Electromagnetic Wave Propagation and Scattering in Rain and Other Hydrometeors

Proceedings of the IEEE

Volumn 71, Issue 9, 1983, Pages 1029-1078

  Oguchi, Tomohiro ^a  

^a Ministry of Posts and Telecommunications   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

HYDROMETEORS;

MICROWAVES - SCATTERING; RAIN AND RAINFALL; TELECOMMUNICATION LINKS, SATELLITE;

ELECTROMAGNETIC WAVES;

EID: 0020821752     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1983.12724     Document Type: Article

References (306)

1. J.W. Ryde, “Echo intensity and attenuation due to clouds, rain, hail, sand and duststorms at centimetre wavelengths,”? Rep. 7831, General Electric Co. Research Labs., Wembley, England, Oct. 1941.
2. J.W. Ryde and D. Ryde, “Attenuation of centimetre waves by rain, hail and clouds,”? Rep. 8516, General Electric Co. Research Labs., Wembley, England, Aug. 1944.
3. J.W. Ryde, “Attenuation of centimetre and millimetre wave by rain, hail, fogs and clouds,”? Rep. 8670, General Electric Co. Research Labs., Wembley, England, May 1945.
4. D.E. Kerr, Ed., Propagation of Short Radio Waves (M.I.T. Radiation Lab. Series, 13). New York: McGraw-Hill, 1951.
5. K.L.S. Gunn and T.W.R. East, “The microwave properties of precipitation particles,”? Quart. J.R. Met. Soc., vol. 80, pp. 522–545, Oct. 1954.
6. P.A. Watson, “Survey of measurements of attenuation by rain and other hydrometeors,”? Proc. Inst. Elec. Eng., vol. 123, pp. 863–871, Sept. 1976.
7. S. Okamura, K. Funakawa, H. Uda, J. Kato, and T. Oguchi, “Effect of polarization on the attenuation by rain at millimeter-wave length,”? J. Radio Res. Labs. (Japan), vol. 8, pp. 73–80, Mar. 1961.
8. D. Atlas, M. Kerker, and W. Hitschfeld, “Scattering and attenuation by non-spherical atmospheric particles,”? J. Atmos. Terr. Phys., vol. 3, pp. 108–119, 1953.
9. R.A. Semplak, “Effect of oblate raindrops on attenuation at 30.9 GHz,”? Radio Sci., vol. 5, pp. 559–564, Mar. 1970.
10. M.J. Saunders, “Cross polarization at 18 and 30 GHz due to rain,”? IEEE Trans. Antennas Propagat.,vol. AP-19, pp. 273–277, Mar. 1971.
11. D.T. Thomas, “Cross-polarization distortion in microwave radio transmission due to rain,”? Radio Sci., vol. 6, pp. 833–839, Oct. 1971.
12. C.W. Bostian and J. E Allnutt, “Ice-crystal depolarisation on satellite-earth microwave radio paths,”? Proc. Inst. Elec. Eng., vol. 126, pp. 951–960, Oct. 1979.
13. J.P. Mon, “Backward and forward scattering of microwaves by ice particles: A review,”? Radio Sci., vol. 17, pp. 953–971, Sept.-Oct. 1982.
14. P.S. Ray, “Broadband complex refractive indices of ice and water,”? Appl. Opt., vol. 11, pp. 1836–1844, Aug. 1972.
15. K.S. Cole and R.H. Cole, “Dispersion and absorption in dielectrics,”? J. Chem. Phys., vol. 9, pp. 341–351, Apr. 1941.
16. O. Worz and R.H. Cole, “Dielectric properties of ice I,”? J. Chem. Phys., vol. 51, pp. 1546–1551, Aug. 1969.
17. C.F. Bohren and L.J. Battan, “Radar backscattering by inhomoge-neous precipitation particles,”? J. Atmos. Sci., vol. 37, pp. 1821–1827, Aug. 1980.
18. K. Lichtenecker, “Die Dielektrizitätskonstante naturlicher und kunstlicher Mischkörper,”? Physikalische Z., vol. 27, pp. 115–158, Mar. 1926.
19. Y. Ozawa and D. Kuroiwa, “Dielectric properties of ice, snow and supercooled water,”? in Microwave Propagation in Snowy Districts, Y. Asami, Ed. (Monograph Ser. of the Res. Inst, of Appl. Electricity, Hokkaido Univ., Sapporo, Japan), no. 6, pp. 31–71, 1958.
20. A. Matsumoto and A. Nishitsuji, Ed., SHF and EHF Propagation in Snowy Districts (Monograph Ser. of the Res. Inst, of Appl. Electricity, Hokkaido Univ., Sapporo, Japan), no. 19, 1971.
21. W.A. Cumming, “The dielectric properties of ice and snow at 3.2 centimeters,”? J. Appl. Phys., vol. 23, pp. 768–773, July 1952.
22. D.A.G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,”? Ann. Physik. (Leipzig), vol. 24, pp. 636–679, Nov. 1935.
23. D.C. Blanchard, “The behavior of water drops at terminal velocity in air,”? Trans. Amer. Geophys. Union, vol. 31, pp. 836–842, Dec. 1950.
24. H.R. Pruppacher and K.V. Beard, “A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air,”? Quart. J.R. Met. Soc., vol. 96, pp. 247–256, Apr. 1970.
25. A.R. Nelson and N.R. Gokhale, “Oscillation frequencies of freely suspended water drops,”? J. Geophys. Res., vol. 77, pp. 2724–2727, May 1972.
26. C. Magono, “On the shape of water drops falling in stagnant air,”? J. Meteorol., vol. 11, pp. 77–79, Feb. 1954.
27. D.M.A. Jones, “The shape of raindrops,”? J. Meteorol., vol. 16, pp. 504–510, Oct. 1959.
28. S. Ugai, K. Kato, M. Nishijima, T. Kan, and K. Tazaki, “Fine structure of rainfall,” Ann. Télécommunic., vol. 32, pp. 422–429, Nov.-Dee. 1977.
29. A.F. Spilhaus, “Raindrop size, shape, and falling speed,”? J. Meteorol., vol. 5, pp. 108–110, June 1948.
30. I. Imai, “On the velocity of falling raindrops,”? Geophys. Mag. (Tokyo), vol. 21, pp. 244–249, 1950
31. H.R. Pruppacher and R.L. Pitter, “A semi-empirical determination of the shape of cloud and rain drops,”? J. Atmos. Sci., vol. 28, pp. 86–94, Jan. 1971.
32. R. Gunn and G.D. Kinzer, “The terminal velocity of fall for water droplets in stagnant air,”? J. Meteorol., vol. 6, pp. 243–248, Aug. 1949.
33. R.G. Medhurst, “Rainfall attenuation of centimeter waves: comparison of theory and measurement,”? IEEE Trans. Antennas Propagat., vol. AP-13, pp. 550–564, July 1965.
34. A.C. Best, “Empirical formulae for the terminal velocity of water drops falling through the atmosphere,”? Quart. J.R. Met. Soc., vol. 76, pp. 302–311, July 1950.
35. A. Vander Vorst, “Cross-polarization on a terrestrial path,”? Alta Freq., vol. 48, pp. 201–209, Apr. 1979.
36. R.L. Olsen, “Cross polarization during precipitation on terrestrial links: A review,”? Radio Sci., vol. 16, pp. 761–779, Sept.-Oct. 1981.
37. S. Ugai and H. Akimoto, private communication.
38. G. Brussaard, “A meteorological model for rain-induced cross polarization,”? IEEE Trans. Antennas Propagat., vol. AP-24, pp. 5–11, Jan. 1976.
39. R.A. Semplak, “Measurements of rain-induced polarization rotation at 30.9 GHz,”? Radio Sci., vol. 9, pp. 425–429, Apr. 1974.
40. B.O. Maher, P.J. Murphy, and M.C. Sexton, “A theoretical model of the effect of wind-gusting on rain-induced cross-polarization,”? Ann. Télécommunic., vol. 32, pp. 404–408, Nov.-Dee. 1977.
41. J. Howard and M. Gerogiokas, “A statistical raindrop canting angle model,”? IEEE Trans. Antennas Propagat., vol. AP-30, pp. 141–147, Jan. 1982.
42. A.G. Davenport, “The spectrum of horizontal gustiness near the ground in high winds,”? Quart. J.R. Met. Soc., vol. 87, pp. 194–211, Apr. 1961.
43. A.J. Dunlop, “De-polarisation due to non-symmetry in raindrops,”? in IEE Conf. Publ. 195, vol. 2, pp. 101–104 (Inst. Elec. Eng., London), 1981.
44. J. Wiesner, “Beiträge zur Kenntniss des tropischen Regens,”? Akad. Wiss. Vienna, Math. Nat. Klasse, Sitzungsb., vol. 104, pp. 1397–1434, 1895.
45. J.O. Laws and D.A. Parsons, “The relation of raindrop-size to intensity,”? Trans. Amer. Geophys. Union, vol. 24, pp. 452–460, 1943.
46. J.S. Marshall and W. MclC Palmer, “The distribution of raindrops with size,”? J. Meteorol., vol. 5, pp. 165–166, Aug. 1948.
47. J. Joss and A. Waldvogel, “Ein Spektrograph fur Niederschlagstropfen mit automatischer Auswertung,”? Pure Appl. Geophys., vol. 68, pp. 240–246, 1967.
48. U.H.W. Lammers, “Electrostatic analysis of raindrop distributions,”? J. Appl. Meteorolvol. 8, pp. 330–334, June 1969.
49. G. Donnadieu, “Measure de la vitesse terminale des gouttes de pluie au sol ä Paide du spectropluviométre VIDIAZ,”? J. Rech. Atmos., vol. 12, pp. 245–259, 1978.
50. J. Joss, J.C. Thams, and A. Waldvogel, “The variation of raindrop size distributions at Locarno,”? in Proc. Int. Conf. on Cloud Physics (Toronto, Ont., Canada, 1968), pp. 369–373.
51. P.I.A. Kinnell, “Some observations on the Joss-Waldvogel rainfall disdrometer,”? J. Appl. Meteorol., vol. 15, pp. 499–502, May 1976.
52. G. Donnadieu, “Comparison of results obtained with the VIDIAZ spectropluviometer and the Joss-Waldvogel rainfall disdrometer in a Rain of a thundery type,”? J. Appl. Meteorol., vol. 19, pp. 593–597, May 1980.
53. P.G.F. Caton, “A study of raindrop-size distributions in the free atmosphere,”? Quart. J.R. Met. Soc., vol. 92, pp. 15–30, Jan. 1966.
54. R.S. Sekhon and R.C. Srivastava, “Doppler radar observations of drop-size distributions in a thunderstorm,”? J. Atmos. Sci., vol. 28, pp. 983–994, Sept. 1971.
55. P.R. Brazier-Smith, S.G. Jennings, and J. Latham, “Raindrop interactions and rainfall rates within clouds,”? Quart. J.R. Met. Soc., vol. 99, pp. 260–272, Apr. 1973.
56. K.C. Young, “The evolution of drop spectra due to condensation, coalescence and breakup,”? J. Atmos. Sci., vol. 32, pp. 965–973, May 1975.
57. R.C. Srivastava, “The cloud physics of particle size distributions. A review,”?j. Rech. Atmos., vol. 8, pp. 23–39, Jan.-June 1974.
58. H.R. Pruppacher and J.D. Klett, Microphysics of Clouds and Precipitation. Boston, MA: Reidel, 1978.
59. C. Magono and T. Nakamura, “Aerodynamic studies of falling snowflakes,”? J. Meteorol. Soc. Japan, vol. 43, pp. 139–147, June 1965.
60. Y. Sasyö, “The collection efficiency of simulated snow particles for water droplets (II)-on the oscillatory angular motion of the snowflake-,”? papers in Meteorol. and Geophys. (Tokyo), vol. 28, pp. 159–168, Dec. 1977.
61. K.L.S. Gunn and J.S. Marshall, “The distribution with size of aggregate snowflakes,”? J. Meteorol., vol. 15, pp. 452–461, Oct. 1958.
62. R.S. Sekhon and R.C. Srivastava, “Snow size spectra and radar reflectivity,”? J. Atmos. Sci., vol. 27, pp. 299–307, Mar. 1970.
63. T. Ohtake, “Observations of size distributions of hydrometeors through the melting layer,”? J. Atmos. Sci., vol. 26, pp. 545–557, May 1969.
64. T. Ihara, Y. Furuhama, and K. Tohma, “Measurement of depolarization due to snowfall at 34.5 GHz,”? Trans. Inst. Electron. Commun. Eng. Japan, vol. E65, pp. 16–22, Jan. 1982.
65. C. Magono and C.W. Lee, “Meteorological classification of natural snow crystals,”? J. Fac. Sci. (Hokkaido Univ., Sapporo, Japan), ser. VII, vol. 2, pp. 321–362, 1966.
66. A.H. Auer, Jr., and D.L. Veal, “The dimension of ice crystals in natural clouds,”? J. Atmos. Sci., vol. 27, pp. 919–926, Sept. 1970.
67. J. Zikmunda and G. Vali, “Fall patterns and fall velocities of rimed ice crystals,”?j. Atmos. Sci., vol. 29, pp. 1334–1347, Oct. 1972.
68. H.-R. Cho, J.V. Iribame, and W.G. Richards, “On the orientation of ice crystals in a cumulonimbus cloud,”? J. Atmos. Sci., vol. 38, pp. 1111–1114, May 1981.
69. P.V. Hobbs, L.F. Radke, J.D. Locatelli, D.G. Atkinson, C.E. Robertson, R.R. Weiss, F.M. Turner, and R.R. Brown, “Field observations and theoretical studies of clouds and precipitation over the Cascade Mountains and their modifications by artificial seeding (1971–72),”? Univ. of Washington, Seattie, Wash., Dept. Atmos. Sci., Res. Rep. VII, Dec. 1972.
70. R. List, “Wachstum von Eis-Wassergemischen im Hagelversuchskanal,”? Helvetica Phys. Acta, vol. 32, pp. 293–296, 1959.
71. D.S. Saxon, “Tensor scattering matrix for the electromagnetic field,”? Phys. Rev., vol. 100, pp. 1771–1775, Dec. 1955.
72. J.A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941.
73. J.A. Saxton and J.A. Lane, “Electrical properties of sea water,”? Wireless Eng., vol. 29, pp. 269–275, 1952.
74. H.C. van de Hulst, Light Scattering by Small Particles. New York: Wiley, 1957, p. 107.
75. A.F. Stevenson, “Solution of electromagnetic scattering problems as power series in the ratio (dimension of scatterer)/wavelength,”? J. Appl. Phys., vol. 24, pp. 1134–1142, Sept. 1953.
76. A.F. Stevenson, “Electromagnetic scattering by an ellipsoid in the third approximation,”? J. Appl. Phys., vol. 24, pp. 1143–1151, Sept. 1953.
77. T. Oguchi, “Attenuation of electromagnetic wave due to rain with distorted raindrops,”? J. Radio Res. Labs. (Japan), vol. 7, pp. 467–485, Sept. 1960.
78. T. Oguchi, “Attenuation and phase rotation of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,”? Radio Sci., vol. 8, pp. 31–38, Jan. 1973.
79. T. Oguchi, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain: Calculations at 19.3 and 34.8 GHz,”? J. Radio Res. Labs. (Japan), vol. 20, pp. 79–118, 1973.
80. P.A. Watson and M. Arbabi, “Rainfall crosspolarisation at microwave frequencies,”? Proc. Inst. Elec. Eng., vol. 120, pp. 413–418, Apr. 1973.
81. J.A. Morrison and T.S. Chu, “Perturbation calculations of rain-induced differential attenuation and differential phase shift at microwave frequencies,”? Bell Syst. Tech. J., vol. 52, pp. 1907–1913, Dec. 1973.
82. J.A. Morrison and M.-J. Cross, “Scattering of a plane electromagnetic wave by axisymmetric raindrops,”? Bell Syst. Tech. J., vol. 53, pp. 955–1019, July-Aug. 1974.
83. S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,”? Appl. Opt., vol. 14, pp. 29–49, Jan. 1975.
84. S. Asano, “Light scattering properties of spheroidal particles,”? Appl. Opt., vol. 18, pp. 712–723, Mar. 1979.
85. J.A. Morrison, M.-J. Cross, and T.S. Chu, “Rain-induced differential attenuation and differential phase shift at microwave frequencies,”? Bell Syst. Tech. J., vol. 52, pp. 599–604, Apr. 1973.
86. T. Oguchi and Y. Hosoya, “Scattering properties of oblate raindrops and cross polarization of radio waves due to rain (Part II): Calculations at microwave and millimeter wave regions,”? J. Radio Res. Labs. (Japan), vol. 21, pp. 191–259, 1974.
87. A.W. Dissanayake and P.A. Watson, “Forward scatter and crosspolarisation from spheroidal ice particles,”? Electron. Lett., vol. 13, pp. 140–142, Mar. 1977.
88. P.C. Waterman, “Matrix formulation of electromagnetic scattering,”? Proc. IEEE, vol. 53, pp. 805–812, Aug. 1965.
89. P.C. Waterman, “Scattering by dielectric obstacles,”? Alta Freq., vol. 38 (speciale), pp. 348–352, 1969.
90. P. Barber and C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,”? Appl. Opt., vol. 14, pp. 2864–2872, Dec. 1975.
91. C. Warner and A. Hizal, “Scattering and depolarization of microwaves by spheroidal raindrops,”? Radio Sci., vol. 11, pp. 921–930, Nov. 1976.
92. B. Peterson, “Numerical computation of electromagnetic scattering by raindrops-A comparison of methods,”? Internal Rep. TMF76–1, Inst. Theor. Phys. (G-teborg, Sweden), 1976.
93. V.N. Bringi and T.A. Seliga, “Scattering from non-spherical hydrometeors,”? Ann. Télécommunic., vol. 32, pp. 392–397, Nov.-Dee. 1977.
94. A.R. Holt, N.K. Uzunoglu, and B.G. Evans, “An integral equation solution to the scattering of electromagnetic radiation by dielectric spheroids and ellipsoids,”? IEEE Trans. Antennas Propagat., vol. AP-26, pp. 706–712, Sept. 1978.
95. N.K. Uzunoglu, B.G. Evans, and A.R. Holt, “Scattering of electromagnetic radiation by precipitation particles and propagation characteristics of terrestrial and space communication systems,”? Proc. Inst. Elec. Eng., vol. 124, pp. 417–424, May 1977.
96. N.K. Uzunoglu and A.R. Holt, “The scattering of electromagnetic radiation from dielectric scatterers,”? J. Phys. A: Math. Gen., vol. 10, pp. 413–424, Mar. 1977.
97. J.W. Shepherd and A.R. Holt, “Some shape effects in the scattering of electromagnetic waves by ice particles,”? in Proc. Commission F Int. Symp. on Effects of the Lower Atmosphere on Radio Propagation at Frequencies above 1 GHz (Union Radio Sci. Int., Lennoxville, Que., May 26-30, 1980), pp. 1.2.1–1.2.5.
98. A.R. Holt, “The Fredholm integral equation method and comparison with T-matrix approach.” in Acoustic, Electromagnetic and Elastic Wave Scattering-Focus on the T-Matrix Approach, V.K. Varadan and V.V. Varadan, Eds. New York: Pergamon, 1980, pp. 255–268.
99. K.K. Mei, “Unimoment method of solving antenna and scattering problems,”? IEEE Trans. Antennas Propagat., vol. AP-22, pp. 760–766, Nov. 1974.
100. S.-K. Chang and K.K. Mei, “Application of the unimoment method to electromagnetic scattering of dielectric cylinders,”? IEEE Trans. Antennas Propagat., vol. AP-24, pp. 35–42, Jan. 1976.
101. D.J. Fang and F.J. Lee, “Tabulations of raindrop induced forward and backward scattering amplitudes,”? COMSAT Tech. Rev., vol. 8, pp. 455–486, Fall 1978.
102. D.J. Fang, “Microwave scattering amplitudes for raindrops,”? Tech. Memo., CL-13–78, Commun. Satell. Corp. Lab., Clarksburg, MD, 1978.
103. M.A. Morgan, “Finite element computation of microwave scattering by raindrops,”? Radio Sci., vol. 15, pp. 1109–1119, Nov.-Dee. 1980.
104. T. Oguchi, “Scattering from hydrometeors: A survey,”? Radio Sci., vol. 16, pp. 691–730, Sept.-Oct- 1981.
105. A.R. Holt, “The scattering of electromagnetic waves by single hydrometeors,”? Radio Sci., vol. 17, pp. 929–945, Sept.-Oct. 1982.
106. T. Oguchi, “Eigenvalues of spheroidal wave functions and their branch points for complex values of propagation constants,”? Radio Sci., vol. 5, pp. 1207–1214, Aug.-Sept. 1970.
107. P.M. van den Berg and J.T. Fokkema, “The Rayleigh hypothesis in the theory of diffraction by a cylindrical obstacle,”? IEEE Trans. Antennas Propagat., vol. AP-27, pp. 577–583, Sept. 1979.
108. K. Yasuura, “A view of numerical methods in diffraction problems,”? in Radio Waves and Circuits: Radio Electronics, W.V. Tilston and M. Sauzade, Eds. (vol. 3 of Progress in Radio Science 1966-1969, C.M. Minnis, Ed.). Brussels: Union Radio Scien. Internat. (URSI), 1971, pp. 257–270.
109. P. Barber and C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric scatterers,”? Univ. of Calif., at Los Angeles, Rep. UCLA-ENG-7431, 1974.
110. J.W. Shepherd, A.R. Holt, and B.G. Evans, “The effects of shape on electromagnetic scattering by ice particles,”? in IEE Conference Publ. 195, vol. 2, pp. 96–100 (Inst. Elec. Bag., London), 1981.
111. A.R. Holt and B.G. Evans, “Some resonance effects in scattering of microwaves by hydrometeors,”? Proc. Inst. Elec. Eng., vol. 124, pp. 1114–1116, Dec. 1977.
112. T. Oguchi, “Summary of studies on scattering of centimetre and millimetre waves due to rain and hail,”? Ann. Télécommunic., vol. 36, pp. 383–399, July-Aug. 1981.
113. T.A. Seliga and V.N. Bringi, “Differential reflectivity and differential phase shift: Application in radar meteorology,”? Radio Sci., vol. 13, pp. 271–275, Mar.-Apr. 1978.
114. W. Franz and K. Deppermann, “Theorie der Beugung am Zylinder unter Beriicksichtigung der Kriechwelle,”? Ann. Physik. (Leipzig), vol. 6, pp. 361–373, 1952.
115. J.R. Probert-Jones, “Surface waves associated with the backscattering of microwave radiation by large ice spheres,”? in Electromagnetic Scattering, M. Kerker, Ed. New York: Pergamon, 1963, pp. 237–250.
116. T. Oguchi, “Scattering and absorption of a millimeter wave due to rain and melting hailstones,”? J. Radio Res. Labs. (Japan), vol. 13, pp. 141–172, May 1966.
117. S.A.J. Upton, B.G. Evans, and A.R. Holt, “Variations with model parameters of earth/space path attenuation derived from radiometer and radar measurements,”? in Proc. Commission F Int. Symp. on Effects of the Lower Atmosphere on Radio Propagation at Frequencies above 1 GHz (Union Radio Sci. Int., Lennoxville, Que., May 26-30, 1980), pp. 1.6.1–1.6.6.
118. C. Warner, “Effects of shape and orientation of spheroidal raindrops on microwave scattering,”? Electron. Lett., vol. 11, pp. 328–330, July 1975.
119. A.R. Holt and J.W. Shepherd, “Electromagnetic scattering by dielectric spheroids in the forward and backward directions,”? J. Phys. A : Math. Gen., vol. 12, pp. 159–166, Jan. 1979.
120. B.G. Evans and J. Troughton, “Calculation of crosspolarisation due to precipitation,”? in IEE Conf. Publ. 98, pp. 162–171 (Inst. Elec. Eng., London), 1973.
121. T.S. Chu, “Rain-induced cross-polarization at centimeter and millimeter wavelengths,”? Bell Syst. Tech. J., vol. 53, pp. 1557–1579, Oct. 1974.
122. T. Ihara, private communication.
123. A.R. Holt and B.G. Evans, “The scattering of millimeter waves by precipitation particles,”? in Proc. Commission F Int. Symp. on Effects of the Lower Atmosphere on Radio Propagation at Frequencies above 1 GHz (Union Radio Sci. Int., Lennoxville, Que., May 26-30, 1980), pp. 1.1.1–1.1.6.
124. B.G. Evans and A.R. Holt, “Frequency scaling at millimetre wave frequencies,”? in IEE Conf. Publ. 195, vol. 2, pp. 93–95 (Inst. Elec. Eng., London), 1981.
125. URSI Workshop Session Chairmen, “URSI workshop report: Effects of the lower atmosphere on radio propagation at frequencies above 1 GHz,”? Radio Sci., vol. 16, pp. 813–824, Sept.-Oct. 1981.
126. K. Funakawa, “Measurement of total cross sections of water drops at 5 mm wavelength utilizing the “shadow theorem',”? J. Radio Res. Labs. (Japan), vol. 12, pp. 111–126, Mar. 1965.
127. D.J. Harris and T.M. Teo, “Extinction cross-section measurements on single falling water drops at 100 GHz,”? Electron. Lett., vol. 17, pp. 7–8, Jan. 1981.
128. N.A. Mathews, F. Good all, and P.A. Watson, “Amplitude and phase measurements of forward-scattered microwave radiation from water-drops,”? Electron. Lett., vol. 12, pp. 157–158, Apr. 1976.
129. A. Nishitsuji and A. Matsumoto, “Calculation of radio wave attenuation due to snowfall,”? in SHF and EHF Propagation in Snowy Districts, A. Matsumoto and A. Nishitsuji, Eds. (Monograph Ser. of the Res. Inst, of Appl. Electricity, Hokkaido Univ., Sapporo, Japan), no. 19, 1971, pp. 63–78.
130. N.R. Labrum, “The scattering of radio waves by meteorological particles,”? J. Appl. Phys., vol. 23, pp. 1324–1330, Dec. 1952.
131. C. Yeh, R. Woo, A. Ishimaru, and J. Armstrong, “Scattering by single ice needles and plates at 30 GHz,”? Radio Sci., vol. 17, pp. 1503–1510, Nov.-Dee. 1982.
132. N.K. Uzimoglu, N.G. Alexopoulos, and J.G. Fikioris, “Scattering from thin and finite dielectric fibers,”? J. Opt. Soc. Am., vol. 68, pp. 194–197, Feb. 1978.
133. H. Weil and C.-M. Chu, “Scattering and absorption of electromagnetic radiation by thin dielectric discs,”? Appl. Opt., vol. 15, pp. 1832–1836, July 1976.
134. H. Weil, “Scattering and absorption of electromagnetic radiation by clouds of disc shaped ions,”? Radiat. Lab., Univ. of Mich., Ann Arbor, Rep. 016234–1-F, Dec. 1978.
135. A.J. Mallmann and R.G. Greenler, “Origins of anthelic arcs, the anthelic pillar, and the anthelion,”? J. Opt. Soc. Am., vol. 69, pp. 1107–1112, Aug. 1979.
136. R.F. Coleman and K.N. Liou, “Light scattering by hexagonal ice crystals,”? J. Atmos. Sci., vol. 38, pp. 1260–1271, June 1981.
137. T.B.A. Senior and H. Weil, “Electromagnetic scattering and absorption by thin walled dielectric cylinders with application to ice crystals,”? Appl. Opt., vol. 16, pp. 2979–2985, Nov. 1977.
138. A. Nelson and L. Eyges, “Electromagnetic scattering from dielectric rods of arbitrary cross section,”? J. Opt. Soc. Am., vol. 66, pp. 254–259, Mar. 1976.
139. B.M. Herman and L.J. Battan, “Calculations of Mie back-scattering of microwaves from ice spheres,”? Quart. J.R. Met. Soc., vol. 87, pp. 223–230, Apr. 1961.
140. D. Atlas and K.M. Glover, “Back-scatter by dielectric spheres with and without metal caps,”? in Electromagnetic Scattering, M. Kerker, Ed. New York: Pergamon, 1963, pp. 213–236.
141. M.P. Langleben and K.L.S. Gunn, “Scattering and absorption of microwaves by a melting ice sphere,”? Stormy Weather Res. Group, McGill Univ., Montreal, Canada, Rep. MW-5, 1952.
142. B.M. Herman and L.J. Battan, “Calculations of Mie back-scattering from melting ice spheres,”? J. Meteorol., vol. 18, pp. 468–478, Aug. 1961.
143. A.L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,”? J. Appl. Phys., vol. 22, pp. 1242–1246, Oct. 1951.
144. L.J. Battan and B.M. Herman, “The radar cross sections of “spongy' ice spheres,”? J. Geophys. Res., vol. 67, pp. 5139–5145, Dec. 1962.
145. A.R. Holt, “Electromagnetic wave scattering by spheroids: A comparison of experimental and theoretical results,”? IEEE Trans. Antennas Propagat., vol. AP-30, pp. 758–760, July 1982.
146. N.R. Labrum, “Some experiments on centimeter-wavelength scattering by small obstacles,”? J. Appl. Phys., vol. 23, pp. 1320–1323, Dec. 1952.
147. J. Nicolis, “The wavelength dependence (between 18 to 25 Gc/s) of back-reflected energy from small ice particles during the melting process,”? Proc. IEEE, vol. 53, pp. 551–552, May 1965.
148. J.R. Gerhardt, C.W. Tolbert, S.A. Brunstein, and W.W. Bahn, “Experimental determinations of the back-scattering cross-sections of water drops and of wet and dry ice spheres at 3.2 centimeters,”? J. Meteorol., vol. 18, pp. 340–347, June 1961.
149. J.R. Gerhardt, C.W. Tolbert, and S.A. Brunstein, “Further studies of the back-scattering cross-sections of water drops and wet and dry ice spheres,”? J. Meteorol., vol. 18, pp. 688–691, Oct. 1961.
150. J. Joss and A.N. Aufdermaur, “Experimental determination of the radar cross sections of artificial hailstones containing water,”? J. Appl. Meteorolvol. 4, pp. 723–726, Dec. 1965.
151. L.J. Auchterlonie and D.L. Bryant, “Experimental study of millimetre-wave scattering from simulated hailstones in an open resonator,”? Proc. Inst. Elec. Eng., vol. 128, pt H, pp. 236–242, Oct. 1981.
152. L. E Allan and G.C. McCormick, “Measurements of the backscatter matrix of dielectric spheroids,”? IEEE Trans. Antennas Propagat., vol. AP-26, pp. 579–587, July 1978.
153. “Measurements of the backscatter matrix of dielectric bodies,”? IEEE Trans. Antennas Propagat., vol. AP-28, pp. 166–169, Mar. 1980.
154. G.C. McCormick, L.E. Allan, and A. Hendry, “The backscatter matrix of ice samples: Its relation to the identification of hail by radar,”? J. Appl. Meteorol., vol. 18, pp. 77–84, Jan. 1979.
155. K. Sassen and K.N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,”?. Atmos. Sci., vol. 36, pp. 838–851, May 1979.
156. K. Sassen, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part II: Angular depolarizing and multiple-scattering behavior,”? J. Atmos. Sci., vol. 36, pp. 852–861, May 1979.
157. R.K. Crane, “The rain range experiment-propagation through a simulated rain environment,”? IEEE Trans. Antennas Propagat., vol. AP-22, pp. 321–328, Mar. 1974.
158. D.C. Hogg and T.S. Chu, “The role of rain in satellite communications,”? Proc. IEEE, vol. 63, pp. 1308–1331, Sept. 1975.
159. D.V. Rogers and R.L. Olsen, “Calculation of radiowave attenuation due to rain at frequencies up to 1000 GHz,”? Rep. 1299, Communications Res. Cen., Dept, of Commun. (Ottawa, Canada), Nov. 1976.
160. R.L. Olsen, “A review of theories of coherent radio wave propagation through precipitation media of randomly oriented scatterers, and the role of multiple scattering,”? Radio Sci., vol. 17, pp. 913–928, Sept.-Oct. 1982.
161. R.L. Olsen, D.V. Rogers, and D.B. Hodge, “The aRb relation in the calculation of rain attenuation,”? IEEE Trans. Antennas Propagat., vol. AP-26, pp. 318–329, Mar. 1978.
162. T. Manabe, T. Ihara, and Y. Furuhama, “Inference of raindrop size distribution from attenuation and rain rate measurements” (in Japanese), Paper of Tech. Group, TGAP81–107, Inst. Electron. Commun. Eng. Japan, Dec. 1981.
163. P. Waldteufel, “Attenuation des ondes hyperfréquences par la pluie: Une mise au point,”? Ann. Télécommunic., vol. 28, pp. 255–272, May-June 1973.
164. T. Oguchi, “Scattering properties of Pruppacher-and-Pitter form raindrops and cross polarization due to rain: calculations at 11, 13, 19.3, and 34.8 GHz,”? Radio Sci., vol. 12, pp. 41–51, Jan.-Feb. 1977.
165. A.M. Zavody and B.N. Harden, “Attenuation/rain-rate relationships at 36 and 110 GHz,”? Electron. Lett., vol. 12, pp. 422–424, Aug. 1976.
166. Yu. S. Babkin, I.A. Iskhakov, A.V. Sokolov, L.I. Stroganov, and Ye. V. Sukhonin, “Attenuation of radiation at a wavelength of 0.96 mm in snow” Radio Eng. Electron. Phys., vol. 15, pp. 2171–2174, Dec. 1970.
167. T. Oomori and S. Aoyagi, “A presumptive formula for snowfall attenuation of radio waves,”? Trans. Inst. Electron. Commun. Eng. Japan (in Japanese), vol. 54-B, pp. 451–458, Aug. 1971.
168. I.J. Dilworth and B.G. Evans, “Depolarisation due to snow at 11.6 GHz,”? Electron. Lett., vol. 14, pp. 315–317, May 1978.
169. A. Nishitsuji, “Method of calculation of radio-wave attenuation in snowfall,”? Electron. Commun. Japan, vol. 54, pp. 74–81, Jan 1971 (s/p scripta publishing corporation, Washington, DC).
170. A. Nishitsuji and M. Hirayama, “Anomalous attenuation of radio waves due to snowfall,”? Electron. Commun. Japan, vol. 54, pp. 27–33, Nov. 1971 (s/p scripta publishing corporation, Washington, DC).
171. A. Nishitsuji and A. Matsumoto, “The character of falling snow,”? in SHF and EHF Propagation in Snowy Districts, A. Matsumoto and A. Nishitsuji, Eds. (Monograph Ser. of the Res. Inst, of Appl. Electricity, Hokkaido Univ., Sapporo, Japan), no. 19, pp. 45–61, 1971.
172. A. Attisani, C. Capsoni, and A. Paraboni, “Effects of non-spherical hydrometeors on EM propagation through atmospheric precipitation,”? J. Rech. Atmos., vol. 8, pp. 137–145, Jan.-June 1974.
173. G.C. McCormick, “Propagation through a precipitation medium: Theory and measurement,”? IEEE Trans. Antennas Propagat., vol. AP-23, pp. 266–269, Mar. 1975.
174. D.J. Fang, “Attenuation and phase shift of microwaves due to canted raindrops,”? COMSAT Tech. Rev., vol. 5, pp. 135–156, Spring 1975.
175. K. Ostberg, “Effect of drop canting-angle distribution on depolarization of microwaves in rain,”? FOA Rep., vol. 10, pp. 1–8 (Nat. Def. Res. Inst., Stockholm, Sweden), Feb. 1976.
176. I.P. Shkarofsky, “Depolarization due to precipitation in satellite communications,”? RCA Rev., vol. 38, pp. 257–309, June 1977.
177. P. Beckmann, The Depolarization of Electromagnetic Waves. Boulder, CO: Golem Press, 1968.
178. P.A. Watson, “Working group report III: Microphysics of hydrometeors and polarisation,”? J. Rech. Atmos., vol. 8, pp. 477–484, Jan.-June 1974.
179. B.G. Evans, S.A.J. Upton, and A.R. Holt, “Effect of raindrop shape on crosspolarisation/attenuation relationships,”? Electron. Lett., vol. 17, pp. 22–24, Jan. 1981.
180. I.P. Shkarofsky, “Dependence on rain attenuation and cross-polarization on drop size distribution,”? IEEE Trans. Antennas Propagat., vol. AP-27, pp. 538–542, July 1979.
181. J. Howard and N.A. Mathews, “Effects of sizes of nonspherical raindrops on crosspolarization of transmitted microwave signals,”? IEEE Trans. Antennas Propagatvol. AP-27, pp. 891–893, Nov. 1979.
182. P.F. Shutie, J.E. Allnutt, and E.G. Mackenzie, “Satellite-earth signal depolarisation at 30 GHz in the absence of significant fading,”? Electron. Lett., vol. 13, pp. 1–2, Jan. 1977.
183. L.J. Ippolito, “Radio propagation for space communications systems,”? Proc. IEEE, vol. 69, pp. 697–727, June 1981.
184. D.C. Cox, “Depolarization of radio waves by atmospheric hydrometeors in earth-space paths: A review,”? Radio Sci., vol. 16, pp. 781–812, Sept.-Oct. 1981.
185. D.C. Cox and H.W. Arnold, “Results from the 19-and 28-GHz COMSTAR satellite propagation experiments at Crawford Hill,”? Proc. IEEE, vol. 70, pp. 458–488, May 1982.
186. P.A. Watson, N.J. McEwan, A.W. Dissanayake, and D.P. Haworth, “Attenuation and cross-polarization measurements at 20 GHz using the ATS-6 satellite with simultaneous radar observations,”? IEEE Trans. Antennas Propagat., vol. AP-27, pp. 11–17, Jan. 1979.
187. J. Thirlwell, D.M. Knox, and R.G. Howell, “Crosspolar variations on a satellite-earth path,”? Electron. Lett., vol. 13, pp. 516–518, Aug. 1977.
188. D.P. Haworth, P.A. Watson, and N.J. McEwan, “Model for the effect of electric fields on satellite-earth microwave radio propagation,”? Electron. Lett., vol. 13, pp. 562–564, Sept. 1977.
189. B.G. Evans and A. R, Holt, “Crosspolarisation phase due to ice crystals on microwave satellite paths,”? Electron. Lett., vol. 13, pp. 664–666, Oct. 1977.
190. N.J. McEwan, “Phase of crosspolarised signals on microwave satellite links,”? Electron. Lett., vol. 13, pp. 489–491, Aug. 1977.
191. N.J. McEwan, A.P. Alves, H.W. Poon, and A.W. Dissanayake, “OTS propagation measurements during thunderstorms,”?.Ann. Télécommunic., vol. 36, pp. 102–110, Jan-Feb. 1981.
192. D.P. Haworth, N.J. McEwan, and P.A. Watson, “Crosspolarisation for linearly and circularly polarised waves propagating through a population of ice particles on satellite-earth paths,”? Electron. Lett., vol. 13, pp. 703–704, Nov. 1977.
193. D.P. Haworth, N.J. McEwan, and P.A. Watson, “Relationship between atmospheric electricity and microwave radio propagation,”? Nature, vol. 266, pp. 703–704, Apr. 1977.
194. A. Hendry and G.C. McCormick, “Radar observations of the alignment of precipitation particles by electrostatic fields in thunderstorms,”? J. Geophys. Res., vol. 81, pp. 5353–5357, Oct. 1976.
195. D.J. Mendez, “Optical polarization induced by electric fields of thunderstorms,”? J. Geophys. Res., vol. 74, pp. 7032–7037, Dec. 1969.
196. H.W. Arnold and D.C. Cox, “Dependence of depolarization on incident polarization for 19-GHz satellite signals,”? Bell Syst. Tech. J., vol. 57, pp. 3267–3276, Nov. 1978.
197. D.C. Cox and H.W. Arnold, “Observations of rapid changes in the orientation and degree of alignment of ice particles along an earth-space radio propagation path,”? J. Geophys. Res., vol. 84, no. C8, pp. 5003–5010, Aug. 1979.
198. A. Hendry, G.C. McCormick, and B.L. Barge, “Ku-band and S-band observations of the differential propagation constant in snow,”? IEEE Trans. Antennas Propagat., vol. AP-24, pp. 521–525, July 1976.
199. A. Hendry, G.C. McCormick, and Y.M.M. Antar, “Differential propagation constants on slant paths through snow and ice crystals as measured by 16.5 GHz polarization-diversity radar,”? Ann. Télécommunic., vol. 36, pp. 133–139, Jan.-Feb. 1981.
200. T. Oguchi, “Rain depolarization studies at centimeter and millimeter wavelengths: Theory and measurement,”? J. Radio Res. Labs. (Japan), vol. 22, pp. 165–211, 1975.
201. I.J. Dilworth and B.G. Evans, “Cumulative crosspolarisation and canting angle distributions,”? Electron. Lett., vol. 15, pp. 603–604, Sept. 1979.
202. G.C. McCormick and A. Hendry, “Polarization properties of transmission through precipitation over a communication link,”? J. Rech. Atmos., vol. 8, pp. 175–187, Jan.-June 1974.
203. G.C. McCormick, A. Hendry, and L.E. Allan, “Depolarization over a link due to rain: Measurements of the parameters,”? Radio Sci., vol. 11, pp. 741–749, Aug.-Sept. 1976.
204. C. Capsoni, A. Paraboni, F. Fedi, and D. Maggiori, “A model-oriented approach to measure rain-induced cross-polarization,”? Ann. Télécommunic., vol. 36, pp. 154–159, Jan.-Feb. 1981.
205. R.L. Olsen, “Thieory for measuring the effective polarization parameters of rain from orthogonal linearly-polarized transmissions,”? Ann. Télécommunic., vol. 36, pp. 471–476, July-Aug. 1981.
206. P. Cologne and P. Sobieski, “Fine structure of microwave cross-polarization due to precipitation,”? Ann. Télécommunic., vol. 32, pp. 377–385, Nov.-Dee. 1977.
207. A.W. Dissanayake, D.P. Haworth, and P.A. Watson, “Analytical models for cross-polarization on earth-space radio paths for frequency range 9-30 GHz,”? Ann. Télécommunic., vol. 35, pp. 398–404, Nov.-Dee. 1980.
208. T.S. Chu, “Microwave depolarization of an earth-space path,”? Bell Syst. Tech. J., vol. 59, pp. 987–1007, July-Aug. 1980.
209. W.L. Nowland, R. L. Olsen, and I.P. Shkarofsky, “Theoretical relationship between rain depolarisation and attenuation,”? Electron. Lett., vol. 13, pp. 676–678, Oct. 1977.
210. R.L. Olsen and W.L. Nowland, “Semi-empirical relations for the prediction of rain depolarization statistics: Their theoretical and experimental basis,”? in Proc. Int. Symp. on Antennas and Propagation. (Japan), pp. 477–480, 1978.
211. T.S. Chu, “A semi-empirical formula for microwave depolarization versus rain attenuation on earth-space paths,”? IEEE Trans. Commun., vol. COM-30, pp. 2550–2554, Dec. 1982.
212. CCIR, Rep. 722-1, “Cross-polarization due to the atmosphere,”? in Recommendations and Reports of the CCIR, vol. 5, pp. 185–193, 1982 (Int. Telecommun. Union, Geneva, Switzerland).
213. T.S. Chu, “Analysis and prediction of cross-polarization on earth-space links,”? Ann. Télécommunic., vol. 36, pp. 140–147, Jan.-Feb. 1981.
214. T.S. Chu, “Restoring the orthogonality of two polarizations in radio communication systems, I,”? Bell Syst. Tech. J., vol. 50, pp. 3063–3069, Nov. 1971.
215. T.S. Chu, “Restoring the orthogonality of two polarizations in radio communication systems, II,”? Bell Syst. Tech. J., vol. 52, pp. 319–327, Mar. 1973.
216. R.W. Kreutel, “The orthogonalization of polarized fields in dualpolarized radio transmission systems,”? COMSAT Tech. Rev., vol. 3, pp. 375–386, Fall 1973.
217. D.F. DiFonzo, W.S. Trachtman, and A. E Williams, “Adaptive polarization control for satellite frequency reuse systems,”? COMSAT Tech. Rev., vol. 6, pp. 253–283, Fall 1976.
218. A.E. Williams and F.L. Frey, “Adaptive polarisation control on a dual-polarised 4/6 GHz SATCOM link in the presence of rain,”? Electron. Lett., vol. 12, pp. 686–687, Dec. 1976.
219. H. Kannowade, “An automatic control system for compensating crosspolarization coupling in Frequency-reuse communication systems,”? IEEE Trans. Commun., vol. COM-24, pp. 986–999, Sept. 1976.
220. A.E. Williams, “A dual-polarized 4/6-GHz adaptive polarization control network,”? COMSAT Tech. Rev., vol. 7, pp. 247–262, Spring 1977.
221. P. DeLogne and P. Sobieski, “Adaptive cancellation of crosspolarisation: Experiments with unmodulated signals,”? Electron. Lett., vol. 14, pp. 770–772, Oct. 1978.
222. W.P. Overstreet and C.W. Bostian, “Crosstalk cancellation on linearly and circularly polarized communications satellite links,”? Radio Sci., vol. 14, pp. 1041–1047, Nov.-Dee. 1979.
223. M. Nouri and M.R. Braine, “Uplink adaptive depolarisation cancellation in a ground-to-satellite link,”? Electron. Lett., vol. 16, pp. 68–69, Jan. 1980.
224. R.R. Persinger, R.W. Gruner, J.E. Effland, and D.F. DiFonzo, “Operational measurements of a 4/6-GHz adaptive polarization compensation network employing up/down-link correlation algorithms,”? in IEE Conf. Publ. 195, vol. 2, pp. 181–187 (Inst. Elec. Eng., London), 1981.
225. N.J. McEwan, M. Günes, and M.S. Mahmoud, “RF methods for adaptive cancellation of cross polarisation in microwave satellite systems,”? in IEE Conf. Publ. 195, vol. 2, pp. 188–192 (Inst. Elec. Eng., London), 1981.
226. M. Yamada, H. Yuki, K. Inagaki, S. Endo, and N. Matsunaka, “Compensation techniques of rain depolarization in satellite communications,”? Radio Sci., vol. 17, pp. 1220–1230, Sept.-Oct. 1982.
227. T. Oguchi and M. Yamada, “Frequency characteristics of attenuation, phase shift, and cross-polarization due to rain within communication bands: Calculations at 4, 6, 11, and 14 GHz bands for INTELSAT satellite communication system,”? J. Radio Res. Labs. (Japan), vol. 28, pp. 97–131, Mar.-July 1981.
228. ITU, Final Acts of the World Administrative Radio Conference. Geneva, Switzerland: ITU, 1979.
229. D. Atlas and C.W. Ulbrich, “The physical basis for attenuation-rainfall relationships and measurement of rainfall parameters by combined attenuation and radar methods,”? J. Rech. Atmos., vol. 8, pp. 275–298, Jan.-June 1974.
230. D. Atlas, “Optical extinction by rainfall,”? J. Meteorol., vol. 10, pp. 486–488, Dec. 1953.
231. L.J. Battan, Radar Observation of the Atmosphere. Chicago, IL: Univ. of Chicago Press, 1973.
232. S.M. Cherry, J.W.F. Goddard, and M.P.M. Hall, “Use of dualpolarization radar data for evaluation of attenuation on a satellite-to-earth path,”? Ann. Télécommunic., vol. 36, pp. 33–39, Jan.-Feb. 1981.
233. CCIR, Rep. 569-1, “The evaluation of propagation factors in interference problems at frequencies greater than 0.6 GHz,”? in Recommendations and Reports of the CCIR, vol. 5, pp. 241–262, 1978 (Int. Telecommun. Union, Geneva, Switzerland).
234. CCIR, Rep. 724, “Propagation data for the evaluation of co-ordination distance in the frequency range 1 to 40 GHz,”? in Recommendations and Reports of the CCIR, vol. 5, pp. 262–279, 1978 (Int. Telecommun. Union, Geneva, Switzerland).
235. L.H. Doherty and S.A. Stone, “Forward scatter from rain,”? IEEE Trans. Antennas Propagat., vol. AP-8, pp. 414–418, July 1960.
236. L.T. Gusler and D.C. Hogg, “Some calculations on coupling between satellite communications and terrestrial radio-relay systems due to scattering by rain,”? Bell Syst. Tech. J., vol. 49, pp. 1491–1512, Sept. 1970.
237. D.E. Setzer, “Anisotropic scattering due to rain at radio-relay frequencies,”? Bell Syst. Tech. J., vol. 50, pp. 861–868, Mar. 1971.
238. R.K. Crane, “Bistatic scatter from rain,”? IEEE Trans. Antennas Propagat., vol. AP-22, pp. 312–320, Mar. 1974.
239. R.K. Crane, “Prediction of the effects of rain on satellite communication systems,”? Proc. IEEE, vol. 65, pp. 456–474, Mar. 1977.
240. T.S. Chu, “Rain-scatter interference on an earth-space path,”? IEEE Trans. Antennas Propagat., vol. AP-25, pp. 287–288, Mar. 1977.
241. T. Li, W.C. Jakes, Jr., and J.A. Morrison, “Forward scattering due to rain at 11 GHz,”? IEEE Trans. Antennas Propagat., vol. AP-25, pp. 646–649, Sept. 1977.
242. S. Sakagarni, “Some experimental results on bistatic scatter from rain,”? IEEE Trans. Antennas Propagat., vol. AP-28, pp. 161–165, Mar. 1980.
243. J. Awaka, “Angular dependence of rain scattering at frequencies below 30 GHz,”? Trans. Inst. Electron. Commun. Eng. Japan, vol. E62, pp. 462–465, July 1979.
244. P. DeLogne and M. Lobelle, “Numerical calculations on microwave propagation through rain,”? Ann. Télécommunic., vol. 32, pp. 386–391, Nov.-Dee. 1977.
245. E. Damosso and D. Tarducci, “Angular scattering of water drops and ice particles,”? Rapporti Tecnici (Centro Studi e Laboratori Telecomun-icazioni, Torino, Italy), vol. 8, pp. 107–109, Mar. 1980.
246. J. Awaka and T. Oguchi, “Bistatic radar reflectivities of Pruppacher-and-Pitter form raindrops at 34.8 GHz,”? Radio Sci., vol. 17, pp. 269–278, Jan.-Feb. 1982.
247. J. Awaka, “Bistatic radar reflectivities of Pruppacher-and-Fitter form raindrops at 14.3 and 5.33 GHz,”? J. Radio Res. Labs. (Japan), vol. 29, pp. 125–150, July 1982.
248. A. Ochs, “Statistical analysis of the directivity of precipitation scattering at 11.5 GHz,”? in IEE Conf. Publ. 195, vol. 2, pp. 193–197 (Inst. Elec. Eng., London), 1981.
249. J. Awaka, private communication.
250. P.J. Eccles and D. Atlas, “A dual-wavelength radar hail detector,”? J. Appl. Meteorol., vol. 12, pp. 847–854, Aug. 1973.
251. M. Yamada, A. Ogawa, O. Furuta, and H. Yokoi, “Measurement of rain attenuation by dual-frequency radar,”? in Proc. Int. Symp. on Antennas and Propagation. (Japan), pp. 469–472, 1978.
252. J. Goldhirsh and I. Katz, “Estimation of raindrop size distribution using multiple wavelength radar systems,”? Radio Sci., vol. 9, pp. 439–446, Apr. 1974.
253. Y. Furuhama and T. Ihara, “Remote sensing of path-averaged raindrop size distributions from microwave scattering measurements,”? IEEE Trans. Antennas Propagat., vol. Ap. 29, pp. 275–281, Mar. 1981.
254. B.L. Barge, “Polarization measurements of precipitation backscatter in Alberta,”? J. Rech. Atmos., vol. 8, pp. 163–173, Jan.-June 1974.
255. R.G. Humphries, “Observations and calculations of depolarization effects at 3 GHz due to precipitation,”? J. Rech. Atmos., vol. 8, pp. 155–161, Jan.-June 1974.
256. G.C. McCormick, A. Hendry, and B.L. Barge, “The anisotropy of precipitation media,”? Nature, vol. 238, pp. 214–216, July 1972.
257. A. Hendry and G.C. McCormick, “Polarization properties of precipitation particles related to storm structure,”? J. Rech. Atmos., vol. 8, pp. 189–200, Jan.-June 1974.
258. G.C. McCormick and A. Hendry, “Principles for the radar determination of the polarization properties of precipitation,”? Radio Sci., vol. 10, pp. 421–434, Apr. 1975.
259. G.C. McCormick, “Polarization-related parameters for rain: Measurements obtained by radar,”? Radio Sci., vol. 11, pp. 731–740, Aug.-Sept. 1976.
260. A. Hendry, G.C. McCormick, and B.L. Barge, “The degree of common orientation of hydrometeors observed by polarization diversity radars,”? J. Appl. Meteorol., vol. 15, pp. 633–640, June 1976.
261. G.C. McCormick and A. Hendry, “Depolarisation by solid hydrometeors,”? Electron. Lett., vol. 13, pp. 83–84, Feb. 1977.
262. T.A. Seliga and V.N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol., vol. 15, pp. 69–76, Jan. 1976.
263. M.P.M. Hall, S.M. Cherry, J.W.F. Goddard, and G.R. Kennedy, “Rain drop sizes and rainfall rate measured by dual-polarization radar,”? Nature, vol. 285, pp. 195–198, May 1980.
264. R.R. Rogers, “Doppler radar investigation of Hawaiian rain,”? Tellus, vol. 19, pp. 432–455, 1967.
265. A.A. Chernikov, V.A. Kapitanov, and Yu. V. Mel'nichuk, “A polarization dependence of Doppler spectra of precipitation radar returns,”? in Proc. Inter-Union Commission on Radio Meteorology, Coloquium (Union Radio Sci. Int., Int. Union of Geod. and Geophys., Nice, France, Oct. 1973), p. Ml.
266. A.B. Shupyatsky, “Echo depolarization as measured with bistatic radar,”? J. Rech. Atmos., vol. 8, pp. 201–204, Jan.-June 1974.
267. D.P. Haworth, N.J. McEwan, and P.A. Watson, “Microwave transmission spectra through rainfall: A new method for identifying hydrometeors,”? in Proc. Commission F Open Symp. (Union Radio Sci. Int., La Baule, France, Apr.-May 1977), pp. 205–209.
268. D.P. Haworth and N.J. McEwan, “Spectral analysis of the received signal on a 20 GHz bistatic scatter link,”? Ann. Télécommunic., vol. 35, pp. 390–397, Nov.-Dec. 1980.
269. J. Neves and P.A. Watson, “Cross-polarisation, differential attenuation and differential phase shift measured on a 36.5 GHz terrestrial link,”? in Proc. Commission F Int. Symp. on Effects of the Lower A tmosphere on Radio Propagation at Frequencies above I GHz (Union Radio Sci. Int., Lennoxville, Que., May 26-30, 1980), pp. 5.1.1–5.1.6.
270. L.L. Foldy, “The multiple scattering of waves,”? Phys. Rev., vol. 67, pp. 107–119, Feb. 1945.
271. M. Lax, “Multiple scattering of waves,”? Rev. Mod. Phys., vol. 23, pp. 287–310, Oct. 1951.
272. M. Lax, “Multiple scattering of waves, 2, The effective field in dense systems,”? Phys. Rev., vol. 85, pp. 621–629, Feb. 1952.
273. V. Twersky, “On scattering of waves by random distributions, I, Free-space scatterer formalism,”? J. Math. Phys., vol. 3, pp. 700–715, July-Aug. 1962.
274. V. Twersky, “On scattering of waves by random distributions, II, Two-space scatterer formalism,”? J. Math. Phys., vol. 3, pp. 724–734, July-Aug. 1962.
275. A. Ishimaru, Wave Propagation and Scattering in Random Media, vols. 1 and 2. New York: Academic Press, 1978.
276. J.C. Lin and A. Ishimaru, “Propagation of millimeter waves in rain,”? Univ. of Washington, Seattle, Wash., Dep. of Elec. Eng., Tech. Rep. 144, 1971.
277. J.C. Lin, “Multiple scattering of waves by a uniform random distribution of discrete isotropic scatterers,”? J. Acoust. Soc. Am., vol. 56, pp. 1695–1700, Dec. 1974.
278. A. Ishimaru and J.C. Lin, “Multiple scattering effects on wave propagation through rain,”? in Proc. Conf. on Telecommunications Aspects of Frequencies between 10 and 100 GHz (Adv. Group for Aeronaut. Res. and Dev., North Atl. Treaty Organ., Norway, Sept. 18–21, 1972), pp. I.1-I.13.
279. S. Chandrasekhar, Radiative Transfer. Oxford, England: Clarendon, 1950.
280. J.B. Keller, “Stochastic equations and wave propagation in random media,”? in Proc. Symp. in Applied Mathematics, vol. 16 (Amer. Math. Soc., Providence, RI, 1964), pp. 145–170.
281. K. Furutsu, “Multiple scattering of waves in a medium of randomly distributed particles and derivation of the transport equation,”? Radio Sci., vol. 10, pp. 29–44, Jan. 1975.
282. K.M. Case, “Elementary solutions of the transport equation and their applications,”? Ann. Phys. N.Y., vol. 9, pp. 1–23, Jan. 1960.
283. N.J. McCormick and I. Kuscer, “Bi-orthogonality relations for solving half-space transport problems,”? J. Math. Phys., vol. 7, pp. 2036–2045, Nov. 1966.
284. R.K. Crane, “Propagation phenomena affecting satellite communication systems operating in the centimeter and millimeter wavelength bands,”? Proc. IEEE, vol. 59, pp. 173–188, Feb. 1971.
285. M. Lobelie, “Resolution numerique de l'équation de Chandrasekhar dans le cas d'une pluie de gouttes sphériques,”? Lab. of Telecommun. and Microwaves, Fac. of Appl. Sci., Cath Univ. of Louvain, Louvain-la-Neuve, Belgium, Internal Rep., 1975.
286. P. DeLogne, P. Osvath, P. Sobieski, and J. van Vyve, “Theory and experimental study of microwave depolarisation due to rain,”? presented at the 18th General Assembly, Union Radio Sci. Int., Lima, Peru, Aug. 11–19, 1975.
287. C. Capsoni, M. Mauri, and A. Paraboni, “Incoherent effects in electromagnetic propagation through rain,”? Ann. Télécommunic., vol. 32, pp. 409–414, Nov.-Dec. 1977.
288. A. Ishimaru and R.L.-T. Cheung, “Multiple scattering effects on wave propagation due to rain,”? Ann. Télécommunic., vol. 35, pp. 373–379, Nov.-Dee. 1980.
289. T. Oguchi, “Effect of incoherent scattering on attenuation and cross polarization of millimeter wave due to rain: Preliminary calculations at 34.8 and 82 GHz for spherical raindrops,”? J. Radio Res. Labs. (Japan), vol. 27, pp. 1–51, Mar.-July 1980.
290. T. Oguchi, “Effect of incoherent scattering on attenuation and cross polarization of millimeter waves due to rain: Preliminary calculations at 34.8 and 82 GHz for spherical raindrops,”? Ann. Télécommunic., vol. 35, pp. 380–389, Nov.-Dec. 1980.
291. J. Canosa and H.R. Penafiel, “A direct solution of the radiative transfer equation: Application to Rayleigh and Mie atmospheres,”? J. Quant. Spectrosc. Radiat. Transfer, vol. 13, pp. 21–39, Jan. 1973.
292. J.V. Dave and J. Canosa, “A direct solution of the radiative transfer equation: Application to atmospheric models with arbitrary vertical nonhomogeneities,”? J. Atmos. Sci., vol. 31, pp. 1089–1101, May 1974.
293. A. Ishimaru, R. Woo, J.W. Armstrong, and D.C. Blackman, “Multiple scattering calculations of rain effects,”? Radio Sci., vol. 17, pp. 1425–1433, Nov.-Dee. 1982.
294. A.M. Zavody, “Effect of scattering by rain on radiometer measurements at millimeter wavelengths,”? Proc. Inst. Elec. Eng., vol. 121, pp. 257–263, Apr. 1974.
295. A. Ishimaru and R.L.-T. Cheung, “Multiple-scattering effect on radio-metric determination of rain attenuation at millimeter wavelengths,”? Radio Sci., vol. 15, pp. 507–516, May-June 1980.
296. L. Tsang and J.A. Kong, “Radiative transfer theory for active remote sensing of half-space random media,”? Radio Sci., vol. 13, pp. 763–773, Sept.-Oct. 1978.
297. A. Ishimaru and S.T. Hong, “Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles,”? Radio Sci., vol. 10, pp. 637–644, June 1975.
298. S.T. Hong and A. Ishimaru, “Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence,”? Radio Sci., vol. 11, pp. 551–559, June 1976.
299. S. Ito, “On the theory of pulse wave propagation in media of discrete random scatterers,”? Radio Sci., vol. 15, pp. 893–901, Sept.-Oct. 1980.
300. S. Ito and K. Furutsu, “Theory of light pulse propagation through thick clouds,”? J. Opt. Soc. Am., vol. 70, pp. 366–374, Apr. 1980.
301. C. Capsoni and A. Paraboni, “Properties of the forward-scattered incoherent radiation through intense precipitation,”? IEEE Trans. Antennas Propagat., vol. AP-26, pp. 804–809, Nov. 1978.
302. C.I. Beard and V. Twersky, “Propagation through random distributions of spheres,”? Rep. EDL-M156, Sylvania Electron. Def. Lab., Mountain View, CA, 1958.
303. C.I. Beard and V. Twersky, “Forward coherent and incoherent scattering from random volume distributions of spheres” Rep. EDL-E46, Sylvania Electron. Def. Lab., Mountain View, CA, 1960.
304. R.L. Olsen and M.M.Z. Kharadly, “Experimental investigation of the scattering of electromagnetic waves from a model random medium of discrete scatterers,”? Radio Sci., vol. 11, pp. 39–48, Jan. 1976.
305. L.J. Ippolito, “ATS-6 millimeter wave propagation and communications experiments at 20 and 30 GHz,”? IEEE Trans. Aerospace Electron. Syst., vol. AES-11, pp. 1067–1082, Nov. 1975.
306. D.C. Cox, H.W. Arnold, and R.P. Leck, “Phase and amplitude dispersion for earth-satellite propagation in the 20-to 30-GHz frequency range,”? IEEE Trans. Antennas Propagat., vol. AP-28, pp. 359–366, May 1980.