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Efficient and accurate computation of the single‐scattering properties of black carbon (BC) aerosols is fundamental in various fields, including remote sensing and climate simulations. In this study, we developed a composite model of fractal aggregates of BC encapsulated with hygroscopic aerosols to represent the ambient BC. We used the invariant imbedding T‐matrix method to compute the optical properties of fully and partially encapsulated BC aerosols. In this new model, the traditional assumption of unoverlapped surfaces in the super‐position T‐matrix method is unnecessary. After extensive simulations, we established a database of single‐scattering properties, including the extinction efficiency, the single‐scattering albedo, the asymmetry factor and six phase matrix elements. Moreover, we obtained deep neural networks (DNNs) from this database using a deep learning method. These DNN models provide a universal interface for predicting the optical properties of ambient BC aerosols. Specifically, through a modified architecture of the DNN, we trained two models based on the database to predict three integrated optical properties (extinction efficiency, single‐scattering albedo, and asymmetry factor) and six phase matrix elements. We performed statistical assessments based on the true values in the database and the predicted values from the DNNs, demonstrating that the DNNs accurately predicted all single‐scattering properties. Therefore, the developed DNN models can be conveniently implemented in aerosol optical parameterization for remote sensing studies and atmospheric models. Plain Language Summary: Black carbon (BC) aerosol plays a significant role in the atmosphere, influencing climate through its interactions with radiation, such as scattering and absorbing. The accurate determination of the single‐scattering properties of BC, including the extinction efficiency, the single‐scattering albedo, the asymmetry factor and six phase matrix elements, is crucial for understanding its radiation effects. In this study, we developed a comprehensive model for BC particles that incorporates complex morphological characteristics and the mixing of BC with other hygroscopic aerosols. We established a database of single‐scattering properties for these models using the invariant imbedding T‐matrix method. However, the large storage space required by this database (over 20 GB) makes it impractical for widespread applications. Therefore, we employed a deep learning method to compress the storage consumption. Two deep neural networks (DNNs) were trained using the database, enabling the prediction of all single‐scattering properties. Remarkably, the performance of the DNNs was excellent, with a coefficient of determination greater than 0.99 for all single‐scattering properties, as determined through statistical assessment. These DNN models hold great potential for various atmospheric radiation and remote sensing studies in the future. Key Points: A flexible model of partially and fully encapsulated fractal black carbon particles was developedA database of single‐scattering properties of encapsulated fractal black carbon particles was constructedTwo deep neural networks were obtained, offering a flexible approach to calculating the optical properties of black carbon aerosols [ABSTRACT FROM AUTHOR]

• Machine learning excelled at extrapolating optical properties of non-spherical particles with larger size parameters. • Deep Neural Networks (DNN) outperformed the improved geometric optics method for particles with moderate size parameters, accounting for edge effects. • DNN efficiently computed optical properties of super-spheroids across a wide range of size parameters. This study investigates the use of machine learning techniques, specifically deep neural networks (DNN), to compute the optical properties of non-spherical particles across a wide range of size parameters. The approach involves training a DNN using a T-matrix database of super-spheroids with size parameters below 50. The DNN is then able to predict optical properties for size parameters beyond this limit, with exceptional accuracy observed for size parameters between 50–100. These predictions outperform the improved geometric optics method (IGOM). To further enhance accuracy and broaden the range of size parameters, databases are merged, combining the T-matrix results for small (0.1–50) and some moderate size parameters (50–100), the DNN predicted values for moderate size parameters (50–100), and the IGOM results for large size parameters (>100). This merged database is used to train a new DNN. This comprehensive training enables the neural networks to calculate the optical properties for super-spheroids across the entire size parameter spectrum, considering various shape parameters and refractive indices. This technique effectively bridges the gap between full-electromagnetic wave results and geometric-optics approximations, providing an efficient method for computing the optical properties of non-spherical particles from Rayleigh to geometric optics domains. Notably, the DNNs automatically consider edge effects, eliminating the need for deriving complex analytical formulas for non-spherical particles. [ABSTRACT FROM AUTHOR]

Sea salt aerosols were assumed to be homogeneous spheres in most climate models. However, observations show that sea salt particles are inhomogeneous during the deliquesce and crystallization processes. Using a two‐layer sphere model, we found that backscattering of solar radiation associated with sea salts is underestimated in homogeneous sea salt models. The Community Earth System Model is used to assess the inhomogeneity effect on direct radiative forcing. For global climate model simulation, the inhomogeneity effect on radiative transfer is found to be small as high RHs over widespread oceans suppress the impact of inhomogeneity. On the other hand, in coastal regions, the inhomogeneity effect can cause up to 10% radiative forcing difference of sea salt aerosols. The inhomogeneity effect of sea salt aerosols has to be considered over coastal regions, especially in the Mediterranean, Australia, and the eastern coast of South America. Plain Language Summary: In a humid environment, solid sea salt particles can be coated with water. Sea salt aerosol has a cooling effect on the Earth, but coated sea salt has even stronger cooling effect. However, in most climate models, coated sea salt is not considered. This study confirms that coated sea salt aerosols may not significantly affect the global radiation budget, but they should definitely be considered in the coastal climate where large changes in relative humidity are evident. Key Points: For some range of relative humidity (50‐80%), sea salt is assumed to be an inhomogeneous two‐layer sphereThe inhomogeneity of sea salt decreases the asymmetry factor and increases backscattering of solar radiationInhomogeneity has a relatively large impact (up to 10%) on sea salt radiative forcing over coastal waters [ABSTRACT FROM AUTHOR]

Abstract: The nonsphericity and inhomogeneity of marine aerosols (sea salts) have not been addressed in pertinent radiative transfer calculations and remote sensing studies. This study investigates the optical properties of nonspherical and inhomogeneous sea salts using invariant imbedding T‐matrix simulations. Dry sea salt aerosols are modeled based on superellipsoidal geometries with a prescribed aspect ratio and roundness parameter. Wet sea salt particles are modeled as coated superellipsoids, as spherical particles with a superellipsoidal core, and as homogeneous spheres depending on the level of relative humidity. Aspect ratio and roundness parameters are found to be critical to interpreting the linear depolarization ratios (LDRs) of NaCl crystals from laboratory measurements. The optimal morphology parameters of NaCl necessary to reproduce the measurements are found to be consistent with data gleaned from an electron micrograph. The LDRs of wet sea salts are computed based on inhomogeneous models and compared with the measured data from ground‐based LiDAR. The dependence of the LDR on relative humidity is explicitly considered. The increase in the LDR with relative humidity at the initial phase of deliquescence is attributed to both the size increase and the inhomogeneity effect. For large humidity values, the LDR substantially decreases because the overall particle shape becomes more spherical and the inhomogeneity effect in a particle on the LDR is suppressed for submicron sea salts. However, the effect of inhomogeneity on optical properties is pronounced for coarse‐mode sea salts. These findings have important implications for atmospheric radiative transfer and remote sensing involving sea salt aerosols. [ABSTRACT FROM AUTHOR]

An ice crystal single-scattering property database is developed in the microwave spectral region (1 to 874 GHz) to provide the scattering, absorption, and polarization properties of 12 ice crystal habits (10-plate aggregate, 5-plate aggregate, 8-column aggregate, solid hexagonal column, hollow hexagonal column, hexagonal plate, solid bullet rosette, hollow bullet rosette, droxtal, oblate spheroid, prolate spheroid, and sphere) with particle maximum dimensions from 2 µm to 10 mm. For each habit, four temperatures (160, 200, 230, and 270 K) are selected to account for temperature dependence of the ice refractive index. The microphysical and scattering properties include projected area, volume, extinction efficiency, single-scattering albedo, asymmetry factor, and six independent nonzero phase matrix elements (i.e. P 11 , P 12 , P 22 , P 33 , P 43 and P 44 ). The scattering properties are computed by the Invariant Imbedding T-Matrix (II-TM) method and the Improved Geometric Optics Method (IGOM). The computation results show that the temperature dependence of the ice single-scattering properties in the microwave region is significant, particularly at high frequencies. Potential active and passive remote sensing applications of the database are illustrated through radar reflectivity and radiative transfer calculations. For cloud radar applications, ignoring temperature dependence has little effect on ice water content measurements. For passive microwave remote sensing, ignoring temperature dependence may lead to brightness temperature biases up to 5 K in the case of a large ice water path. [ABSTRACT FROM AUTHOR]

To derive the bulk radiative properties of ice clouds, aircraft contrails and snow grains, which are fundamental to atmospheric radiative transfer calculations in downstream applications, it is necessary to accurately simulate the scattering of light by individual ice particles. An ice particle optical property database reported in 2013 (hereafter, TAMUice2013) is updated (hereafter, TAMUice2016) to incorporate recent advances in computation of the optical properties of nonspherical particles. Specifically, we employ the invariant imbedding T-matrix (II-TM) method to compute the optical properties of particles with small to moderate size parameters. Both versions use the Improved Geometric Optics Method (IGOM) to compute the optical properties of large ice crystals, but TAMUice2016 improves the treatment of inhomogeneous waves inside the scattering particles in the case where ice is absorptive such as at infrared wavelengths. To bridge the gap between the extinction efficiencies computed from the II-TM and the IGOM, TAMUice2016 includes spectrally dependent higher order terms of the edge effect in addition to the first order counterpart considered in TAMUice2013. Furthermore, the differences between TAMUice2013 and TAMUice2016 are quantified with respect to the computation of the bulk optical properties of ice clouds. [ABSTRACT FROM AUTHOR]

Constructing an appropriate particle morphology model is essential for realistic simulation of optical properties of atmospheric particles. This paper presents a model for generating surface roughness based on a combination of methods from discrete differential geometry combined with a stochastic partial differential equation for surface evolution introduced by Edwards and Wilkinson. Scattering of light by roughened particles is simulated using the Invariant Imbedding T-Matrix (II-TM) method. The effects of surface roughness on the single-scattering properties, namely, the phase matrix, asymmetry factor, and extinction efficiency, are investigated for a single wavelength in the visible range and for a range of size parameters up to x =50. Three different smooth shapes are considered: spherical, spheroidal, and hexagonal, the latter two in just the “compact particle” case of unit aspect ratio. It is shown that roughness has negligible effects on the optical scattering properties for size parameters less than 20. For size parameters ranging from 20 to 50, the phase matrix elements are more sensitive to the surface roughness than are two important integral optical properties, the extinction efficiency and asymmetry factor. As has been seen in studies using other forms of roughening, the phase function is progressively smoothed as roughness increases. The effect on extinction efficiency is to increase it, and on asymmetry factor is to decrease it. Each of these effects is relatively modest in the size range considered, but the trend of results suggests that greater effects will be seen for size parameters larger than ones considered here. [ABSTRACT FROM AUTHOR]

Abstract: A fundamental problem in remote sensing and radiative transfer simulations involving ice clouds is the ability to compute accurate optical properties for individual ice particles. While relatively simple and intuitively appealing, the conventional geometric-optics method (CGOM) is used frequently for the solution of light scattering by ice crystals. Due to the approximations in the ray-tracing technique, the CGOM accuracy is not well quantified. The result is that the uncertainties are introduced that can impact many applications. Improvements in the Invariant Imbedding T-matrix method (II-TM) and the Improved Geometric-Optics Method (IGOM) provide a mechanism to assess the aforementioned uncertainties. The results computed by the II-TM+IGOM are considered as a benchmark because the II-TM solves Maxwell׳s equations from first principles and is applicable to particle size parameters ranging into the domain at which the IGOM has reasonable accuracy. To assess the uncertainties with the CGOM in remote sensing and radiative transfer simulations, two independent optical property datasets of hexagonal columns are developed for sensitivity studies by using the CGOM and the II-TM+IGOM, respectively. Ice cloud bulk optical properties obtained from the two datasets are compared and subsequently applied to retrieve the optical thickness and effective diameter from Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Additionally, the bulk optical properties are tested in broadband radiative transfer (RT) simulations using the general circulation model (GCM) version of the Rapid Radiative Transfer Model (RRTMG) that is adopted in the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM, version 5.1). For MODIS retrievals, the mean bias of uncertainties of applying the CGOM in shortwave bands (0.86 and 2.13μm) can be up to 5% in the optical thickness and as high as 20% in the effective diameter, depending on cloud optical thickness and effective diameter. In the MODIS infrared window bands centered at 8.5, 11, and 12μm, biases in the optical thickness and effective diameter are up to 12% and 10%, respectively. The CGOM-based simulation errors in ice cloud radiative forcing calculations are on the order of 10Wm−2. [Copyright &y& Elsevier]

Abstract: The invariant imbedding T-matrix method (II-TM) is employed to compute the optical properties of randomly oriented ice crystals of various shapes including hexagonal columns, hollow columns, droxtals, bullet rosettes and aggregates. The II-TM is shown to be numerically stable and capable of obtaining the single-scattering properties of hexagonal ice crystals with size parameters up to 150. The 22° and 46° halo peaks in the phase function of compact hexagonal ice crystals begin to emerge at a size parameter of approximately 80 and tend to become insensitive to particle size as the corresponding size parameter approaches 150. Furthermore, the II-TM solutions are shown to be in agreement with their counterparts based on the discrete dipole approximation (DDA) method and the pseudo-spectral time-domain (PSTD) method. In addition, the accuracy of the improved geometric-optics method (IGOM) is examined for randomly oriented hexagonal ice crystal cases over a wide size-parameter range from the resonant to geometric-optics regimes. The II-TM is also used to study the effects of particle surface roughness and internal inclusions on the single-scattering properties of ice particles. [Copyright &y& Elsevier]

Abstract: The extended boundary condition method (EBCM) and invariant imbedding method (IIM) are two fundamentally different T-matrix methods for the solution of light scattering by nonspherical particles. The standard EBCM is very efficient but encounters a loss of precision when the particle size is large, the maximum size being sensitive to the particle aspect ratio. The IIM can be applied to particles in a relatively large size parameter range but requires extensive computational time due to the number of spherical layers in the particle volume discretization. A numerical combination of the EBCM and the IIM (hereafter, the EBCM+IIM) is proposed to overcome the aforementioned disadvantages of each method. Even though the EBCM can fail to obtain the T-matrix of a considered particle, it is valuable for decreasing the computational domain (i.e., the number of spherical layers) of the IIM by providing the initial T-matrix associated with an iterative procedure in the IIM. The EBCM+IIM is demonstrated to be more efficient than the IIM in obtaining the optical properties of large size parameter particles beyond the convergence limit of the EBCM. The numerical performance of the EBCM+IIM is illustrated through representative calculations in spheroidal and cylindrical particle cases. [Copyright &y& Elsevier]

Abstract: Three terms, “Waterman''s T-matrix method”, “extended boundary condition method (EBCM)”, and “null field method”, have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIM+SOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIM+SOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIM+SOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIM+SOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging. [Copyright &y& Elsevier]

Abstract: A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method. [Copyright &y& Elsevier]

Abstract: The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM. [ABSTRACT FROM AUTHOR]

Electromagnetic wave scattering by ice particles is commonly modeled by defining representative habits, including droxtals, columns, plates, and aggregates, although actual particles in the atmosphere can be even much more complex. In this study, we examined a superspheroidal approximation method for modeling electromagnetic wave scattering by ice crystals. Superspheroid can be associated with a shape index (SI) defined by the particle volume and average projected area. Corresponding to realistic ice crystals, suitable superspheroid models with the same SI (that means, identical volume and average projected area) and aspect ratio can be identified as surrogates for optical property calculations. We systematically compared the optical properties of ice crystals and superspheroids at 33 microwave bands in the range of 3–640 GHz and at three representative visible or infrared wavelengths (0.66, 2.13, and 11 μm). It was found that the single-scattering properties of compact ice crystal habits and their superspheroidal model particles were quite close. For an aggregate with sparse distribution of elements, a superspheroid model produces relatively large errors because the aspect ratio may not be sufficient to describe a particle shape. However, the optical similarity of a superspheroid and an aggregate is still encouraging. [ABSTRACT FROM AUTHOR]

Inclusions of air bubbles or soot particles have significant effects on the single-scattering properties of ice crystals, effects that in turn have significant impacts on the radiation budget of an atmosphere containing the crystals. This study investigates some of the single-scattering effects in the case of hexagonal ice crystals, including effects on the backscattering depolarization ratio, a quantity of practical importance in the interpretation of lidar observations. One distinguishing feature of the study is an investigation of scattering properties at a visible wavelength for a crystal with size parameter ( x ) above 100, a size regime where one expects some agreement between exact methods and geometrical optics methods. This expectation is generally borne out in a test comparison of how the sensitivity of scattering properties to the distribution of a given volume fraction of included air is represented using (i) an approximate Monte Carlo Ray Tracing (MCRT) method and (ii) a numerically exact pseudo-spectral time-domain (PSTD) method. Another distinguishing feature of the study is a close examination, using the numerically exact Invariant-Imbedding T-Matrix (II-TM) method, of how some optical properties of importance to satellite remote sensing vary as the volume fraction of inclusions and size of crystal are varied. Although such an investigation of properties in the x >100 regime faces serious computational burdens that force a large number of idealizations and simplifications in the study, the results nevertheless provide an intriguing glimpse of what is evidently a quite complex sensitivity of optical scattering properties to inclusions of air or soot as volume fraction and size parameter are varied. [ABSTRACT FROM AUTHOR]