In this paper we examined an ensemble of 50 large ice crystals of irregular shapes. To optimize calculations, each particle has no more than 20 faces that were randomly generated. The calculations were performed for particles with a size of 15 microns, with an incident radiation length of 0.532 microns. It is shown that for an ensemble of particles a coherent peak appears in the vicinity of the backward scattering direction, as well as the effect of negative polarization, which we studied in detail on a fixed shape of a single particle.
Previously, we built a database for a single particle with a random polyhedral shape. The solution was obtained for a size range from of 10 to 300 microns at a wavelength of 0.532 microns. The particle selected was the one closest to the average in the ensemble of generated particles. In this work, a different approach to building the database is implemented: an arbitrary particle with a random shape and size is generated from the range of particle sizes attached to the database. The report examines the differences between the two approaches in building the database.
The paper presents a comparison of numerical solutions for the problem of light scattering on ice particles using methods of geometric and physical optics. The solutions were developed for irregularly shaped particles ranging in size from 10 to 100 μm, with a wavelength of 0.532 μm. The results of the comparison of the light scattering matrix over the entire direction sphere indicate that the solution within the framework of geometric optics approximation is in good agreement with the solution within the framework of physical optics over the entire scattering sphere, except for the vicinity of scattering in the forward and backward directions.
The paper presents the problem of scattering of a plane monochromatic wave by small nonspherical dielectric particles that prevail in cirrus clouds is considered: hexagonal plates and columns, droxtalls and particles of arbitrary shape. The calculations were carried out at wavelengths 0.532 μm and refractive indices 1.3116. The solutions were obtained by the discrete dipole method (ADDA v. 1.4) and complement the previously obtained database for large particles, which is used to interpret the lidar signal. All calculations were performed for randomly oriented particles and far field.
This paper it is shown that for an effective study of cirrus clouds by the method of laser polarization sensing, it is necessary to have: at least two wavelengths (for example, 0.532 and 1.064 μm); the ability to construct a color ratio for this pair of wavelengths; and the ability to measure the lidar and depolarization ratios at any from wavelengths. The use of a wavelength with strong absorption for ice (for example, 1.55 or 2.15 μm) is demonstrated to be promising for retrieving the average particle size in the cloud. Therefore, the combined use backscatter ratios measured by lidar (color, lidar, and depolarization ratios) demonstrates its effectiveness both in retrieving the shape and size of cirrus cloud particles.
The paper presents the elements of the light scattering matrix for atmospheric ice aggregated particles, consisting of "bullets" with the number of particles from 1 to 6. The calculation of the scattering matrices was carried out within the geometric optics approximation and single scattering. The spatial orientation of aggregates is random, the refractive index is 1.3116 (for a wavelength of 0.532 μm). The dependence of the light scattering matrix elements on the number of particles in aggregates is presented. The results can be used for interpretation of the data retrieved from laser sensing of crystalline clouds from ground and space.
Among the ice crystals of cirrus clouds, there are crystals of irregular shape. The imperfection of ice crystals can be both internal (e.g. inclusions such as air bubbles or soot particles) and external (e.g. surface roughness). Advanced studies showed that these imperfections have to be taken into account, because they affect significantly on the single-scattering properties of the ice crystal. The paper presents a solution to the problem of light scattering on ice crystal hexagonal tubes. This particle shape is the simplest model of a particle with internal inclusions. The model was based on the most common shape of a crystal observed in cirrus clouds - a hexagonal column with a ratio of base diameter to height of 0.69, in which a through hole was made, with a variable geometry. The solution was obtained within the geometrical optics approximation for the refractive index of ice 1.3116. The optical characteristics of hexagonal tubes are compared with non-convex particles (hollow columns) available in the database.
The paper presents the phenomenon of negative polarization for large randomly oriented irregular particles what occurs as a result of interference between specific reflected waves associated with geometric optical trajectories of light beams for four refraction/reflection events. All calculations were performed for randomly oriented particles with a convex irregular shape. We used our physical optics approximation computer algorithm where the light scattered inside the particle consists of many plane-parallel beams. It is shown that the appearance of a backscattering peak is characteristic of the trajectories of light beams with any number of refraction/reflection events; however, only trajectories with four events (two internal reflections and two refractions at the exit faces of the particle) create negative polarization.
The paper presents the light backscattering matrices for crystal particle of an irregular convex shape of the size of 200 micrometers with different refractive indices within the physical optics approximation. The calculation of matrices was carried out at the wavelengths of incident light of 0.532 micrometers, for the case of an arbitrary spatial orientation of particles. The matrices can be used to study mineral dust cloud particles.
This paper presents the results of calculations and analyzes the backscattering matrices of random oriented ice crystals, typical for cirrus clouds. The backscattering matrices were calculated within the physical optics approximation for lidar (wavelength 0.355 μm) and the discrete dipole approximation for 94 GHz radar (wavelength 3189 μm) with the refractive indices of ice – 1.3249+0i and 1.7864+0.0032i respectively. For the first time, it was possible to correctly calculate the ratio of radar and lidar signals in the direction of backscatter, called the radar-lidar ratio. The radar-lidar ratio is obtained for a wide particle size distribution for typical ice crystal shapes in cirrus clouds: hexagonal column and plate, bullet, droxtal, aggregate, bullet-rosette, arbitrary shape and sphere. As a result, it is shown that the radar-lidar ratio can be used to estimate the ice crystals size in cirrus clouds. The radar-lidar ratio for the EarthCARE satellite was unambiguously obtained for an adequate model of the sizes and shapes of ice crystals of a cirrus cloud.
Publisher’s Note: This paper was originally published on 7 December 2022, and a revised version of this manuscript was published on 17 March 2023. If you downloaded the original PDF but are unable to access the revision, please contact SPIE Digital Library Customer Service for assistance.
The paper presents the results of numerical simulation of the signal of a scanning lidar probing cirrus clouds. Two types of clouds were studied: clouds consisting of randomly oriented particles of arbitrary shape and predominantly oriented hexagonal columns, and clouds consisting of randomly oriented particles of arbitrary shape and predominantly oriented hexagonal plates. The obtained results show good agreement between the calculated data and the results of experimental observations on the scanning lidar of the V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Sciences. The capability of a scanning lidar to determine the flutter angle of oriented particles based on the analysis of the lidar signal intensity and the depolarization ratio is demonstrated.
The paper presents the results of comparing numerical solutions to the problem of light scattering on atmospheric ice particles by methods of geometric and physical optics. The solution was constructed for hexagonal shaped particles (hexagonal ice column) and droxtals. The results of the comparison of the light scattering matrix over the entire sphere of the direction showed that in the direction of scattering strictly backward, the use of the geometric optics approximation can lead to significant errors, especially for hexagonal particles, which are characterized by the presence of angular reflection
A technique is proposed that makes it possible to significantly accelerate the solution of the problem of light scattering in the exact backscattering direction on particles larger than 100 microns within the framework of the physical optics method. The peculiarities of this technique is that the solution is constructed within the vicinity of a small number of nodal points. Then, in the resulting solution, one complete period of interference oscillations is allocated and the light scattering matrix is averaged in this range. The average value is entered into the database. In this way, it was possible to build a complete database of backscattering matrices for atmospheric ice particles with sizes from 10 to 1000 microns for wavelengths of 0.355, 0.532, 1.064, 1.55, 2 and 2.15 microns. The results obtained make it possible to improve the algorithms for interpreting the data of laser sensing of cirrus clouds.
The paper presents a solution to the problem of light scattering by small randomly oriented hexagonal ice crystals of cirrus clouds. The solution was obtained both within the discrete dipole approximation and within the physical optics approximation. The particle sizes ranged from 0.2 to 6 μm. The wavelength of the incident radiation is 0.532 μm, the refractive index is 1.3116. The results of the comparison of the solutions obtained within the framework of the discrete dipole approximation with the physical optics approximation are shown. It is found that the solutions are in good agreement, however, to solve the problem of light scattering in the vicinity of the backward direction, which is important for the interpretation of lidar data, it is necessary to continue the calculations by the discrete dipole approximation up to particle sizes of about 10 μm.
The paper presents a solution to the problem of light scattering by small randomly oriented ice crystals of arbitrary shape. The solution was obtained within the discrete dipole approximation. The particle sizes ranged from 0.02 up to 4 μm. The wavelength of the incident radiation is 0.532 μm, the refractive index is 1.3116. The influence of the number of dipoles per lambda and number of orientations on the convergence of the solution is shown. It is shown that the computation time has an exponential law dependence on particle size.
The paper presents peculiarities of polarization at vicinity of near backscattering direction for large randomly oriented irregular particles. We used our physical optics approximation where the light scattered inside the particle consists of many plane-parallel beams. It is shown that the backscattering peak is caused by of interference between the light beams with any number of refraction/reflection events; however, only pair of conjugate beams with four events (two internal reflections and two refractions at the exit faces of the particle) lead to local minimum in polarization element in scattering (Mueller) matrixes and create negative polarization.
Scattering of light by ice crystals of cirrus clouds is an important problem for remote sensing of clouds and the atmosphere. Such a solution is necessary for the interpretation of data obtained be the active and passive remote sensing instruments, such as lidars and photometers. Ice crystals in cirrus clouds are large non-spherical particles. To solve the problem of light scattering by large non-spherical particles, it is not possible to apply rigorous numerical methods such as FDTD, DDA, PSDT, due to their high computational complexity for large particles. This problem also cannot be solved within the framework of the classical geometric optics approximation, since this method does not take into account such phenomena as diffraction and interference, which have a significant effect in the vicinity of the backscattering direction. This report presents the solution for the problem of light scattering by non-spherical particles with sizes from 10 to 1000 μm. The results were obtained within the framework of the physical optics approximation. The obtained database of light scattering matrices allows one to improve the accuracy of interpretation of laser sounding data of atmospheric aerosol and crystal clouds for lidars and remote sensing applications.
The elements of light backscattering matrix for atmospheric ice hexagonal particles with distorted shapes with random spatial orientation were calculated within the physical optics approximation. Three different set of particle geometry shapes was created by distortion of a solid hexagonal column for calculation. The distortion angle for each method is 0- 50 degrees. The wavelength of the incident radiation was 1.064 μm. The backscattering cross section, the linear depolarization ratio, and the lidar ratio are presented.
The paper presents a solution to the problem of light scattering by randomly oriented particles of irregular shape for particles with sizes of 100, 140, 170 and 200 microns for a wavelength of 0.532 microns for various refractive indices. The solution was constructed both within the framework of physical optics (for the backward scattering direction) and geometric optics (for scattering angles in the range from 0 to 180 degrees). The obtained solutions made it possible to construct a diagram of the dependence of the geometric albedo of a particle on the maximum degree of polarization to verify the Umov effect. It was found that when the imaginary part of the refractive index is less than 0.001, the Umov effect is performed with good accuracy. However, for the case when the imaginary part of the refractive index is greater than 0.001 and the specular component of the scattered radiation begins to dominate in the solution, the Umov effect is violated.
The optical characteristics of atmospheric ice particles are usually calculated within the framework of the physical optics approximation, since particle sizes generally vary from 10 to 1000 microns. However, the results of experimental measurements show that ice crystals up to 10 microns in size are observed in cirrus clouds of the upper tier. The report presents a solution to the problem of light scattering for particles, obtained in the framework of the methods of the physical optics and discrete dipoles. Based on the solution, such important optical characteristics as depolarization and spectral ratios were calculated. Two limiting cases are considered: ideal hexagonal particles and randomly shaped particles.
This work presents the results of calculation and analysis of the light scattering matrix for aggregates of atmospheric hexagonal ice particles, which are occurred in cirrus clouds. The two types of base particle shape for aggregates were considered: hexagonal column and hexagonal plate. For both shapes the two types of arrangement of particles in aggregates were chosen: compact and non-compact. As the result the 4 sets of aggregates were built: 1) compact hexagonal columns, 2) non-compact hexagonal columns, 3) compact hexagonal plates, and 4) non-compact hexagonal plate. Each set consist of 9 aggregates distinguished by number of particles (1-9) in them, and particles in every single aggregate are with the same shape and size but with different spatial orientation. The calculations of light scattering matrices for all (36 in total) aggregates were performed for the case of arbitrary orientation within the geometric optics approximation. Dependences of the first matrix element on number of particles in aggregate, with different types of arrangement of particles, and for two types of shapes are presented.
Calculations of reflected solar radiation in crystal clouds composed of horizontally oriented plates or Parry columns are presented. The radiation intensity was simulated for a limited set of observation and illumination conditions using the optical characteristics of clouds calculated by the geometric optics method for particles with shape parameters 0.1 (plates) and 2.5 (Parry columns).
The paper presents a solution to the problem of light scattering on atmospheric ice crystals of irregular shape. In this work, the calculation and study of backscatter ratios: the backscattering cross section, lidar and depolarization ratios of ice hexagonal particles, the right dihedral angle ξ of which was distorted in the range from 0° (regular particle) to 50°, were carried out. The calculation was performed for random oriented ice crystal particles of irregular shape: a double hexagonal bullet, hollow and distorted hexagonal columns. The calculations were carried out within the physical optics approximation, the wavelength of the incident light was taken equal to 1.064 μm, and the refractive index was 1.3004. The results of a comparison of the optical properties of the investigated particles are presented.
The solution to the problem of light scattering by atmospheric hexagonal plates and columns, as well as arbitrary shaped particles with sizes from 10 to 100 microns, is presented. The solution is presented as a databank of light backscattering matrices and is intended for interpretation of data from ground-based and space-based lidars. The solution is obtained for typical wavelengths used in laser sensing problems: 0.355; 0.532; 1.064; as well as for the wavelengths of the near infrared range: 1.55; 2 and 2.15 μm. The solution was obtained within the framework of the physical optics method.
When solving the problem of light scattering on ice crystals of cirrus clouds, two limiting cases can be distinguished: a model of ideal hexagonal particles and a model of randomly shaped particles. As already shown, the optical characteristics of particles that are closer to the real forms of atmospheric crystals are not go beyond these limiting cases. Before solving the problem of light scattering within the framework of the physical optics method, it is necessary to carry out a number of basic estimates. These estimates include the study of the convergence of the numerical solution on the number of iterations of the beam splitting algorithm and the number of spatial orientations of the particle during its averaging. The results of this study are presented in the report.
The optical characteristics of arbitrary shaped atmospheric ice crystals are necessary both for solving the problem of radiation transfer in the atmosphere and for interpreting lidar data. At the same time, there is an acute problem of studying the influence of the particle shape on its optical characteristics. Since the construction of a databank of the optical characteristics of cirrus clouds is a laborious task, it is necessary to reduce as much as possible the number of different particles, the superposition of which represent the values averaged over the entire ensemble of particles in the cloud. The report presents the results of calculations of the light scattering matrix for 500 different arbitrary shaped particles with 25 facets and the same particle size. The calculations were performed within the geometric optics approximation. According to the results of the analysis, several particles were selected whose optical properties are as close as possible to the optical properties of the entire ensemble.
The purpose of this work is to solve an important issue: the light scattering problem for ice crystals of cirrus clouds less than 10 μm and matching the obtained solution with the existing solution obtained within the physical optics approximation. The article presents a solution to the problem of light scattering by hexagonal ice particles of cirrus clouds with sizes from 0.05 to 5.17 μm for a wavelength 0.532 μm, obtained within the discrete dipole approximation. It is found that the obtained solution is in good agreement with the physical optics approximation in the vicinity of scattering angles of 0–10° (the vicinity of forward direction scattering). However, to solve the problem of light scattering in the vicinity of the backward scattering direction, which is important for the interpretation of lidar data, it is necessary to continue the calculations to sizes of the order of 20 μm. The results obtained are necessary for constructing algorithms for the interpretation of lidar data obtained by sounding cirrus clouds.
The paper presents a solution to the problem of light scattering by hexagonal atmospheric plates and columns, as well as irregularly shaped particles with sizes from 10 to 100 microns. The solution is presented in the form of a databank of light backscattering matrices. The solution was obtained for typical wavelengths used in laser sensing problems: 0.355, 0.532, 1.064 μm; as well as for the wavelengths of the near infrared range: 1.55, 2 and 2.15 μm. At wavelengths of 0.532 and 1.064 μm, in addition to the refractive index of ice, the refractive index of the dust aerosol was used: 1.48+i•0.002 and 1.6+i•0.002, respectively. The solution was obtained within the framework of the physical optics method developed by the authors. Based on the calculated light backscattering matrices, the values of the color and linear depolarization ratios were obtained. It is shown that the power laws previously identified by the authors are violated in the presence of absorption, in particular, for hexagonal particles with sizes up to 100μm, with an imaginary part of the refractive index greater than i•0.0004, significant deviations from the power law are observed. For irregularly shaped particles at wavelengths for which there is no absorption, smooth power law dependences are seen.
This paper presents the results of calculation and analyzes the light scattering matrix of random oriented ice particles of non-convex shape (hollow column) with cavity angles from 0 to 50 degrees for lidar wavelengths of 0.355, 0.532, and 1.064 microns and refractive indices of 1.3249, 1.3116, and 1.3004. The calculation was carried out within both physical and geometrical optics approximation methods for particle sizes varied from 10 to 100 microns. As a result, it is shown that differential scattering cross-section for non-convex shape (hollow column) demonstrates a power-law dependence on the particle size. However, the linear depolarization ratio has no simple dependence on particle size and is practically independent of wavelength for small particles (L<50μm). The linear depolarization ratio increases from 0.2 up to 0.5–0.8 with an increase of the cavity angle of the crystal. The elements of the light scattering matrix depending on scattering and cavity angle are given.
This paper presents the results of calculating and analyzing the light scattering matrix of aggregates of atmospheric hexagonal ice particles located in cirrus clouds. Two types of basic particle shapes for aggregates are considered: a hexagonal column and a hexagonal plate. For both forms, two types of particle arrangement in aggregates were chosen: compact and non-compact. As a result, 4 sets of aggregates were built: compact hexagonal columns, non-compact hexagonal columns, compact hexagonal plates, and non-compact hexagonal plates. Each set consists of 9 aggregates differing in the number of particles in them, and the particles in each individual aggregate have the same shape and size, but different spatial orientation. The light scattering matrices for all aggregates were calculated for the case of arbitrary orientation in the geometric optics approximation. Dependences of the first element of the matrix on the number of particles in aggregate, with different types of particle arrangement, and for two types of shapes are given.
The Umov effect is the inverse correlation between the maximum of the linear polarization of the light scattered on an object and the geometrically albedo of this object. The importance of studying this effect should be considered in the context of one of the complex and important tasks of remote sensing: determining the concentration of particles in optically thin clouds. Since the intensity of the scattered light depends on two unknown quantities: the concentration of particles in the cloud and the phase function of the particles of the cloud. Then to retrieve the concentration from the measured signal, it is necessary to know the phase function in advance. In real observations, the phase function is, usually, not known. The Umov effect will make it possible to estimate some necessary unknown characteristics of particles in a cloud, which determine the phase function. This paper is devoted to the study of this effect for particles with sizes much larger than the wavelength of the incident light. The report presents a solution to the problem of light scattering by randomly oriented particles of irregular shape for particles with sizes of 100 and 200 microns, for a wavelength of 0.532 microns. The solution was obtained within the both frameworks: the physical optics method and the geometric optics approximation. It was found that if the imaginary part of the refractive index less than 0.001, the Umov effect is observed with good accuracy for particles of size from 100 to 200 microns. However, the Umov effect is violated when the imaginary part of the refractive index is greater than 0.001.
Simultaneous measurement of lidar and radar signals returned from the same cirrus clouds is a prospective method for retrieving the cloud microphysics, i.e. size and shape of the ice crystals constituting the cloud. In this study, the ratio of the backscattered signals of lidar and radar called the lidar-radar ratio has been calculated for the first time for typical shapes of ice crystals and wide distribution of the crystals over their sizes. It is shown that it is the lidar-radar ratio that is most sensitive to crystal sizes while the lidar depolarization ratio is most sensitive to crystal shapes.
The report presents database of microwave radiation scattering matrices for ice particles of cirrus clouds. The calculations were performed for meteorological radars operating at frequencies of 35 and 94 GHz. The calculation was carried out for randomly oriented ice particles of the following shapes: hexagonal plates and columns, aggregate, bulletrosette, droxtal and irregular shape particle. The particle size ranges from 10 to 10000 microns. It has been found out that the Rayleigh scattering theory for these radar wavelengths is not applicable to the full spectrum of ice crystals observed in the clouds. Specific threshold sizes are determine for each crystal shape. The results can be used to interpret joint radar-lidar measurements.
The paper presents the results of numerical calculations of the scattered light intensity by large randomly oriented particles of arbitrary shapes with flat faces in the backscattering cone [170°, 180°], performed in the physical optics approximation. It is shown that light scattered in the backscattering direction for a single large particle of arbitrary shape is divided into coherent and incoherent parts, similar to a phenomenon well known in the field of multiple scattering. For models of crystalline particles of arbitrary shapes used in this work, the coherent part forms a coherent backscattering peak, whose angular dimensions are approximately equal to the ratio of wavelength/(particle size). The incoherent part is close to smooth geometrical optical solutions.
The paper presents the characteristics of light scattering on ice particles of cirrus clouds within the physical optics approximation for wavelengths of 0.355, 0.532, 1.064, 1.55 and 2 μm. The calculation was carried out for hexagonal ice columns and particle with arbitrary shape with their random spatial orientation. Particle sizes range from 10 to 1000 microns. It is shown that the color ratio of a polarization lidar operating at wavelengths of 0.532, 1.064, and 1.55 μm allows one to construct algorithms for retrieving the particle size in cirrus clouds.
The article presents the data bank of light scattering matrices for ice hexagonal particles with a preferentially horizontal spatial orientation. The calculations were performed within the geometric optics approximation for flutter angles from 0 to 180 degrees in increments of 1 degree. It is shown that the light scattering matrix for randomly oriented ice crystals of cirrus clouds is fundamentally different from the light scattering matrix for particles with a preferentially horizontal spatial orientation. This fact can play a significant role in solving the radiation transfer problem through cirrus clouds and have to be taken into account in climate modeling.
In this work the result of calculation of backscattering matrices for non-spherical ice particles for 1.55 μm and 2 μm wavelengths is presented. The Physical Optics approximation method was used for solving this problem. The maximal dimension of particles varies from 10 μm to 1000 μm according to D. Mitchel dependency. The calculations were performed for random spatial orientation of particles. The results can be used for retrieving of microphysical properties (i.e. size and habit) of cirrus particles.
We present a solution to the problem of light scattering by spherical particles, adapted for interpreting the signals of portable lidars for autonomous vehicles. The solution was obtained for typical wavelengths used in laser sensing tasks: 0.355, 0.532, 0.905, 0.940, 1.064, 1.55, 2.15, and 10.6 μm. The solution was obtained within the framework of the Mie scattering theory for water and ice. The inherent high-frequency oscillations in the backscattering direction are smoothed out by means of a moving average, which allows one to construct fast and efficient algorithms for particle size distributions observed in the atmosphere. The resulting solution is presented in the form of a data bank, which is available in the public domain.
Results of the experiments on polarization laser sensing of aircraft contrails performed with the lidar developed at the National Research Tomsk State University are described. The altitudes of the lower and upper borders, backscattering phase matrices, optical thickness, and scattering ratios of the observed aerosol formations are determined. Microstructure parameters of the contrails are estimated by comparing the elements of backscattering phase matrices not only obtained from lidar experiments, but also calculated theoretically. The meteorological conditions for the formation of the preferred horizontal spatial orientation of ice crystals in contrails are established.
The paper presents the calculations of the light scattering matrix for quasi-horizontally oriented crystal ice particles. It is shown that in the general case the light scattering matrix for the transport equation is the function of seven variables, and for its calculation it is necessary to have a complete scattering matrix, depending on 9 independent variables. The report provides a number of simplifications that allow us to use of a light scattering matrix, depending on five variables, in radiation transfer problems, and that need the matrix as a function of four variables to calculate it. This approach significantly (millions of times) speeds up the calculations.
Possibilities to retrieve the microphysical properties of cirrus clouds consisting of ice crystals from lidar and radar signals simultaneously reflected from the same cloud are discussed. It is stated that the measurements of the radar-lidar color ratio is promising. This ratio is easy calculated with the available data obtained in the physical-optics and discrete dipole approximations.
Angular distributions of intensity of microwave radiation scattered by ice crystals of cirrus clouds are calculated with the discrete dipole approximation. The wavelength of the incident radiation is chosen as 3.2 mm and the ice crystals are the hexagonal plates and columns with both regular and irregular shapes with particle sizes up to 20 mm. The cases of both fixed and random particle orientations are considered.
The way for taking absorption impact into account for light scattering on atmospheric ice particles within physical optics approximation is presented. For arbitrarily shaped particle the calculations with three different conditions within physical optics approximation were conducted: without absorption accounting; simple absorption accounting before diffraction; absorption accounting based on diffraction on beam shape. The results show that with absorption accounting with using of all vertices of beam shape the different face function near backscattering direction.
In this work light absorption effect for atmospheric ice crystals for near-infrared electromagnetic spectrum is presented. The software for calculating the scattering matrices was modified for a crystal with absorption. The dependence of the M11 element of the scattering matrix on the zenith angle has been received within the physical optics approximation for three wavelengths: 0.532 μm, 1.064 μm, 1.6 μm, for convex and non-convex crystals, and for two conditions: with absorption factor and without it. The comparison of the M11 element of the scattering matrix for these conditions shows negligible changing of intensity for 0.532 μm and 1.064 μm wavelengths and significant decrease of intensity for 1.6 μm.
The paper presents the extinction matrix for an ensemble of ice hexagonal plates and columns. The calculations were carried out for particles with characteristic sizes from 10 to 100 μm, for wavelengths from 0.3 to 10 μm, assuming the gamma distribution over particles size width parameter μ<4. It is shown that for the visible range of wavelengths, the extinction matrix of an ensemble of atmospheric ice crystals is unit with a coefficient being equal to the double area of the particle projection. It is also shown that in the IR region this representation of the extinction matrix is valid only for hexagonal columns, bullets and similar crystals with a characteristic size larger than 20 μm for wavelengths less than 8 μm.
Microphysical properties of the cirrus cloud ice crystals with the horizontal orientation are required for numerical models of radiation balance. Retrieving the orientation distributions function of the crystals from a vertically pointing lidar is a very complicated problem because of lake of the information. The paper shows that the lidars with zenith scanning can be effectively used to retrieve the degree of the horizontally oriented particles (flutter). It is also shown that all the elements of the Mueller matrix give no extra information as far as the depolarization ratio compare to the lidar ratio. Optical properties of the hexagonal ice plates with the size of 10, 30, 100 and 300 μm for the wavelengths of 0.355, 0.532 and 1.064 μm were obtained within the physical optics approximation.
New algorithm for light scattering by concave ice crystals was developed. It is based on the beam-splitting algorithm for
convex type of crystals that was developed in IAO RAS. For implementation of this algorithm the program for
calculation of the light scattering matrices was created. The results of test calculations that were carried out within the
geometrical optics (GO) approximation show good agreement with the ray-tracing algorithm. The light scattering
diagram for hollow columns with various cavity angles within the GO approximation and the dependence of M11
element of scattering matrix on zenith angle for various angle of crystal cavity within physical (PO) approximation were
received.
The current state of the problem of light scattering by ice crystal particles of cirrus clouds is presented for the problem of interpreting the lidar signal. A short overview of existing methods and approaches to the solution of the problem of light scattering by nonspherical particles is presented. The results obtained within the framework of the physical optics approximation agree well with the results of experimental observations and can be used to interpret lidar data. The solution of the light scattering problem is available as a data bank of the Mueller matrices.
Optical properties of the cirrus cloud ice crystals with preferred azimuthal orientation are required for current numerical models of the Earth's radiation balance. Retrieving the orientation distributions function of the crystals from a vertically pointing polarization lidar measuring the full Mueller matrix is a very complicated problem because of lake of information. Lidars with zenith scanning can be used only to retrieve the properties of horizontally oriented particles. The paper shows that if the particles have preferred azimuthal orientation, the polarization lidars with azimuthal scanning should be used. It is also shown that all the elements of the Mueller matrix give no extra information compare to the depolarization ratio. Optical properties of preferred azimuthal oriented hexagonal ice columns with size from 10 to 1000 μm for wavelengths of 0.355, 0.532 and 1.064 μm were collected as a data bank.
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