations, ranging from 0.02 to 102 µg m⁻³, and $\mathrm{OM}/\mathrm{SNA}$, ranging from 0.13 to 55. Simulated R_eff extends from 15 nm when both M_SNAOM and $\mathrm{OM}/\mathrm{SNA}$ are low (0.09 µg m⁻³ and 1.3, respectively), up to 282 nm when M_SNAOM and $\mathrm{OM}/\mathrm{SNA}$ are high (about 44 µg m⁻³ and 14, respectively). The background color indicates our parameterized R_eff. A high degree of consistency exists between the parameterized R_eff and simulated R_eff, especially in the free troposphere, where large gradients in R_eff exist, with an R² of 0.72 overall for the troposphere and a slope of 0.81 (Fig. B1, bottom right). At the lower end of R_eff, the agreement between simulation and the parameterization can also be found in Fig. B1, which shows that the small R_eff values are reproduced by the parameterization. Despite the overall consistency, a few differences exist. When the aerosol mass concentration is high, the parameterization tends to yield a higher R_eff than in the GEOS-Chem-TOMAS simulation, since the adjustment using aircraft measurements led to 11 % increase in R_eff. At M_SNAOM near 10 µg m⁻³ and $\mathrm{OM}/\mathrm{SNA}$ near 10, the simulation indicates higher R_eff than the parameterization, reflecting dilution downwind of biomass burning that reduces the aerosol mass concentration but has less influence on particle size in GEOS-Chem-TOMAS (Park et al., 2013; Rissler et al., 2006; Sakamoto et al., 2016). A 10 %–20 % underestimation in the parameterization at low $\mathrm{OM}/\mathrm{SNA}$ reflects the advection and dilution downwind of urban areas and in the free troposphere (Yue et al., 2010; Asmi et al., 2011). Evaluation of our parameterization versus the GEOS-Chem-TOMAS simulation of 2^∘ × 2.5^∘ for October yields similar results but explains an additional 14 % of the variance in simulated R_eff, providing additional evidence of the fidelity of the parameterization.

Figure 4 Dry R_eff as a function of M_SNAOM and $\mathrm{OM}/\mathrm{SNA}$ when SNA and OM are dominant (>90 %). Each circle represents the mean value of the GEOS-Chem-TOMAS-simulated R_eff in each bin. The background color indicates the parameterized R_eff.

Figure 5 (a) Surface dry R_eff for SNA and OM calculated using Eq. (5) and GEOS-Chem bulk-model-simulated SNA and OM mass. R_eff is shown when M_SNAOM is greater than 80 % of the total aerosol mass. (b) The GEOS-Chem-simulated AOD using inferred R_eff. (c) The absolute difference between the updated AOD and default AOD using dry R_eff=101 nm.

Figure 6 (a, b) Percent increase in GEOS-Chem-simulated AOD minus AERONET AOD as a function of parameterized surface dry R_eff for SNA and OM. Black lines represent the mean values of ΔAOD in each 35 nm bin; error bars represent the corresponding standard deviation. (c) Scatterplot of AERONET versus simulated AOD with the default R_eff (blue dots, line, and text) and with the parameterized R_eff (red dots, line, and text). The 1 : 1 line is dashed. NRMSD is the normalized root mean square deviation between the two datasets. N is the number of points in each dataset.

When applied to the airborne measurements, this parameterization only slightly overestimates the measured R_eff from DISCOVER-AQ (139 nm vs. 138 nm) and slightly underestimates R_eff from KORUS-AQ (157 nm vs. 164 nm). Discrepancies between the calculated and measured extinction from aircraft campaigns are largely reduced (Fig. 2, bottom panel), with AOD biases of 0.01 and 0.08 for DISCOVER-AQ and KORUS-AQ, respectively. Minor differences are still present in the aerosol extinction above 4 km for KORUS-AQ, but a physical explanation remains elusive, since the calculated extinction is biased, even if the measured aerosol size and composition are used because instrument uncertainties may play a role. Nonetheless, the effects on columnar AOD from these disagreements aloft are minor (<5 %).

We then apply Eq. (5) to a GEOS-Chem bulk simulation to calculate R_eff and AOD. The top panel of Fig. 5 shows the annual mean dry R_eff for surface SNA and OM aerosol. The parameterized R_eff is usually higher than the default value of about 100 nm in GEOS-Chem over land and lower than that over the ocean, with a normalized root mean square deviation (NRMSD) of 43.8 %. The parameterized R_eff is the highest in biomass burning regions in South America and central Africa, in addition to industrial regions in Asia, which is similar to the pattern found in the GEOS-Chem-TOMAS simulation. The parameterized R_eff and its horizontal variation diminish with altitude (Fig. B2), with the mean R_eff of 85 nm at the surface decreasing by 18.8 % to 69 nm at about 5 km. By design, the parameterization has little effect in regions and seasons where and when M_SNAOM is not dominant, since the parameterization only affects R_eff of SNA and OM.

The middle panel of Fig. 5 shows the simulated AOD, with the corresponding difference between the base simulation and the updated simulation in the bottom panel. To accommodate the parameterized R_eff, a lookup table with a wide range of R_eff (0.02 to 1.7 µm) and the corresponding extinction efficiencies for OM and SNA is created based on the Mie theory (Mishchenko et al., 2002, 1999). This update generally increases the aerosol mass scattering by increasing the mass extinction efficiency and, in turn, increasing AOD over regions with strong anthropogenic sources, such as East Asia (by 0.10 and 28.3 %) and South Asia (by 0.14 and 31.1 %). It also slightly increases AOD over regions influenced by wildfires, such as South America (by 0.02 and 19.7 %), central Africa (by 0.03 and 22.7 %), and the boreal forests in Europe (by 0.01 and 9.9 %). Most increases occur near the surface (Fig. B3), where the highest aerosol mass loading and mass extinction efficiency exist. The NRMSD between original and updated GEOS-Chem simulated AOD is 18.9 % globally and 25.6 % over continents.

Although R_eff is only one of many processes affecting AOD, we evaluate the effect of the parameterization on the GEOS-Chem simulation of AOD to assess its implications. The left and middle panels of Fig. 6 show the discrepancy between GEOS-Chem-simulated AOD and AERONET AOD as a function of the parameterized surface R_eff for SNA and OM. The simulation using the default R_eff (Fig. 6, left panel) slightly overestimates AOD at sites with small parameterized R_eff and underestimates AOD at sites with large parameterized R_eff. The overestimates occur primarily in western Europe, where SNA and OM concentrations are low, while the underestimates happen mainly over industrial regions in East Asia, Southeast Asia, and biomass burning areas in South America and central Africa, where the SNA and OM mass loading are high (Fig. B4). The underestimates are mitigated when applying the parameterized R_eff in GEOS-Chem (Fig. 6, middle panel), yielding increased consistency between the measured (AERONET) AOD and simulated AOD (Fig. 6, right; R² change from 0.68 to 0.74; slope from 0.75 to 0.94).

4 Conclusion

Aerosol size strongly determines mass scattering efficiency, with implications for the calculation of aerosol optical properties. Prior work found that the global mean dry aerosol size used in a bulk-aerosol-model-induced low bias versus measured extinction in a region with a high aerosol loading (Zhai et al., 2021). We interpreted aircraft measurements from DISCOVER-AQ and KORUS-AQ with a chemical transport model (GEOS-Chem) to better understand the regional variation in aerosol size. The measurements had a strong positive correlation (r=0.83) between the aerosol size and the mass of sulfate–nitrate–ammonium (SNA) and organic matter (OM), reflecting the high condensation and coagulation rates where emissions of particles and the gaseous precursors are abundant, indicating the possibility of using aerosol mass as a predictor of aerosol size.

To gain a broader perspective of the global variation in aerosol size, we used the TOMAS microphysics package of the GEOS-Chem model to simulate the monthly mean aerosol mass, composition, and size distribution. We used an effective radius (R_eff) as a surrogate for aerosol size and examined its relationship with aerosol mass and components where SNA and OM were dominant. We found that the sum of SNA and OM concentration, and the ratio between them, were the major predictors of R_eff. We used GEOS-Chem-TOMAS model output to derive a parameterization of R_eff, which reproduced R_eff measured from the aircraft campaigns well (R²=0.74). When applied in the bulk GEOS-Chem high-performance model, the parameterization tended to increase the R_eff of SNA and OM over regions with high concentrations of SNA and OM and decrease R_eff elsewhere, relative to the standard model. This led to a global normalized root mean square deviation (NRMSD) of 43.8 % between the original and updated surface R_eff. The parameterized R_eff tended to increase the vertical gradient in the extinction relative to the standard model, due to the decrease in R_eff with altitude. The NRMSD of global mean AOD between the original and updated simulations was 18.9 %, with the most significant regional AOD increase of 0.14 in South Asia, where aerosol mass loadings are high. This parameterization led to the improved consistency of GEOS-Chem-simulated AOD with AERONET AOD (R² from 0.68 to 0.74; slope from 0.75 to 0.94) by increasing AOD at high R_eff.

Overall, the simple parameterization of R_eff derived in this study improved the accuracy in modeling aerosol optical properties without imposing an additional computational expense. Other chemical transport models and modeling of other size-related processes, such as heterogeneous chemistry, photolysis frequencies, and dry deposition, may also benefit from the parameterized R_eff. Future work could include additional parameters to better summarize the aerosol size distribution (Nair et al., 2021; Sakamoto et al., 2016). Further developments in computational efficiency of aerosol microphysics models and more abundant measurements of aerosol size and optical properties would both offer opportunities for further advances.

Appendix A

A1 Application of spatially and temporally varying $\mathrm{OM}/\mathrm{OC}$ ratio

The top panel of Fig. A1 shows scatterplots of the estimated and measured $\mathrm{OM}/\mathrm{OC}$ and OM during the KORUS-AQ campaign. The estimation is obtained by applying a NO₂-inferred $\mathrm{OM}/\mathrm{OC}$ (from Philip et al., 2014) to the OC measurement, with a subsequent correction factor of 1.09 (suggested by Canagaratna et al., 2015). Estimated OM is compared with the measured OM by AMS during the campaign. Overall consistency is evident between NO₂-derived $\mathrm{OM}/\mathrm{OC}$ and measured $\mathrm{OM}/\mathrm{OC}$. The agreement is better below 500 m than above (left panel; R² = 0.62 vs. 0.33). The discrepancy at high altitudes is mainly due to the low NO₂ (<0.2 ppbv, parts per billion by volume), where the Philip et al. (2014) equation is not applicable. An average $\mathrm{OM}/\mathrm{OC}$ ratio (2.1) is applied in this case. A high degree of consistency exists between the estimated OM and measured OM, with R²=0.99 and slope = 0.91 for data from all altitudes (right panel), thus supporting the use of estimated OM in our analyses. The bottom-left panel compares the vertical profile of the estimates and measurements, yielding overall consistency.

Table A1 Dry aerosol properties in the GEOS-Chem bulk model.

A2 Aerosol extinction calculation in GEOS-Chem

The extinction (Ext) of radiation by aerosols is represented as the sum of extinction due to each of the aerosol components using the following equation:

$$\begin{array}{}\text{(A1)}& {\mathrm{Ext}}_k={\displaystyle \frac{\mathrm{3}{Q}_{\mathrm{ext},k}{M}_k}{\mathrm{4}{\mathit{\rho }}_k{R}_{\mathrm{eff},k}}},\end{array}$$

where subscript k indicates the property for the kth component. R_eff is the effective radius, which is defined as the area-weighted mean radius. Q_ext is the area-weighted mean extinction efficiency. M is the aerosol mass loading per unit volume. ρ is the aerosol density. Aerosol optical depth (AOD) is the integral of aerosol extinction across the vertical domain.

For each component, the extinction is calculated for assumed lognormal size distribution, with a corresponding dry geometric mean radius R_g and geometric standard deviation σ, hygroscopicity, refractive index (RI), and density (ρ) for individual aerosol components, as listed in Table A1. Sulfate, nitrate, and ammonium are grouped into SNA for convenience. R_eff and Q_ext are calculated using the Mie theory (Mishchenko et al., 1999, 2002), based on assumptions in aerosol size and RI. Hygroscopicity for SNA and OM is represented using a κ-Kohler hygroscopic growth scheme (Kreidenweis et al., 2008), as implemented by Latimer and Martin (2019).

Figure A1 Scatterplots of estimated and measured $\mathrm{OM}/\mathrm{OC}$ (a) and OM (b) during KORUS-AQ. Each point represents a mean value of the AMS measurement for a 1 h interval. Red diamonds, lines, and text represent data from 0–500 m altitude. Blue dots, lines, and text represent data above 500 m from the ground. Solid black lines and text represent the line of the best fit for all the data. The 1 : 1 line is dashed. NRMSD is the normalized root mean square deviation between the two datasets. N is the number of points in each dataset. (c) Mean values of $\mathrm{OM}/\mathrm{OC}$ and OM from measurements and estimations along the altitude. (d) Flight tracks during KORUS-AQ.

Appendix B

Figure B1 (a, b) Scatterplot of parameterized R_eff and measured R_eff from DISCOVER-AQ and KORUS-AQ. Each point represents a daily mean measurement. (c, d) Scatterplot of parameterized R_eff and GEOS-Chem-TOMAS-simulated R_eff for the planetary boundary layer (blue dots, line, and text) and for the free troposphere (yellow dots, line, and text). Solid black lines and the text indicate the entire troposphere with the sum of SNA and OM > 90 % of aerosol mass. The 1 : 1 line is dashed. NRMSD is the normalized root mean square deviation between the two datasets. N is the number of points in each dataset. Panels (a) and (c) indicate the original parameterization from multiple linear regression. Panels (b) and (d) show the adjusted parameterization using aircraft measurements.

Figure B2 Annual mean R_eff for SNA and OM at (a) about 5 km, (b) about 1 km, and (c) surface, calculated using Eq. (5) and simulated SNA and OM mass from the GEOS-Chem bulk model. R_eff is shown only if M_SNAOM is greater than 80 % of the total aerosol mass. Boxes in panel (c) define the regions referred to in Fig. B3.

Figure B3 Global and regional aerosol extinction coefficient simulated by GEOS-Chem bulk model with original R_eff (solid lines) and parameterized R_eff (dashed lines). Regions are defined by the boxes in Fig. B2.

Figure B4 Difference between AERONET AOD minus the default GEOS-Chem-simulated AOD (dots) and difference between the simulated AOD with the parameterized R_eff minus AOD with default R_eff (background).