1 Introduction

1.1 Light-absorbing aerosols

Light-absorbing aerosol components exert complex perturbations to the climate system through their shortwave absorption in the atmosphere and snowpack (Stier et al. 2007; Samset et al. 2018). The atmospheric heating by aerosol’s shortwave absorption alters the circulation and precipitation from regional-to-global scales (Lau et al. 2006; Samset et al. 2022). Known significant contributors to aerosol’s shortwave absorption are light-absorbing constituents of carbonaceous compounds (i.e., black carbon, brown carbon) and iron oxides (i.e., goethite, hematite, magnetite) from both anthropogenic and non-anthropogenic origins (e.g., Moteki et al. 2017).

Carbonaceous aerosol emitted as a byproduct of the combustions of fossil fuels, biofuels, and biomass is a mixture of a large variety of organic molecules and partly graphitized solid carbon (Lighty et al. 2000; Simoneit 2000). In addition, other organic molecules and polymers as secondary constituents of carbonaceous aerosol are produced in the atmosphere through gas-phase photochemical reactions and aqueous reactions in cloud droplets (Kalberer et al. 2004; Kanakidou et al. 2005; Ervens et al. 2011; Shrivastava et al. 2017). Carbonaceous aerosol materials can be categorized on the continuous spectrum of the imaginary part of the refractive index (Andreae and Gelencsér 2006; Corbin et al. 2019). One extreme of the spectrum is the group of non-refractory organic molecules with negligible imaginary refractive index, which is referred to as organic carbon (OC). Another spectrum extreme is the group of partly graphitized solid-state refractory material with a high imaginary refractive index, black carbon (BC) (Bond et al. 2013). The middle of the spectrum is a group of yellowish-to-brownish organic compounds with a moderate imaginary refractive index, commonly referred to as brown carbon (BrC) (Laskin et al. 2015). The BrC can also secondarily form through photochemical reactions in the atmosphere from primary and secondary OC materials (Updyke et al. 2012). The imaginary refractive index of BrC material can rapidly change as the BrC particles photochemically age in the atmosphere (Zhao et al. 2015). By contrast, BC is chemically inert in the atmosphere and even persistent after deposition on timescales from centuries to millennia (Coppola et al. 2022).

In this review, the author focused only on BC among all the light-absorbing aerosol components to elaborate on the recent advances in the in situ BC measurements and their contributions to the fundamental understanding of aerosol processes and the developments of the aerosol-climate model.

1.2 Black carbon

Owing to its high imaginary refractive index and relatively long atmospheric lifetime, BC is the largest contributor to global shortwave absorption in the present atmosphere among all the light-absorbing aerosol compounds (Samset et al. 2018; Sand et al. 2021). Atmospheric heating by BC reduces the global mean precipitation by compensating for the latent-heat transport from the surface to the atmosphere (Pendergrass and Hartmann 2012). BC deposited on snow-covered surfaces contributes to albedo reduction and accelerates the snowmelt (Flanner et al. 2007).

The morphology of each BC particle is known to be an aggregate of nanospheres. The diameter of each primary nanosphere (monomer) is typically 10–100 nm (Buseck et al. 2014). Each monomer consists of an onion-shell-like arrangement of graphene nanolayers (Buseck et al. 2014). The refractive index of each carbon monomer depends on the electronic structure of the carbon material, which is related to the degree of graphitization (Stagg and Charalampopoulos 1993; Bond and Bergstrom 2006). As the degree of graphitization of BC particles depends on the flame environment (Apicella et al. 2018), the refractive index of atmospheric BC could be variable depending on emission sources. The optical properties, such as the mass absorption cross section (MAC m2/g), of each BC particle depend on the refractive index of consisting monomers, morphological parameters of aggregate, and aggregate’s volume-equivalent size relative to the wavelength (Zheng and Wu 2021).

Each BC particle emitted from the combusting flame to the atmosphere rapidly undergoes internal mixing with other aerosol components (e.g., organic matter, sulfate, nitrate) through the condensation and coagulation process. Low-efficiency combustions such as wildfire produce high-concentration condensable organic molecules and carbonaceous aerosols with a high OC-to-BC ratio, resulting in instantaneous internal mixing of BC and OC within the dense smoke (Schwarz et al. 2008b). By contrast, relatively high-efficiency combustions such as vehicle engines produce carbonaceous aerosols with a much lower OC-to-BC ratio, resulting in the release of uncoated pure BC particles into the atmosphere (Schwarz et al. 2008b). Such BC particles undergo internal mixing with secondary aerosols (e.g., organics, sulfate) formed through the photochemical production of condensable gases from precursors (i.e., volatile organic compounds, sulfur dioxide, ammonia, etc.) (Shiraiwa et al. 2007; Riemer et al. 2010). Two dominant aerosol components mixed with BC are considered to be sulfate and organics because of the pervasiveness of these compounds in the atmosphere (Murphy et al. 1998; Thompson et al. 2022).

The BC-containing particles consisting of BC and non-BC materials are very different in climate-relevant properties from pure BC particles. Firstly, BC-containing particles consisting of BC core and non-absorbing coating materials have larger MAC per unit BC mass than pure BC particles due to enhancement of the electric field incident onto the BC core through “lensing effects” by the coating materials (Fuller et al. 1999). The MAC enhancement of ambient BC by coating may be up to ~ 60% depending on sources and aging (Liu et al. 2017). Secondly, BC-containing particles would be able to be cloud condensation nuclei (CCN) under modest supersaturations (~ 0.1%) in environmental clouds, whereas the pure BC particles are CCN inactive for their hydrophobic surface (Dusek et al. 2006; Kuwata et al. 2009). The coating materials on the BC core tend to become more hygroscopic with the aging of the plume (Ohata et al. 2016; Perring et al. 2017). The coating strongly affects the critical supersaturation of BC-containing particles in less-aged urban plumes (Zaveri et al. 2010). The thickness and hygroscopicity of the coating are, therefore, critical factors controlling the efficiency of vertical transport of BC through moist convection at the proximity of urban emission sources (Moteki et al. 2019).

In this review, we provide the historical backgrounds and recent advances of the in situ techniques for identifying and quantifying the BC and BC-containing particles after the mid-2000s. We clarify the unique roles of in situ BC measurements in recent advances in physical science basis on evaluating the effects of BC and other aerosols on climate (Fig. 1). This review on BC is intentionally focused on the research areas the author (N. Moteki) has made some original contributions, avoiding the areas already reviewed by previous studies (e.g., Bond and Bergstrom 2006; Ramanathan and Carmichael 2008; Moosmüller et al. 2009; Bond et al. 2013; Petzold et al. 2013; Kang et al. 2020; Liu et al. 2020a, b; Coppola et al. 2022).

Fig. 1
figure 1

Roles and relationships of the four different approaches in aerosol-climate research. Laboratory analyses of collected samples, in situ measurements, and remote sensing provide complementary observational information needed for reducing assumptions in the atmospheric chemical transport model (sub-module of the climate model)

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2 Measurement techniques

2.1 Backgrounds

BC is a ubiquitous aerosol component from the troposphere to the stratosphere, but its abundance is only a tiny fraction (< 2%) of total submicron aerosols mass in the global atmosphere, most of which is contributed by sulfate and organics (Gao et al. 2022). The minority of BC in the total aerosol carbon with various physicochemical properties makes the robust thermochemical identification of BC difficult (Cavalli et al. 2010; Karanasiou et al. 2015). Bulk optical methods for quantifying BC according to the absorption spectrum of a population of aerosol particles require the assumptions of the spectral refractive index of every potential contributor to the measured light absorption (Yang et al. 2009; Schuster et al. 2016). In addition to the uncertainties of the spectral refractive index, the change of light absorption efficiency of each absorbing component with particle’s size, morphology, and mixing state with non-absorbing compounds makes the bulk optical methods more susceptible to bias (Bond et al. 1999; Nakayama et al. 2010; Moteki et al. 2010a).

An observable particle-size measure of each BC aggregate depends on the measurement principle and procedure due to the non-spherical particle shape and internal mixing with other components (Kasper 1982; McMurry et al. 2002; Slowik et al. 2004; Kazemimanesh et al. 2022). BC aggregates change their original lacy shape to be more compact in the atmosphere as they experience collapsing through their aging and cloud processing (Bhandari et al. 2019). For these reasons, it has been difficult to quantify the size-resolved BC concentration with a size-sorting aerosol sampling followed by bulk BC analyses.

The single-particle laser-induced incandescence (LII) using an intracavity laser beam introduced around the mid-2000s (Stephens et al. 2003), a commercial version is known as single-particle soot photometer (SP2; Droplet Measurement Technologies Inc., Boulder, CO.), has extended our capability of identifying and quantifying atmospheric BC and BC-containing particles largely overcoming the difficulties mentioned above. The in situ data obtained by the SP2 instruments are routinely used in the aerosol-climate research community for investigating aerosol processes and testing and prescribing assumptions in other BC monitoring methods, aerosol remote sensing algorithms, and aerosol-climate models. We review the development history, principle, and known limitations of the single-particle LII in Sect. 2.2. We would use the word single-particle LII instead of SP2 as we focus here on the physical principle, independent of the supplier’s actual implementation of the hardware and software.

Section 2.3 reviews complex amplitude sensing (CAS) (Moteki 2021), a generic method for single-particle optical characterization of liquid-borne particles, which is also useful as a new approach for in situ BC measurements and explorations of BC refractive index.

2.2 Laser-induced incandescence

The laser-induced incandescence (LII) using pulsed lasers has long been used in combustion sciences for the noninvasive characterization of concentrations and microphysical properties of soot particles in flame (Vander Wal and Weiland 1994; Schulz et al. 2006; Michelsen et al. 2015). In the pulse LII approach, each high-energy pulse of a laser beam emitted from the light source (e.g., Nd:YAG laser) is expanded to irradiate a flaming volume that contains a population of soot particles. Then, the thermal radiation at visible-to-near-infrared wavelengths, also called incandescence, emitted from soot particles heated up to their vaporization point ~ 4200 K, is detected at several wavelength bands by photodetectors or image sensors. The simultaneous LII measurement at several (at least two) wavelength bands is needed for estimating the soot temperature from the spectral dependence of emitted thermal radiation. LII signal intensity at each wavelength band is proportional to the soot volume concentration within the sensing region. Imaging LII intensity distributions resolves the soot-forming regions and soot population growth within the flame (Ni et al. 1995). The rate of cooling of soot particles after the excitation pulse inferred from a fast time-resolved measurement of LII signals is used to estimate the mean monomer size of soot aggregates (Vander Wal et al. 1999; Axelsson et al. 2000). The pulse energy density for LII excitation within the sensing volume is determined between the lower limit that is needed to heat soot particles to vaporization point and the upper limit at which vaporization loss of soot during the pulse excitation starts to be apparent (Vander Wal and Jensen 1998). The laser wavelength for LII excitation should be selected to reduce the interferences from fluorescence emission of clusters of carbon atoms (Goulay et al. 2009). The longer excitation wavelengths are preferable to suppress fluorescence at the LII monitoring visible wavelengths, whereas the particle’s heating efficiency is higher in shorter excitation wavelengths (Schulz et al. 2006). The near-infrared 1064 nm wavelength of Nd:YAG laser or its second harmonic 532 nm was primarily employed for LII excitation in practice (Michelsen et al. 2015).

Although the pulse LII approach is used for monitoring the volume concentration of BC particles in engine exhaust gases (Snelling et al. 1999), it is not practical for field observations due to the very low and highly variable BC concentrations in the atmosphere. Pulse-hit probability can be increased if the excitation pulse is triggered by the particle’s scattering signal from another continuous wave (CW)-operating laser beam just upstream of the LII excitation region, as has been done in the single-particle laser mass spectrometers (Murphy 2007). Even so, BC detection frequency in ambient air samples will remain too low to obtain size-resolved statistics in real-time as the fraction of aerosol particles containing BC aggregate will be one-to-several orders of magnitude lower than BC-free particles (Matsui et al. 2011).

The particle detection frequency drawback of pulse LII for atmospheric applications has been concisely solved by the single-particle LII technique using an intracavity CW-laser beam (Stephens et al. 2003). The single-particle LII uses the CW-laser beam building up inside a solid-state laser cavity to excite the LII signal from every BC (and other metallic) particle in the sample gas jet focused into the intracavity beam. The original single-particle LII instrument by Stephens et al. (2003) employed the 1064 nm Nd:YAG laser cavity pumped by an 808 nm fiber-coupled diode laser (< ~ 4W). This diode-pumped Nd:YAG 1064 nm laser system has been employed by most of the single-particle LII instruments developed so far for its practical energy efficiency, stability, and cost advantages. The original instrument by Stephens et al. (2003) integrated four independent light-collection optics with different optical filters to be able to simultaneously monitor four different signals from each particle during its transition across the intracavity beam: three of which were used for LII signals at various wavelength bands, one of which was used for scattering signal at 1064 wavelength. The waveform of the scattering signal was initially used as an indicator of the particle’s vaporization in the laser beam. An appreciable shrink of an incandescing particle in the laser beam is experimental evidence that the particle’s temperature has reached the material-specific vaporization point at the peak of LII signals. The signal intensity ratios between the three LII channels were used for identifying incandescing material according to the difference in vaporization temperature. Although Stephens et al. (2003) demonstrated single-particle LII’s capability to identify individual flame soot, graphite, and several metallic particles, they did not investigate the possibility of quantifying the climate-relevant properties of single BC particles (e.g., size, mixing state).

Baumgardner et al. (2004) reported the first application of a single-particle LII instrument (single-particle soot photometer: SP2 commercialized by Droplet Measurement Technologies) to field observations. Determining single-particle BC mass from the LII signal in field observations requires a laboratory calibration of their empirical relationship using an appropriate standard BC sample. Baumgardner et al. (2004) used a spherical glassy carbon powder to sort particle mass using a conventional electrical mobility particle-size classifier (Knutson and Whitby 1975). The potential artifacts of using the spherical glassy carbon as an LII calibration standard material for quantifying non-spherical BC aggregates were not evaluated then.

Schwarz et al. (2006) and Slowik et al. (2007) employed flame-generated soot as more similar materials with ambient BC aggregates for calibrating the LII-to-mass relationship within 2–30 fg mass range (130–320 nm volume-equivalent diameter dv, assuming 1.8 g cm−3 density). In the calibration, they indirectly estimated the mass of flame-generated soot particles sorted at a particular mobility diameter by scanning their distribution in vacuum aerodynamic diameter, as a direct method for sorting the mass of non-spherical aerosol particles had not yet been available. Schwarz et al. (2006) observed that the LII signal amplitude was linearly proportional to the mass of flame-generated soot at 2–30 fg and that the linear relationship (e.g., slope) was unchanged with the fractal dimension of soot aggregates. They employed the linear LII-to-mass relationship for ambient BC measurements, extrapolating the calibration line at mass ≤ 30 fg to larger particles up to ~ 800 fg (dv ~ 950 nm). Although the accuracy of this extrapolation had not been thoroughly evaluated then, Schwarz et al. (2006) are regarded as a pioneering work providing quantitative altitude profiles of ambient BC concentration from the troposphere to the lower stratosphere for the first time by using a well-characterized single-particle LII instrument.

Moteki and Kondo (2007) have experimentally shown that even thick coating on the BC core by low-volatility organic materials (glycerol and oleic acid) does not affect the single-particle LII signals from the BC core. They also provided physical interpretations of the observed LII and scattering signal waveforms of BC-containing particles using a numerical model simulating the time-dependent particle’s properties in an intracavity laser beam.

Gao et al. (2007) developed a novel method to directly measure the time-dependent position of the particle translating across an intracavity Gaussian laser beam by using a position-sensitive multi-element scattering detector placed at one of the four optical detection channels in the SP2 instrument. The scattering signal waveform from the position-sensitive detector enables a reconstruction of the scattering amplitude of each particle before evaporation. The coating thickness on the BC core can be theoretically estimated from the scattering amplitude of the BC-containing particle before evaporation. Moteki and Kondo (2008) developed another method to estimate the time-dependent position of each scattering particle translating across a Gaussian laser beam from the normalized derivative of the scattering signal waveform. This method enables a single-particle quantification of coating thickness on the BC core without installing a multi-element photodetector instead of a single-element photodetector. Although the random measurement error in Moteki and Kondo (2008)’s method is more susceptible to background noise in scattering signal waveform than Gao et al. (2007)’s method, the former will also be practically advantageous as it enables a reconstruction of the time-dependent scattering cross section of BC-containing particle using only a signal waveform from a single light-scattering photodetector. Later, the time-dependent scattering cross section of each incandescing particle was found to help identify the morphological type (attached or coated type) of BC-containing particles (Moteki et al. 2014) as well as for categorizing incandescing iron oxide particles either of anthropogenic or desert dust origin (Moteki et al. 2017).

Moteki and Kondo (2010) characterized the LII-to-mass relationships for various BC samples using a newly available device for sorting the mass of aerosol particles accurately according to the balance between centrifugal and electrostatic forces acting on the aerosols (aerosol particle mass analyzer (APM); Ehara et al. 1996). APM enabled for the first time a sorting of aerosols by mass without particle shape-dependent bias and allowed the accurate calibration of single-particle LII instruments using non-spherical BC particles. Moteki and Kondo (2010) showed that the LII-to-mass relationship depends on both particle’s refractive index and shape. The observed dependences were physically interpretable by the generalized Kirchhoff’s law (Rytov 1953), as experimentally confirmed by Moteki et al. (2009) and Moteki et al. (2011). The linear proportionality between LII signal amplitude and BC mass, frequently assumed in SP2-related publications, is satisfied only if the radiation at the wavelengths used for incandescence detection (typically within 300–750 nm) can penetrate the entire volume of a BC particle if the radiation counterpropagating from the observation point incident onto the BC particle. This condition is satisfied when the size of BC aggregate is smaller than the wavelengths. In larger particle-size domains, the LII-to-mass relationship becomes nonlinear and strongly depends on the compactness of particle shape. Moteki and Kondo (2010) could not concretely demonstrate the dependence of the LII-to-mass linear slope to the BC refractive index at the smaller particle-size domain because of the several theoretical assumptions in their method for refractive index estimation (Moteki et al. 2010b). An experimental determination of the refractive index of BC at visible wavelengths has been one of the open problems in aerosol-climate sciences, which will be discussed again in Sect. 3.

Because of the similarity in LII-to-mass linear slope at the smaller size domain with ambient BC and diesel soot particles (Laborde et al. 2012) and the ease of particle generation, fullerene soot (Alfa Aesar Inc.) has been recommended as a standard BC powder material for calibrating single-particle LII instruments (Baumgardner et al. 2012). At the larger particle-size domain (i.e., size >  ~ LII wavelength), nonlinearity due to the shape effects should be considered. This consideration is crucial in measurements of BC mass concentration in rain and snow samples, wherein the BC size distributions tend to shift larger than in the atmosphere (e.g., Schwarz et al. 2013; Kinase et al. 2020; Mori et al. 2021).

The single-particle LII method is also able to detect light-absorbing iron oxides from desert dust (Liu et al. 2018) and anthropogenic combustion sources (e.g., vehicles) (Moteki et al. 2017; Ohata et al. 2018). Laboratory experiments showed that the particle’s incandescence efficiency in a given operating laser power of black-colored iron oxides (magnetite and wüstite) is comparable to BC, whereas red-colored hematite showed lower efficiency. Notably, the LII-to-Fe-mass relationship was observed to be identical among wüstite, magnetite, and hematite (Yoshida et al. 2016; Mori et al. 2023). In addition, the LII signal’s particle-size and spectral dependences agreed with the theoretical emission cross section according to Mie theory (Yoshida et al. 2018). These results suggest that each solid non-spherical particle consisting of any of wüstite (Fe(II)), magnetite (Fe(II, III)), and hematite (Fe(III)) has transformed into a molten iron (Fe) droplet in a laser beam before it starts to incandesce at boiling point (~ 3300 K). This fact allows theoretical extrapolation of the LII-to-Fe-mass relationship assuming spherical Fe particle beyond the upper particle mass limit sortable using the APM, that is, ~ 1000 fg or ~ 700 nm in volume-equivalent diameter (Yoshida et al. 2016; Mori et al. 2023). This extrapolation is essential in atmospheric measurements as most of the anthropogenic iron oxide mass concentration is distributed beyond ~ 700 nm volume-equivalent diameter (Moteki et al. 2017; Yoshida et al. 2020).

After the above development efforts over two decades, the single-particle LII method, also known as commercialized instrument SP2, has become a standard method for identifying and quantifying BC and BC-containing particles in the atmosphere essentially without the limit of lowest detectable number concentration. The single-particle LII with a nebulizer has also been the quantitative method for measuring BC in precipitated freshwater samples (e.g., rainwater, snowpack, ice sheets).

Corbin and Gysel-Beer et al. (2019) demonstrate the possibility of identifying strongly light-absorbing spherical BrC particles (i.e., tarball; Pósfai et al. 2004) using the single-particle LII.

2.3 Complex amplitude sensor

We briefly review another recent method for optical particle characterization, the complex amplitude sensor, which is useful for in-line BC measurements. The complex scattering amplitude S = ReS + iImS =|S|ei∆ represents the amplitude |S| and phase shift ∆ of the scattered field relative to those of the plane-wave field incident to the scattering particle (van de Hulst 1957). The S is a function of the angle θ between the incident beam and observation direction. The S reflects the physical properties of the scattering particle, such as refractive index, volume, shape, and orientation, and thus plays pivotal roles in optical particle characterizations and remote sensing of aerosols and clouds (Jones 1999; Romanov and Yurkin 2021). Light-scattering sensors, including the optical particle counters, nephelometers, and remote sensing methods for reflected and scattered radiations, are designed to measure the power of the scattered field |S(θ)|2 at θ ≠ 0°, avoiding the direct optical beam of the incident field. On the other hand, light extinction sensors, including occultation single-particle sensors, cavity-ringdown extinction spectroscopies, and remote sensing methods for direct radiation, are designed to measure the interference power of the scattered and incident fields in the forward direction ImS(0°) by monitoring the direct beam (Mishchenko 2014). Simultaneous measurement of both \(\mathrm{Re}S\) and \(\mathrm{Im}S\) of suspended single particles has not been possible until recently because of its technical difficulties, as reviewed in Moteki (2021).

The self-reference interferometry of a forward-scattered field of single particles excited by a focused Gaussian beam, proposed by Giglio and Potenza (2011) and demonstrated by Potenza et al. (2015), has been further refined by Moteki (2021) as a principle to be able to measure the complex forward-scattering amplitude S(0°) of single particles in liquid flow. We refer to it as complex amplitude sensor/sensing (CAS). The theoretical principle and hardware requirements for CAS have been described in Moteki (2021). The single-particle S(0°)-measurements with CAS enable a rigorous optical characterization of single spherical non-absorbing particles, which have only two unknown parameters (i.e., the real part of refractive index and diameter). The single-particle S(0°)-measurements enable the identification and classification of different particle populations (e.g., black carbon, mineral dust, bacteria) coexisting in an environmental water sample, thanks to the sensitivity of the location of S(0°)-cluster to the difference in material properties (complex refractive index, shape) of the size-distributed particle population (Yoshida et al. 2022). Moteki (2020) proposed an algorithm to constrain each particle population’s complex refractive index, shape, and volume-equivalent size distribution from a distinct S(0°)-cluster. This algorithm has been further refined by Moteki et al. (2023) and used to constrain the real and imaginary parts of the refractive index of ambient BC, as to be detailed in Sect. 3.4.

3 Observational findings

3.1 BC in the global atmosphere

BC mass concentration in the atmosphere had been nearly unknown before the single-particle LII (SP2 and its modified versions) became available for field observations. Here, we review the basic knowledge of atmospheric BC revealed from the single-particle LII. BC mass mixing ratio in the midlatitude continental atmosphere shows a steep vertical gradient in the lower troposphere, decreasing from ~ 100 ng (kg air)−1 near the surface to ~ 1 − 10 ng (kg air)−1 in the middle troposphere (Schwarz et al. 2006). BC mass mixing ratio level could be ~ 10 times larger than this profile in the regions around large emission sources (e.g., East Asia) (Oshima et al. 2012; Kondo et al. 2016). BC mass mixing ratio in the remote Pacific ocean was within the range of ~ 0.1 − 10 ng (kg air)−1 with a weak vertical gradient in the lower-to-upper troposphere (Schwarz et al. 2010; Katich et al. 2018). BC mass mixing ratio over the remote Atlantic Ocean tends to be substantially higher than the Pacific Ocean due to the proximity to continental sources in midlatitudes and the strong influence of African biomass burning in tropical latitudes (Katich et al. 2018). The BC mass fraction was ~ 1–2% or less of the total submicron aerosol mass (Schwarz et al. 2006; Gao et al. 2022). BC mass mixing ratio in the tropical tropopause layer, which is a gateway of injection of tropospheric aerosols into the stratosphere, was found to be ~ 1 ng (kg air)−1 (Gao et al. 2008), which was similar to the average value in the upper troposphere to lower stratosphere over the midlatitude (Schwarz et al. 2006). The global atmospheric BC data from the surface to upper troposphere are essential to evaluate the model assumptions on the emission and transport processes, as the new atmospheric BC dataset had revealed the model bias of a factor of ~ 10 or more in remote regions and higher altitudes (e.g., Koch et al. 2009; Wang et al. 2014; Katich et al. 2018). The observational datasets of BC mass mixing ratio in the global troposphere play critical roles in testing the assumptions of the parameters controlling the BC lifetime (e.g., the timescale of hydrophobic to hygroscopic conversion, in-cloud scavenging efficiency) in global models (Kipling et al. 2013; Hodnebrog et al. 2014; Lund et al. 2018; Liu and Matsui 2021).

Particle-size distribution of BC mass mixing ratio is approximated well with a log-normal distribution with the mode at ~ 200 ± 50 nm volume-equivalent BC core diameter, being reasonably independent of location and altitude up to the lower stratosphere (Schwarz et al. 2008a, 2010; Spackman et al. 2010; Kondo et al. 2011a; Laborde et al. 2013; Reddington et al. 2013; Schulz et al. 2019; Yang et al. 2019; Yoshida et al. 2020; Ohata et al. 2021b). Even though fresh urban plumes could exhibit smaller BC core size distribution <  ~ 150 nm (Schwarz et al. 2008a; Laborde et al. 2013), the smaller distribution near the urban area will be of minor significance in regional-to-global scale as it transforms via coagulations to the stable distribution with the mode at ~ 200 nm in ~ 1 day after emission (Moteki et al. 2007; Miyakawa et al. 2017). Simultaneous observations of BC core size distribution in the atmosphere and rainwater provided observational evidence of the predominance of nucleation scavenging as a process controlling the efficiency of wet removal of submicron aerosols (Ohata et al. 2016; Moteki et al. 2019). Preferential removal of larger aerosol particles (with less critical supersaturation) through moist convections tends to shift the BC size distribution to smaller in cleaner, particle-free air masses (Moteki et al. 2012; Taylor et al. 2014; Schulz et al. 2019). The two opposite size-regulating processes control the size distribution of BC in the atmosphere: the coagulation growth in the dense plumes just after emission and the preferential removal of larger BC through cloud-precipitation processes.

The number fraction of internally mixed BC particles, as well as the thickness of the coating on the BC core (evaluated at ~ 200 nm BC core size), showed marked contrast between fresh urban plumes and fresh biomass-burning plumes: Thickly coated BC particles are far more dominant in biomass-burning plumes (Schwarz et al. 2008b; Kondo et al. 2011a). The thickness of the coating on BC particles in a fresh urban plume was found to increase with the production of secondary aerosols (e.g., sulfate and organics) as the plume ages in the atmosphere (Moteki et al. 2007; Shiraiwa et al. 2007; Miyakawa et al. 2017). The average coating thickness (evaluated at ~ 200 nm BC core diameter) was larger in the upper troposphere to lower stratosphere than in the lower-to-middle troposphere (Schwarz et al. 2008a). BC coating thickness over the Arctic region, dominated by a mixture of aged and cloud-processed aerosols, was approximately independent of altitude from the surface to ~ 5 km (Kodros et al. 2018; Ohata et al. 2021b). The degree of internal mixing of BC tends to be positively correlated with the total aerosol mass to BC mass ratio, which is an indicator of secondary aerosol production in the urban plume or the degree of contribution of the biomass-burning plume (Schwarz et al. 2008a, b; Moteki et al. 2014). Moteki et al. (2014) developed a method to classify the morphology of BC-containing particles into coated type and attached type according to the single-particle LII signals. They found that the number fraction of attached type was only ~ 1% even in fresh urban air (Adachi et al. 2016), suggesting that the attached-type BC-containing particles are negligible in the atmosphere. Recent re-analyses of worldwide ground-based observation datasets revealed that the coating thickness of BC-containing particles universally follows exponential distributions, the parameters of which were pretty independent of BC core size and location (Wang et al. 2022). This suggests a possibility of a succinct but accurate representation of the BC mixing state in global aerosol models.

Observational results on microphysical properties of BC-containing particles obtained by the single-particle LII have been used for testing the recent aerosol models that explicitly simulate the BC aging process (Oshima et al. 2009; Matsui et al. 2013; Oshima and Koike 2013). Simulation accuracy of particle-size distribution and mixing state of BC is of fundamental importance for predicting atmospheric BC burden and its radiative effects, as the aging and cloud-droplet activation parameterizations are considered to be significant sources of uncertainty (Textor et al. 2006; Vignati et al. 2010; Moteki et al. 2019; Yu et al. 2019a, b; Holopainen et al. 2020; Matsui and Moteki 2020).

The new observational results obtained by the single-particle LII have also been used for updating the aerosol optical models for remote sensing algorithms (Schuster et al. 2022).

3.2 Comparison of single-particle LII with other BC measurements

The thermal-optical and filer-based light absorption methods were two primary techniques used for measuring BC mass concentration in ambient air, snow, and ice samples before the invention of single-particle LII. A notable advantage of thermal-optical and filter-based light absorption methods compared with the single-particle LII is their applicability to BC samples with any particle-size range. Pileci et al. (2021) reported that ambient-mass concentrations of refractory carbon derived from thermal-optical and single-particle LII methods could differ within a factor of ~ 2. The BC measurement bias in filter-based light absorption methods can be largely suppressed by removing volatile aerosol components using a heated aerosol inlet (Kondo et al. 2009; Irwin et al. 2013; Ohata et al. 2019), as demonstrated in fresh urban pollutions (Kondo et al. 2011b) and Arctic atmosphere (Ohata et al. 2021a).

3.3 Anthropogenic iron oxide

The in situ aerosol measurements using single-particle LII and laboratory analyses of collected aerosol samples using a transmission electron microscope (TEM) revealed that anthropogenic light-absorbing iron oxides (FeOx) consisting of an aggregate of magnetite nanoparticles are ubiquitous in the urban plumes and the East Asian and Arctic troposphere (Moteki et al. 2017; Ohata et al. 2018; Yoshida et al. 2018). The mass mixing ratio of anthropogenic FeOx in these regions was ~ 20–60% of BC (Yoshida et al. 2020). The anthropogenic FeOx aerosol is likely ubiquitous in the global troposphere (Lamb et al. 2021) and will be one of the contributors to regional-to-global-scale aerosol’s shortwave absorption (Moteki et al. 2017; Matsui et al. 2018; Ito et al. 2018). These new observation data provided further evidence to constrain the magnitude and spatial distribution of anthropogenic Fe emission (Rathod et al. 2020; Liu et al. 2022), which is an essential factor for investigating the effects of Fe-bearing aerosols on ocean fertilization (Hamilton et al. 2020; Ito et al. 2021).

3.4 BC refractive index

The complex refractive index \(m={m}_{r}+i{m}_{i}\) is possibly the most critical climate-relevant property of atmospheric aerosols as it largely determines the efficiency of absorption and scattering of solar radiation by particles. Refractive indices of non-light-absorbing aerosol materials (e.g., sulfate, organics, aluminosilicates, sea salt) at visible wavelengths are around \({m}_{r}\) ~1.5 ± 0.05 under dry conditions. By contrast, refractive indices of insoluble light-absorbing materials (BC, iron oxides, insoluble BrC) are still not sufficiently known.

Experimental determination of the refractive index of a particulate material always requires a close comparison between rigorous light-scattering theory and accurate optical measurements. The theory-to-measurement comparisons have been technically challenging for BC aggregates in the atmosphere due to their wavelength-scale irregularity of particle shape and mixing with other aerosol components.

Currently, assumptions of BC refractive index at visible wavelengths are mostly chosen between the lower and upper limits recommended by Bond and Bergstrom (2006), 1.75 + 0.63i (BB06-l) and 1.95 + 0.79i (BB06-h), respectively. The recommendation was based on a compilation of experimental results for synthetic BC samples (e.g., propane–oxygen flame soot, carbon black) obtained earlier than the early-2000s. The validity of the BB06 is still being determined as experimental methods in the early-2000s include various assumptions (e.g., spherical BC shape). The refractive index of atmospheric BC material could be variable and different from any synthetic carbon material.

Liu et al. (2020b) pointed out that the theoretically computed mass absorption cross section (MAC, m2/g) of uncoated BC aggregates using BB06 refractive indices underestimated the experimental MAC values by ~ 30%. This systematic discrepancy suggests that further investigations on BC refractive index are still needed.

Moteki (2020) proposed a method for estimating the refractive index of waterborne particles from the measured distribution in complex forward-scattering amplitude S(0°). Moteki et al. (2023) improved this approach using an updated S(0°)-measurement protocol (Moteki 2021) and a more sophisticated inverse-scattering model for BC aggregates. They applied the method to constrain the ambient BC refractive index collected from the atmosphere over the northwestern Pacific Ocean at 633 nm wavelength. From the new S(0°) data for atmospheric BC and recently reported MAC values for various types of flame-generated BC, Moteki et al. (2023) constrained a plausible (mr, mi) domain that contains the BC refractive index at 633 nm wavelength:

$$\left\{\begin{aligned} 0.51 & + 0.014{m_{r}^{5.2}} \le {m_{i}} \le 2.5{m_{r}} - 3.5 \; {\text{if}} \; 1.7 \le {m_{r}} \le 1.8 \\ & 0.51 + 0.014{m_{r}^{5.2}} \le {m_{i}} \le 1.5 \; {\text{if}} \; 1.8 < {m_{r}} \le 2.2. \end{aligned}\right.$$

Even though the BB06 values are currently “accepted” in the climate and atmospheric science community, they are located outside the plausible (mr, mi) domain constrained from the new experimental evidence. The persistent ~ 30% underpredictions of MAC using the BB06-l or BB06-h value pointed out by Liu et al. (2020b) will be mitigated if its imaginary part is increased to a value inside the suggested (mr, mi) domain.

For straightforward applications of the new constraint of BC refractive index by climate and atmospheric research, Moteki et al. (2023) suggested a recommendable mr + mi value from the constrained (mr, mi) domain, 1.95 + 0.96i, which was determined by increasing the imaginary part of the BB06-h to the lower mi boundary of the plausible (mr, mi) domain (Fig. 2). Assuming the 1.95 + 0.96i instead of the BB06-h (1.95 + 0.79i) will result in a ~ 16% increase of calculated shortwave absorption by BC-containing aerosols. This implies a non-negligible underestimate of shortwave absorption by black carbon aerosols in current climate simulations using BB06-h.

Fig. 2
figure 2

Illustrating the three-different (mr, mi) domains for the complex refractive index of BC.: 1) The domain consistent with measured S(0°) for atmospheric BC (enclosed by black-dashed lines), 2) the domain consistent with measured MAC for various flame-generated BCs (red-filled area), and 3) the domain constrained by both MAC- and S(0°)-measurements (Moteki et al. 2023). The conventional assumptions BB06-l (1.75 + 0.63i) and BB06-h (1.95 + 0.79i) (gray-filled circles) and the recommendable value for practical uses 1.95 + 0.96i (blue-filled circle) suggested by Moteki et al. (2023) are also plotted

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4 Open problems and suggestions

4.1 BC measurement techniques

The most important open issue of the current single-particle LII technique is the uncertainty or difficulty of measuring BC particles much larger than the visible wavelengths. Current commercial single-particle LII instruments (e.g., SP2 from Droplet Measurement Technologies, Inc.) are designed to detect BC core within ~ 70–500 nm volume-equivalent diameter. The NOAA SP2 instruments used for global-scale aircraft observations were intended to measure ~ 70–550 nm BC core (Schwarz et al. 2010; Katich et al. 2018). Aircraft and ground observations using the single-particle LII instrument of The University of Tokyo (a modified version of SP2; Moteki and Kondo 2010), which detects 70–850 nm BC core, indicated a non-negligible contribution of BC with >  ~ 500 nm diameter to size-integrated BC mass mixing ratio (Kondo et al. 2016; Yoshida et al. 2020). This implies the significance of extending the upper limit of the BC core size range observable by single-particle LII instruments at least up to ~ 1000 nm. The importance of extending the LII-detectable particle-size range is even more evident for FeOx (Moteki et al. 2017; Lamb et al. 2021). The author therefore suggests fundamental investigations for extending the upper limit of the observable particle-size range in the single-particle LII.

Another important open issue on the current BC measurement technique is the lack of measurement principles applicable to various types of sample fluids. For example, single-particle LII is currently not able to apply to the BC particles suspended in high-solute concentration fluids such as ocean water. One of the unique advantages of the CAS compared with single-particle LII is its applicability to in situ single-particle measurements of any insoluble particles suspended in any transparent liquids (e.g., freshwater, ocean water, organic solvents). The CAS is a potential tool for in situ real-time measurements of BC in ocean water. In addition, the CAS will be able to measure both BC and mineral dust particles coexisting in an environmental water sample (Yoshida et al. 2022). The author suggests investigations on CAS technique to be able to use it for in-line measurement of size-resolved number concentrations of BC particles in various types of environmental fluids. Before the wide applications, consistencies in the quantified physical properties (e.g., BC mass) between single-particle LII and CAS should also be established.

4.2 BC outside the troposphere

Observational understandings of BC outside the troposphere still need to be improved. BC exerts stronger radiative effects per unit mass in the stratosphere than in the troposphere due to its longer lifetime and higher actinic flux. It was known that biomass-burning (BB) plumes from wildfires could penetrate the tropopause and intrude into the lower stratosphere through strong convective systems (Jost et al. 2004; Ansmann et al. 2018). Sporadic intrusions of BB plumes enhance the annual mean BC mass mixing ratio of the lowermost stratosphere over Europe and North America by about ~ 75% from the regional background (Ditas et al. 2018). Strong shortwave absorption by BC drives buoyant uplift of the injected plumes in the stratosphere (Yu et al. 2019b, 2021; Gao et al. 2021). Further understanding of the origins, physicochemical properties, and removal processes of stratospheric aerosols are needed (Kremser et al. 2016; Murphy et al. 2021) to predict the effects and side-effects of the stratospheric aerosol injection for solar radiation management (e.g., Niemeier and Timmreck 2015). The author suggests that in situ BC measurements in the stratosphere help to develop the fundamental understanding as BC is an inert particle tracer of combustion-originated tropospheric materials.

BC in the cryosphere has been actively investigated for its importance as a climate forcer and as a proxy of historical environmental changes (Kang et al. 2020). BC embedded in the ice sheets can provide information on the historical record of atmospheric concentration of combustion-induced aerosols (e.g., McConnell et al. 2007; Winstrup et al. 2019). BC significantly contributes to snow albedo reduction in polar regions and midlatitude glaciers (Flanner et al. 2007; Skiles et al. 2018). It was estimated that BC is the second largest contributor to positive radiative forcing among all the anthropogenic gases and aerosols in Arctic regions due mainly to its effects on snow albedo reduction (Oshima et al. 2020). However, the interpretation of BC-in-snow observations is still controversial due to the complex processes that affect BC concentration and microphysical properties after deposition (e.g., Schmitt et al. 2019). Particle-size distribution of BC-in-snow and BC-in-glacier tends to be substantially larger than the BC-in-atmosphere for unknown physical mechanisms (Schwarz et al. 2013; Zhang et al. 2017; Mori et al. 2019; Kinase et al. 2020). The larger shift of BC size distribution might cause an underestimate of BC mass concentration measured by some commercial single-particle LII instruments without extending the detectable BC size range. The author suggests the importance of further improvements of BC measurement techniques for snow and ice-sheet samples in terms of accuracy and ease of operation. That should help to accelerate understanding of the physical properties and processes of BC in the cryosphere.

BC is persistent in the natural environment on timescales of centuries to millennia (Goldberg 1985). Occurrences of wildfires and burnings of fossil fuel and biofuel modify the turnover rate of the global carbon cycle by converting relatively labile organic carbon to more environmentally persistent, slowly cycling BC (Coppola et al. 2022). A large fraction of BC particles emitted into the atmosphere will be input into the ocean. BC is the largest slow-cycling organic carbon reservoir in the ocean (e.g., Yamashita et al. 2022). The current standard analytical methods for BC in ocean water were designed to quantify the dissolved refractory aromatic molecules (dissolved BC) (e.g., Dittmar 2008), which is different from the analytical methods for particulate BC in the atmosphere (Coppola et al. 2022). A quantitative estimate of the oceanic BC budget requires atmospheric BC data (Bao et al. 2017). However, the consistency of the current BC datasets available from atmospheric and oceanic disciplines is nearly unknown. The author suggests that the CAS would help to provide consistent particulate BC datasets in the atmosphere, cryosphere, and ocean.

5 Conclusive remarks

We reviewed recent advances in in situ measurement methods and observational findings since the mid-2000s on atmospheric BC aerosol, one of the most important short-lived climate forcers. Quantification of climate-relevant properties of atmospheric BC and BC-containing particles has been continually updated over two decades. The single-particle LII has been playing an important role in field observations and observation-based updates of assumptions in climate models and remote sensing algorithms. Although the global anthropogenic BC emission from fossil fuel burning is expected to decrease owing to the clean air act, natural BC emissions from wildfires and the occurrence of BC injection to the stratosphere may increase globally with greenhouse gas-induced climate change. Further developments in the measurement methods and observational knowledge on environmental BC should help improve the predictabilities of short-term climate response to atmospheric composition and the long-term global carbon cycle.