Optical Characterization of Marine Aerosols Using a Morphologically Realistic Model With Varying Water Content: Implications for Lidar Applications and Passive Polarimetric Remote Sensing

Retrieving the physical properties and water content of marine aerosols requires understanding the links between the particles' optical and microphysical properties. By using a morphologically realistic model with varying salt mass fractions fm, describing the transition from irregularly shaped, dry salt crystals to brine‐coated geometries, optical properties relevant to polarimetric remote sensing are computed at wavelengths of 532 and 1,064 nm. The extinction cross section and its color ratio depend on particle size, but are insensitive to changes in fm; thus, measured extinction coefficients at two wavelengths contain information on both particle number and size. The lidar ratio's dependence on both size and wavelength has implications for inverting the lidar equation. The results suggest that active observations of the backscattering cross section's color ratio and the depolarization ratio, as well as, passive observations of the degree of linear polarization offer avenues to obtain the water content of marine aerosols.


Introduction
Global sea salt emissions amount to more than 4,700 Tg/year, which exceeds emissions of all other types of aerosols combined (H.Wang et al., 2020).Sea salt acts as cloud condensation nuclei, thus influencing cloud optical properties, cloud lifetime, and the hydrological cycle.This amounts to a substantial effect on the radiative balance in the climate system, owing to the high amount of global emissions, the vast extent of marine cloud fields, and the high albedo contrast between clouds and the ocean surface.Also, long-range transported marine aerosols are important for ecosystem modeling, because deposition of sea salt over land can counteract the effect of acidifying pollutants.
In aerosol transport models, one simulates emission of marine aerosols from bubble bursting and spume drops by use of empirical parameterizations (Soares et al., 2016;Sofiev et al., 2011) that are derived from laboratory observations (Mårtensson et al., 2003;Monahan et al., 1986).The number density of emitted particles depends on the surface wind speed, while the size distribution is dependent on sea-surface temperature and salinity (Sofiev et al., 2011).Hygroscopic growth of marine particles is important to accurately describe gravitational settling and dry deposition, as well as optical properties (Soares et al., 2016).The wet radius of the particles can be computed from their dry radius and the ambient relative humidity by use of Köhler theory (Z.Wang et al., 2019) or by approximate formulas (Fitzgerald, 1975).However, solving these equations can be time-consuming.Therefore, in large-scale aerosol transport models one typically employs simple empirical parameterizations of the wet radius as a function of dry radius and relative humidity (Gerber, 1985;Sofiev et al., 2011).
How can we evaluate parameterizations of marine aerosol emission fluxes, size distribution, and hygroscopic growth on the regional and global scale?Satellite observations provide consistent long-term data records with global coverage that can, potentially, be used to constrain models and to improve parameterizations of aerosol emission and water content.A recent analysis of a 10-year data record of CALIPSO observations during winter months over the Southern Ocean (Thomas et al., 2022) revealed that the backscattering coefficient increases with surface wind speed, while the depolarization ratio monotonically decreases with growing relative humidity.This can be understood in terms of an increase in the emission flux with wind speed, and an increase in water content with increasing relative humidity (which makes the particles more spherical, thus less depolarizing).A similar relation between depolarization and relative humidity in marine aerosols has been reported from lidar campaign measurements (Haarig et al., 2017) and from airborne campaigns (Ferrare et al., 2023).This illustrates the potential usefulness of satellite data in studying emission and water adsorption processes of marine aerosols.However, these studies presently only provide a qualitative interpretation of physical aerosol properties in terms of observed optical properties.Further progress will depend on a better understanding of the relation between physical and optical properties.A most challenging problem is to understand how complex morphological properties, such as irregularly shaped salt crystals and the inhomogeneous composition of partially dissolved, water-coated crystals, manifest themselves in polarimetric optical properties, which are known to be highly sensitive to morphology and composition.Here, a morphologically realistic model for marine aerosols is employed to investigate which optical parameters are most promising for obtaining information on particle number density, effective radius, and water content.This study is of high relevance for the interpretation of observations by the Aerosol and Carbon dioxide Detection Lidar onboard the DQ-1 satellite, a High Spectral Resolution Lidar with polarization detection capabilities, which uses wavelengths of 532 and 1,064 nm (Dai et al., 2023;Liu et al., 2023).Also, accounting for the impact of inhomogeneity in brine-coated salt aerosols on optical properties can be important for modeling the direct radiative forcing effect of marine aerosols (Z.Wang et al., 2019) and the radiative impact on precipitation in tropical cyclones (Zhu et al., 2022).
It is noted that there have been a number of different model particles in use for marine aerosols, such as cubes (David et al., 2013), distorted cubes (Kanngießer & Kahnert, 2021a), homogeneous superellipsoids (Bi, Lin, Liu, & Zhang, 2018;Kanngießer & Kahnert, 2021b), inhomogeneous superspheroids (Bi, Lin, Wang, et al., 2018;Kanngießer & Kahnert, 2021b), cube-sphere hybrid particles (Kanngießer & Kahnert, 2021b), and non-concentric core-mantle spheres (Kanngießer & Kahnert, 2021b).All of these particles introduce various simplifying assumptions, the validity of which are not yet fully explored.However, a recent comparison of our reference model with homogeneous superellipsoids (Kanngießer & Kahnert, 2021b) revealed that by a suitable tuning of the roundness parameter and aspect ratio of the superellipsoids one can reasonably well reproduce the lidar ratio and backscatter linear depolarization ratio obtained with the reference model at 532 nm.Also, the results in Bi, Lin, Wang, et al. (2018) show that variation of the roundness parameter and aspect ratio of super-spheroids results in a significant variation in the linear depolarization ratio, which indicates that this model is highly tunable.A main advantage of simplified models is that they allow for simplifications in numerical computations, while a main concern is their robustness.An instance of a simple model that has been tuned to reproduce specific optical properties at a certain wavelength may not be applicable to other optical properties or wavelengths.

Particle Model
While pure sodium chloride crystals display cubic shape, dry marine aerosols in nature are often irregular particles resembling distorted cubes (Gwaze et al., 2007;Haarig et al., 2017;King et al., 2012;McInnes et al., 1994;Patterson et al., 2016;Peart & Evans, 2011;Wise et al., 2005;Zeng et al., 2013).Polarimetric optical properties of marine particles are well described by a realistic distorted cube model based on convex polyhedra, which was developed in Kanngießer and Kahnert (2021a).Figure 1 (top row) shows four stochastic realizations of that model.

10.1029/2023GL107541
Condensation of water modulates the optical properties.Here, the model described in Kahnert and Kanngießer (2023a) is employed, which uses a pseudo-potential model (Ishimoto et al., 2019) to realistically describe the morphological changes due to condensation of water.More specifically, (a) water condenses first onto parts of the particle with a low surface potential (corresponding to a large number of neighboring atoms); (b) solid material in contact with the liquid coating is first dissolved at those points where the surface potential is high (corresponding to few neighboring atoms); (c) salt that becomes dissolved can be relocated so that the liquid coating becomes rearranged in a state of low surface potential; and (d) the brine coating consists of 36 g salt per 100 ml water with a density of 1,210 kg/m 3 , while pure water and dry sea salt are assumed to have densities of 1,000 and 2,240 kg/m 3 , respectively.Note that a mass-weighted average of the densities of salt and water would result in a density of 1,328 kg/m 3 , which would be larger than the true density of brine.Thus, owing to the lower density of 1,210 kg/m 3 , the composite particle of brine and salt has a larger volume than the sum of the volumes of salt and water.The model accounts for this effect in calculating the wet radius as a function of the dry radius and the salt-mass fraction.A detailed model description and the transformation from salt-volume fraction to salt-mass fractions is given in Kahnert and Kanngießer (2023a).Tests at a wavelength of 532 nm showed that the range of lidar ratios and linear depolarization ratios obtained with the model is consistent with existing field and satellite observations (Kahnert & Kanngießer, 2023a).Figure 1 (bottom row) shows four realization of the model with salt-mass fractions (from left to right) f m = 1.00, 0.97, 0.94, 0.91, where f m = m salt /(m salt + m water ), and m salt and m water represent the masses of salt and water in the composite particle.
The model is employed to generate 74 dry salt crystals with radii r = 0.04, 0.06, …, 1.5 μm, where r is the radius of a mass-equivalent sphere.(An upper cut-off of 1.5 μm had to be imposed due to numerical limitations in the light-scattering computations.)Each of these particles is a different stochastic realization of the distorted cube model (Kanngießer & Kahnert, 2021a), so that the ensemble of marine aerosols is described by a size-shape distribution.In addition to dry particles ( f m = 1.00), brine-coated model particles are generated for salt-mass fractions f m = 0.97, 0.94, 0.91.As discussed in Kahnert and Kanngießer (2023a), and as illustrated in Figure 1 (bottom), this braces the range within which the transition from dry nonspherical to wet spherical marine particles occurs.Although it is not straightforward to relate these mass fractions to relative humidity, it is estimated that, for pure sodium chloride crystals, this range would roughly correspond to a relative humidity of 43%-48% for efflorescence, and 60%-72% for deliquescence (Kahnert & Kanngießer, 2023a).However, field and satellite observations of lidar depolarization ratios of marine aerosols as a function of relative humidity suggest that in nature the transition from dry depolarizing to wet non-depolarizing particles is rather smooth and extends over a broad range of the relative humidity between 40% and 90% (Haarig et al., 2017;Thomas et al., 2022).

Dielectric Properties and Light-Scattering Computations
The marine-aerosol model had previously been tested by modeling lidar-relevant quantities at a single wavelength of 532 nm (Kahnert & Kanngießer, 2023a;Kanngießer & Kahnert, 2021b).Here, a more comprehensive study is presented with additional computations at a wavelength of 1,064 nm (thus allowing the computation of color ratios), as well as an investigation of the degree of linear polarization and its dependence on wavelength.The degree of linear polarization is relevant for passive polarimetric remote sensing.Also, the optical properties at 532 nm have been computed here with an updated value of the complex refractive index of the brine coating, as explained below.As the light-scattering computations are numerically demanding, these computations required several months of wall-clock time.
At a wavelength of λ = 532 nm, the complex refractive indices of sea salt and brine are assumed to be m = 1.5484 + 0i (Eldridge & Palik, 1997) and 1.3844 + 2.5330 ⋅ 10 8 i, respectively.The latter is an updated value different from the one in Kahnert and Kanngießer (2023a), which accounts for the corrigendum in X. Li et al. (2018) to the parameterization given in X. Li et al. (2015).At λ = 1,064 nm, the corresponding complex refractive indices are 1.5312 + 0i and 1.3674 + 3.309 ⋅ 10 5 i, respectively.
Optical properties were computed by use of the discrete-dipole approximation (DDA), using ADDA version 1.3b4 (Yurkin & Hoekstra, 2011).The particles were represented by a Cartesian grid of dipoles.The main parameter controlling the numerical accuracy of the solution is the number of dipoles per wavelength dpl.The optical properties were averaged over three Euler angles α, β, γ by use of Romberg integration, assuming randomly oriented particles.In ADDA, each Euler angle uses a range of subdivisions J min , J max .In this study, dpl ≥ 25 is used, as well as J min = 2 and J max = 4 for α and γ in the interval [0, 360°], and J min = 2 and J max = 3 for β in the interval [0, 180°].At these settings, the results of the computations have converged for this kind of particle geometry (Kanngießer & Kahnert, 2021a).

Size Distribution
The size distribution of marine aerosols is often modeled by either multi-modal lognormal or by power-law functions.What all models have in common is that the size distribution is rather broad.Here, the modified power-law distribution proposed by Sofiev et al. (2011)  ) N 1 is proportional to the total number density, and the volume-equivalent dry radius r is given in μm.This model has been derived from two earlier models, which were based on observations of bubble-bursting aerosols and spume drops (Monahan et al., 1986) as well as laboratory measurements in a bubble chamber (Mårtensson et al., 2003).The model is used in several chemical transport models and parametrizations of wind-driven emission processes, for example, in the Multiple-scale Atmospheric Transport and Chemistry model (Andersson et al., 2015), in the System for Integrated Modelling of Atmospheric Composition (Sofiev et al., 2011), and in the model of the Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe (Simpson et al., 2012).While multi-modal lognormal distributions can have a large number of free parameters, the power-law distribution only depends on N 1 and α, which makes it attractive for retrievals.N 1 depends mainly on wind speed, while α can be modeled as a function of salinity and sea-surface temperature (Sofiev et al., 2011).Over the oceans, α typically varies between 0 and 1, but for freshwater it can be as high as 3 (Sofiev et al., 2011).In place of α, the effective dry radius will be used to describe the optical size of an ensemble of particles, which is defined by where n(r) describes the size-distribution of volume-equivalent dry radii r.This quantity describes that effective radius that the ensemble of particles would have if all water were removed.It provides a convenient size-measure to compare particles with different water content (i.e., different salt-mass fractions f m ).But it is emphasized that the hygroscopic growth of the particles is explicitly accounted for in the model.For each salt-mass fraction the distribution of wet radii is computed from that of dry radii based on the method outlined in Section 2.1-see also Kahnert and Kanngießer (2023a).

Optical Properties Relevant for Active Remote Sensing
Figure 2 shows size-averaged optical properties for different values of the salt mass fraction f m .The left column displays results obtained for λ 1 = 1,064 nm, and the right column shows the corresponding color ratios with respect to λ 1 and λ 2 = 532 nm.Optical properties are shown as a function of the effective dry radius r dry eff .However, it is emphasized that wet particles ( f m < 1) have wet radii that are slightly larger than the dry radii due to the addition of water, which is accounted for in the model (see Section 2.1).We chose to use the dry radii as a common reference in this figure in order to show more clearly to what extent the addition of water (decreasing f m < 1) impacts the optical cross sections.
The extinction cross section Cext (top right) is strongly dependent on r dry eff , yet quite insensitive to changes in f m .This is because within the limited range of salt-mass fraction considered here, the wet radius is not dramatically larger than the corresponding dry radius.(As an example, a particle with dry radius 1.5 μm and a salt-mass fraction of 0.91 would have a wet radius of 1.6 μm-see also Figure 11 by Kahnert and Kanngießer (2023a).)Further, the corresponding color ratio (top right) is also insensitive to a variation in f m .In lidar remote sensing, one can use the extinction cross section k = N Cext and its color ratio k(λ 1 )/k(λ 2 ) = Cext (λ 1 )/ Cext (λ 2 ) to retrieve the aerosol number density N and the effective radius of the particles (as the color ratio is only dependent on size, but not N).The results indicate that, within the range of salt-mass fractions considered here, this is a robust approach unaffected by varying values of f m .
By contrast, the color ratio of the backscattering cross section (2nd row right) is monotonically decreasing with decreasing f m .This indicates that independent observations of extinction and backscattering at two wavelengths should allow us to simultaneously retrieve N, r dry eff , and f m .
The third row shows that the lidar ratio S(λ 1 ) is strongly dependent on both r dry eff and f m ; it varies between 25 and 43 sr.The color ratio of S ranges between about 1 and 2.5.In the processing of CALIPSO observations, backscattering and extinction coefficients are obtained from attenuated backscattering measurements by assuming fixed lidar ratios for each type of aerosol.For instance, Omar et al. (2009) list lidar ratios for clean marine aerosols of 20 and 45 sr at 532 and 1,064 nm, respectively, corresponding to S(λ 1 )/ S(λ 2 ) = 2.25.According to the results obtained here, S(λ 1 ) = 45 sr would be representative of r dry eff = 0.1 μm and f m = 0.91, while a color ratio of 2.25 would be characteristic of r dry eff = 0.5 μm and f m = 0.91.In the latest version 4 of the CALIPSO automated aerosol classification and lidar ratio selection algorithm (Kim et al., 2018), a spectrally neutral lidar ratio of 23 ± 5 sr at 532 and 1,064 nm is being assumed.This is based on several recent studies (Haarig et al., 2017;Josset et al., 2012;Müller et al., 2007;Papagiannopoulos et al., 2016;Rogers et al., 2014;Sayer et al., 2012).According to the modeling results in Figure 2 (third row), a lidar ratio of 23 at 1,064 nm would be representative of relatively dry, large particles with r dry eff ≥ 0.6 μm, while a color ratio of 1 would suggest particles with r dry eff ≤ 0.05 μm.This shows that there are some remaining challenges in reconciling light-scattering models with lidar-ratio assumptions made in the retrieval of backscattering and extinction coefficients.The model considered here suggests that both S and its color ratio depend on both r dry eff and f m .
Similarly, the linear depolarization ratio δ L (bottom left) depends strongly on r dry eff and f m .As more water is being adsorbed (and f m decreases), the particles become more spherical, resulting in a quenching of δ L .Thus, depolarization provides useful information on the water content of marine aerosol, but only to the point at which the particles become spherical.The relatively low color ratios (bottom right) show that depolarization is strongest in the visible part of the spectrum.Also, for f m ≤ 0.94 the color ratio of δ L is probably not helpful, as it is based on division of two very small values.Thus, to constrain the water content of marine aerosols in the transition regime from nonspherical crystals to spherical droplets it is likely to be sufficient to measure δ L at a single wavelength, that is, at λ 2 = 532 nm.

Optical Properties Relevant for Passive Remote Sensing
The phase function (not shown) is relatively flat and featureless at side-scattering angles, which is typical for sizeshape distributions of aerosols.The diffraction peak in the forward direction becomes more intense and more narrow with increasing size parameter x = 2πr dry eff /λ.
The phase-matrix element F 12 /F 11 has some distinct properties.This quantity describes the degree of linear polarization generated in single-scattering events of unpolarized sunlight.Figure 3 presents F 12 /F 11 as a function of the scattering angle and r dry eff for different values of f m (across rows), as well as for two wavelengths (across columns), as indicated in the panels.A most prominent feature is the negative polarization peaking at scattering angles around 161-163°.A similar feature has been observed by Bi, Lin, Wang, et al. (2018), using a geometrically simpler model of core-mantle superellipsoids.Inspection of Figures 12 and 13 in that paper indicates that the negative polarization branch is more pronounced for spherical particles, and it is enhanced by inhomogeneity.A comparison of homogeneous spheres, two super-spheroids, and three inhomogeneous spheres with both spherical and nonspherical cores presented by M. Li et al. (2022) arrived at conclusions consistent with those by Bi, Lin, Wang, et al. (2018).Similarly, it can be seen here in Figure 3 that the negative polarization intensifies with increasing water content (decreasing f m ), that is, as the particles become more spherical.Further, Geophysical Research Letters 10.1029/2023GL107541 the negative polarization peak is more pronounced in the IR (left) than in the visible part of the spectrum (right), and it intensifies with growing r dry eff .These findings suggest that observation of linearly polarized scattered sunlight in the near infrared (NIR) at scattering angles around 162°could provide a passive polarimetric method for inferring the water content of marine aerosols.M. Li et al. (2023) employed coated super-spheroids, including coated spheres, to investigate the range of size parameters, shell-core ratios, and refractive indices for which the negative polarization at near-backscattering directions is most pronounced.They concluded that the negative polarization is most pronounced for weakly absorbing particles with size parameters ≤14.5 and shell-core ratios around 1.4-1.9,where the latter is defined as the ratio of the size parameters of the shell and the core, respectively.

Conclusions
A study of the optical properties of morphologically realistic brine-coated sea salt particles has been presented, which led to the following findings.
1.The ensemble-averaged extinction cross section Cext strongly depends on the effective radius of the particles.
The same is true for the color ratio Cext (λ 1 )/ Cext (λ 2 ), where λ 1 = 1,064 nm and λ 2 = 532 nm.Neither the extinction cross section nor the corresponding color ratio changes much with the salt mass fraction f m .The extinction coefficient k = N Cext depends on both the number density and the extinction cross section.Thus, the color ratio of k, which does not depend on N, can be used to retrieve particle size.Simultaneous measurements of k at two wavelengths should provide a robust method for simultaneous retrieval of particle size and number density, unperturbed by variations in water content.Although measurements of the extinction coefficient at NIR wavelengths is challenging, encouraging progress with Raman lidar techniques has been reported (Haarig et al., 2016).2. The lidar ratio varies considerably with particle size and salt mass fraction (between 25 and 43 sr at λ = 1,064 nm); its color ratio varies between 1 and 2.5.High-level lidar products (such as level 2 and level 3 CALIPSO products) assume fixed values of the lidar ratio in retrieving extinction and backscattering coefficients from attenuated backscattering signals.The results of the present study suggest that such retrievals may have systematic errors owning to the pronounced dependence of the lidar ratio on particle size and water content.A reliable retrieval of particle size, composition, and number density would need to invert the lidar equation by taking the size-and wavelength-dependence of the lidar ratio into account.This is a challenging inverse problem, since the lidar ratio required for solving the lidar equation is size dependent, but the size of the particles is one of the quantities one wants to retrieve from the solution of the lidar equation.3.Both the color ratio Cbsc (λ 1 )/ Cbsc (λ 2 ) of the backscattering cross section (or the backscattering coefficient) and the depolarization ratio δ L generally increase with growing salt mass fraction f m and with particle size.δ L is larger in the visible than in the NIR part of the spectrum.Hence, both the backscattering color ratio and δ L at 532 nm provide quantitative information on the water content of marine aerosols.Additional observation of δ L at 1,064 nm is not expected to provide much extra information on the water content.4. The degree of linear polarization of sunlight scattered at specific angles can be strongly modulated by the water content of the aerosols.This effect is most pronounced in the NIR part of the spectrum at scattering angles around 162°, which could open up new possibilities in passive polarimetric remote sensing to estimate the water content of marine aerosols.5.At λ 2 = 532 nm, dry sea salt particles can have a depolarization ratio δ L up to 0.15, which is higher than that of uncoated soot aerosols (e.g., Burton et al., 2015;Kanngießer & Kahnert, 2018;Kahnert & Kanngießer, 2020), and considerably lower than that of mineral dust aerosols (e.g., Burton et al., 2015;Kahnert et al., 2020).This can help to disentangle mixed aerosol populations, as is done in CALIPSO aerosol classifications (Omar et al., 2009), but also in quantitative retrievals based on field measurements (e.g., David et al. (2013)).
The computations performed in this study were limited to dry radii up to 1.5 μm and wet radii up to roughly 1.6 μm.Marine aerosols in nature can contain larger particles, typically up to or even exceeding 5 μm radius, even though larger particles often have low number densities.This limits the model to serving, mostly, as a reference model in theoretical studies.In quantitative applications, such as retrieval methods in remote sensing or chemical data assimilation, one will need to rely on simpler and faster models that are capable of covering the full range of relevant particle sizes, at least up to 5 μm.

Figure 1 .
Figure 1.Top: four stochastic realizations of the convex polyhedra model for dry marine aerosols; bottom: model particles with decreasing salt mass fractions (from left to right) f m = 1.00, 0.97, 0.94, and 0.91.

Figure 2 .
Figure 2. Left: size-averaged optical properties at 1,064 nm wavelength as a function of effective dry radius for different salt mass fractions f m , first row: extinction cross section, 2nd row: backscattering cross section, third row: lidar ratio, fourth row: linear depolarization ratio.Right: corresponding color ratios of optical properties at 1,064 nm and 532 nm.

Figure 3 .
Figure 3. Degree of linear polarzation F 12 /F 11 as a function of scattering angle and effective dry radius for different f m (across rows), and for λ 1 = 1,064 nm (left column) and λ 2 = 532 nm (right column).