Modelling light-absorbing particle–snow–radiation interactions and impacts on snow albedo: fundamentals, recent advances and future directions

Keywords: aerosol, climate, global cryosphere, light absorption and scattering, light-absorbing particles, snow albedo, snow radiative transfer, solar radiation.

Snowpack is a key component of the Earth system, which modulates the surface energy balance, hydrological cycle and climate feedback. It also provides critical water resources for drinking, irrigation, hydropower and fishery (Barnett et al. 2005; Bales et al. 2006). Snow albedo, one of the most important snowpack properties, alters snowpack evolution and surface water and energy balance through a positive albedo feedback (Qu and Hall 2006; Painter et al. 2010; Flanner et al. 2011; Oaida et al. 2015). Snow albedo is affected by a number of key factors, including snow grain properties (e.g. size and shape), snowpack properties (e.g. density and depth), snow impurities and illumination conditions (e.g. solar zenith angle, direct/diffuse radiation and downward solar spectrum) (He and Flanner 2020, and references therein).

Light-absorbing particles (LAPs; Fig. 1), including black carbon (BC), mineral dust, brown carbon (BrC), volcanic ash and snow algae, have been found to significantly reduce snow albedo and cause a positive surface radiative forcing across the global cryosphere, which hence accelerates snow melting and glacier retreat (e.g. Jacobson 2004; Painter et al. 2010; Dumont et al. 2014; Peltoniemi et al. 2015; Qian et al. 2015; Di Mauro et al. 2017; Lee et al. 2017; Skiles et al. 2018; Pu et al. 2019; Tuzet et al. 2019; Gul et al. 2021). Numerous observational and modelling studies have been conducted in the past few decades to estimate the radiative forcing and hydroclimatic effects of LAPs in snow/ice, which have been nicely reviewed by a few recent papers (Qian et al. 2015; Skiles et al. 2018; Kang et al. 2020; Wang et al. 2020; Dumont and Tuzet 2022). However, there are still large uncertainties in the fundamental understanding and modelling of LAP–snow albedo interactions and associated radiative effects. In particular, several recent studies have revealed the important role of LAP–snow–radiation interactions at the particle level (e.g. LAP–snow mixing state, LAP coating and particle structure and snow microstructure) in altering snow albedo and radiative effects (e.g. Picard et al. 2009; Flanner et al. 2012; Liou et al. 2014; Dang et al. 2016; He et al. 2017a, 2019; Dumont et al. 2021; Pu et al. 2021; Shi et al. 2022a), which have not been systematically summarised. Therefore, this study seeks to synthesise recent advances, challenges and future directions in modelling LAP–snow–radiation interactions from microscopic (particle level) to macroscopic (bulk snow optical properties and albedo) perspectives, which makes it a unique review.

Fig. 1.  Demonstration of five major light-absorbing particles in snow obtained from transmission electron microscopy (TEM), including BC (a), mineral dust (b), BrC (c), ash (d) and snow algae (e). Adapted from Ren et al. (2017) with permission.

This paper is organised as follows. The fundamentals of LAP–snow–radiation interactions are first introduced. Pure snow optical properties and albedo are then described. The interactions between snow and BC, dust, BrC, volcanic ash and snow algae, respectively, and their impacts on snow albedo are then summarised. Finally, the key challenges and future directions in improving the understanding and modelling of LAP–snow–radiation interactions are presented.

He and Flanner (2020) present a comprehensive review of snowpack radiative transfer theory and albedo modelling. Thus, here we focus on the fundamentals of LAP effects on snow optical properties and albedo. Fig. 1 demonstrates typical transmission electron microscopy (TEM) images of different LAPs in snow. Fig. 2 summarises the key elements involved in LAP–snow–radiation interactions through snowpack radiative transfer. In general, snowpack radiative transfer computations require three key snow optical properties, including mass extinction cross section, asymmetry factor and single-scattering albedo (Wiscombe and Warren 1980). Mass extinction cross section represents the total light absorption and scattering per unit particle mass. Single-scattering albedo reflects the light scattering capability. Asymmetry factor indicates the forward scattering ability. These snow optical properties are determined by ice refractive index, snow grain size and shape via particle-optics computations such as Mie theory and geometric optics ray-tracing theory (Liou 2002; Liou et al. 2014).

Fig. 2.  A general flowchart for key elements in modelling the light-absorbing particle (LAP)–snow–radiation interaction and impact on snow albedo.

The ice refractive index database has been updated several times in the past decades (Warren 1984; Warren and Brandt 2008; Picard et al. 2016), which leads to several orders of magnitude differences in the imaginary part (i.e. light absorption ability) of ice refractive indices at ultraviolet (UV) and visible wavelengths and hence up to 0.1 differences in snow albedo at these wavelengths for large snow grains (Flanner et al. 2021). Typically, larger snow grain sizes lead to smaller single-scattering albedo (particularly at near-infrared (NIR) wavelengths) and mass extinction cross section but higher asymmetry factor (i.e. stronger forward scattering), resulting in stronger light penetration in snowpack and hence more light absorption by snowpack (if optically thick snowpack) or underlying ground (if optically shallow snowpack) and hence lower snow albedo (Wiscombe and Warren 1980; Flanner et al. 2021). Compared to spherical snow grains with equivalent specific surface area (or effective size), non-spherical snow grains (Fig. 3) have a lower asymmetry factor (i.e. weaker forward scattering, primarily at wavelengths <3 μm), which reduces solar radiation penetration in snowpack and hence light absorption by snowpack and/or underlying ground and consequently increases snow albedo (Libois et al. 2013; Dang et al. 2016; He et al. 2017a; Räisänen et al. 2017). Snow non-sphericity only has minor (<10%) effects on snow single-scattering albedo and mass extinction cross section (Liou et al. 2014; He et al. 2017a; Räisänen et al. 2017). In fact, previous studies proposed to represent non-spherical snow grains by effective spherical grains with the same specific surface area (or volume-to-area ratio) (e.g. Fu et al. 1999; Grenfell and Warren 1999; Neshyba et al. 2003; Grenfell et al. 2005), which works reasonably well for snow extinction efficiency and single-scattering albedo but is less accurate for asymmetry factor (Dang et al. 2016).

Fig. 3.  A demonstration of four typical non-spherical snow grain shapes (Liou et al. 2014) and light-absorbing particle (LAP)–snow external and internal mixing. Adapted from He et al. (2019).

LAPs can alter snow optical properties when mixed with snow grains because of the differences in LAP and snow optical properties. Specifically, pure snow has a very weak absorption of solar radiation (i.e. high single-scattering albedo > 0.99) at UV and visible wavelengths (Wiscombe and Warren 1980), whereas LAPs have a strong absorption at visible and/or UV wavelengths (Qian et al. 2015; Flanner et al. 2021), which leads to a lower single-scattering albedo (i.e. stronger light absorbing capability) of snow–LAP mixtures and hence lower snow albedo relative to pure snow (Warren and Wiscombe 1980). Snow albedo at UV and visible wavelengths are very sensitive to the change in snow single-scattering albedo and hence the inclusion of LAPs in snowpack (Warren and Wiscombe 1980). Traditionally, LAPs are assumed to be externally mixed with snow grains (Fig. 3), which results in the computation of optical properties of LAP–snow mixtures by averaging snow and LAP optical properties with the weights of their corresponding total and/or scattering optical depths (Flanner et al. 2007). However, recent studies found that different LAP–snow mixing states (external or internal mixing; Fig. 3) can result in substantial variations of LAP effects on snow light-absorbing ability, with strong absorption enhancements by LAP–snow internal mixing relative to external mixing (Flanner et al. 2012; Liou et al. 2014; He et al. 2017a, 2019; see also sections on BC–snow albedo and dust–snow albedo interactions below for details). LAPs only have minor effects on the mass extinction cross section and asymmetry factor of snow–LAP mixtures (Liou et al. 2014) partially due to the several orders of magnitude larger snow mass compared to LAP mass. In addition, LAPs can further interact with snow non-sphericity because the weaker forward scattering and hence reduced light penetration in snowpack caused by non-spherical snow grains relative to their spherical counterparts will reduce the light absorption by LAPs in snow and hence weaken the LAP effects on snow albedo (He et al. 2017a, 2018a).

In addition to the microscopic snow and LAP properties at the particle level, macroscopic snowpack properties (thickness and density), underlying ground albedo and illumination conditions (diffuse/direct radiation type and solar zenith angle) also alter snowpack albedo through radiative transfer processes (He and Flanner 2020 and references therein; see also Fig. 2), which further modulates the LAP effects on snow albedo (see further below for details). In general, larger snowpack density, snowpack thickness and solar zenith angle tend to reduce light penetration through snowpack and hence light absorption by snowpack and/or underlying ground, which increases snow albedo (Wiscombe and Warren 1980; Aoki et al. 2003; Flanner et al. 2021). Visible snow albedo is found to be very similar under direct and diffuse radiation, but NIR snow albedo varies noticeably with the fraction of diffuse radiation (Wiscombe and Warren 1980; Aoki et al. 2003; Dang et al. 2015). Recent studies also revealed the important role of small-scale snowpack surface roughness in leading to additional multiple surface light scattering and hence enhanced snow absorption of sunlight and reduced snow albedo (e.g. Warren et al. 1998; Zhuravleva and Kokhanovsky 2011; Larue et al. 2020; Manninen et al. 2021), which further complicates the LAP–snow–radiation interactions.

Moreover, a conventional assumption of snowpack radiative transfer calculations is the independent scattering approximation, where light absorption and scattering processes of each snow grain are independent of surrounding grains. This assumption is not always valid considering snow is often a densely packed medium particularly for wet snow (e.g. Colbeck 1982). Some studies (e.g. Kokhanovsky 1998) found that the snow asymmetry factor tends to be reduced by densely packed grain structures, while others (e.g. Peltoniemi 2007; He et al. 2017b) showed that densely packed snow grain aggregates lead to an overall reduction of snow albedo particularly at NIR wavelengths, mainly contributed by an increase of the effective snow grain size due to aggregating structures. This dense-packing effect further enhances the LAP effects on snow albedo (He et al. 2017b), which adds another complexity level to the LAP–snow interaction and needs to be investigated in more detail in future studies.

The effects of snow grain size, snowpack properties and illumination conditions on pure snow albedo have been documented in previous literature (e.g. Wiscombe and Warren 1980; Warren 1982; Aoki et al. 2003; He and Flanner 2020). Here we mainly discuss the effect of snow grain shapes on snow optical properties and albedo, which has recently gained renewed attention. For example, Kokhanovsky and Zege (2004) developed an Approximate Asymptotic Radiative Transfer (AART) theory for snow albedo calculation, which includes two key parameters (asymmetry factor and absorption enhancement parameter) dependent on snow grain shapes. Optical measurements showed large variations in the asymmetry factor and absorption enhancement parameter retrieved by the AART theory due to different observed snow grain microstructures (Libois et al. 2013, 2014). Recent measurements (Dumont et al. 2021) further indicated that, besides the snow grain specific surface area, snow microstructure such as grain shape plays an important role in controlling snow bidirectional reflectance, with faceted grains generally exhibiting stronger anisotropic reflectance than fragmented grains.

In addition, Räisänen et al. (2015) proposed a parameterisation of snow optical properties for a combination of three non-spherical snow shapes, including strongly distorted Koch fractals, severely rough droxtals and aggregates of severely rough plates, which showed large differences in optical properties (mainly asymmetry factor) compared to snow spheres. Using this parameterisation in a climate model, their follow-up study (Räisänen et al. 2017) found that snow non-sphericity leads to a higher broadband albedo by 0.02–0.03 and hence a global mean radiative effect of −0.22 W m⁻² and surface temperature cooling of 1.17 K. Dang et al. (2016) connected the asymmetry factor of non-spherical snow grains to grain effective size and aspect ratio using a physically based parameterisation for hexagonal ice crystals (Fu 2007), which leads to 0.03–0.05 higher broadband albedo for non-spherical snow grains than snow spheres. He et al. (2017a) further extended the Fu (2007) parameterisation of the snow asymmetry factor for two other typical shapes (spheroid and Koch snowflake/fractal; Fig. 3) based on explicit geometric-optics surface-wave (GOS) ray tracing calculations (Liou et al. 2014), which revealed up to a 0.15 lower asymmetry factor mainly at wavelengths <3 μm for non-spherical snow grains relative to spherical grains. This parameterisation has been implemented into a widely used snowpack radiative transfer model, the Snow, Ice, and Aerosol Radiative model (SNICAR; Flanner et al. 2007), which shows up to a 0.05 broadband albedo increase due to snow non-sphericity with greater increases for larger snow grain sizes (He et al. 2018a, 2018b; Flanner et al. 2021).

Moreover, the effect of snow grain shapes on snow albedo is modulated by snowpack properties and illumination conditions. Specifically, the snow albedo increase caused by snow non-sphericity reduces at wavelengths <~1.5 μm as the solar zenith angle (SZA) increases, whereas the opposite is true at wavelengths >~1.5 μm (Fig. 4a). The overall non-sphericity effect on visible and NIR narrowband snow albedo still decreases with an increasing SZA (Dang et al. 2016). The snow non-sphericity effect on albedo under diffuse radiation tends to be similar to that under direct radiation with a SZA of ~50° (Fig. 4a). A larger snowpack thickness or higher density (for a thin snowpack) generally reduce the effect of snow grain shapes mainly at wavelengths <1.0 μm (Fig. 4b, c). Overall, snow grain non-sphericity can increase broadband pure snow albedo by up to 0.15 depending on snow grain size, snowpack thickness, snow density and illumination conditions.

Fig. 4.  Differences between snow spheres and Koch snowflakes in pure snow albedo (the latter minus the former) vary with solar zenith angle (SZA; panel a), snowpack thickness (dz; panel b) and snowpack density (ρ; panel c) based on the Snow, Ice, and Aerosol Radiative (SNICAR) model (Flanner et al. 2021; https://github.com/mflanner/SNICARv3). The snowpack thickness is assumed to be 10 cm in panel (c).

BC (also known as soot) is an important carbonaceous aerosol component with the strongest light-absorbing ability among all LAPs (Bond et al. 2013). Traditionally, BC is assumed to be externally mixed with spherical snow grains (e.g. Warren and Wiscombe 1980; Hansen and Nazarenko 2004; Flanner et al. 2007; Aoki et al. 2011; Dang et al. 2015). The BC-induced snow albedo reduction varies with BC concentration in snow, snow grain size, wavelength, snowpack properties and illumination conditions (Fig. 5). In general, BC-induced albedo reductions tend to be stronger with higher BC concentrations in snow, larger snow grain sizes, larger snowpack thicknesses or higher snowpack densities (Warren and Wiscombe 1980; Aoki et al. 2011; Dang et al. 2015; see also Fig. 5). This is because larger snow grain sizes enhance light penetration in snowpack that contributes to more light absorption and albedo reduction by BC, while larger snowpack thicknesses or densities reduce the light absorption by underlying ground and hence enhance BC effects on snow albedo. The BC effect on snow albedo reduces with an increasing SZA under direct radiation (Fig. 5f), due to less light penetration in snowpack and hence less BC absorption in snow under a higher SZA. Assuming BC external mixing with snow spheres, the global annual mean BC-induced snow albedo forcing was estimated to be 0.01–0.09 W m⁻² (Bond et al. 2013) with hotspots over the Tibetan Plateau and northern China particularly during springtime (regional mean of >~5 W m⁻²; Flanner et al. 2007; He et al. 2014; Skiles et al. 2018; Pu et al. 2019; Yi et al. 2019). Based on in situ measurements of BC concentration in snowpack and BC–snow external mixing, Dang et al. (2017) estimated regional (snow-covered area) mean BC-induced snow albedo reductions of 0.005, 0.005 and 0.031 for fresh snow over the Arctic, North America and northern China, respectively, leading to snow albedo radiative effects of 0.06, 0.3 and 3 W m⁻². The aged melting snow further enhances the preceding BC-induced snow albedo reduction by a factor of two and hence 3–8 times stronger snow albedo effects partially due to higher downward solar radiation during melting seasons (Dang et al. 2017).

Fig. 5.  BC-induced snow albedo reductions for BC–snow external (dashed lines) and internal (solid lines) mixing as a function of BC concentration in snow (a), snow grain radius (b), snow grain shape (c), snowpack thickness (d), snowpack density (e) and solar zenith angle (f) based on the SNICAR model enhanced with BC–snow internal mixing parameterisations (He et al. 2018b). The BC concentration in snow in panels b–f is assumed to be 500 ppb.

However, the conventional assumption of BC–snow external mixing may not be always valid in reality since BC can be internally mixed with snow grains through complex BC atmospheric wet deposition processes (Flanner et al. 2012). Specifically, compared to BC–snow external mixing, BC–snow internal mixing can substantially increase snow single-scattering co-albedo (defined as one minus single-scattering albedo) and light absorption (Liou et al. 2014; He et al. 2017a) and hence enhance BC-induced snow albedo reductions and radiative effects by 30–86% (Jacobson 2004; Flanner et al. 2012; He et al. 2018a, 2018b; Dombrovsky and Kokhanovsky 2020; Shi et al. 2022a). Liou et al. (2014) further showed that BC–snow internal mixing by treating multiple BC particles randomly distributed within each snow grain results in much stronger albedo reductions than the internal mixing by treating all BC mass as one single large BC particle locating in the centre of each snow grain. In addition, the differences in snow albedo reductions caused by BC–snow internal and external mixing tend to be larger under higher BC concentrations in snow, larger snow grain sizes, thicker snowpack, higher snowpack densities, lower SZA and more spherical snow grains (Fig. 5).

Moreover, several other important factors can influence BC-induced snow albedo reductions. Specifically, snow non-sphericity has been shown to reduce BC-induced snow albedo reductions and radiative effects by up to 50% compared with snow spheres (Dang et al. 2016; He et al. 2018a, 2018b; Flanner et al. 2021; Shi et al. 2022a). Larger BC particle sizes tend to weaken the BC-induced snow albedo reductions (Warren and Wiscombe 1980; He et al. 2018c) mainly due to smaller BC mass absorption cross sections for larger BC sizes (Dang et al. 2015). Schwarz et al. (2013) observed larger effective particle sizes for BC in snow than those for BC in the atmosphere (typically used in BC–snow albedo calculations), which has important implications for model estimates of BC effects in snow. He et al. (2018c) further showed weaker BC-induced snow albedo reductions for polydisperse (log normal) BC size distribution than monodisperse BC size distribution with the same effective radius and BC concentration in snow, which is due to a lower BC mass absorption cross section for polydisperse BC than for monodisperse BC with the same effective radii and concentration (Flanner et al. 2012). BC particle structures also affect the induced snow albedo reductions, with stronger albedo reductions caused by irregular BC aggregates than the volume-equivalent BC spheres (Liou et al. 2014), primarily due to the stronger light absorption and scattering by the BC aggregates than their spherical counterparts (Bond and Bergstrom 2006). Note that BC particles are more towards spherical shapes when depositing onto snowpack after atmospheric aging processes (Zhang et al. 2008). Pu et al. (2021) recently pointed out that BC particles coated by other soluble aerosol components (e.g. sulfate and organics) through atmospheric aging processes can further enhance BC-induced snow albedo reductions by a factor of 1.1–1.8 for a non-absorbing coating and 1.1–1.3 for an absorbing coating, compared to uncoated BC particles. However, due to the lack of observations, it remains unclear how much coated BC particles could exist in real snowpack considering the soluble coating materials may dissolve into rain/cloud droplets before they freeze during BC wet deposition. Further complicating the problem, He et al. (2017b) showed that the dense/close packing of snow grains enhances BC-induced snow albedo reductions by up to 20%, compared to the conventional independent scattering approximation treatment of snow grains. This is because snow grain packing leads to decreases in snow extinction coefficient, single-scattering albedo and asymmetry factor, with an overall effect to enhance light penetration within snowpack and hence light absorption by BC, which is similar to the effect of an increased effective snow grain size.

Therefore, accurate estimates of BC-induced snow albedo reductions and associated radiative effects require careful considerations of the aforementioned important factors, most of which, however, are not accounted for in current snow/land/climate models. To facilitate model improvements, a number of BC–snow albedo parameterisations that account for different aspects of the aforementioned key factors have been recently developed (e.g. Dang et al. 2015, 2016; He et al. 2017a, 2018a; Saito et al. 2019; Pu et al. 2021; Shi et al. 2022a), to which we refer readers who are interested.

Mineral dust (hereinafter dust) is the most abundant light-absorbing aerosol by mass in the climate system (Shao et al. 2011). Although dust has a much weaker light-absorbing ability than BC, dust mass content in snow is typically several orders of magnitude higher than that of BC (e.g. Painter et al. 2012; Qian et al. 2015), which could lead to comparable or even higher snow albedo reductions and radiative forcing compared to BC (Skiles et al. 2018). Similar to BC–snow studies, dust is traditionally assumed to be externally mixed with spherical snow grains in snow radiative transfer calculations (e.g. Warren and Wiscombe 1980; Flanner et al. 2009; Dang et al. 2015), with dust-induced snow albedo reductions dependent on dust concentration in snow, snow grain size, wavelength, snowpack properties and illumination conditions (Fig. 6). Consistent with the pattern of BC-induced albedo reductions, dust-induced snow albedo reductions are stronger under higher dust content in snow, larger snow grain size, higher snowpack density, larger snowpack thickness or smaller SZA under direct radiation (Warren and Wiscombe 1980; Dang et al. 2015; see also Fig. 6). Assuming dust external mixing with snow spheres, dust can lead to broadband snow albedo reductions of up to 0.3 with 100 ppm dust content in aged snow (snow grain radius of 1000 μm) (Dang et al. 2015; He et al. 2019; Shi et al. 2021). Dust in snow leads to a springtime regional mean surface radiative forcing of up to 5 W m⁻² over the globe, with particularly strong forcing (>10 W m⁻²) over the polluted mid-latitude seasonal snowpack (Painter et al. 2010; Skiles et al. 2018; Dumont et al. 2020; Shi et al. 2022a).

Fig. 6.  Dust-induced snow albedo reductions for dust–snow external (dashed lines) and internal (solid lines) mixing as a function of dust concentration in snow (a), snow grain radius (b), snow grain shape (c), snowpack thickness (d), snowpack density (e) and solar zenith angle (f) based on the SNICAR model enhanced with dust–snow internal mixing parameterisations (He et al. 2019). The dust concentration in snow in panels b–f is assumed to be 100 ppm.

Recent studies pointed out that dust can also be internally mixed with snow grains through dust atmospheric wet deposition (e.g. serving as ice nuclei; Hoose and Möhler 2012), which enhances dust-induced snow albedo reductions by up to 40% (Liou et al. 2014; He et al. 2019; Shi et al. 2021). For example, He et al. (2019) estimated that dust–snow internal mixing leads to about 20% higher snow albedo reductions in the Colorado River Basin (US) than external mixing, which is equivalent to an increase of 6–16 W m⁻² for dust-induced springtime surface radiative effects. Shi et al. (2021) further tested the impact of three different dust–snow internal mixing configurations for spherical snow grains, including dust distributed uniformly, in the centre or in the peripheral within each snow grain. They found that the uniform dust–snow internal mixing configuration leads to smaller snow albedo reductions than the central internal mixing configuration but larger albedo reductions than the peripheral internal mixing configuration. In addition, the differences in snow albedo reductions caused by dust–snow internal and external mixing tend to become larger with increasing dust content in snow, snow grain size, snowpack thickness or snowpack density (Fig. 6), while the differences become smaller under higher SZA (Fig. 6f) or non-spherical snow grains (Fig. 6c).

Furthermore, a number of other factors can impact dust-induced snow albedo reductions. Specifically, non-spherical snow grains have been found to reduce dust-induced snow albedo reduction by up to 45% compared to their spherical counterparts (He et al. 2019; Shi et al. 2022a). Similar to BC–snow interaction, dust particle non-sphericity and smaller dust particle sizes enhance the dust effect on snow albedo (He et al. 2019; Shi et al. 2022b). The dust-induced snow albedo reduction may also be enhanced by the dense packing of snow grains and dust particles coated with other aerosol components during atmospheric aging processes, both of which however lack direct observational evidence or quantitative model estimates so far. Another important factor that controls dust absorption in snowpack is the dust particle refractive index, which is associated with large uncertainties and depends on dust particle composition. Recent studies showed that dust from different sources have more than a factor of two differences in their refractive indices and hence mass absorption cross sections, which results in up to 0.1 difference in dust-induced snow albedo reductions (He et al. 2019; Flanner et al. 2021).

Thus, accurate quantifications of dust-induced snow albedo reductions and associated radiative effects require taking into account all the aforementioned factors. Although these detailed dust–snow interactions are not fully included in the current snow and climate models, several dust–snow albedo parameterisations have been recently developed to account for dust–snow internal mixing and snow non-sphericity effects (e.g. Dang et al. 2015, 2016; He et al. 2019; Shi et al. 2022a), which could facilitate a better representation of dust effects on snow albedo in climate models.

Brown carbon (BrC) is the light-absorbing component of organic carbonaceous aerosol, which absorbs strongly in the UV and short (blue) visible wavelengths but very weakly in the red visible wavelengths (Kirchstetter et al. 2004; Andreae and Gelencsér 2006). The overall BrC light-absorbing ability integrated across the solar spectrum is much smaller than BC. Compared with BC and dust, the effect of BrC on snow albedo has been much less studied and quantified. Most snow and climate models do not account for BrC in snow partially due to the substantial uncertainty associated with BrC refractive index, size distribution, solubility and chemical composition (Sun et al. 2007; Laskin et al. 2015; Liu et al. 2020; Flanner et al. 2021). Flanner et al. (2009) conducted simulations and radiative effect estimates for both BC and BrC in global snowpack but did not separate their individual contributions. Recent measurements (Beres et al. 2020) found a BrC-induced instantaneous local snow albedo radiative effect of ~2.7 W m⁻² per ppm of BrC deposited onto clean snow in spring over Sierra Nevada, USA. There are also measurements of water-insoluble and water-soluble BrC concentrations in mid-latitude snowpack (e.g. Zhang et al. 2019; Li et al. 2020), which could help constrain the modelling of BrC evolution in snow but these are still rather scarce. We note that the soluble BrC dissolved in snow cannot be treated in the same manner as insoluble solid BrC particles in snowpack radiative transfer (Liu et al. 2020).

Although less quantified and constrained, the patterns of BrC effects changing with snowpack properties and illumination conditions are theoretically similar to those of BC and dust. Specifically, Fig. 7 shows an example of BrC effects on snow by using the BrC refractive index from a widely used database (Kirchstetter et al. 2004). The BrC-induced snow albedo reductions are enhanced by increasing BrC content in snow, snow grain size, snowpack thickness and density, but weakened by higher SZA under direct radiation and snow non-sphericity (Fig. 7). Flanner et al. (2021) further showed that BrC coating with sulfate significantly increases BrC light absorption and hence leads to stronger snow albedo reductions by up to 25% (see also Fig. 7). In addition, organic aerosol can act as cloud or ice nuclei (Tobo et al. 2014), suggesting the possibility of forming BrC–snow internal mixtures during BrC wet deposition in snowfall events. However, there are currently neither observations nor model quantifications for the effect of BrC–snow internal mixing. Overall, more measurements of BrC optical properties and concentrations in snow are needed to constrain model estimates of BrC effects on snow albedo.

Fig. 7.  Brown carbon (BrC)-induced snow albedo reductions for uncoated BrC (dashed lines) and sulfate-coated BrC (solid lines) as a function of BrC concentration in snow (a), snow grain radius (b), snow grain shape (c), snowpack thickness (d), snowpack density (e) and solar zenith angle (f) based on the SNICAR model (Flanner et al. 2021). The BrC concentration in snow in panels b–f is assumed to be 500 ppb.

Volcanic ash can largely reduce snow albedo after deposition onto snowpack (e.g. Young et al. 2014; Gelman Constantin et al. 2020), although it only occurs episodically after volcanic eruptions. This is one of the reasons why the effect of volcanic ash on snow albedo is much less studied and quantified compared to BC and dust. Young et al. (2014) estimated snow albedo reductions of up to 0.6 and 0.85 caused by volcanic ash deposition in new and aged Arctic snowpack, respectively, which results in up to 96 W m⁻² daily mean surface radiative effects. However, the refractive index of volcanic ash is currently associated with large uncertainties. Flanner et al. (2014) summarised a series of volcanic ash refractive indices based on previous measurements, which shows an order of magnitude variation in ash absorptivity. The mass absorption cross section of volcanic ash derived from the central value of the Flanner et al. (2014) database tends to be lower than that of most dust particles (Flanner et al. 2021).

Moreover, other volcanic ash particle properties (e.g. size, shape and density) are also less constrained (Flanner et al. 2021). For example, ash particle non-sphericity is found to cause up to 16% differences in ash mass absorption cross section compared to spherical ash grains (Flanner et al. 2014). Increasing ash particle sizes from 0.5 to 5 μm tends to result in weaker snow albedo reductions due to the decreasing mass absorption cross section with larger sizes, while the ash particle with a size of 0.05–0.5 μm shows some special patterns due to its optical characteristics (Flanner et al. 2021; see also Fig. 8). In addition, the effect of volcanic ash on snow albedo is modulated by snowpack properties and illumination conditions. Similar to the patterns of BC/dust/BrC–snow albedo interaction, the ash-induced snow albedo reduction is enhanced by increasing snow grain size, snowpack thickness and snowpack density, while it is reduced by increasing SZA under direct radiation and snow non-sphericity (Fig. 8). Detailed measurements of volcanic ash particle properties (e.g. optics, size and shape) and its content in snowpack are still imperative in order for more accurate modelling of volcanic ash-induced snow albedo reductions and associated radiative effects.

Fig. 8.  Volcanic ash-induced snow albedo reductions for five ash size bins (r; five coloured lines) as a function of ash concentration in snow (a), snow grain radius (b), snow grain shape (c), snowpack thickness (d), snowpack density (e) and solar zenith angle (f) based on the SNICAR model (Flanner et al. 2021). The ash concentration in snow in panels b–f is assumed to be 100 ppm.

Pigmented algae, which occur in both seasonal snowpack and glacier/ice sheet ablation zones (Painter et al. 2001; Cook et al. 2017; Wang et al. 2018), is another important light-absorbing constituent that is not treated in traditional snowpack radiative transfer and albedo calculations. In the past few years, the effects of snow/ice algae on snow albedo and glacier melting have been gaining increasing attention (e.g. Cook et al. 2017, 2020; Stibal et al. 2017; Williamson et al. 2020; Tedstone et al. 2020). For example, Cook et al. (2017) measured a visible snow albedo reduction of up to 0.4 caused by algae in the Greenland ice sheet. Stibal et al. (2017) observed a broadband albedo reduction of 0.04 for each algal population doubling in the Greenland ice sheet. Williamson et al. (2020) further showed that the secondary phenolic pigmentation of algae can substantially increase algae light absorption with a 50-fold increase in total cellular energy absorption by the phenolic pigmentation.

Because of the complex and less-constrained snow algae physiological properties (e.g. algae type, cell size, cell shape and pigment types), there are currently substantial uncertainties in snow algae optical properties and hence the impact on snow albedo. Cook et al. (2017) provides a set of cell-specific optical properties for snow algae to facilitate the modelling of algae spectroscopic characteristics and induced albedo reductions. Flanner et al. (2021) and Whicker et al. (2022) have recently updated the database of snow and glacier algae optical properties by assuming homogeneous mixing of a few common types of pigments within spherical algae cells. In general, large algae cell sizes and higher algae concentrations in snow lead to stronger snow albedo reductions (Flanner et al. 2021; see also Fig. 9). Similar to the other LAPs mentioned above, algae-induced snow albedo reductions are enhanced by larger snow grain size, snowpack thickness and snowpack density, but are weakened by increasing SZA under direct radiation and snow non-sphericity (Fig. 9).

Fig. 9.  Snow-algae-induced snow albedo reductions for five algae cell sizes (r; five coloured lines) as a function of algae concentration in snow (a), snow grain radius (b), snow grain shape (c), snowpack thickness (d), snowpack density (e) and solar zenith angle (f) based on the SNICAR model (Flanner et al. 2021). The algae concentrations in snow in panels b–f are assumed to be 10⁴ cells mL^–1. The default SNICAR pigment mass fractions are used in all the panels, including 1.5% chlorophyll-a, 0.5% chlorophyll-b, 5% photoprotective carotenoids and 0% photosynthetic carotenoids.

However, current model treatments of snow algae are still at an early stage, with several deficiencies such as the assumption of spherical cells and homogeneous mixing of pigments as well as less knowledge of pigment types (Flanner et al. 2021). Overall, the impact of algae on snow albedo is less understood and quantified compared to other LAPs like BC/dust. There is an urgent need to improve observational constraints on snow algae optical properties and model representations of irregularly shaped and heterogeneous algae cells (Cook et al. 2020).

In the past few decades, substantial scientific and technical advances have been made to improve the modelling of LAP–snow–radiation interactions and impacts on snow albedo, as summarised above. However, several key challenges and large uncertainties still exist, hindering a better understanding and quantification of LAP–snow albedo effects. Here, we highlight a few problems that require more attention, which hopefully could shed light on future studies.

1. LAP optical properties: The optical properties of LAPs are controlled by particle size, shape and refractive index (or chemical composition). Most previous studies have focused on constraining BC optical properties, which thus show a relatively smaller uncertainty compared to the other LAPs. However, large uncertainties are associated with refractive indices of dust, BrC, ash and snow algae (Flanner et al. 2021), due to their complex but less-constrained particle types and composition. The particle size and structure (e.g. irregular shapes) in snowpack are also poorly constrained. BC and BrC particles appear to be spherical after atmospheric aging processes (Zhang et al. 2008; Liu et al. 2020), whereas dust, ash, and algae tend to have non-spherical structures (Flanner et al. 2014; Cook et al. 2020; Shi et al. 2022b). Measurements of LAP particle size distributions in snowpack are rather scarce and mostly for BC (e.g. Schwarz et al. 2013; Marquetto et al. 2020). Therefore, more measurements of LAP particle size, shape and refractive index in snowpack are needed to better constrain LAP optical properties and associated impacts on snow albedo.

2. LAP distribution and evolution in snowpack: The concentration of LAPs in snow is one first-order controlling factor for their impacts on snow albedo. The LAP concentration in snowpack is determined by atmospheric deposition flux of LAPs (except for snow algae) and evolution of LAPs in snowpack. Due to the rather limited measurements of LAP deposition flux over global snowpack (e.g. Li et al. 2021; Qi et al. 2017; Yan et al. 2019; Liu et al. 2020), current model estimates of LAPs input to global snowpack are poorly constrained. Large uncertainties also exist for modelling the LAP evolution in snowpack, due to little knowledge about LAP scavenging by meltwater (Qian et al. 2014) and LAP distribution changes during snowpack melting–refreezing and other metamorphism processes (Rosenthal et al. 2007; Domine et al. 2009). For snow algae in particular, there are very limited observations and knowledge about how it evolves and how its optical properties are affected by dynamic growth in snowpack (Williamson et al. 2020). Recently, numerous field measurements of BC, BrC and dust concentrations in snowpack have been conducted over Asia, North America, Arctic and South America (e.g. Doherty et al. 2010, 2014; Painter et al. 2010; Dang and Hegg 2014; Wang et al. 2017; Rowe et al. 2019), which provide direct constraints for modelling LAP content in snow but are still limited in spatial and temporal coverage. Satellite observations, with a much larger spatial and temporal coverage than field measurements, can be used to retrieve LAP-induced snow albedo changes and associated radiative forcing (e.g. Painter et al. 2013; Pu et al. 2019) but may be only reliable with sufficiently large signal-to-noise ratios under large LAP concentrations in snow (Warren 2013).

3. Snow grain evolution and metamorphism/aging: Snow aging processes alter snow grain size, grain shape, snowpack density and thickness, which all contribute to modulating snow albedo and albedo reductions by LAPs (as presented in previous sections above). The dry snow grain growth through vapour diffusion can be simulated reasonably well in current snow models (Flanner et al. 2007), whereas there is still large uncertainty in representing grain growth during wet snow aging (e.g. melting/refreezing) processes (Brun 1989). Moreover, the dynamic evolution of snow grain shapes/structures is not included in any current snow and climate models, partially due to the lack of observations and physical understanding. There is also a lack of physical representations for other complex snow metamorphism processes (e.g. sintering, sieving of blowing snow and melt–freeze crust transformation), which can substantially change snow grain structures and hence snow albedo (Rosenthal et al. 2007; Domine et al. 2009). Therefore, more field and laboratory measurements of the dynamic evolution of snow grain properties are key to better model representations of those processes and hence improved estimates of snow albedo and interactions with LAPs.

4. LAP–snow mixing structures: The microscopic LAP–snow mixing structures can have substantial impacts on LAP-induced snow albedo reductions (as presented in previous sections above). Some recent studies explored the effects of dust and BC internally mixed with snow grains and snow non-sphericity through modelling experiments (e.g. Flanner et al. 2012; Dang et al. 2016; He et al. 2017a, 2019; Shi et al. 2021), which however have not been validated by direct observations. Currently, no theoretical or observational studies on BrC/ash/algae–snow mixing structures and impacts on snow albedo are available. Uncertainties also exist in representing the specific configuration of LAP–snow internal mixing, such as LAPs randomly distributed within snow grains, LAPs concentrated in the centre of snow grains or LAPs distributed in the peripheral of snow grains (Shi et al. 2021), which lack observational constraints. Moreover, current models cannot treat internal mixing between snow grains and multiple types of LAPs simultaneously, which requires future work. In addition to LAP–snow mixing, the synergistic effects of LAP coating, size distribution and particle structures have not been quantified and accounted for in snow and climate models. Overall, future measurements of detailed LAP–snow particle mixing structures will be helpful for enhancing model estimates of LAP–snow albedo interactions.

5. Snowpack radiative transfer: The basic snowpack radiative transfer algorithms, such as the traditional two-stream approximation and adding–doubling method, have been widely accepted and applied to snow albedo calculations (Warren and Wiscombe 1980; Flanner et al. 2007; Dang et al. 2019). However, some treatments in snow radiative transfer are still imperfect and can exert non-trivial impacts on snow albedo. For example, liquid water in snowpack is typically excluded in snowpack radiative transfer calculations in most models, which has been found to noticeably change snow optical properties and albedo (Green et al. 2002; Gardner and Sharp 2010). The way of treating liquid water mixing with snow grains (e.g. locating in the voids among snow grains or coating on the surface of snow grains) also matters (Green et al. 2002). The dense packing of snow grains during snow metamorphism/compaction processes also raises a question about the validity of the independent scattering approximation assumption commonly used in the snowpack radiative transfer calculations. Some studies found important effects of densely packed snow grains compared to the results with independent scattering of snow grains (Kokhanovsky 1998; Peltoniemi 2007; He et al. 2017b). Moreover, smooth snowpack surfaces are commonly assumed in snow radiative transfer calculations, whereas recent studies have found reduced albedo caused by small-scale snowpack surface roughness that enhances the surface ‘trapping’ effect of incoming photons (e.g. Zhuravleva and Kokhanovsky 2011; Larue et al. 2020; Manninen et al. 2021). It is also unclear how the preceding factors affect LAP–snow albedo interactions. Thus, the coupling of traditional snow radiative transfer calculations with the aforementioned factors will be needed for a more realistic representation of LAP–snow–radiation interactions.

6. Snow albedo parameterisations: For the consideration of computational efficiency, many weather and climate models (particularly operational modelling systems) do not adopt the sophisticated snowpack radiative transfer schemes but leverage simplified bulk snow albedo parameterisations. As a result, many empirical or semi-empirical snow albedo parameterisations that quantitatively link snow albedo to snow grain properties, snowpack properties, illumination conditions and/or snow impurities have been developed and applied in the past decades (He and Flanner 2020, and references therein). However, those snow albedo parameterisations still have uncertainties and limitations and often only account for a very limited number of factors that impact snow albedo. The parameterisations developed for a specific region or time period may not be applicable to other regions or other years/seasons. Therefore, it is important to assess, constrain and improve the snow albedo parameterisations for specific applications in order to better predict snowpack evolution in weather and climate models.

This study used the SNICAR model version 3 code and database at https://github.com/mflanner/SNICARv3, and the SNICAR model version 2 code and database enhanced with BC–snow and dust–snow internal mixing parameterisations at https://github.com/cenlinhe/SNICARv2/tree/SNICARv2_dustint.

The author declares no conflict of interest.

NCAR is sponsored by the National Science Foundation. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation. This study did not receive any specific funding.