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 M<sub>11</sub> 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 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.
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.
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.
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 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.
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.
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.
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.
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.
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
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 <i>m</i><sub>44</sub> 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.
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.
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.
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.
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.
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 M<sub>34</sub> carries additional information for interpreting the azimuthal distribution.
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.
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.
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.
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.
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.
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.
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.
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