Sensitivity of depolarized lidar signals to cloud and aerosol particle properties

Measurements from depolarized lidars provide a promising method to retrieve both cloud and aerosol properties and a versatile complement to passive satellite-based sensors. For lidar observations of clouds and aerosols, multiple scattering plays an important role in the scattering process. Monte Carlo simulations are carried out to investigate the sensitivity of lidar backscattering depolarization to cloud and aerosol properties. Lidar parameters are chosen to be similar to those of the upcoming space-based CALIPSO lidar. Cases are considered that consist of a single cloud or aerosol layer, as well as a case in which cirrus clouds overlay different types of aerosols. It is demonstrated that besides thermodynamic cloud phase, the depolarized lidar signal may provide additional information on ice or aerosol particle shapes. However, our results show little sensitivity to ice or aerosol particle sizes. Additionally, for the case of multiple but overlapping layers involving both clouds and aerosols, the depolarized lidar contains information that can help identify the particle properties of each layer.     

On the far field in the Lorenz-Mie theory and T-matrix formulation

The far field within the context of the Lorenz-Mie theory and the T-matrix formulation is usually expressed on the basis of the asymptotic properties of vector spherical waves. The radiation condition is taken into account by employing proper vector spherical functions as the expansion basis of the scattered field. The asymptotic behavior of the Hankel function is obtained from differential equations. The asymptotic far field can also be obtained from the Kirchhoff surface integral equation, in which the radiation condition has been implemented when it is derived from the Maxwell equations. This note is to present an explicit establishment of the relationship between the asymptotic far field and the near field in the Lorenz-Mie theory and the T-matrix formulation through the Kirchhoff surface integral.     

Effect of ice crystal shape and effective size on snow bidirectional reflectance

We tested the applicability of three rigorous radiative transfer computational approaches, namely, the discrete ordinates radiative transfer (DISORT) method, the adding–doubling approach, and an efficient computational technique based on Ambartsumian's nonlinear integral equation for computing the bidirectional reflectance of a semi-infinite layer. It was found that each of these three models, in a combination with the truncation of the forward peak of the bulk scattering phase functions of ice particles, can be used to simulate the bidirectional reflectance of a semi-infinite snow layer with appropriate accuracy. Furthermore, we investigate the sensitivity of the bidirectional reflectance of a homogeneous and optically infinite snow layer to ice crystal habit and effective particle size. It is shown that the bidirectional reflectance is not sensitive to the particle effective size in the visible spectrum. The sensitivity of the bidirectional reflectance in the near-infrared spectrum to the particle effective size increases with the increase of the incident wavelength. The sensitivity of the bidirectional reflectance to the effective particle size and shape is attributed fundamentally to the sensitivity of the single-scattering properties to particle size and shape. For a specific ice crystal habit, the truncated phase function used in the radiative transfer computations is not sensitive to particle effective size. Thus, the single-scattering albedo is primarily responsible for the sensitivity of the bidirectional reflectance to particle size, particularly, at a near-infrared wavelength.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.     

Dependence of extinction cross-section on incident polarization state and particle orientation

This note reports on the effects of the polarization state of an incident quasi-monochromatic parallel beam of radiation and the orientation of a hexagonal ice particle with respect to the incident direction on the extinction process. When the incident beam is aligned with the six-fold rotational symmetry axis, the extinction is independent of the polarization state of the incident light. For other orientations, the extinction cross-section for linearly polarized light can be either larger or smaller than its counterpart for an unpolarized incident beam. Therefore, the attenuation of a quasi-monochromatic radiation beam by an ice cloud depends on the polarization state of the beam if ice crystals within the cloud are not randomly oriented. Furthermore, a case study of the extinction of light by a quartz particle is also presented to illustrate the dependence of the extinction cross-section on the polarization state of the incident light.     

Optical properties of ice particles in young contrails

The single-scattering properties of four types of ice crystals (pure ice crystals, ice crystals with an internal mixture of ice and black carbon, ice crystals coated with black carbon, and soot coated with ice) in young contrails are investigated at wavelengths 0.65 and 2.13 μm using Mie codes for coated spheres. The four types of ice crystals show differences in their single-scattering properties because of the embedded black carbon whose volume ratio is assumed to be 5%. The bulk-scattering properties of young contrails consisting of the four types of ice crystals are further investigated by averaging their single-scattering properties over a typical ice particle size distribution found in young contrails. The effect of the radiative properties of the four types of ice particles on the Stokes parameters I, Q, U, and V is also investigated for different viewing zenith angles and relative azimuth angles with a solar zenith angle of 30° using a vector radiative transfer model based on the adding-doubling technique. The Stokes parameters at a wavelength of 0.65 μm show pronounced differences for the four types of ice crystals, whereas the counterparts at a wavelength of 2.13 μm show similar variations with the viewing zenith angle and relative azimuth angle. However, the values of the results for the two wavelengths are noticeably different.     

Theorems on symmetries and flux conservation in radiative transfer using the matrix operator theory

The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.     

Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium

We present both experimental and Monte Carlo-based simulation results for the diffusely backscattered intensity patterns that arise from illumination of a turbid medium with a polarized laser beam. A numerical method that allows the calculation of all 16 elements of the two-dimensional Muller matrix is used; moreover, it is shown that only seven matrix elements are independent. To validate our method, we compared our simulations with experimental measurements, using a turbid medium consisting of 2.02-microm -diameter polystyrene spheres suspended in deionized water. By varying the incident polarization and the analyzer optics for the experimental measurements, we obtained the diffuse backscattering Mueller matrix elements. The experimental and the numerical results are in good agreement.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

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.     

Interior radiances in optically deep absorbing media—I Exact solutions for one-dimensional model

The exact solutions are obtained for a one-dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth-order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values. Except for extremely large values of the optical thickness of a layer, the reflection and transmission operators calculated from accurate starting values obtained by the Runge-Kutta method are orders of magnitude (a factor of 10¹¹ better in a typical case at unit optical depth) more accurate than those obtained by the use of the single scattering approximation for an optically thin layer. The relative error in the reflection and transmission operators is less than 10^-12 and 10^-8 respectively up to an optical thickness of 32,768 when calculated by this procedure, while the relative error in the interior radiance is less than 10^-8 at all points within a layer of optical thickness 32,768. It is shown that flux conservation is a poor test of the accuracy of a numerical method, since flux is conserved to all orders for a conservative medium when the doubling method is used, no matter how inaccurate the starting values may be.