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.
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.
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 report presents the results of a numerical simulation of the optical properties of cirrus clouds containing quasi-horizontally oriented crystals, as observed by a scanning lidar. Two models of the spatial orientation of plate-like crystals in a cirrus cloud are considered. In the first model, the orientation of the crystals was determined by the normal law, while in the second case, it was determined by the exponential law. The numerical results were used to interpret the experimental observation data. It is demonstrated that the use of the exponential law leads to a better agreement between theoretical and experimental data, particularly at small scanning angles.
The physical optics method occupies a leading position in solving the problem of light scattering by atmospheric ice particles for active remote sensing problems. At the same time, insufficient attention has been paid to the study of the lower limit of applicability of this method. In this report, the limit of applicability of the method of physical optics is studied on the example of five Platonic solids. For the validation of the method of physical optics developed at the Institute of Atmospheric Optics of the Siberian Branch of the Russian Academy of Sciences, the invariant imbedding Tmatrix method (IITM), the physical geometric optics method (PGOM), the discrete dipole approximation (ADDA) were used.
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 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.
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 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.
In this paper we show that in the problem of light scattering by one randomly oriented irregularly shaped particle, the effect of negative polarization arises. In addition, we indicate a physical mechanism that explains this effect, namely, negative polarization appears as a result of the contribution to the scattered radiation from conjugated quasi-planar light trajectories inside a particle that interfere with each other.
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.
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 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.
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 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.
Corner-reflection effect is the main feature at lidar soundings of cirrus clouds. In this paper, this effect is numerically studied in the case of plate-like quasi-horizontally oriented ice crystals of cirrus clouds. It is shown that the lidar signal as function of lidar tilt relative to the vertical can be used for inferring microphysical properties of ice crystals. In particular, if depolarization ratio at small lidar tilts is a small quantity it means that the crystals are plate-like and the plates are quasi-horizontally oriented. Appearance of a sharp step of depolarization ratio at the tilts of about 30° means that the transversal shapes of the crystals are regular. Otherwise, the transversal shapes are irregular.
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.
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.
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 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.
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 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.
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.
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.
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 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.
Phase matrixes for polyhedron particles of both regular and irregular shapes, where particle sizes exceed the wavelength of the incident light about 50 times, has been calculated numerically by use of both geometrical optics and physical optics approximations. The results are presented as the visual figures demonstrating the azimuthal symmetry of the phase matrixes.
The scattering matrixes for randomly oriented large particles of faceted shapes have been calculated using both the geometrical optics and physical optics approximations. We showed that the scattering matrixes are different for regular and irregular particle shapes since the corner reflection effect is predominant at the backward direction for the regular shapes. In the case of irregular shapes, the scattering matrixes have the common feature. Namely, the elements of the matrix reveal near the backward scattering direction some typical peaks that are explained by interference of the backscattered waves. In particular, the negative polarization effect known in astrophysics can be explained by the interference.
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.
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.
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.
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 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.
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 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 report presents the solution to the problem of light scattering on large ice spherical particles. The solution was obtained within the framework of the Lorenz-Mie light scattering theory. Since the solution in the exact backscattering direction has the interference oscillations that impede the analysis and comparison of the obtained data, the obtained solution has been averaged according to the moving average. Comparison of the obtained results with the existing solution for large nonspherical atmospheric crystals showed that irregular particles are in good agreement with spherical ones, while hexagonal particles have a significant discrepancy.
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 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.
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.
Lidar and radar are two useful tools for cirus clouds, which can provide the possibility to retrieve the vertical profiles of both the number density of particles and their microphysical characteristics, especially, when they operate together simultaneously. In this study, a multi-wavelength Lidar and a 35 Ghz Radar with polarization channels are employed to measure the properties of cirrus clouds in Hefei. The backscattering coefficient at 0.532 μm from lidar, and the effective reflectivity factor from radar are inversed for use. Furthermore, the quantities responsible for microphysics can be extracted and explained as the dimensionless values, such as the depolarization ratio and color ratio. Then these optical properties for cirrus cloud during campaigns are analyzed and compared with calculating results.
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.
Cirrus clouds consisting mainly of ice crystals are important components of the atmosphere which essentially modulate the radiative budget of the Earth. Until now, the microphysical properties (i.e., size and shape) of the ice crystals, as well as their number density are poorly known because of their great variability in time and space and difficulties of field measurements. At present, cirrus clouds are widely studied by various ground-based, airborne and spaceborne instruments. Among such instruments, lidars and radars are promising devices providing active remote sensing of the clouds. In the report, we present the results of the calculations the radar-lidar ratio explicitly at a reasonable model for the size and shapes of the cirrus ice crystals using the physical-optics approximation. We show that it is the radar-lidar ratio that is mainly informative for retrieving crystal sizes. Also, we calculate the depolarization ratios for both lidar and radar. We obtain that the lidar depolarization ratio is effective for estimating crystal shapes in cirrus clouds. Such data would be useful for interpreting any data obtained simultaneously by radars and lidars.
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 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.
The light scattering matrix is calculated for particles of the large-scale fraction of dust aerosols. It is shown that for randomly oriented particles the number of particle orientations needed for numerical calculations by exact methods like DDA becomes a crucial parameter. In particular, for particle with size parameters larger than 40 the number of orientations should be more than 1000.
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 work presents the solution for the light scattering problem by arbitrarily-shaped particles in all directions of scattering, in particular in the vicinity of the backward scattering direction. The solution was obtained within the framework of the geometrical optics approximation. The refractive index was equal to 1.3116. It was shown that the general contribution of scattering light for arbitrarily-shaped particles in the vicinity of the backscattering direction consists of the specular reflection of the particles and two types of non-specular optical beams. It is shown that the optical characteristics of the ice particles with arbitrary shapes correspond to experimental data.
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.
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.
In this study, a multi-wavelength Raman-mie Lidar, and a 35 Ghz Radar are employed to measure the properties of aerosol and cloud. The extinction at 0.355μm and 0.532μm and backscattering at 0.355μm, 0.532μm and 1.064μm coefficients from lidar, and the effective reflectivity factor from radar are inversed for use. Furthermore, the quantities responsible for microphysics can be extracted and explained as the dimensionless values, such as the linear depolarization ratio, the color ratio, and the other ratios. Then these microphysical properties for aerosol and cloud during campaigns are analyzed for further use.
In the paper the analyses of the lidar measurements data of optical parameters of the cirrus clouds over the Tomsk city are presented. The valuation of the microphysical properties of the cirrus clouds was done by the backscattering matrices that were measured by the high-altitude polarization lidar (wavelength is 0.532 μm) from National Research Tomsk State University in 2016-2018. For the interpretation of the laser sensing data we used the backscattering matrices database designed in V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, Siberian Branch. An attempt to interpret the measured matrix using the quasi-horizontal orientated hexagonal columns with the 1000 μm modal size Lmod is incorrect in view of the fact that the particles with this size are very unlikely in existence of nature. It was demonstrated that the calculated backscattering matrices together with proposed algorithm could be used for the valuation of microphysical properties of the measured backscattering matrices.
The scattering (Mueller) matrix has been calculated for the ice crystals of cirrus clouds within the framework of both the geometrical-optics and physical-optics approximations. It is shown that the geometrical-optics solution matches its physical-optics counterpart rather well at the intervals of the zenith scattering angles between 20° – 160° except some deviations in the regions of the halos of 22° and 46°. However, the difference between these solutions is essential in the vicinity of the forward and backward scattering directions. In particular, we show that the geometrical-optical singularity known for the element M11 at the backward scattering direction is accompanied by sign-changing contributions from different ray-trajectories for other elements of the Mueller matrix that was known earlier. These sign-changing peculiarities are inherent to the physical-optics solution as well.
In this paper, the calculation and the theoretical investigation of backscattering cross section were carried out as well as a lidar and linear depolarization ratios for the random oriented hexagonal ice columns. The right dihedral angle of the hexagonal ice column was distorted in a range from 0°(regular particle) to 50°. All calculations were obtained within the framework of the physical optics approximation. A wavelength of the incident light was assumed to be 1.064 μm, an index of refraction was taken as 1.3004. It has been shown that if the distortion of a right dihedral angle of the hexagonal ice column is larger than 10°, the secondary maximums in the backscattering cross section become observable due to a new type of the optical beams trajectory. Also, during the averaging over the particle distortion angle a linear depolarization ratio for the column could reach the value close to 0.7 relative units.
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.
The physical optics approximation is applied to calculate the backscattering Mueller matrix and the depolarization and color ratios for quasi-horizontally oriented hexagonal ice plates of cirrus clouds in the case of a tilted lidar. It is shown that the backscatter reveals some features caused by the corner reflection effect that is inherent to the pristine hexagonal ice plates. In particular, the backscatter creates sharp peaks of both the backscattering cross section and depolarization ratio at the lidar tilts of about 30 degrees off zenith. The experimental results obtained recently by Veselovskii et al. JQSRT, 2017;202:74–80 at the lidar tilt of 43 degrees have been interpreted as a partial manifestation of the corner reflection effect.
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.
This work presents the estimation of contribution of the main types of optical beams to the light backscatter for randomly oriented hexagonal ice column, the right dihedral angle of which was distorted within the range of 0° (regular particle) to 10°. Calculations were obtained within the physical optics approximation. The wavelength was 532 nm and the refractive index was 1.3116. The results showed that the total contribution of the main types of optical beams to the total backscattering cross section reach the value of 85% at small distortion angle of the hexagonal column and at substantial distortion angle the total contribution of the main types of optical beams decrease up to 55% of the total backscattering cross section. The obtained conclusions can significantly reduce the calculation time in the case when there is no need for high accuracy of the calculation.
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.
The data bank for the backscattering matrixes of cirrus clouds that was calculated earlier by the authors and was available in the internet for free access has been replaced in the case of randomly oriented crystals by simple analytic equations. Four microphysical ratios conventionally measured by lidars have been calculated for different shapes and the effective size of the crystals. These values could be used for retrieving shapes of the crystals in cirrus clouds.
The paper presets the research results of the influence of hexagonal ice column’s dihedral angle of 90° distortions on the backscattering matrix. The solution of the light scattering problem for hexagonal ice columns is obtained within the physical optics approximation. The results are obtained for hexagonal ice columns with lengths of 10, 31, 100, 316, 562, 1000 microns and diameters of 7, 22, 70, 123, 165, 220 microns, respectively. The distortion angle of the dihedral angle of 90° runs within the range of 0° (regular particle) to 10°. The calculations were carried out for the wavelength of 532 nm. The refractive index was assumed to be 1.3116. In addition to the backscattering matrix, the geometric scattering cross section and the important optical characteristics such as the lidar and depolarization ratios were calculated. The results showed that the influence of deformation on the optical characteristics increases with the particle size.
The paper presents the result of simultaneous observation of cirrus clouds by a lidar and an all-sky camera. The observation was started at 17:00, 24 March, 2016 and finished at 09:00, 25 March, 2016. The polarization lidar of V.E. Zuev Institute of Atmospheric Optics was used. The cirrus cloud was formed at 8000 m and went down to 4000 m at the end of observation. The linear depolarization ratio varied from 60% to less than 1%. The layer of quasi-horizontally oriented ice crystals was observed. Simultaneously, the all-sky camera pictured the 22 degrees halos while the lidar measured high depolarization ratio, which means that randomly oriented hexagonal ice particles were forming the cloud. The camera also pictured the Sundogs when the depolarization ratio tended to zero at about 21:30 that definitely indicates the quasi-horizontally oriented hexagonal plates. Absence of the Sundogs in the all-sky pictures while both the lidar sense low depolarization ratio, strong intensity and the specular reflection appears means that the cloud was formed by quasi-horizontally oriented particles with complex shape, i.e. snowflakes. The simultaneous lidar and all-sky camera observations seems to be a very prospective method to retrieve the microphysical properties of cirrus clouds.
In the problem of light scattering by ice crystals of cirrus clouds, two exact methods (FDTD – finite difference time domain and DGTD – discontinuous Galerkin time domain) and the physical-optics approximation are used for numerical calculations of the Mueller matrix in the case of ice hexagonal plates and columns. It is shown that for the crystals larger than 10 μm at the wavelength of 0.532 μm the exact methods and physical-optics approximation closely agreed within three diffraction fringes about the centers of the diffraction patterns. As a result, in the case of random orientation of these crystals, the physical-optics approximation provides accuracy 95% for the averaged Mueller matrix.
In the problem of light scattering by ice crystals of cirrus clouds, a new quantity characterizing microphysics of the clouds is determined. This quantity appears at simultaneous use of lidar and radar signals reflected from the same cloud. The quantity is the ratio of the backscattering cross section averaged over a statistical crystal ensemble to the averaged crystal volume. It is shown that this new characteristics can be effective if it is used together with the color ratio for retrieving microphysics of quasi-horizontally oriented crystals
Cirrus clouds cover about 30% of the Earth surface and they essentially impact on the radiative budget of the Earth and, consequently, on the climate. This study investigated the properties of cirrus cloud by used observations obtained from the three-wavelength lidar system over Tomsk and Hefei. The backscatter ratios (polarization ratio, color ratio and lidar ratio) for cirrus cloud are compared with each other from these two regions. Some differences are found that are caused by aerosol conditions. These differences have been mitigated by use of the appropriate microphysical model.
Orientation probability densities of ice crystals constituting cirrus clouds are required for correct interpretation of the lidar signals. It is shown that in the case of the azimuthal orientation, the probability density function can be constructed as a superposition of azimuthal and zenith distribution functions. However, such a superposition has a discontinuity in the poles of the orientation unit sphere, so it would be preferable to use Fisher or Kent distributions. The backscattering Mueller matrix has been calculated for the hexagonal ice columns and plates for the first time. Possibility of retrieving the orientation distributions of the crystals from a vertically pointing polarization lidar measuring the full Mueller matrix is considered. It is shown that for the columns the element m44 or, equivalently, the circular depolarization ratio distinguishes between the low and high zenith tilts of the crystals. Then, at their low or high zenith tilts, off-diagonal elements should be measured to retrieve the azimuth tilts.
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.
Interference effects between the scattered beams in the problem of light scattering by atmospheric ice crystals have been studied. Since the crystals are much larger than the wavelength, it is shown that the interference effects can be neglected if the crystal sizes are statistically varied more than 5% of the mean size. As a result, any calculations of the optical properties of the crystals performing an averaging over crystal sizes can be effectively replaced by the procedure of the incoherent addition of the scattered beams. This procedure allows us decrease the execution time up to 100 times.
The paper presents the first results of observations of cirrus clouds by polarization lidars with conical scanning, which were developed in Hefei (China) and in Tomsk (Russia). The light scattering matrix of ice crystal particles of cirrus clouds has been calculated for the first by the authors within the framework of the physical optics approximations in the case of conical scanning lidar. It is found that in this case the Mueller matrix consists of ten non-zero elements, four of which are small and can’t be applied to interpret the azimuthal distribution of particle orientation. All the diagonal elements have a strong azimuthal dependence. Among the off-diagonal elements only one element M34 carries additional information for interpreting the azimuthal distribution.
It is shown that light backscattering by hexagonal ice crystals of cirrus clouds is formed by both diffraction and interference phenomena. Diffraction determines the angular width of the backscattering peak and interference produces the interference rings inside the peak. By use of a simplest model for distortion of the pristine hexagonal shape, we show that the shape distortion leads to both oscillations of the scattering (Mueller) matrix within the backscattering peak and to a strong increase of the depolarization, color, and lidar ratios needed for interpretation of lidar signals.
A comparison of the physical optics code and GOIE method to solve the problem of light scattering by hexagonal ice crystals has been presented. It was found that in the case of diffraction on a hole in the perpendicular screen, both methods give the same diffraction scattering cross section for the diffraction angles up to 60 degrees. The polarization elements of the Mueller matrix in this case differ significantly even for the angles of 15-30 degrees. It is also shown that in the case of diffraction on the tilted screen, the difference between these methods may be significant. The comparison of the results with the exact solution obtained by FDTD has confirmed that the difference between these methods is not significant for the case of diffraction on the perpendicular screen, but it is slightly preferable to use the GOIE for the calculations. The good agreement with the exact solution confirms the possibility of using the method of physical optics to solve the problem of light scattering by particles with characteristic size greater than 10 microns.
At the present time quasi-horizontally oriented ice plates of cirrus clouds become the object of active research. Experimental observations of such kind of objects are carried out using multiwave and polarization lidars. The interpretation of lidar signals is now based on the solutions obtained in the approximation of both physical and geometrical optics. The article compares these approximations for the solution of light backscattering by quasihorizontally oriented hexagonal ice plates. Special attention is paid to the limits of applicability of geometrical optics method for solving such problems.
Three microphysical backscatter ratios (color ratio, depolarization ratio, and lidar ratio) widely used for interpretation of lidar signals returned from cirrus clouds have been calculated for the first time. The physical-optics code developed earlier by the authors is applied. Though the data are obtained for the hexagonal ice plates and columns, that are the simplest crystal shapes, their arbitrary spatial orientation has been taken into account. The lidar experimental data measuring simultaneously the depolarization ratio and color ratio in cirrus clouds are also presented.
Comparison of two approaches within the framework of geometric optics, called the ray-tracing and beam-tracing methods, is considered in application to the problem of light scattering by ice crystal particles of cirrus clouds. A good conformity between the numerical data obtained by these algorithms is demonstrated. The computer time spent for the calculations by these algorithms is analyzed depending on spatial orientations of the particles. It is shown that the beamtracing methods exceeds its counterpart at small number of reflection/refraction events (up to 5) while the situation becomes opposite if this number is larger than 5.
Experimental results of polarization laser sensing of cirrus with anomalous backscattering are presented. The technique of determining the optical and geometrical characteristics of clouds is described. Experimental data are compared with the meteorological conditions at altitudes of cirrus above the lidar location and with the results of numerical modeling of phase matrices in the approximation of physical optics. The recurrence frequency of meteorological characteristics of “mirror” cirrus is estimated.
The paper focuses on retrieving the microphysical characteristics of cirrus clouds from lidar data. The beam-splitting algorithm developed by the authors within framework of physical optics approximation has been used to solve the problem of light scattering by the hexagonal ice crystals. The paper presents the color ratio, depolarization ratio, and lidar ratio that have been calculated for the first time for quasi-horizontally and randomly oriented hexagonal ice particles. The lidar experimental data measuring simultaneously the depolarization ratio and color ratio in cirrus clouds are also presented.
This paper is a revision of a paper presented at the SPIE conference on Laser Radar Technology for Remote Sensing, Sep. 2003, Barcelona, Spain. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5240.
Light scattering by large, as compared to wavelength, ice crystal particles is considered within the framework of geometric optics. Certain general equations for the scattering matrices and for an averaging procedure over an arbitrary distribution of particle orientations are considered. The appearance of a strong backscattering peak is explained by the occurrence of right dihedral angles in the crystals. An analytical equation for the peak including the polarization properties is proposed.
Light scattering by hexagonal ice columns and plates is considered within the framework of both the geometric optics and physical optics approaches. The vicinity of the backward scattering direction that is of interest for lidar measurements is discussed in details. It is shown that the angular distribution of the backscatter reveals a fine interference structure.
An optical model for cirrus clouds consisting of ice crystal particles is considered for random particle orientations. In this model, two points and four intervals of the scattering zenith angle are introduced. They are the points of forward and backward scattering and the intervals of 0° - 22°,- 22° - 46°, 46° - 60°, and 60° - 180°. It is argued that light scattering into these intervals are caused by different physical reasons. Therefore, the behavior of the phase functions in these intervals can be modeled independently. It is assumed that these behaviors of the phase functions are scarcely determined by the exact particle shapes but they are mainly determined by certain weight coefficients for wedges that are inherent to the particle shapes. So, the optical model is based on the weight coefficients for the wedges.
Lidar backscatter by hexagonal ice cylinders of cirrus clouds is considered within the framework of both geometric optics and physical optics approaches. Within geometric optics, reasons of great backscattering peak and of large magnitudes of the depolarization ratio are investigated and explained. An approach including diffraction and interference phenomena is discussed.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.