Abstract

The relation between the orientation of particles in ice-crystal clouds and backscattering phase matrices (BSPMs) is considered. Parameters characterizing the predominant orientation of particles in the azimuthal direction and in the horizontal position are presented. The parameters are expressed through BSPM elements. A technique for measuring BSPM elements with lidar is described. Examples of some measurements are presented along with a statistical generalization of the results from more than 400 BSPM measurements. It is found that the orientation of coarse particles with large diameters in an azimuthal direction and in a horizontal position is more probable than in a random direction. However, the orientation of large particles is often masked by small particles that are not subject to the effect of orienting factors. Thus the mean parameters characterizing the state of orientation of particles in clouds as a whole correspond to weak orientation. It is supposed that the orientation of particles in the azimuthal direction is caused by wind-velocity pulsations.

© 2004 Optical Society of America

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References

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  1. K. Sassen, D. K. Lynch, “What are cirrus clouds?,” in Cirrus, 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–3.
  2. C.-R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatter,” Appl. Opt. 26, 4159–4173 (1987).
    [CrossRef] [PubMed]
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  4. C. F. Boren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  5. J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices: a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
    [CrossRef]
  6. B. V. Kaul, “Symmetry of light backscattering matrices related to orientation of nonspherical aerosol particles,” Atmos. Oceanic Opt. 13, 829–833 (2000).
  7. D. N. Romashov, R. F. Rakhimov, “Determination of the axially symmetric elongated particles orientation from data of polarization sounding,” Atmos. Oceanic Opt. 6, 515–521 (1993).
  8. D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).
  9. M. P. McCormick, ed., Third International Lidar Researchers DirectoryAtmospheric Sciences Division, NASA Langley Research Center, Hampton, Va., 1993), p. 71.
  10. A. Gerrard, J. M. Burch, Introduction to the Matrix Method in Optics (Wiley, New York, 1975).
  11. B. V. Kaul, “Equation for laser sounding of weakly anisotropy medium,” Atmos. Oceanic Opt. 11, 338–342 (1998).
  12. B. V. Kaul, D. N. Romashov, “Estimate of influence of ice cylindrical particles on extinction matrix,” Atmos. Oceanic Opt. 10, 931–936 (1998).
  13. S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).
  14. P. B. Rassel., J. Y. Swissler, P. M. McCormick, “Methodology of error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3790 (1979).
  15. J. Bard, Nonlinear Parameter Estimation (Academic, New York, 1974).
  16. J. Zikmunda, G. Vali, “Fall patterns and fall velocities of rimed ice crystals,” J. Atmos. Sci. 29, 1334–1347 (1972).
    [CrossRef]

2002 (1)

S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).

2000 (2)

B. V. Kaul, “Symmetry of light backscattering matrices related to orientation of nonspherical aerosol particles,” Atmos. Oceanic Opt. 13, 829–833 (2000).

D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).

1998 (2)

B. V. Kaul, “Equation for laser sounding of weakly anisotropy medium,” Atmos. Oceanic Opt. 11, 338–342 (1998).

B. V. Kaul, D. N. Romashov, “Estimate of influence of ice cylindrical particles on extinction matrix,” Atmos. Oceanic Opt. 10, 931–936 (1998).

1996 (1)

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices: a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

1993 (1)

D. N. Romashov, R. F. Rakhimov, “Determination of the axially symmetric elongated particles orientation from data of polarization sounding,” Atmos. Oceanic Opt. 6, 515–521 (1993).

1987 (1)

1979 (1)

1972 (1)

J. Zikmunda, G. Vali, “Fall patterns and fall velocities of rimed ice crystals,” J. Atmos. Sci. 29, 1334–1347 (1972).
[CrossRef]

Bard, J.

J. Bard, Nonlinear Parameter Estimation (Academic, New York, 1974).

Boren, C. F.

C. F. Boren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Burch, J. M.

A. Gerrard, J. M. Burch, Introduction to the Matrix Method in Optics (Wiley, New York, 1975).

Gerrard, A.

A. Gerrard, J. M. Burch, Introduction to the Matrix Method in Optics (Wiley, New York, 1975).

Herb, P.

Hovenier, J. W.

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices: a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

Hu, C.-R.

Huffman, D. R.

C. F. Boren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kattawar, G. W.

Kaul, B. V.

S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).

B. V. Kaul, “Symmetry of light backscattering matrices related to orientation of nonspherical aerosol particles,” Atmos. Oceanic Opt. 13, 829–833 (2000).

D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).

B. V. Kaul, “Equation for laser sounding of weakly anisotropy medium,” Atmos. Oceanic Opt. 11, 338–342 (1998).

B. V. Kaul, D. N. Romashov, “Estimate of influence of ice cylindrical particles on extinction matrix,” Atmos. Oceanic Opt. 10, 931–936 (1998).

Lynch, D. K.

K. Sassen, D. K. Lynch, “What are cirrus clouds?,” in Cirrus, 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–3.

McCormick, P. M.

Parkin, M. E.

Rakhimov, R. F.

D. N. Romashov, R. F. Rakhimov, “Determination of the axially symmetric elongated particles orientation from data of polarization sounding,” Atmos. Oceanic Opt. 6, 515–521 (1993).

Rassel., P. B.

Romashov, D. N.

D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).

B. V. Kaul, D. N. Romashov, “Estimate of influence of ice cylindrical particles on extinction matrix,” Atmos. Oceanic Opt. 10, 931–936 (1998).

D. N. Romashov, R. F. Rakhimov, “Determination of the axially symmetric elongated particles orientation from data of polarization sounding,” Atmos. Oceanic Opt. 6, 515–521 (1993).

Samokhvalov, I. V.

S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).

D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).

Sassen, K.

K. Sassen, D. K. Lynch, “What are cirrus clouds?,” in Cirrus, 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–3.

Swissler, J. Y.

Vali, G.

J. Zikmunda, G. Vali, “Fall patterns and fall velocities of rimed ice crystals,” J. Atmos. Sci. 29, 1334–1347 (1972).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van der Mee, C. V. M.

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices: a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

Volkov, S. N.

S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).

Zikmunda, J.

J. Zikmunda, G. Vali, “Fall patterns and fall velocities of rimed ice crystals,” J. Atmos. Sci. 29, 1334–1347 (1972).
[CrossRef]

Appl. Opt. (2)

Atmos. Oceanic Opt. (6)

B. V. Kaul, “Symmetry of light backscattering matrices related to orientation of nonspherical aerosol particles,” Atmos. Oceanic Opt. 13, 829–833 (2000).

D. N. Romashov, R. F. Rakhimov, “Determination of the axially symmetric elongated particles orientation from data of polarization sounding,” Atmos. Oceanic Opt. 6, 515–521 (1993).

D. N. Romashov, B. V. Kaul, I. V. Samokhvalov, “Databank for interpretation of results of the crystalline clouds polarized sensing,” Atmos. Oceanic Opt. 13, 794–800 (2000).

B. V. Kaul, “Equation for laser sounding of weakly anisotropy medium,” Atmos. Oceanic Opt. 11, 338–342 (1998).

B. V. Kaul, D. N. Romashov, “Estimate of influence of ice cylindrical particles on extinction matrix,” Atmos. Oceanic Opt. 10, 931–936 (1998).

S. N. Volkov, B. V. Kaul, I. V. Samokhvalov, “A technique for processing of lidar measurements of backscattering matrices,” Atmos. Oceanic Opt. 15, 891–895 (2002).

J. Atmos. Sci. (1)

J. Zikmunda, G. Vali, “Fall patterns and fall velocities of rimed ice crystals,” J. Atmos. Sci. 29, 1334–1347 (1972).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices: a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

Other (6)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. F. Boren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

K. Sassen, D. K. Lynch, “What are cirrus clouds?,” in Cirrus, 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 2–3.

J. Bard, Nonlinear Parameter Estimation (Academic, New York, 1974).

M. P. McCormick, ed., Third International Lidar Researchers DirectoryAtmospheric Sciences Division, NASA Langley Research Center, Hampton, Va., 1993), p. 71.

A. Gerrard, J. M. Burch, Introduction to the Matrix Method in Optics (Wiley, New York, 1975).

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Figures (6)

Fig. 1
Fig. 1

Dependence of element a 44 of the normalized BSPM on the parameter of the distribution in Eq. (16) that characterizes the degree of orientation of hexgonal columns and plates with large dimensions near the plane perpendicular to the wave vector of the incident (and scattered) radiation.8

Fig. 2
Fig. 2

Lidar: 1, laser; 2, λ/4 phase plates; 3, lens collimator; 4, Cassegrainian objective; 5, field stop; 6, interference filter; 7, λ/4 phase plate; 8, Wollaston prism; 9, photon counter; 10, computer.

Fig. 3
Fig. 3

Demonstration of the experiment at the determination stage of C k (h) [see Eq. (19)]. The normalized Stokes parameters of the laser radiation s 0 i are shown: a, s 0 1 = (1100); b, s 0 4 = (1001). Left-hand curves, C k (h) obtained owing to the effect of a polarizer characterized by a pair of instrument vectors G j and G j* on the scattered radiation: G 1 = 12(1100), G 1* (curve q), G 2 = 12(1010), G 2* (curve u), G 3 = 12(1001), G 3* (curve v). Right-hand curves, scattering ratio R(h) obtained when the corresponding C k (h), k = 3(i - 1) + j is determined.

Fig. 4
Fig. 4

Part of the experiment illustrating the situation in which Eqs. (29) were obtained (see the text). The normalized Stokes parameters are q, u, and v. On the left is the scattering ratio averaged over the results from the three measurements to the right.

Fig. 5
Fig. 5

Relative frequencies for the values of the a ij ′ elements of the normalized reduced backscattering phase matrices of ice-crystal clouds and of the orientation parameter χ calculated by χ = (a 22′ + a 33′)/(1 + a 44′) [see Eq. (15) and comments concerning Eq. (26)]. The value of the element (dimensionless) is plotted on the abscissa, and the frequencies are plotted on the ordinate.

Fig. 6
Fig. 6

Relative frequencies of azimuthal directions Φ obtained from the reduction in the experimental BSPM to form Eq. (11) [see Eqs. (25)–(28)]. According to the accepted condition, a 12′ ≤ 0, it is assumed that the particles are oriented with their large diameters mainly in these directions. The angles are shown in the lidar-based coordinate system. Dark arrow, the meridian position, light arrow, the latitudinal direction. The geographic azimuth is calculated by Eq. (30).

Equations (33)

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S=1/r2MS0ΔV.
ΔV=πθr2cτ/2,
Mij=Mji if i or j3, ij; Mij=-Mji if i or j=3, ij,
M11-M22+M33-M44=0.
Λ12π+Λ21π=0.
M=RΦMRΦ=M,
RΦ=10000cos 2Φsin 2Φ00-sin 2Φcos 2Φ00001.
M=A00H0E0000-E0H00C,
ρΨ=ρ-Ψ,
2Φ=a tan-M13/M12=a tan-M24/M34; 4Φ=a tan-2M23/M22+M33.
M=M11M120M14M21M220000M33M34M410M43M44
F=1ΔVi=1mσ22+σ33i2cos4ΨiρΨi, M12=1ΔVi=1mσ12i cos2ΨiρΨi, M34=1ΔVi=1mσ34i cos2ΨiρΨi.
M11=M11, M14=M14, M44=M44, M12=M12C2-M13S2, M13=M12S2+M13C2, M24=M24C2+M34S2, M34=-M24S2+M34C2, M23=M23C4+M22+M332S4.
M22=E+FC4-M23S4, M33=-E+FC4-M23S4,
E=M11-M442, F=M11+M442, Ck=cos kΦ, Sk=sin kΦ.
χ=M22+M33/M11+M44.
ρΨ, k=exp2k cos 2Ψ/πJ0, k0, Ψ-π/2, π/2,
L0°, L*0°, Φ0°; L45°, L*45°; Φ45°;L0°, L*0°, Φ45°,
Gj=121, xj, yj, zj, Gj*=121,-xj,-yj,-zj, j=1, 2, 3.
Phsh=12 cW0Ah-2Mhs0×exp-20hεh, φ, θdh,
Nhlij=12cN0Ahl-2κjnΔτlGjMhls0i×exp-20h εh, φ, θdh, N*hlij=12cN0Ahl-2κj*nΔτlGj*Mhls0i×exp-20h εh, φ, θdh,
Ckhl=Nhlij-N*hlijNhlij+N*hlij=Gj-αjGj*Mhls0iGj+αjGj*Mhls0i, i=1, 2, 3, 4; j=1, 2, 3; k=3i-1+j; αj=κj*/κj.
Mkh=A11,khah+1Rkh-1a1hSiσ,
f=Kr.
r=a12, a13, a14, a22, a23, a24, a33, a34T.
rˆ=KTD-1fK-1KTD-1ff,
Dr=KTD1fK-1.
a13=0, a23=0, a24=0.
a120, a22+a330.
Y=Y1, Y2, Y3T,Y1=a tan-a13a12+mπ,Y2=12a tan-2a23a22+a33+nπ2,Y3=a tan-a24a34+kπ,m=1, 0, 1, n=-2, -1, 0, 1, 2, k=-1, 0, 1.
2Φ=ATD-1AATD-1Y,
a6.00 km=1-0.510.000.04-0.510.89-0.040.020.000.04-0.5130.080.040.02-0.08-0.40,Φ=-83.2°±1.9, χ=0.62±0.04,a6.77 km=1-0.820.00-0.07-0.820.93-0.06-0.040.000.06-0.75-0.010.07-0.040.01-0.63,Φ=8.5°±1.7, χ=0.49±0.05.
Φg=Φ-17.5°+180°.

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