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 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.
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 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 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.
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 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.
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.
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.
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.
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.
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 report analyzes the data of microscopic observation of atmospheric ice crystal particles in the surface layer of the atmosphere. Observations were conducted in Tomsk during the winter of 2017-2018. The results of observations are used to create an adequate microphysical model of atmospheric ice crystals for solving the light scattering problem by the method of the physical optics.
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.
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 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.
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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