Urban aerosol size distributions: a global perspective

Urban aerosol measurements are necessary to establish associations between air pollution and human health outcomes and to evaluate the efficacy of air quality legislation and emissions standards. The measurement of urban aerosol particle size distributions (PSDs) is of particular importance as they enable characterization of size-dependent processes that govern a particle's transport, transformation, and fate in the urban atmosphere. PSDs also improve our ability to link air pollution to health effects through evaluation of particle deposition in the respiratory system and inhalation toxicity. To inform future measurements of urban aerosol observations, this paper reviews and critically analyzes the current state of knowledge on urban aerosol PSD measurements by synthesizing 737 PSD observations made between 1998 to 2017 in 114 cities in 43 countries around the globe. Significant variations in the shape and magnitude of urban aerosol number and mass PSDs were identified among different geographical regions. In general, number PSDs in Europe (EU) and North America, Australia, and New Zealand (NAAN) are dominated by nucleation- and Aitken-mode particles. PSDs in Central, South, and Southeast Asia (CSSA) and East Asia (EA) are shifted to larger sizes, with a meaningful contribution from the accumulation mode. Urban mass PSDs are typically bimodal, presenting a dominant mode in the accumulation mode and a secondary mode in the coarse mode. Most PSD observations published in the literature are short-term, with only 14 % providing data for longer than 6 months. There is a paucity of PSDs measured in Africa (AF), CSSA, Latin America (LA), and West Asia (WA), demonstrating the need for long-term aerosol measurements across wide size ranges in many cities around the globe.

Geographical variations in urban aerosol effective densities were also reviewed. Size-resolved urban aerosol effective density functions from 3 to 10 000 nm were established for different geographical regions and intra-city sampling locations in order to accurately translate number PSDs to mass PSDs, with significant variations observed between near-road and urban background sites. The results of this study demonstrate that global initiatives are urgently needed to develop infrastructure for routine and long-term monitoring of urban aerosol PSDs spanning the nucleation to coarse mode. Doing so will advance our understanding of spatiotemporal trends in urban PSDs throughout the world and provide a foundation to more reliably elucidate the impact of urban aerosols on atmospheric processes, human health, and climate.

1 Introduction

Urban air pollution is a major global environmental health challenge. Aerosols are a key constituent of urban air pollution and include a diverse mixture of liquid and solid particles spanning in size from several nanometers to tens of micrometers. Urban aerosol measurements are critical for monitoring the extent of urban air pollution, identifying pollutant sources, understanding aerosol transport and transformation mechanisms, and evaluating human exposure and health outcomes (Asmi et al., 2011; Azimi et al., 2014; Harrison et al., 2011; Hussein et al., 2004; Morawska et al., 1998; Peng et al., 2014; Shi et al., 1999; Shiraiwa et al., 2017; Vu et al., 2015; Wu et al., 2008). Human exposure to aerosols in urban environments is responsible for adverse health effects, including mortality and morbidity due to cardiovascular and respiratory diseases, asthma, and neural diseases (Allen et al., 2017; Burnett et al., 2018; Delfino et al., 2005; Meldrum et al., 2017; Oberdörster et al., 2005; Rychlik et al., 2019; Shiraiwa et al., 2017; Sioutas et al., 2005). Improved characterization of urban aerosols is needed to better understand the impact of aerosol exposure on human health and to evaluate the efficacy of current and future air quality legislation.

Of particular importance are measurements of urban aerosol particle size distributions (PSDs). The ambient aerosol PSD is the result of direct particle emissions, in situ formation processes, atmospheric interactions between particles or between particles and gaseous compounds, and deposition processes. Typically, nucleation-mode particles (3 to ∼ 20 nm) are freshly formed via the nucleation of gaseous molecules and ions (Brines et al., 2015; Charron and Harrison, 2003; Zhu et al., 2002a). Aitken- (∼ 20 to 100 nm) and accumulation-mode (100 to 1000 nm) particles are often associated with primary emissions from combustion sources and condensation of secondary materials (Yue et al., 2009). Coarse-mode particles (> 1000 nm) generally result from mechanical processes, such as aerodynamic resuspension and abrasion. Nucleation-mode particles can be removed relatively quickly via coagulation due to their high diffusivity (Hinds, 2012). They can also grow into the Aitken mode during new particle formation (NPF) events (Cai et al., 2017; Xiao et al., 2015). Aitken-mode particles may further form accumulation-mode particles via coagulation and condensation. Accumulation-mode particles can have a long lifetime due to their low gravitational settling velocities and slow coagulation rates among themselves. In the urban environment, nucleation- and Aitken-mode particles generally dominate number PSDs due to the abundance of primary emission sources, such as power generation, traffic, and industrial activities. Their concentrations are high close to emission sources, while decreasing rapidly with distance from the source (Zhu et al., 2002a). Particle size can grow during transport by condensation of secondary materials. Coarse-mode particles in the urban environment often contain road dust (Almeida et al., 2006), tire debris (Adachi and Tainosho, 2004; Rogge et al., 1993), and biological particles (e.g., pollen) (Saari et al., 2015). Due to their high gravitational settling velocities, their number concentrations can be 2–4 orders of magnitudes lower than other modes.

Measurement of urban aerosol PSDs provides a basis for in-depth evaluation of size-resolved aerosol transport and transformation processes in the urban atmosphere (e.g., Hussein et al., 2004; Peng et al., 2014; Salma et al., 2011; Wehner et al., 2008; Wu et al., 2008), air pollution source apportionment (e.g., Harrison et al., 2011; Sowlat et al., 2016; Wang et al., 2013b), aerosol deposition in the human respiratory system (e.g., Hussein et al., 2019, 2020; Kodros et al., 2018; Zwozdziak et al., 2017), and associated toxicological effects on the human body (e.g., Bentayeb et al., 2015; Burnett et al., 2014; Oberdürster, 2000; Shiraiwa et al., 2017; Tseng et al., 2015; Wong et al., 2015). In addition, the measurement of aerosol PSDs is important for evaluating global climate change as particle size strongly affects the interaction of particles with solar radiation and their ability to form fog and cloud droplets (Mahowald, 2011; Seinfeld and Pandis, 2012; Zhang et al., 2012). Despite the atmospheric and health relevance of urban PSDs, long-term aerosol measurements are often focused on size-integrated concentration metrics, such as PM_2.5, that lack essential size-resolved information. While urban aerosol PSD measurements have been conducted in cities around the globe, they are often short in duration and not performed as part of routine air quality monitoring. Urban PSDs provide a more complete assessment of an aerosol population, beyond what can be achieved with size-integrated metrics. Of particular importance are urban PSDs that capture the ultrafine particle (UFP) regime. UFPs tend to dominate number PSDs, which can penetrate deep into the lung and translocate to different organs and are associated with various deleterious human health outcomes (Allen et al., 2017; Delfino et al., 2005; Jiang et al., 2009; Li et al., 2016, 2017; Oberdörster, 2001; Oberdörster et al., 2004, 2005; Rychlik et al., 2019; Sioutas et al., 2005; Weichenthal et al., 2017).

A future urban aerosol PSD observation network will improve our ability to more fully understand the health implications of urban aerosols. Measurements of PSDs incorporating the UFP regime are needed given the importance of UFPs on human health and the size dependency of deposition in the human respiratory tract. The health effects of UFPs are increasingly receiving more attention due to their high number concentrations in the urban environment, high surface area to mass ratios, and higher oxidative stress compared to larger particles (Allen et al., 2017; Burnett et al., 2018; Delfino et al., 2005; Li et al., 2016, 2017; Oberdörster et al., 2004, 2005; Pieters et al., 2015; Pietropaoli et al., 2004; Rychlik et al., 2019). Human exposure to UFPs has been associated with the development of cardiopulmonary and cardiovascular diseases, lung cancer, and asthma (Anderson et al., 2012; Delfino et al., 2005; Li et al., 2016; Meldrum et al., 2017; Oberdörster et al., 2005; Pietropaoli et al., 2004; Rychlik et al., 2019; Tsiouri et al., 2015; Valavanidis et al., 2008). Inhaled deposited dose rates on a number basis are dominated by UFPs in nearly all geographical and respiratory tract regions. The deposition fraction in the pulmonary region, which is often assumed to be more relevant for respiratory diseases, shows a maximum in the UFP regime, which overlaps with the prominent modes of many urban aerosol number PSDs.

Presently, there are no comprehensive literature reviews synthesizing urban aerosol PSD observations from around the globe in order to identify geospatial trends in the structure of number and mass PSDs. Previous literature reviews of urban aerosol PSDs have focused on major emission sources and source apportionment techniques (Vu et al., 2015) and the implications of urban aerosol PSDs on indoor air quality (Azimi et al., 2014). There has been a large number of urban aerosol PSD observations conducted over the past few decades. The objective of this study is to provide a comprehensive overview of urban aerosol PSD observations from around the globe.

This study reviews urban aerosol PSD observations measured between 1998 to 2017. Urban aerosol PSD data spanning the nucleation to coarse mode (3 to 10 000 nm as electrical mobility diameter) were extracted from the literature, fit to multi-modal lognormal distribution functions, and agglomerated by geographical region in order to identify trends in the physical characteristics of aerosol populations from different regions. This represents the first attempt, to the best of the authors' knowledge, to understand geographical variations in urban aerosol PSDs at a global scale. The geographical distribution of measurement locations and the categorization of the collected PSDs enables the identification of gaps in urban aerosol PSD measurements. This will help motivate future research efforts and frame forthcoming urban air pollution measurement needs. As climate models have been improved significantly in terms of spatial resolution, a compilation of urban PSDs can also serve as useful input for models to estimate the direct and indirect influence of aerosols on regional and global climates. Along with urban aerosol PSDs, size-resolved urban aerosol effective densities were also reviewed. The effective density is an important aerosol morphological parameter that provides a basis to reliably translate measured number PSDs to mass PSDs.

2 Methodology for establishing the current state of knowledge on urban aerosol PSD observations

An expansive literature search was conducted on short- and long-term stationary and mobile measurements of urban aerosol number and mass PSDs between 1998 and 2017. The aim was to capture any potentially relevant peer-reviewed resources in which urban aerosol PSDs have been reported. Two academic search indices, Web of Science and ScienceDirect, along with Google Scholar, were used to conduct the literature search. Search terms included urban aerosol, particle size distribution, urban aerosol size distribution, aerosol size distribution, urban particulate matter, scanning mobility particle sizer urban, differential mobility particle sizer urban, and urban aerosol MOUDI (micro-orifice uniform deposit impactor), among others. Approximately 3400 peer-reviewed journal articles and reports were initially screened to determine if they contained suitable information. Approximately 200 of them, which reported urban or semi-urban aerosol PSDs in the submicron regime (< 1000 nm), with some also covering the coarse regime (> 1000 nm), were selected for detailed analysis. These articles presented 737 individual PSDs (182 of which covered both the submicron and coarse regime) which have been reported in previous peer-reviewed journal articles in the form of figures or fitting parameters, from 114 cities in 43 countries around the globe (Table S1). All the PSDs are the result of a time average over certain sampling periods. Most PSDs reported number-based concentrations [e.g., measured with a scanning mobility particle sizer (SMPS), aerodynamic particle sizer (APS), or optical particle sizer (OPS)], while some report mass-based concentrations (e.g., measured by inertial impactors). For PSDs reported only in the form of figures without lognormal fitting parameters, as was most common among the references, the GRABIT tool in MATLAB (The MathWorks, Inc., Natick, MA, USA) and WebPlotDigitizer (https://automeris.io/WebPlotDigitizer, last access: 27 February 2021, Version 4.0) were utilized to extract the data points of the PSDs. The PSDs were subsequently reproduced in MATLAB. A consistent particle size definition, the electrical mobility diameter (D_em), was used for all PSDs, as described in Sects. 3 and 4.

The PSDs were classified by geographical region: Africa (AF), Central, South, and Southeast Asia (CSSA), East Asia (EA), Europe (EU), Latin America (LA), North America, Australia, and New Zealand (NAAN), and West Asia (WA) (Table S1). The PSDs in each geographical region were separated into two site types depending on the measurement location within the city. “Urban” indicates that the measurement was conducted in urban areas that are not strongly affected by localized traffic emissions. “Traffic (near-road)” indicates that the environment was strongly influenced by traffic emissions, e.g., street canyon or roadside.

3 Geographical trends in size-resolved urban aerosol effective densities

3.1 Introduction to size-resolved urban aerosol effective density functions

Evaluation of geographical variations in size-resolved aerosol morphological features is needed to better characterize urban aerosol populations around the world. This section outlines the development of size-resolved urban aerosol effective density (ρ_eff) functions from D_em=3 to 10 000 nm. Size-dependent differences in the aerosol particle density (ρ_p) and dynamic shape factor (χ) are best captured together through ρ_eff. The ρ_eff functions serve three purposes in this study: (1) to translate urban aerosol number PSDs to mass PSDs, (2) to convert aerodynamic diameter (D_a)-based PSDs to D_em-based PSDs, and (3) to provide a summary of ρ_eff measurements in the urban atmosphere. Point (2) is necessary to enable a consistent particle size definition to be used in compiling PSD observations from around the globe, as described in Sect. 4. The size-resolved ρ_eff functions include a combination of direct measurements of ρ_eff in the urban atmosphere (Sect. 3.2) and approximations for size fractions where direct measurements have not yet been reported in the literature, such as sub-10 nm and coarse-mode particles (Sect. 3.3–3.5). The integration of the size-resolved ρ_eff functions with the urban aerosol PSD observations is presented in Sect. 3.6.

Different definitions of ρ_eff have been used in previous studies (DeCarlo et al., 2004). In the current study, ρ_eff is defined as the ratio of the measured particle mass (m_p) to the volume calculated from D_em assuming spheres (DeCarlo et al., 2004; Hu et al., 2012; McMurry et al., 2002; Qiao et al., 2018) (Eq. 1):

$$\begin{array}{}\text{(1)}& {\mathit{\rho }}_{\mathrm{eff}}={\displaystyle \frac{\mathrm{6}{m}_{\mathrm{p}}}{\mathit{\pi }{D}_{\mathrm{em}}^{\mathrm{3}}}}.\end{array}$$

Only empirical ρ_eff values defined in this manner were collected from the literature. The particle volume (V_p) is defined as the volume taken up by all of the solid and liquid material in the particle and void space enclosed within the particle envelope (DeCarlo et al., 2004). For an irregular particle, the volume equivalent diameter (D_ve) represents the diameter of a sphere that has the same volume as V_p (DeCarlo et al., 2004; Hinds, 2012; Seinfeld and Pandis, 2012) (Eq. 2):

$$\begin{array}{}\text{(2)}& V_{\mathrm{p}}={\displaystyle \frac{\mathit{\pi }}{\mathrm{6}}}{D}_{\mathrm{ve}}^{\mathrm{3}}.\end{array}$$

The ratio of m_p to V_p is referred to as the particle density (ρ_p), as shown in Eq. (3):

$$\begin{array}{}\text{(3)}& {\mathit{\rho }}_{\mathrm{p}}={\displaystyle \frac{\mathrm{6}{m}_{\mathrm{p}}}{\mathit{\pi }{D}_{\mathrm{ve}}^{\mathrm{3}}}}.\end{array}$$

The relationship between D_em and D_ve is given by DeCarlo et al. (2004) and Seinfeld and Pandis (2012):

$$\begin{array}{}\text{(4)}& {\displaystyle \frac{D_{\mathrm{em}}}{C_{\mathrm{c}}\left(D_{\mathrm{em}}\right)}}={\displaystyle \frac{D_{\mathrm{ve}}\mathit{\chi }}{C_{\mathrm{c}}\left(D_{\mathrm{ve}}\right)}},\end{array}$$

where C_c is the Cunningham slip correction factor (Allen and Raabe, 1982, 1985; Hinds, 2012). For a spherical particle, χ is equal to 1; D_em is equal to D_ve; and ρ_eff is equal to ρ_p. For particles with irregular shapes, χ is greater than 1; D_em is greater than D_ve; and ρ_eff is less than ρ_p.

For coarse-mode particles, the value of $\frac{C_{\mathrm{c}}\left(D_{\mathrm{ve}}\right)}{C_{\mathrm{c}}\left(D_{\mathrm{em}}\right)}$ is approximately unity, such that the Cunningham slip correction factors in Eq. (4) can be reasonably neglected. Therefore, Eq. (4) becomes D_em=D_veχ. Plugging this into Eq. (1), we arrive at Eq. (5):

$$\begin{array}{}\text{(5)}& {\mathit{\rho }}_{\mathrm{eff}}={\displaystyle \frac{\mathrm{6}{m}_{\mathrm{p}}}{\mathit{\pi }{\mathit{\chi }}^{\mathrm{3}}{D}_{\mathrm{ve}}^{\mathrm{3}}}}.\end{array}$$

Combining Eqs. (3) and (5), we can derive Eq. (6), which describes the relationship between ρ_eff, ρ_p, and χ for coarse- mode particles (an example is given in Fig. 2):

$$\begin{array}{}\text{(6)}& {\mathit{\rho }}_{\mathrm{eff}}={\displaystyle \frac{{\mathit{\rho }}_{\mathrm{p}}}{{\mathit{\chi }}^{\mathrm{3}}}}.\end{array}$$

3.2 Urban aerosol effective densities: summary of direct measurements

Direct measurements of ρ_eff in urban environments are limited. However, sufficient data are available in the literature to identify trends in ρ_eff among geographical regions and intra-city site types (urban or traffic). Size-resolved urban aerosol ρ_eff values were extracted from nine studies conducted in Denmark, China, the United States, and Finland (Table S2). The studies report direct measurements of ρ_eff, primarily in the submicron regime through use of various aerosol instrument configurations, such as those evaluating the mass–mobility relationship of an aerosol population through a differential mobility analyzer (DMA)–aerosol particle mass analyzer (APM) system (e.g., McMurry et al., 2002). The measured ρ_eff values and measurement information, including measurement technique, duration, and site (city, country), are summarized in Table S2. All the results are the averages over given sampling periods.

As the PSD and direct ρ_eff measurements were conducted in different cities and at different site types within the city, it is reasonable to apply ρ_eff values which were measured under a condition consistent with a PSD measurement when converting number PSDs to mass PSDs and D_a to D_em. In order to apply the most reasonable ρ_eff to a PSD observation, the collected size-resolved ρ_eff values were divided into three groups according to the geographical region where the direct measurement was conducted and the site type (urban or traffic). Direct measurements conducted in China in “urban” environments were incorporated into Group A. Direct measurements in the United States in “urban” environments were incorporated into Group B. Direct measurements conducted in the United States, Finland, and Denmark in “traffic” environments were incorporated into Group C. None of the direct ρ_eff measurements in China were conducted in “traffic” environments. The ρ_eff values for the size range of 3200 to 5600 nm reported by Hu et al. (2012) were not included as the high ρ_eff values associated with the abundance of minerals in coarse particles in Beijing might bias the analysis (Guo et al., 2010; Zhang et al., 2010).

Figure 1 Size-resolved urban aerosol effective density functions (ρ_eff) for Group A (“urban”; obtained from measurements in China), Group B (“urban”; obtained from measurements in the United States), and Group C (“traffic”; obtained from measurements in the United States, Finland, and Denmark). Details of the ρ_eff measurements are summarized in Table S2. ρ_eff values for different combinations of χ and ρ_p are illustrated in Fig. 2. Measurement technique nomenclature: DMA: differential mobility analyzer, APM: aerosol particle mass analyzer, SMPS: scanning mobility particle sizer, APS: aerodynamic particle sizer, MOUDI: micro-orifice uniform deposit impactor.

Figure 2 Effective densities (ρ_eff) as derived from different values of dynamic shape factors (χ) and particle densities (ρ_p), assuming the value of $\frac{C_{\mathrm{c}}\left(D_{\mathrm{ve}}\right)}{C_{\mathrm{c}}\left(D_{\mathrm{em}}\right)}$ is approximately unity for coarse particles.

Representative size-resolved ρ_eff functions were estimated for Groups A, B, and C (Fig. 1). For the direct ρ_eff measurements tabulated in Table S2, the collected values were often reported as a function of particle size discretely. In order to convert them to a continuous ρ_eff function with respect to size, which can be easily applied when converting number PSDs to mass PSDs and D_a to D_em, a few assumptions were made. For particles greater than 10 nm, if the particles at a certain diameter D_em,1 were reported to have an effective density of ρ_eff,1, we assume the particles in the size range from ($D_{\mathrm{em},\mathrm{1}}-\mathrm{50}$ nm) to ($D_{\mathrm{em},\mathrm{1}}+\mathrm{50}$ nm) also have the same effective density of ρ_eff,1. If the particles at diameter D_em,2 (D_em,2 > D_em,1) were reported to have an effective density of ρ_eff,2 in the same study, and D_em,2 is within the size range from D_em,1 to ($D_{\mathrm{em},\mathrm{1}}+\mathrm{50}$ nm), we assume the particles with the size from ($D_{\mathrm{em},\mathrm{1}}-\mathrm{50}$ nm) to $(D_{\mathrm{em},\mathrm{1}}+D_{\mathrm{em},\mathrm{2}})/\mathrm{2}$ to have the effective density of ρ_eff,1, while the particles with the size from $(D_{\mathrm{em},\mathrm{1}}+D_{\mathrm{em},\mathrm{2}})/\mathrm{2}$ to ($D_{\mathrm{em},\mathrm{2}}+\mathrm{50}$ nm) have the effective density of ρ_eff,2. By doing this, we obtained several continuous size-resolved ρ_eff functions ranging from approximately 10 nm to several hundreds of nanometers. We then took the mean of the size-resolved ρ_eff values derived from direct measurements in each of the three groups, illustrated as blue lines in the gray regions of Fig. 1.

3.3 Urban aerosol effective densities: considerations for sub-10 nm particles without direct measurements

Direct measurements of ρ_eff from D_em=3 to 10 nm have not been previously reported in the literature. Particles in this size range are typically formed by homogeneous or heterogeneous nucleation, which can involve sulfuric acid (H₂SO₄), amines, ammonia, and organic vapors (e.g., Kulmala et al., 2013). H₂SO₄ and highly oxygenated molecules (HOMs) or extremely low-volatility organic compounds (ELVOCs) are often involved in the nucleation and initial growth of particles during an atmospheric new particle formation event. Previous studies have assumed nucleated particles formed in experimental chambers in the size range of 4 to 12 nm to have a density of 1.5 g cm⁻³ (Wang et al., 2010). ELVOCs and HOMs are assumed to have a density of 1.5 and 1.4 g cm⁻³, respectively (Ehn et al., 2014; Tröstl et al., 2016). For simplicity, we used the ρ_p of condensed ELVOCs (Ehn et al., 2014) (1.5 g cm⁻³) and the condensed-phase density of H₂SO₄ (Xiao et al., 2015) (1.83 g cm⁻³) to estimate the lower and upper limits of ρ_eff for particles from D_em=3 to 10 nm, assuming the particles adopt a spherical shape with χ=1. The mean value of the two limits was used as the representative ρ_eff for all three groups (dark red lines in light blue regions of Fig. 1). Despite uncertainties in the assumed ρ_eff values, particles from D_em=3 to 10 nm contribute negligibly to particle mass concentrations and are seldom measured with aerodynamic-based techniques, thus conversion from D_a to D_em is often unnecessary.

3.4 Urban aerosol effective densities: considerations for accumulation-mode particles without direct measurements

There is a lack of direct measurements of ρ_eff in Groups B and C for particles greater than approximately 400 nm in size. Pitz et al. (2008b) conducted measurements of apparent particle density for particles with a D_a≤2500 nm (PM_2.5) at an urban background site in Germany. The apparent particle density ranged from 1.05 to 2.36 g cm⁻³, with a mean value of 1.65 g cm⁻³. As particles in the accumulation mode strongly contribute to urban aerosol mass concentrations (e.g., PM₁, PM_2.5), we assume the mean apparent particle density of 1.65 g cm⁻³ to be the representative ρ_eff for particles in the size range from D_em=400 to 2500 nm in Group B (dark red line in yellow region of Fig. 1). Rissler et al. (2014) measured the ρ_eff of urban aerosols from 50 to 400 nm in a street canyon in central Copenhagen and identified two different groups of aerosols with distinctive ρ_eff: loose chain-like soot aggregates and more dense particles. The ρ_eff of the dense particles from D_em=50 to 400 nm was in the range of 1.3 to 1.65 g cm⁻³, of which the main constituents were inorganic salts, such as sulfate, nitrate, and ammonium, along with organics. Previous studies that have investigated the chemical composition of near-road aerosols indicated that the mass fraction of black carbon (elemental carbon) to the total mass of particles from D_em=400 to 1000 nm was 6.4 % to 26.7 % (Brüggemann et al., 2009; Daher et al., 2013; Fushimi et al., 2008; Massoli et al., 2012; Song et al., 2012). Here, we assume that loose chain-like soot aggregates do not contribute significantly to particle mass concentrations in this size range and applied the mean value of ρ_eff for “dense” particles as measured by Rissler et al. (2014) as the representative ρ_eff for particles from D_em=400 to 1000 nm in Group C (dark red line in orange region of Fig. 1). Although soot particles, which have a ρ_eff less than that of the dense particles, exist in the size range of D_em=400 to 1000 nm, denser components, such as organics, mineral dusts, and crustal materials, may also exist in this size range.

3.5 Urban aerosol effective densities: considerations for coarse-mode particles without direct measurements

Direct measurements of urban aerosol ρ_eff have been rarely conducted in the coarse mode, in part due to the difficulty of extending mass–mobility measurements (e.g., DMA–APM) to this size range. Coarse particles can be composed of organics, ions, dusts, crustal material, brake and tire wear, sea salt, black carbon, and other trace elements (Brüggemann et al., 2009; Cheung et al., 2011; Cozic et al., 2008; Daher et al., 2013; Kim et al., 2003; Koçak et al., 2007; Koulouri et al., 2008; Pakkanen et al., 2001; Song et al., 2012). These materials are associated with a wide range in ρ_p. Secondary organic aerosol (SOA) synthesized in the laboratory is reported to have ρ_p ranging from 1 to 1.65 g cm⁻³, depending on formation conditions and gas-phase precursors (Kostenidou et al., 2007; Malloy et al., 2009; Nakao et al., 2013; Zelenyuk et al., 2008). The ρ_p values of (NH₄)₂SO₄ and NH₄NO₃, which represent sulfate and nitrate compounds dominant in ionic mass, were reported to be approximately 1.7 g cm⁻³ (Lide, 2005; Mikhailov et al., 2013; Neusüß et al., 2002; Tang, 1996). The ρ_p of dust varies with the associated components, including amorphous silicon oxide (2.1 to 2.3 g cm⁻³), illite/muscovite (2.7 to 3.1 g cm⁻³), montmorillonite (2.2 to 2.7 g cm⁻³), and quartz (2.65 g cm⁻³) (Reid et al., 2003).

The shape of coarse-mode particles is often composition-dependent. The value of χ depends on the shape of the particle. For a sphere, χ=1; for a cylinder with an axial ratio of 2, χ=1.1; for a cylinder with an axial ratio of 5, χ=1.35; and for a compact cluster of four spheres, χ=1.17 (Hinds, 2012). Some studies indicate that SOA has a spherical shape, suggestive of χ ∼ 1 (Abramson et al., 2013; Pajunoja et al., 2014; Virtanen et al., 2010). Coarse-mode dust particles often exhibit large values of χ. The χ of Saharan mineral dusts measured in Morocco with a D_em = 1200 nm is 1.25 (Kaaden et al., 2009). Davies (1979) reported χ to be 1.36 to 1.82 for quartz, 2.04 for talc, and 1.57 for sand. The complicated mixing state of urban aerosols introduces additional uncertainties in estimating the ρ_eff for both accumulation- and coarse-mode particles (Riemer et al., 2019).

The values of ρ_eff were estimated for coarse-mode particles in Group C, for particles larger than 2500 nm in Group B, and for particles larger than 3200 nm in Group A. The ρ_p and χ of three types of aerosols, including inorganic aerosol, SOA, and mineral dust, were used to estimate a range of values for ρ_eff. (NH₄)₂SO₄ and NH₄NO₃, with a ρ_p of approximately 1.7 g cm⁻³ and a χ of 1.01 (Hudson et al., 2007; Lide, 2005; Mikhailov et al., 2013; Neusüß et al., 2002; Tang, 1996), were selected as the representative inorganic aerosol to calculate ρ_eff. Nearly spherical SOA was assumed to adopt ρ_eff of 1 to 1.65 g cm⁻³ (Kostenidou et al., 2007; Malloy et al., 2009; Nakao et al., 2013; Zelenyuk et al., 2008). Illite, kaolinite, and montmorillonite were chosen to represent mineral dust, with ρ_p of 2.7 to 3.1, 2.6, and 2.2 to 2.7 g cm⁻³, and with χ of 1.3, 1.05, and 1.11, respectively (Hudson et al., 2007, 2008; Reid et al., 2003).

With the different combinations of ρ_p and χ described above, Eq. (6) was applied to calculate ρ_eff values for the three types of aerosols. The values span from 1 to approximately 2 g cm⁻³ (light green region of Fig. 1). The ρ_eff values within this range are used as the representative ρ_eff for coarse-mode particles in Group C, for particles larger than 2500 nm in Group B, and for particles larger than 3200 nm in Group A.

3.6 Integration of size-resolved urban aerosol effective density functions with urban aerosol PSD observations

The combination of directly measured and estimated ρ_eff values between D_em = 3 to 10 000 nm provides a basis to establish continuous, size-resolved urban aerosol ρ_eff functions for Groups A (${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$), B (${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{B}}$), and C (${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{C}}$), as illustrated in Fig. 1. When converting number PSDs to mass PSDs and D_a to D_em, ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$ was applied to number PSDs measured in the “urban” environment in cities in CSSA, WA, LA, AF, and China. The group ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{B}}$ was applied to number PSDs measured in the “urban” environment in cities in EU, NAAN, Japan, and South Korea. The group ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{C}}$ was applied to number PSDs measured in the “traffic” areas in cities around the globe, excluding China.

The group ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$ was applied to the number PSDs measured at both urban and traffic sites in China. The urban PSD measurements in China collected in this study were mainly from megacities, such as Beijing, Shanghai, and Guangzhou. Heavy-duty diesel trucks are prohibited to enter many urban areas during the daytime in these megacities (Wu et al., 2008). In addition, the fraction of diesel-powered cars in cities in China is much lower than that in Europe or North America. It is shown that gasoline-powered passenger cars contribute 91 % of the total number of vehicles in Beijing (Wu et al., 2008). Therefore, the relative fraction of soot particles in the near-road region was expected to be lower than that in North America and Europe. Previous studies suggest that the contribution of black carbon to PM_2.5 mass concentrations was less than 4 % in Shanghai (Cao et al., 2013; Feng et al., 2009). In addition, soot particles from gasoline engine vehicles might be more compact due to the relatively sulfur-rich fuel used in China (Yin et al., 2015). Soot particles may also be heavily aged or internally mixed with other condensable materials due to the higher pollution levels in megacities, resulting in a higher ρ_eff than freshly emitted soot particles. Huang et al. (2014) indicated that the number fraction of pure black carbon was 1.9 % in Shanghai during polluted periods. Therefore, the near-road size-resolved ρ_eff was assumed to be closer to the values compiled for ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$, rather than those for ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{C}}$.

3.7 Summary of size-resolved urban aerosol effective densities

The size-resolved ρ_eff functions for Groups A, B, and C are illustrated in Fig. 1. Across the size range covered by direct ρ_eff measurements in Groups A and B, there is no clear size dependency of ρ_eff, in part because organics and secondary inorganic ions are dominant in this size range. The directly measured ρ_eff values collected from cities in the United States (Group B) are between 1.1 to 1.6 g cm⁻³, while those measured in China (Group A) are slightly greater, with values between 1.3 to 1.9 g cm⁻³, possibly due to a greater abundance of secondary inorganic species. The directly measured ρ_eff in the “traffic” environment (Group C) presents a decreasing trend with the increase in particle size for 50 nm < D_em < 400 nm. This is largely due to primary emissions of soot particles from vehicle exhaust, which typically adopt a loose, chain-like agglomerated morphology with a fractal dimension (mass–mobility exponent) less than 3 (Barone et al., 2011; Pagels et al., 2009; Rawat et al., 2016; Rissler et al., 2013, 2014). Numerous studies have revealed the decrease of ρ_eff with the increase in particle size for vehicle exhaust aerosol (Barone et al., 2011; Maricq et al., 2000; Olfert et al., 2007; Park et al., 2003; Rissler et al., 2013; Virtanen et al., 2006).

ρ_eff is dependent on the chemical composition and morphological features (χ and ρ_p) of an urban aerosol population. Typically, direct ρ_eff measurements are conducted between D_em = 30 and 400 nm. Particles in this size range often consist of organics, secondary inorganic material, and black carbon. As discussed in Sect. 3.5, studies have found SOA to have ρ_eff values between 1 and 1.65 g cm⁻³ and secondary inorganic material, such as H₂SO₄, (NH₄)₂SO₄, and NH₄NO₃ to have ρ_eff values between 1.7 and 1.83 g cm⁻³ (Kostenidou et al., 2007; Lide, 2005; Malloy et al., 2009; Mikhailov et al., 2013; Nakao et al., 2013; Neusüß et al., 2002; Tang, 1996; Xiao et al., 2015; Zelenyuk et al., 2008). The ρ_eff of soot particles can fall below 1 g cm⁻³, with a decreasing trend with the increase in particle size. The relative fraction of various species in an urban air mass, such as organics, secondary inorganic materials, and loosely agglomerated soot particles, among others, will determine the size dependency of the ρ_eff for the externally and internally mixed aerosol population. For example, previous direct ρ_eff measurements conducted in Los Angeles, Copenhagen, and Beijing found ρ_eff to be inversely proportional to particle size when the fraction of soot particles from vehicle emissions was relatively abundant due to elevated traffic intensity (Geller et al., 2006; Rissler et al., 2014; Qiao et al., 2018). Conversely, a study in Shanghai observed an increase in ρ_eff with particle size (Table S2), which was attributed to an abundance of hygroscopic species, such as (NH₄)₂SO₄ and NH₄NO₃ (Ye et al., 2011; Yin et al., 2015).

Urban aerosol ρ_eff is expected to be temporally variant at a given sampling location due to the transient nature of emission sources. For example, in the urban environment, diurnal patterns in traffic density can drive time-dependent shifts in ρ_eff as the relative fraction of soot particles changes throughout the day. A low fraction of soot particles was observed in Copenhagen during the nighttime due to the low traffic density (Rissler et al., 2014). Two minima in ρ_eff were found in Houston in the morning at 07:00 local time (GMT−5) and in the evening at 19:00 to 20:00 LT, likely due to increased emissions of soot particles during rush hours (Levy et al., 2013). In Beijing, one study found ρ_eff to decrease during the nighttime due to an increase in the abundance of soot particles (Hu et al., 2012). This temporal shift in the urban aerosol ρ_eff was found to be due to the emissions of heavy trucks, which are only allowed to enter the fifth ring road in Beijing during the night, as well as more intense coal burning for domestic heating in the night during the heating season.

Urban aerosol ρ_eff is also influenced by air pollution events and air mass origins. Direct ρ_eff measurements in Beijing observed higher ρ_eff values during clean air quality episodes compared to polluted air quality episodes (Hu et al., 2012). This finding was attributed to the greater relative fraction of mineral dust during the clean episodes and abundance of organics and secondary inorganic ions in the particle phase during the polluted episodes (Hu et al., 2012). The ρ_eff can shift during atmospheric NPF events, depending on the dominant condensable vapor during the particle growth period. Qiao et al. (2018) found ρ_eff to decrease during a NPF event in Beijing, indicating that the condensable vapors were dominated by organics, which corresponded to the increase in the fraction of organic material in submicron particle mass concentrations. In contrast, ρ_eff measurements in Shanghai observed an increase in ρ_eff during NPF events, suggesting that relatively heavier secondary inorganic materials were the primary driver for particle condensational growth (Xie et al., 2017; Yin et al., 2015). Wind direction can affect ρ_eff by changing the air mass origin. Direct ρ_eff measurements in a street canyon in central Copenhagen showed higher fractions of dense-mode particles when the air mass traveled over more polluted regions than when the air mass came from clean sea/ocean areas (Rissler et al., 2014).

While the studies summarized in Fig. 1 and Table S2 provide valuable insights into variations of ρ_eff with particle size, geographical location, and intra-city environments (urban vs. traffic), more measurements are clearly needed in many cities around the world to develop a more comprehensive understanding of the nature of urban aerosol morphology and the factors that drive changes in size-resolved ρ_eff. In particular, direct ρ_eff measurements are needed in the accumulation and coarse mode given the variability identified in this study and the contribution of both modes to urban aerosol mass PSDs (Sect. 6). Doing so will provide a basis to better translate measured number PSDs to mass PSDs and D_a-based PSDs to D_em-based PSDs.

The constructed size-resolved urban aerosol ρ_eff functions represent the first attempt to compile previous measured data and extend those to unmeasured size ranges to obtain a continuous function that can be applied in PSD conversions when direct measurements of the size-resolved ρ_eff are unavailable. With the method and measured data detailed in this paper, one can adjust or reconstruct the ρ_eff functions according to their own use. It is acknowledged that the number of compiled data is limited, and uncertainties could be significant for size ranges where direct measurements are unavailable. To reduce uncertainties, more direct measurements are needed in the future. The effective density can be affected by different atmospheric processes and is often site-specific and temporally variant. Caution should be taken when applying the ρ_eff functions. In addition, we compiled the data in a step-wise manner, which resulted in sudden changes at the border of certain size ranges. Other interpolation methods can be used to smooth the ρ_eff functions.

4 Methodology for analyzing urban aerosol PSD observations

4.1 Introduction to multi-modal lognormal fitting and transformations of urban aerosol PSDs

The urban aerosol PSDs were fit to the multi-modal lognormal distribution function and translated across number (cm⁻³), surface area (µm² cm⁻³), volume (µm³ cm⁻³), and mass (µg m⁻³) domains following different strategies depending on the measurement technique and size range, as described in Sect. 4.1.1–4.1.4. Lognormal fitting parameters, including the geometric mean diameter, geometric standard deviation, and concentration for each mode, along with measurement information, for all 737 PSDs are compiled in the Supplement (Tables S3–S6 and individual PSD figures). For a few selected studies where the measured PSDs were already fit to the multi-modal lognormal distribution function, the listed fitting parameters were used directly. The fitting parameters provide a basis to characterize the shape and magnitude of the PSDs, as well as a mathematical parameterization to reproduce the measured PSDs for subsequent analysis by the atmospheric aerosol research community.

4.1.1 Urban aerosol number PSDs in the submicron regime

Urban aerosol number PSDs that only included modes in the submicron regime (nucleation, Aitken, and accumulation) were typically measured via electrical mobility-based techniques as number-based concentrations (e.g., SMPS). The extracted measured data for these PSDs were fit to the multi-modal lognormal distribution function ($\mathrm{d}N/\mathrm{dLog}{D}_{\mathrm{p}}$, cm⁻³, Eq. 7; logarithm base 10) by using a lognormal fitting code in MATLAB based on the nonlinear least-squares curve fitting function, lsqcurvefit.m:

$$\begin{array}{}\text{(7)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}N}{\mathrm{dLog}{D}_{\mathrm{p}}}}& =\sum _{i=\mathrm{1}}^n{\displaystyle \frac{N_i}{\left(\mathrm{2}\mathit{\pi }{)}^{\mathrm{1}/\mathrm{2}}\log \right({\mathit{\sigma }}_i)}}\\ & \times \exp \left[-{\displaystyle \frac{{\left(\log D_{\mathrm{p}}-\log \stackrel{\mathrm{‾}}{D_{\mathrm{p},\mathrm{i}}}\right)}^{\mathrm{2}}}{\mathrm{2}{\log }^{\mathrm{2}}\left({\mathit{\sigma }}_i\right)}}\right].\end{array}\end{array}$$

The geometric mean diameter ($\stackrel{\mathrm{‾}}{D_{\mathrm{p},\mathrm{i}}}$), geometric standard deviation (σ_i), and particle number concentration or amplitude (N_i) for each mode (i) were determined. The number of modes was based upon what was needed to achieve the best fit to the measured data. Two or three modes can achieve the best fit. Fitting parameters and measurement information for urban aerosol number PSDs in the submicron regime are provided in Table S3, as well as in individual PSD figures presented in the Supplement, an example of which is shown in Fig. S1. The fitted number PSDs were converted to surface area PSDs ($\mathrm{d}S/\mathrm{dLog}{D}_{\mathrm{p}}$, µm² cm⁻³) and volume PSDs ($\mathrm{d}V/\mathrm{dLog}{D}_{\mathrm{p}}$, µm³ cm⁻³) assuming spherical particles and converted to mass PSDs ($\mathrm{d}M/\mathrm{dLog}{D}_{\mathrm{p}}$, µg m⁻³) using the representative size-resolved ρ_eff functions for Groups A, B, or C (Sect. 3, Fig. 1). Size-integrated concentrations were also calculated.

4.1.2 Urban aerosol number PSDs that cover both the submicron and coarse regime

Urban aerosol number PSDs that cover both the submicron and coarse regime typically utilize a combination of different aerosol measurement techniques. Electrical mobility-based techniques (e.g., SMPS) are often used for the submicron regime and aerodynamic-based techniques (e.g., APS), or optical-based techniques [e.g., optical particle counter (OPC) or optical particle sizer (OPS)] are used for the coarse regime and a fraction of the accumulation mode. The amplitude of number PSDs can span 1–3 orders of magnitude over the submicron and coarse regimes. When both regimes are measured concurrently, the coarse mode is often present as the tail of the accumulation mode in the number PSDs. Thus, the lognormal fitting of the number PSDs often ignores the coarse-mode particles, which can result in an inaccurate estimation of the volume and mass concentrations of large particles when converting the fitted number PSDs to volume and mass PSDs. Therefore, the PSDs that cover both the submicron and coarse regime were separated into two segments, each of which was individually fitted to the multi-modal lognormal distribution function in order to reproduce the measured data more accurately.

Electrical mobility-based techniques typically cover size fractions that contribute significantly to number PSDs in the urban atmosphere (e.g., D_em ≤ 100 nm). Thus, the segment of the number PSDs measured by such techniques was directly fitted with the multi-modal lognormal distribution function by Eq. (7), and the fitted number PSDs were converted to surface area, volume, and mass PSDs as described in Sect. 4.1.1. Size fractions measured by aerodynamic- or optical-based techniques often cover a fraction of the accumulation mode and the coarse mode, both of which contribute significantly to volume and mass PSDs. Therefore, to best reproduce the volume and mass PSDs, a different approach was employed to fit the PSDs measured by these two techniques.

For aerodynamic-based measurements, D_a needs to be converted to D_em so that a consistent particle size definition can be used. In some studies, the authors did this by converting the measured D_a-based PSD to a D_em-based PSD using the value for ρ_eff that gave the best fit between the converted D_em-based PSD with the measured D_em-based PSD in an overlap region (often the accumulation mode) that was covered by both electrical mobility- and aerodynamic-based techniques (e.g., Pitz et al., 2008a). Most urban aerosol number PSDs measured with an APS were reported as D_a-based PSDs (e.g., Morawska et al., 1998) or converted to Stokes' or geometric diameter-based PSDs by assuming values for χ and ρ_p (e.g., Babu et al., 2016; Bäumer et al., 2008; Wehner et al., 2004a; Wu et al., 2008; Yue et al., 2009, 2010). For the latter, such diameters were first converted back to D_a, and then to D_em. Equation (8) shows the relationship between D_a and D_ve (DeCarlo et al., 2004; Hinds, 2012), where ρ₀ is the standard density of 1 g cm⁻³:

$$\begin{array}{}\text{(8)}& D_{\mathrm{ve}}=D_{\mathrm{a}}\sqrt{{\displaystyle \frac{\mathit{\chi }{\mathit{\rho }}_{\mathrm{0}}{C}_{\mathrm{c}}(D_{\mathrm{a})}}{{\mathit{\rho }}_{\mathrm{p}}{C}_{\mathrm{c}}(D_{\mathrm{ve})}}}}.\end{array}$$

For coarse-mode particles, it is assumed that $\frac{C_{\mathrm{c}}\left(D_{\mathrm{ve}}\right)}{C_{\mathrm{c}}\left(D_{\mathrm{a}}\right)}$ is approximately unity. As mentioned in Sect. 3.1, $D_{\mathrm{ve}}=D_{\mathrm{em}}/\mathit{\chi }$; combining this with Eq. (8), we arrive at Eq. (9):

$$\begin{array}{}\text{(9)}& {\displaystyle \frac{{\mathit{\rho }}_{\mathrm{p}}^{\mathrm{1}/\mathrm{2}}}{{\mathit{\chi }}^{\mathrm{3}/\mathrm{2}}{\mathit{\rho }}_{\mathrm{0}}^{\mathrm{1}/\mathrm{2}}}}={\displaystyle \frac{D_{\mathrm{a}}}{D_{\mathrm{em}}}}.\end{array}$$

From Eqs. (9) and (6), we can derive the relationship between D_a and D_em (Eq. 10), which is used to convert D_a to D_em:

$$\begin{array}{}\text{(10)}& {\mathit{\rho }}_{\mathrm{eff}}={\mathit{\rho }}_{\mathrm{0}}{\left({\displaystyle \frac{D_{\mathrm{a}}}{D_{\mathrm{em}}}}\right)}^{\mathrm{2}}.\end{array}$$

As described in Sect. 3, a series of ρ_eff values were generated from different combinations of χ and ρ_p (Fig. 2 and light green region of Fig. 1) for a fraction of the coarse mode without direct ρ_eff measurements in Groups A, B, and C. When converting D_a to D_em for these particles, each D_a was converted to multiple D_em corresponding to a series of ρ_eff to account for the uncertainty in ρ_eff. Therefore, for each of the D_a-based number PSDs in the size range where direct ρ_eff data are lacking, a series of D_em-based number PSDs were determined. Figure S2 shows the ratio of D_a to D_em when translating between the two diameters for different values of χ and ρ_p (assuming $\frac{C_{\mathrm{c}}\left(D_{\mathrm{ve}}\right)}{C_{\mathrm{c}}\left(D_{\mathrm{a}}\right)}\approx \mathrm{1}$). In general, $D_{\mathrm{a}}/D_{\mathrm{em}}$ increases with decreasing χ and increasing ρ_p.

The converted D_em-based number PSDs were transformed to D_em-based volume PSDs. For the size fraction of the coarse mode where the ρ_eff was estimated by different combinations of χ and ρ_p, multiple D_em-based volume PSDs were obtained from the series of D_em-based number PSDs. An example is shown in Fig. S3. We took the mean D_em-based volume PSD of that series of D_em-based volume PSDs and then conducted the multi-modal lognormal fitting via Eq. (11):

$$\begin{array}{}\text{(11)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}V}{\mathrm{dLog}{D}_{\mathrm{p}}}}& =\sum _{i=\mathrm{1}}^n{\displaystyle \frac{V_i}{\left(\mathrm{2}\mathit{\pi }{)}^{\mathrm{1}/\mathrm{2}}\log \right({\mathit{\sigma }}_i)}}\\ & \times \exp \left[-{\displaystyle \frac{{\left(\log D_{\mathrm{p}}-\log \stackrel{\mathrm{‾}}{D_{\mathrm{p},\mathrm{i}}}\right)}^{\mathrm{2}}}{\mathrm{2}{\log }^{\mathrm{2}}\left({\mathit{\sigma }}_i\right)}}\right],\end{array}\end{array}$$

where V_i is the volume concentration of mode i. Typically three modes are enough to achieve the best fit, but sometimes four modes are needed. The fitted D_em-based volume PSDs were then converted back to number and surface area D_em-based PSDs. This was done to prevent possible amplification in the difference between the measured and lognormally fitted PSDs when converting number PSDs to volume PSDs.

The converted D_em-based number PSDs were also transformed into D_em-based mass PSDs by applying the effective density functions ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$, ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{B}}$, or ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{C}}$, according to the measurement location and site type (Sect. 3, Fig. 1). For the size fraction of the coarse mode where the ρ_eff was estimated by different combinations of χ and ρ_p, multiple D_em-based mass PSDs were obtained from a series of D_em-based number PSDs. Similar to the volume PSDs, we took the mean D_em-based mass PSD of that series of D_em-based mass PSDs and then conducted the multi-modal lognormal fitting via Eq. (12):

$$\begin{array}{}\text{(12)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}M}{\mathrm{dLog}{D}_{\mathrm{p}}}}& =\sum _{i=\mathrm{1}}^n{\displaystyle \frac{M_i}{\left(\mathrm{2}\mathit{\pi }{)}^{\mathrm{1}/\mathrm{2}}\log \right({\mathit{\sigma }}_i)}}\\ & \times \exp \left[-{\displaystyle \frac{{\left(\log D_{\mathrm{p}}-\log \stackrel{\mathrm{‾}}{D_{\mathrm{p},\mathrm{i}}}\right)}^{\mathrm{2}}}{\mathrm{2}{\log }^{\mathrm{2}}\left({\mathit{\sigma }}_i\right)}}\right],\end{array}\end{array}$$

where M_i is the mass concentration of mode i. Typically three modes are enough to achieve the best fit, but sometimes four modes are needed. Now the number, surface area, volume, and mass PSDs in the size range that covered both the electrical mobility- and aerodynamic-based techniques can be reproduced. The goal of this stage is to apply the most appropriate size-resolved ρ_eff to a given number PSD measurement, thereby accurately estimating its volume and mass PSD and taking into consideration the uncertainties of the unknown size-resolved ρ_eff values for the coarse mode. Fitting parameters and measurement information for urban aerosol PSD measurements made with both electrical mobility- and aerodynamic-based techniques covering the submicron and coarse regimes are provided in Table S4.

For optical-based measurements, we assume the optical diameter is equivalent to D_em due to the lack of information needed to convert one to the other. The number PSDs measured by optical-based techniques were transformed to mass PSDs assuming a uniform apparent density of 1.65 g cm⁻³ (Pitz et al., 2008b). The mass PSDs were then fitted with the multi-modal lognormal distribution function using Eq. (12). The fitted mass PSDs were converted back to number, surface area, and volume PSDs. Fitting parameters and measurement information for urban aerosol PSD measurements made with both electrical mobility- and optical-based techniques covering the submicron and coarse regimes are provided in Table S5.

4.1.3 Urban aerosol mass PSDs measured by gravimetric methods employing inertial impactors

For urban aerosol mass PSDs measured by gravimetric methods with inertial impactors, the D_a-based mass PSDs were converted to D_em-based mass PSDs to enable comparison with the other electrical mobility-based measurements. According to the measurement location and site type, D_a was converted to D_em using the ρ_eff functions for Groups A, B, or C, via Eq. (10). For the fraction of the coarse mode where a series of χ and ρ_p were used to estimate ρ_eff, each D_a-based mass PSD was converted to multiple D_em-based mass PSDs, with each PSD corresponding to a particular value of ρ_eff. Then, the mean D_em-based PSD was taken from the series of D_em-based mass PSDs and merged with the rest of the D_em-based mass PSD determined via the effective density functions ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{A}}$, ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{B}}$, or ${\mathit{\rho }}_{\mathrm{eff}}^{\mathrm{C}}$. The multi-modal lognormal fitting was conducted for the D_em-based mass PSDs by using Eq. (12). An example is shown in Fig. S4.

The D_a-based mass PSDs were also converted to D_em-based volume PSDs by using the ρ_eff functions for Groups A, B, or C. Similar to the conversion for mass PSDs, for the fraction of the coarse mode where a series of χ and ρ_p were used to estimate ρ_eff, each D_a-based mass PSD was converted to multiple D_em-based volume PSDs. The mean D_em-based volume PSD was taken from this series of D_em-based volume PSDs and merged with the rest of the D_em-based volume PSD. The multi-modal lognormal fitting was conducted for the D_em-based volume PSDs by using Eq. (11). The fitted D_em-based volume PSDs were converted to D_em-based number and surface area PSDs. For the volume and mass PSDs measured by inertial impactors, typically three modes can achieve the best fit, but sometimes they need four modes. Fitting parameters and measurement information for urban aerosol PSD measurements made with gravimetric methods employing inertial impactors are provided in Table S6.

4.1.4 Considerations for grouping urban aerosol PSD observations by geographical region

The collection of urban aerosol PSD observations from around the globe offers a basis to identify geographical trends in number and mass PSDs. A few considerations were made in grouping the PSDs by geographical region. For urban aerosol number PSDs, the prominent mode is most often present in the UFP regime, which is captured very well by electrical mobility-based techniques (e.g., SMPS). However, PSD measurements made with aerodynamic-based techniques (e.g., APS, inertial impactors) or optical-based techniques (e.g., OPC, OPS) typically cannot accurately characterize number PSDs down to the UFP regime. Thus, when grouping urban aerosol number PSDs by geographical region, only measurements made via electrical mobility-based techniques involving the UFP regime were used. For urban aerosol mass PSDs, the maximum value of the PSD typically exists in either the accumulation mode or the coarse mode. Therefore, urban aerosol PSD measurements made via electrical mobility-based techniques that only cover the submicron regime were not used in the analysis of geographical trends in mass PSDs. Only PSD measurements made with inertial impactors and those combining both electrical mobility- and aerodynamic-/optical-based techniques to cover both the submicron and coarse regime were incorporated into the global mass PSD analysis.

To validate the PSDs compiled in this study, we selected several cities to compare the PM_2.5 derived from the compiled PSDs (Fig. 3, blue circular markers) with those measured by local monitoring stations over the same sampling periods (green diamond markers and error bars). The green diamond markers in Fig. 3 represent the mean values of the PM_2.5 from local sampling stations measured over the sampling period of the corresponding PSD, and the error bars represent the standard deviations. The blue circular markers represent the derived PM_2.5 from mass PSDs. The PSDs from four studies (Cabada et al., 2004; Ding et al., 2017; Harrison et al., 2012; Watson et al., 2002) were selected since long-term PM_2.5 data from a monitoring station near the PSD sampling site are available. Although the PM_2.5 monitoring stations and the sites of the PSDs measurements are not next to each other, the PM_2.5 derived from the PSDs exhibits a good agreement with that measured at local sampling stations, indicating the validity of the collected PSDs. Some discrepancies potentially exist due to the difference in sampling locations between the PSD and local PM_2.5 measurements.

Figure 3 Comparison of size-integrated PM_2.5 mass concentrations derived from the PSDs collected in this study (blue circular markers) with those measured by local monitoring stations in the same city over the same sampling periods (green diamond markers and error bars). The green diamond markers represent the mean values of the PM_2.5 mass concentrations from local sampling stations over the sampling period of the corresponding PSD, and the error bars represent the standard deviations of the mean PM_2.5 mass concentrations. ^a PSDs from Ding et al. (2017) and PM_2.5 from Shanghai Environment Monitoring Center at Hongkou Liangcheng station, including four different sampling periods. ^b PSDs from Cabada et al. (2004) and PM_2.5 from U.S. EPA monitoring station (42-003-0021), including four different sampling periods. ^c PSD from Watson et al. (2002) and PM_2.5 from U.S. EPA monitoring station (06-019-0008). ^d PSDs from Harrison et al. (2012) and PM_2.5 from UK Automatic Urban and Rural Monitoring Network at London Marylebone Road. Three PSDs were measured at three different sampling sites over the same period.

5 Urban aerosol PSD observations around the globe: an overview of existing data

Urban aerosol PSD observations made between 1998 and 2017 were collected and analyzed to evaluate geographical variations in the shape and magnitude of number and mass PSDs and to identify gaps in PSD measurements. The PSD observations are summarized and categorized in the Supplement and are grouped by geographical region: AF, CSSA, EA, EU, LA, NAAN, and WA. Among all PSDs, 14.3 % were long-term measurements (> 6 months), and 33.3 % were moderate-term measurements (1–6 months). The remaining PSDs represent observations made over periods less than 1 month through short-term field measurement campaigns. Figure 4 illustrates the temporal and geographical distribution by year between 1998 and 2017 of the urban aerosol PSD references analyzed in this study. Between 1998 and 2007, there is a clear increase in the number of published studies reporting urban aerosol PSD observations. During this period, the majority of PSD measurements were conducted in cities in EU and NAAN. However, beginning in 2006 and continuing through 2017, a greater fraction of published PSD observations were collected in cities in EA and CSSA. Studies reporting PSD observations in NAAN cities appear to have declined between 2009 and 2017. Urban aerosol PSD observations in LA, WA, and AF remain sparse across the examined time period; however, the frequency of publications reporting PSD measurements in LA has been fairly stable between 2009 and 2017.

Figure 4 Temporal and geographical distribution by year of the urban PSD references analyzed in this study (1998–2017). The geographical regions include North America, Australia, and New Zealand (NAAN), Europe (EU), East Asia (EA), Central, South, and Southeast Asia (CSSA), Latin America (LA), West Asia (WA), and Africa (AF).

Figure 5 Global distribution of urban aerosol PSD measurement locations included in this study.

Figure 5 presents the global distribution of urban aerosol PSD measurement locations included in this study. It is apparent that there are regions where numerous observations have been made (e.g., EU) and others where measurements are scarce (e.g., WA, LA, AF). Among 737 urban aerosol PSD observations collected in this study, 42.6 % of them are from EU, 18.2 % are from North America, and 18.2 % are from EA. Conversely, only 4.7 % are from WA, 6.4 % from LA, and 1 % from AF. The three countries that contribute the most to the collection of urban aerosol PSD observations in this study are the United States (13.7 %), China (12.2 %), and Germany (9.2 %).

A paucity of urban aerosol PSD measurements is clear throughout the entirety of AF, LA, and WA; CSSA excluding India; Canada, although a few measurements have been conducted in the Greater Toronto and Hamilton Area; Russia; Australia; and New Zealand. The few published PSD measurements in AF, CSSA excluding India, and WA were reported. Urban aerosol PSD observations have only been made in five countries in AF. Similarly, in LA, PSD measurements have been made in a few countries, the majority of which have been reported in Brazil (38 PSDs, with 35 from São Paulo), Chile, and Mexico. A total of 35 urban aerosol PSD measurements have been reported in WA, many of which were made in Istanbul, Turkey, Fahaheel, Kuwait, and Yanbu, Saudi Arabia. A total of 69.7 % of the PSD observations in CSSA have been reported in India, with comparatively fewer measurements coming from other countries in the region, including Pakistan, Singapore, Nepal, and Vietnam.

The vast majority of urban aerosol PSD measurements analyzed in this study were made via electrical mobility-based techniques. Comparatively fewer direct measurements of mass PSDs were made via gravimetric methods employing inertial impactors. In total, 82.7 % of the urban aerosol PSDs reported number PSDs down to the UFP fraction of the submicron regime. However, only six of the urban aerosol number PSDs involving the UFP regime are from Southeast Asia; only 13 are from WA, and none are from AF. The lack of urban aerosol PSD measurements down to the UFP regime in many regions of the world makes it very challenging to accurately estimate urban aerosol inhalation exposures. This is of concern given the inhalation toxicity and adverse health effects associated with UFPs (Delfino et al., 2005; Li et al., 2016, 2017; Oberdörster et al., 2004, 2005; Pietropaoli et al., 2004; Rychlik et al., 2019; Sioutas et al., 2005).

6 Urban aerosol PSDs: from number to mass

6.1 Geographical variations in the magnitude and shape of submicron urban aerosol number PSDs

Geographical variations in submicron urban aerosol number PSD measurements ($\mathrm{d}N/\mathrm{dLog}{D}_{\mathrm{em}}$, cm⁻³) are presented in Fig. 6. Each log–log plot incorporates number PSDs measured with electrical mobility-based techniques that cover the submicron regime (624 PSDs, Table S3). Each line represents an individual PSD observation compiled in the Supplement, and the color indicates the occurrence frequency of the number PSDs at a given particle size (D_em) with a certain particle number concentration. Red, orange, and yellow curves indicate the number PSDs where the occurrence frequency is high among the analyzed studies. All number PSD observations are included in the “Global” plot (top left). Number PSDs for EA, CSSA, EU, LA, and NAAN are presented in the remaining plots; however, AF and WA are not included due to the lack of PSD measurements in the submicron regime in the two regions. The solid black lines indicate the median number PSDs for each group, which are also presented in Fig. 7 on a linear y-axis scale. It can be seen that among the geographical regions, the greatest number of submicron number PSDs has been reported for cities in EU, NAAN, and EA; comparatively fewer have been reported in CSSA and LA.

Figure 6 Urban aerosol number PSDs analyzed in this study, grouped by geographical region. The figure incorporates all submicron number PSDs measured by electrical mobility-based techniques (624 PSDs). The color represents the occurrence frequency of the number PSDs at a given particle size with a certain concentration. The black lines indicate the median number PSDs in each group.

Figure 7 Median number PSDs for each geographical region.

The visualization of the global distribution in submicron urban aerosol number PSDs (Fig. 6, top left) demonstrates that there are significant variations in both the magnitude and shape of number PSDs measured across urban environments around the world. For a given particle size (D_em), there can be over 2 orders of magnitude variation in the particle number concentration. This variation in the amplitude of the number PSDs is persistent across the considered size range, from D_em = 3 to 1000 nm, which includes the nucleation, Aitken, and accumulation modes. The red–yellow region of the global plot surrounds the median number PSD (black line). Wide variability in the magnitude of the number PSDs above and below the median PSD is apparent. Thus, defining a globally representative urban aerosol number PSD is challenging given the vast array of factors that can influence the shape of a PSD at a particular sampling location within in a city. However, the red region suggests that on a global basis, some tendencies do exist in regard to the shape and magnitude of urban aerosol number PSDs. Notably, number PSDs are often dominated by particles between D_em = 10 to 100 nm, with varying contributions from the sub-10 nm fraction and accumulation mode, depending on the conditions that exist at the measurement site. Across this size fraction, there is a high occurrence frequency of number PSDs with an amplitude between 5000 and 30 000 cm⁻³​​​​​​​. In some cases, the amplitude can reach or exceed 50 000 to 100 000 cm⁻³, most commonly in the nucleation and Aitken mode. The global median number PSD demonstrates that number PSDs often drop off in magnitude by nearly a factor of 100 across the width of the accumulation mode, from approximately 7000 cm⁻³ at D_em = 100 nm to 50 cm⁻³ as D_em approaches 1000 nm.

The geographically resolved collections of urban aerosol number PSDs presented in Figs. 6 and 7 indicate that there is inter-region variability in the shape and magnitude of number PSDs. Number PSDs in NAAN and EU present similar structural characteristics; similarly, number PSDs in EA and CSSA are alike in both shape and magnitude. Number PSDs measured in cities in NAAN and EU tend to skew to the left and are often dominated by nucleation- and Aitken-mode particles, whereas number PSDs measured in cities in EA and CSSA tend to skew to the right and are often dominated by Aitken- and accumulation-mode particles. The magnitude of the number PSDs in the accumulation mode in EA and CSSA tends to be higher than that in NAAN and EU. This is apparent in the collection of individual PSDs in each of the geographical regions in Fig. 6, as well as in the median number PSDs presented in Fig. 7. Conversely, the magnitude of the number PSDs in the sub-50 nm fraction of the UFP regime in EA and CSSA tends to be lower than of those measured in NAAN and EU. This is especially true for the nucleation mode, which is often much more pronounced in the urban atmospheres of NAAN and EU cities. The median number PSD for LA more closely resembles number PSDs measured in NAAN and EU as compared to those in EA and CSSA. However, the lack of PSD observations in LA makes it difficult to draw conclusions about the shape of PSDs in this region. The D_em values associated with the prominent mode for each of the median number PSDs presented in Fig. 7 are D_em ∼ 20 nm for EU, D_em ∼ 30 nm for NAAN, D_em ∼ 35 nm for LA, and D_em ∼ 60 to 100 nm for EA and CSSA.

The variation in the magnitude of the number PSDs for EA, CSSA, EU, LA, and NAAN is generally consistent with that observed in the global distribution of PSDs presented in Fig. 6. The abundance of number PSD observations in EU provides a basis to more reliably identify a representative PSD for the region. The red–yellow–light green band for EU demonstrates that a large fraction of PSD measurements in EU cities tend to cluster around the median number PSD. Between D_em = 10 to 100 nm, the amplitude of this PSD band varies between 5000 and 20 000 cm⁻³. Less frequently, number PSDs with magnitudes exceeding 30 000 cm⁻³, or as low as 1000 cm⁻³, have been reported in EU cities. A faint band of moderate occurrence frequency can be observed in both EA and NAAN; however, the comparatively few PSD observations in CSSA and LA make it difficult to identify such trends in these two regions.

To better visualize differences in the shape of the urban aerosol number PSDs and to probe the relative fraction of particles in different modes, each number PSD was normalized by its maximum concentration such that variations in the magnitude of the number PSDs can be neglected (Fig. S5). The normalized urban aerosol number PSDs presented in Fig. S5 are grouped by country and geographical region (from top to bottom): WA, NAAN, LA, EU, EA, and CSSA. Many of the normalized number PSDs in EA and CSSA tend to show a mode (red–orange color) at around D_em=100 nm, and few show maxima at or near the nucleation mode. Some of the normalized number PSDs measured in China and India present prominent modes in the accumulation mode, between D_em=100 and 200 nm. However, it can be seen that particles greater than D_em=300 nm contribute negligibly to normalized number PSDs in EA and CSSA. Normalized number PSDs in NAAN and EU generally exhibit maxima at smaller particle sizes (D_em=10 to 50 nm), while a few observations made in Germany, Italy, and the United States present modes near D_em= 100 nm. The normalized number PSDs measured in LA, predominately in São Paulo, Brazil, closely resemble observations reported in NAAN and EU. The prominent nucleation mode in the WA normalized number PSDs is in part due to the few PSD observations collected from the region, which were made at a “traffic” site in Fahaheel, Kuwait.

There are clear distinctions between urban aerosol number PSDs measured in NAAN/EU and EA/CSSA. Figure 8 presents the relationship between total particle number concentration, integrated over the measured size range of a PSD measurement, and the count median diameter (CMD) for each of the submicron number PSDs presented in Fig. 6. Number PSDs in EA and CSSA tend to cluster to the right, from CMD = 50 to 100 nm, whereas number PSDs in NAAN and EU tend to cluster toward the left, from CMD = 20 to 60 nm. There are, however, outliers in each region, such as number PSDs in EA with prominent nucleation modes and CMDs of approximately 10 nm and number PSDs in NAAN with prominent accumulation modes and CMDs approaching 100 nm. There are only a few number PSDs in CSSA that exhibit CMDs below 50 nm. In all geographical regions, there are nearly 2 orders of magnitude variation in total particle number concentrations, which are often bounded by 1000 cm⁻³ at the lower end and 100 000 cm⁻³ at the upper end. Number PSDs in EU, NAAN, and EA that have CMDs < 20 nm are associated with total particle number concentrations exceeding 10 000 cm⁻³. Interestingly, numerous number PSDs in EA and CSSA with CMDs of approximately 100 nm have concentrations > 10 000 cm⁻³. The wide variation in the total particle number concentrations presented in Fig. 8 is consistent with the trends reported in a review of geographical variations in total particle number concentrations across 40 urban roadside measurement sites around the world (Kumar et al., 2014).

Figure 8 Relationship between the total particle number concentration, integrated over the measured size range, and the count median diameter (CMD), determined for each submicron number PSD measured by electrical mobility-based techniques (624 PSDs) and grouped by geographical region.

It should be noted that many factors can influence the magnitude and shape of urban aerosol number PSDs, beyond geographical region, which is the focus of the global-scale analysis presented in Figs. 6–8. Country-wide PSD measurement campaigns have identified significant variations in number PSDs among different cities within the same country (Peng et al., 2014; Tuch et al., 2003) and at different measurement sites within the same city (Birmili et al., 2013; Costabile et al., 2009; Hussein et al., 2005; Ketzel et al., 2004; Tuch et al., 2006; Wehner et al., 2002). Regarding the latter, several studies conducted in EU cities have shown that total particle number concentrations can vary as high as a factor of roughly 9 within the same city (Birmili et al., 2013; Buonanno et al., 2011; Mejía et al., 2008; Mishra et al., 2012). Localized spatial variations in urban aerosol PSDs and number concentrations are due in part to the nature of local emission sources near the measurement site and meteorological conditions, including wind speed and direction, temperature, and relative humidity (Baxla et al., 2009; Birmili et al., 2001; Charron and Harrison, 2003; Kaul et al., 2011; Nieto et al., 1994; Rose et al., 2010; Stanier et al., 2004; Swietlicki et al., 2008; Väkevä et al., 2000; Wehner and Wiedensohler, 2003; Weingartner et al., 1997; Yu et al., 2018). Physiochemical processes that can transform an aerosol population over space and time are also very important, such as particle growth due to coagulation and condensation, particle shrinkage due to evaporation, reactive uptake, and wet and dry deposition (Gaston et al., 2014; Limbeck et al., 2003; Lin et al., 2011; Moise and Rudich, 2002; Salma et al., 2011; Shi and Harrison, 1999; Tang et al., 2010; Zhu et al., 2002a, b).

6.2 Geographical variations in the magnitude and shape of urban aerosol mass PSDs

Global variations in urban aerosol mass PSD measurements ($\mathrm{d}M/\mathrm{dLog}{D}_{\mathrm{em}}$, µg m⁻³) are presented in Fig. 9. The log–log plot incorporates mass PSDs measured by gravimetric methods with inertial impactors and measurements made with electrical mobility- and aerodynamic-/optical-based techniques that cover both the submicron and coarse mode (122 PSDs, Tables S4–S6). As discussed in Sect. 3, the size-resolved ρ_eff functions for Groups A, B, and C (Fig. 1) were used in converting D_a-based PSDs to D_em-based PSDs and translating measured number PSDs to mass PSDs. Similar to Fig. 6, each line represents an individual PSD observation compiled in the Supplement, and the color indicates the occurrence frequency of the mass PSDs at a given particle size (D_em) with a certain particle mass concentration. The solid black line indicates the median mass PSD among the global compilation of observations. In comparing Figs. 6 and 9, it is evident that submicron urban aerosol number PSDs are more commonly reported in the literature compared to mass PSDs or number PSDs spanning the submicron and coarse regimes.

Figure 9 Urban aerosol mass PSDs analyzed in this study from around the globe (122 PSDs). The figure incorporates mass PSDs measured by gravimetric methods with inertial impactors and measurements made with electrical mobility-based and aerodynamic-/optical-based techniques that cover both the submicron and coarse mode. The color represents the occurrence frequency of the mass PSDs at a given particle size with a certain concentration. The black line indicates the median mass PSD.

The visualization of the global distribution in urban aerosol mass PSDs in Fig. 9 demonstrates that there are significant variations in both the magnitude and shape of mass PSDs measured across urban environments around the world. While the limited number of mass PSD observations makes it difficult to discern clear trends in the structure of mass PSDs, some trends are evident. Notably, urban aerosol mass PSDs are dominated by particles with D_em > 100 nm and are typically bimodal, exhibiting maxima in both the accumulation and coarse mode, as indicated by the median mass PSD. The relative contribution of the two modes is variable among the PSD observations. In some cases, urban aerosol mass PSDs are dominated by accumulation-mode particles, while other PSDs present a prominent coarse mode. Within the accumulation mode, the amplitude of the mass PSDs spans 2 orders of magnitude, from 1 to 100 µg m⁻³. The D_em associated with the prominent mode in the accumulation mode is variable. The spread in the magnitude of the mass PSD in the coarse mode is consistent with that observed in the accumulation mode. Some mass PSDs exhibit amplitudes that exceed 100 µg m⁻³; however, their occurrence frequency is very low. The magnitude of mass PSDs in the UFP regime is relatively insignificant and ranges from 0.01 to 10 µg m⁻³. Unlike for the number PSDs in Fig. 6, a band of high occurrence frequency is not evident in Fig. 9. Some degree of clustering of mass PSDs around the median PSD is evident; however, there is clearly more variation in the structure of mass PSDs as compared to number PSDs. This may be due to the variety of measurement techniques employed and uncertainties in translating number PSDs to mass PSDs using the size-resolved ρ_eff functions for Groups A, B, and C.

Figure 10 Normalized urban aerosol mass PSDs analyzed in this study from around the globe. The country codes are listed on the left, and the region codes are listed on the right.

As with the submicron urban aerosol number PSDs, the mass PSDs were normalized by their maximum concentrations such that variations in the magnitude of the mass PSDs can be neglected (Fig. 10). The normalized urban aerosol mass PSDs presented in Fig. 10 are grouped by country and geographical region (from top to bottom): WA, NAAN, LA, EU, EA, CSSA, and AF. The normalized mass PSDs demonstrate that a significant fraction of particle mass exists below D_em = 1000 nm in numerous cities in NAAN, EU, EA, and CSSA. For measurements that included the UFP regime, it is clear that sub-100 nm particles contribute little to urban aerosol mass PSDs. The majority of the normalized mass PSDs in NAAN and EU show a maximum in the accumulation mode (red–orange color) between D_em = 200 to 600 nm, while some show local maxima in both the accumulation and coarse mode. Most of the normalized mass PSDs in EA (predominately from China) are bimodal, with accumulation-mode maxima that span D_em = 300 to 1000 nm and coarse-mode maxima that span D_em = 3000 to 8000 nm. A few mass PSDs in EA (measured in South Korea) are unimodal, with a prominent coarse mode that extends beyond D_em = 10 000 nm. The normalized mass PSDs in CSSA are more variable in shape, with varying contributions from both modes. The D_em = 100 to 200 nm fraction of the accumulation mode in both EA and CSSA, which contributed meaningfully to number PSDs in the two regions, represents a minor component of submicron aerosol mass.

The shape of normalized urban aerosol mass PSDs in WA and AF is uniquely different from the other geographical regions. In WA, the normalized mass PSDs are clearly dominated by coarse-mode particles. Measurements made in Istanbul, Turkey, show a prominent mode between D_em = 6000 and 10 000 nm, with some displaying a second coarse-mode diameter between D_em = 1000 to 2000 nm. Normalized mass PSDs from Yanbu, Saudi Arabia, show a strong mode near D_em = 10 000 nm, with either a very weak or nonexistent mode in the accumulation mode. The prominent coarse modes in WA cities are likely due to frequent dust events and enhanced dust resuspension in WA cities and the relatively large size of mineral dust particles (Al-Mahmodi, 2011). The few PSD observations from AF display a dominant coarse mode, with modes spanning D_em = 1000 to 5000 nm.

6.3 Intra-city variations in urban aerosol number PSDs between urban background and traffic-influenced sites

Urban aerosol PSDs can exhibit intra-city spatial variations depending on the measurement location and its proximity to local emission sources, such as traffic. Figure 11 presents normalized submicron urban aerosol number PSDs divided into UB (urban background, top) and TR (traffic-influenced, bottom) sites. Only PSD observations with a measurement period greater than 1 week are presented. Normalized number PSDs measured at UB sites often show maxima at larger particle sizes compared to those measured at TR sites. UB measurements are typically dominated by Aitken-mode particles, with mode diameters ranging from D_em = 20 to 90 nm, with a mean CMD of 45 nm. In contrast, many of the TR measurements exhibit prominent nucleation modes, with mode diameters falling below D_em = 30 nm, and in some cases, below D_em = 10 nm, with the mean CMD of 33 nm. The mean concentration fraction of the particles smaller than 20 nm is 35 % and 19 % for the PSDs measured at TR and UB sites, respectively. The larger particles observed at UB sites are due in part to various aerosol transformation processes, such as particle growth due to coagulation and the uptake of condensable organic and inorganic vapors during short-range transport (Fine et al., 2004; Wehner et al., 2002). Urban aerosol number PSD observations made at TR sites are strongly influenced by traffic emissions. Vehicle emissions are a major source of UFPs in the urban atmospheric environment (Kumar et al., 2014; Morawska et al., 2008; Pant and Harrison, 2013). Several studies have reviewed the characteristics of aerosol emissions from traffic, including urban SOA formation associated with vehicle exhaust (Gentner et al., 2017; Kittelson et al., 2006; Morawska et al., 2008; Pant and Harrison, 2013; Thorpe and Harrison, 2008). Traffic emissions can be broadly classified as exhaust- and non-exhaust-related. Exhaust-related vehicle emissions include soot particles from incomplete combustion and particles formed via the nucleation and condensation of H₂SO₄ and hydrocarbons as the hot exhaust is cooled and diluted in the ambient atmosphere (Dallmann et al., 2014; Kleeman et al., 2000; Meyer and Ristovski, 2007; Morawska et al., 2008; Shi et al., 2001; Shi and Harrison, 1999; Wehner et al., 2002).

Figure 11 Comparison between normalized urban aerosol number PSDs measured at urban background (UB) and traffic-influenced (TR) sites. Only the number PSDs with a measurement period greater than 1 week are presented. The country codes are listed on the left, and the site type is listed on the right.

As illustrated in Fig. S6, which presents normalized number PSDs for selected urban aerosol sources, vehicle exhaust PSDs are typically dominated by UFPs. Freshly nucleated particles in vehicle exhaust are relatively small, with D_em < 30 nm. They can contribute significantly to number PSDs at TR sites (Buonanno et al., 2009; Fushimi et al., 2008; Ketzel et al., 2003; Shi et al., 1999; Zhu et al., 2002a). However, with the increase of distance from the road, either horizontally or vertically, these particles can grow by coagulation and condensation during transport (Agus et al., 2007; Hitchins et al., 2000; Li et al., 2007; Zhu et al., 2002a, b), while some can shrink due to evaporation (Dall'Osto et al., 2011b; Ning et al., 2010; Zhang et al., 2004). Non-exhaust-related traffic emissions include brake wear, road–tire interactions, and road dust resuspension; brake wear is an important source of submicron particles. As shown in Fig. S6, normalized submicron number PSDs of brake wear aerosol can span from the nucleation mode to the accumulation mode.

6.4 Submicron urban aerosol number PSDs in Asia: factors contributing to the prominent accumulation mode

The results presented in Figs. 6–7 indicate that urban aerosol number PSDs in EA and CSSA are more commonly associated with a significant fraction of accumulation-mode particles and CMDs of approximately 100 nm compared to those reported in NAAN and EU. This indicates that submicron urban aerosol populations in EA and CSSA, and particularly in China and India, are relatively larger in size than those reported in other geographical regions. A multitude of factors are responsible for governing the shape of number PSDs in urban environments in EA and CSSA. The pronounced accumulation mode can be driven by the direct emissions of accumulation-mode particles in both the urban area, as well as regional transport of such particles from rural and industrialized areas. Biomass burning is an important emission source in a number of countries in EA and CSSA. The PSDs of biomass burning aerosol depend on a variety of factors, including: the type of biomass, the condition of the flame, and atmospheric aging processes (Janhäll et al., 2010; Reid and Hobbs, 1998; Rissler et al., 2006; Sakamoto et al., 2016; Zhang et al., 2011). As shown in Fig. S6, the burning of grass, corn straw, and rice straw produces normalized number PSDs with a significant fraction of accumulation-mode particles and CMDs of approximately 100 nm (Janhäll et al., 2010; Reid et al., 2005; Sakamoto et al., 2016). It has been observed that residential biomass burning, possibly for cooking and heating, can contribute to high particle number concentrations of accumulation-mode particles in the evening in New Delhi, India (Mönkkönen et al., 2005). A recent study using the GEOS-Chem-TOMAS model identified significant aerosol emissions from biomass burning in India and Indonesia from residential, agricultural, and wildfire sources (Kodros et al., 2018). Direct burning has been reported to be a common technique to eliminate agricultural residuals in both China and India (Bi et al., 2019). The contribution of biomass burning to urban aerosols was confirmed by the high content of water-soluble potassium in the particle phase (Qi et al., 2015; Zheng et al., 2005). In addition to biomass burning, other urban sources may directly emit accumulation-mode particles, such as vehicle exhaust, power plants, and industrial activities (Vu et al., 2015).

Another factor contributing to the abundance of accumulation-mode particles in EA and CSSA is aging processes that can grow nucleation- and Aitken-mode particles through coagulation and condensation of organic or inorganic vapors (Moffet et al., 2008; Yang et al., 2012). Back trajectories indicate that aerosols transported from industrialized regions south and west of Beijing, China, can grow into larger sizes by condensation within slowly moving air masses, thereby contributing to the pronounced accumulation mode in urban areas (Wu et al., 2008). The abundance of condensable organic and inorganic vapors (e.g., NO_x, SO₂, and volatile organic compounds, VOCs) in polluted areas can aid particle growth to larger sizes. It has been reported that the concentrations of condensable vapors are higher in urban areas in China and India compared to those in NAAN and EU due to heavier air pollution in the former (Gao et al., 2009; Huang et al., 2014; Kodros et al., 2018; Kulmala et al., 2005; Misra et al., 2014; Mönkkönen et al., 2005; Shen et al., 2016a, b; Wang et al., 2013a; Wehner et al., 2004b). High levels of gas-phase precursors in China can result in significant SOA formation, which can contribute to severe haze events that are often dominated by accumulation-mode particles (Huang et al., 2014). The elevated number concentrations of accumulation-mode particles in EA and CSSA have a substantial surface area that can serve as a coagulation sink for nucleation- and Aitken-mode particles. This suppression of UFPs can cause the number PSDs in EA and CSSA to further skew to larger particle sizes.

7 Uncertainties in the extraction and lognormal fitting of urban aerosol PSDs

The urban aerosol PSDs analyzed in this study are the extracted and fitted PSDs from previously reported measurements. The data extraction and lognormal fitting process introduced some uncertainties compared with the original data. Typically, the extraction process can obtain accurate data for the dominant peak of the PSD, where the concentrations are high. However, as the PSDs were primarily reported in the form of figures with a linear y-axis scale, relatively large uncertainties exist for the size ranges with low concentrations due to the limited resolution of the extraction process by using pixel picking in the figures. Similarly, the lognormal fitting process can accurately capture the dominant mode of the PSD, as the high concentrations are weighted greater in the nonlinear least-squares curve fitting (the fitting quality of individual PSDs can be visually checked in the Supplement). However, relatively large uncertainties exist between the originally reported data and the fitted PSDs for the size ranges where the concentrations are relatively low compared with the dominant peak.

These uncertainties, to some extent, affect the comparison of the PSDs in regard to their magnitudes. For example, most of the number PSDs exhibit a dominant mode in the UFP regime, while the accumulation mode often appears as a tail of the dominant mode. Although the number PSDs are fitted well in the UFP regime, the fitted number PSDs in the accumulation mode exhibit relatively large uncertainties. Therefore, we mainly compared the dominant mode in the discussion of geographical variations in urban aerosol PSDs. The uncertainties are expected to affect the comparison of the normalized PSDs to a lesser extent. Since the magnitude of individual PSDs is normalized, only the shape of the main mode is emphasized and compared, while the size ranges with relatively large uncertainties become less important. Therefore, the uncertainties from the data extraction and lognormal fitting would not significantly influence the findings on the geographical variations of the urban aerosol PSDs. The uncertainties potentially affect the absolute concentrations estimated in Fig. 8. Since the fitting quality of the main mode is typically good, and the size range with relatively larger uncertainties does not contribute substantially to the total number concentrations, this influence may not be significant. The mass PSDs include measurements with gravimetric methods employing inertial impactors. These PSDs exhibit low size resolution due to the limited number of size bins of the impactors. The fitted mass PSDs have much greater uncertainties in their shape compared to the number PSDs since the fitted curves were interpolated among the limited data points.

This study constructed size-resolved urban aerosol ρ_eff functions by using measured and assumed ρ_eff in a step-wise manner. This resulted in some sharp changes at the borders of the assumed size ranges. Using the ρ_eff functions in the PSD conversions caused some step-like artifacts. In reality, the ρ_eff and converted PSDs should transition smoothly with particle size. With the construction method and the previously measured data detailed in the paper, readers can reconstruct the ρ_eff functions in an interpolated manner to obtain smooth functions.

8 Framing future research directions for urban aerosol PSD observations at a global scale

Critical gaps in urban aerosol PSD observations were identified in many geographical regions and countries, with a severe lack of ground-based PSD data for cities in AF, LA, WA, and parts of CSSA (Figs. 4 and 5). Available PSD measurement data are often short in duration, with only 14.3 % of the analyzed observations extending beyond 6 months. Similarly, there have been few direct measurements of size-resolved urban aerosol effective densities, and existing data are limited for many size fractions (Fig. 1, Table S2). A greater number of direct measurements of urban aerosol effective densities will enable accurate translation of urban aerosol number PSDs to mass PSDs in a given urban environment.

There are significant geographical variations in the shape and magnitude of urban aerosol PSDs due to differences in primary and secondary aerosol sources and meteorological conditions (Figs. 6 and 9). Such differences have important implications for human exposure and health as they drive large changes in the rate at which particles are deposited in each region of the human respiratory tract. The important contribution of sub-200 nm particles to urban aerosol number PSDs in all regions reinforces the need for routine monitoring of the smallest particles in the urban atmosphere. Urban aerosol PSD observations that span the UFP to coarse regimes are especially lacking, with only 14 % of the analyzed PSDs measuring particles across this wide size range. Coordinated global efforts are needed to build a continuous, long-term, wide size range, and ground-based urban PSD observation network in cities across the world. Such a network is necessary for improving our ability to link urban air pollution with human health and toxicological outcomes, understanding the atmospheric transformations of urban aerosol populations, and supporting air quality legislation and policy decisions that address particles both big and small (Kulmala, 2018).

Existing ground-based air quality monitoring stations are largely focused on measurements of size-integrated PM_2.5 mass concentrations. Expansive observational datasets of PM_2.5 mass concentrations are now available. This has significantly advanced knowledge of the impact of PM_2.5 on urban air pollution and human health in the past 2 decades (Apte et al., 2015; Cheng et al., 2016; Van Donkelaar et al., 2010; Gelencsér et al., 2007; de Jesus et al., 2019; Thunis et al., 2017; West et al., 2016). PM_2.5 measurement gaps do exist, with 141 of 243 countries lacking ground-based PM_2.5 monitoring stations (Martin et al., 2019). The ubiquity of low-cost aerosol sensors (e.g., OPCs) is providing a foundation for large-scale deployment of PM_2.5 monitoring networks (Motlagh et al., 2020). However, given the nature of urban aerosol number and mass PSDs, as illustrated in Figs. 6 and 9, observations of PM_2.5 mass concentrations are insufficient to accurately characterize an urban aerosol population. Of particular importance is the measurement of PSDs that include the UFP regime, given their significant contribution to particle number concentrations (Figs. 6 and 7). This is especially important given that UFP number concentrations and PM_2.5 mass concentrations are not representative of each other, as particles that dominate the two size-integrated metrics often originate from different sources (de Jesus et al., 2019).

The compilation of urban aerosol PSD observations in this study demonstrates the benefit of routinely measuring urban PSDs that include the nucleation, Aitken, accumulation, and coarse mode. CMDs of urban aerosol number PSDs often fall between D_em = 10 and 100 nm (Fig. 8); such particles contribute negligibly to urban aerosol mass PSDs. Many urban aerosol sources, such as biomass burning, traffic emissions (exhaust and non-exhaust), industrial and domestic combustion, cooking, and atmospheric new particle formation events, produce particles in the UFP regime (Fig. S6) (Brines et al., 2015; Kumar et al., 2014; Venecek et al., 2019; Vu et al., 2015). Urban aerosol PSDs provide more detailed information of emission sources than size-integrated concentrations do. Several PSD-based models have been developed using characteristic emission profiles of different sources to identify and apportion the emission sources (Beddows et al., 2009, 2014; Charron et al., 2008; Dall'Osto et al., 2011a; Friend et al., 2012; Gu et al., 2011; Harrison et al., 2011; Kasumba et al., 2009; Kim et al., 2004; Ogulei et al., 2007; Thimmaiah et al., 2009; Tunved et al., 2004; Yue et al., 2013). A detailed review of such models was given by Vu et al. (2015).

Future urban aerosol PSD measurements should aim to span the entirety of the UFP regime. Achieving continuous urban aerosol number PSD observations from the nucleation to coarse mode at the global scale remains a challenge given the cost of sensitive aerosol instrumentation required for the detection of UFPs and the collection of different measurement techniques needed to detect particles across such a wide size range. While advancements in low-cost optical particle sensing for detection of aerosols down to approximately D_em = 300 to 500 nm have been made in recent years, efforts are still needed to develop low-cost condensation particle counters, differential mobility analyzers, and diffusion chargers for measurement of PSDs down to the UFP regime. The combination of routine PM_2.5 measurements with condensation particle counters that measure most of the UFP regime could potentially be a cost-effective approach to routinely monitoring both fine particle mass concentrations and UFP number concentrations in the near future.

Appendix A: List of symbols and abbreviations

AF	Africa
APM	Aerosol particle mass analyzer
APS	Aerodynamic particle sizer
CMD	Count median diameter
CSSA	Central, South, and Southeast Asia
DMA	Differential mobility analyzer
EA	East Asia
ELVOC	Extremely low-volatility organic compound
EU	Europe
HOM	Highly oxygenated molecule
LA	Latin America
MOUDI	Micro-orifice uniform deposit impactor
NAAN	North America, Australia, and New Zealand
NPF	New particle formation
OPC/OPS	Optical particle counter/optical particle sizer
PMX	Integrated mass concentration for particles smaller than X µm
PSD	Particle size distribution
SOA	Secondary organic aerosol
TR	Traffic-influenced
UB	Urban background
UFP	Ultrafine particle (≤ 100 nm)
VOC	Volatile organic compound
WA	West Asia
Dem	Electrical mobility diameter
Da	Aerodynamic diameter
Dop	Optical diameter
Dve	Volume equivalent diameter
ρeff	Aerosol effective density
ρp	Aerosol particle density
χ	Dynamic shape factor
mp	Particle mass
Vp	Particle volume
Cc	Cunningham slip correction factor
Ni	Particle number concentration for mode i
$\stackrel{\mathrm{‾}}{D_{\mathrm{p},\mathrm{i}}}$	Geometric mean diameter for mode i
σi	Geometric standard deviation for mode i
Vi	Particle volume concentration for mode i
Mi	Particle mass concentration for mode i