Abstract

A systematic procedure for calculating the refractive index of snow at microwave frequencies is presented. The refractive index of snow at 0°C was calculated for different snow types (classified in terms of snow wetness as dry, most, wet, and watery) and microwave frequencies. For the sake of completeness, the refractive indices of water and ice were also calculated for the same frequencies.

© 1985 Optical Society of America

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References

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  1. W. A. Cumming, “The Dielectric Properties of Ice and Snow at 3.2 cm,” J. Appl. Phys. 23, 768 (1952).
    [CrossRef]
  2. S. Evans, “Dielectric Properties of Ice and Snow—a Review,” J. Glaciol. 15, 773 (1965).
  3. W. I. Linlor, Advanced Concepts and Techniques in Resources (National Academy of Sciences, Washington D.C., 1974), p. 720.
  4. W. I. Linlor, “Permittivity and Attenuation of Wet Snow Between 4 and 12 GHz,” J. Appl. Phys. 51, 2811 (1980).
    [CrossRef]
  5. P. S. Ray, “Broadband Complex Refractive Indices of Ice and Water,” Appl. Opt. 11, 1836 (1972).
    [CrossRef] [PubMed]
  6. E. R. Pounder, The Physics of Ice (Pergamon, New York, 1965).
  7. P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974).
  8. K. S. Cole, R. H. Cole, “Dispersion and Absorption in Dielectrics,” J. Chem. Phys. 9, 341 (1941).
    [CrossRef]
  9. T. Oguchi, “Electromagnetic Wave Propagation and Scattering in Rain and Other Hydrometeors,” Proc. IEEE 71, 1029 (1983).
    [CrossRef]
  10. T. S. Chu, “Rain-Induced Cross-Polarization at Centimeter and Millimeter Wavelengths,” Bell Syst. Tech. J. 53, 1557 (1974).
  11. D. Polder, J. H. Van Santen, “The Effective Permeability of Mixtures of Solids,” Physica XII, 237 (1946).
  12. L. S. Taylor, “Dielectric Properties of Mixtures,” IEEE Trans. Antennas Propag. AP-13, 943 (1965).
    [CrossRef]
  13. P. Debye, Polar Molecules (Dover, New York, 1929).
  14. A. Nishitsuji, “Method of Calculation of Radio-Wave Attenuation in Snowfall,” Electron. Commun. Jpn. 54-B, 74 (1971).
  15. A. Nishitsuji, M. Hirayama, “Anomalous Attenuation of Radio Waves due to Snowfall,” Electron. Commun. Jpn. 54-B, 27 (1971).

1983

T. Oguchi, “Electromagnetic Wave Propagation and Scattering in Rain and Other Hydrometeors,” Proc. IEEE 71, 1029 (1983).
[CrossRef]

1980

W. I. Linlor, “Permittivity and Attenuation of Wet Snow Between 4 and 12 GHz,” J. Appl. Phys. 51, 2811 (1980).
[CrossRef]

1974

T. S. Chu, “Rain-Induced Cross-Polarization at Centimeter and Millimeter Wavelengths,” Bell Syst. Tech. J. 53, 1557 (1974).

1972

1971

A. Nishitsuji, “Method of Calculation of Radio-Wave Attenuation in Snowfall,” Electron. Commun. Jpn. 54-B, 74 (1971).

A. Nishitsuji, M. Hirayama, “Anomalous Attenuation of Radio Waves due to Snowfall,” Electron. Commun. Jpn. 54-B, 27 (1971).

1965

S. Evans, “Dielectric Properties of Ice and Snow—a Review,” J. Glaciol. 15, 773 (1965).

L. S. Taylor, “Dielectric Properties of Mixtures,” IEEE Trans. Antennas Propag. AP-13, 943 (1965).
[CrossRef]

1952

W. A. Cumming, “The Dielectric Properties of Ice and Snow at 3.2 cm,” J. Appl. Phys. 23, 768 (1952).
[CrossRef]

1946

D. Polder, J. H. Van Santen, “The Effective Permeability of Mixtures of Solids,” Physica XII, 237 (1946).

1941

K. S. Cole, R. H. Cole, “Dispersion and Absorption in Dielectrics,” J. Chem. Phys. 9, 341 (1941).
[CrossRef]

Chu, T. S.

T. S. Chu, “Rain-Induced Cross-Polarization at Centimeter and Millimeter Wavelengths,” Bell Syst. Tech. J. 53, 1557 (1974).

Cole, K. S.

K. S. Cole, R. H. Cole, “Dispersion and Absorption in Dielectrics,” J. Chem. Phys. 9, 341 (1941).
[CrossRef]

Cole, R. H.

K. S. Cole, R. H. Cole, “Dispersion and Absorption in Dielectrics,” J. Chem. Phys. 9, 341 (1941).
[CrossRef]

Cumming, W. A.

W. A. Cumming, “The Dielectric Properties of Ice and Snow at 3.2 cm,” J. Appl. Phys. 23, 768 (1952).
[CrossRef]

Debye, P.

P. Debye, Polar Molecules (Dover, New York, 1929).

Evans, S.

S. Evans, “Dielectric Properties of Ice and Snow—a Review,” J. Glaciol. 15, 773 (1965).

Hirayama, M.

A. Nishitsuji, M. Hirayama, “Anomalous Attenuation of Radio Waves due to Snowfall,” Electron. Commun. Jpn. 54-B, 27 (1971).

Hobbs, P. V.

P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974).

Linlor, W. I.

W. I. Linlor, “Permittivity and Attenuation of Wet Snow Between 4 and 12 GHz,” J. Appl. Phys. 51, 2811 (1980).
[CrossRef]

W. I. Linlor, Advanced Concepts and Techniques in Resources (National Academy of Sciences, Washington D.C., 1974), p. 720.

Nishitsuji, A.

A. Nishitsuji, M. Hirayama, “Anomalous Attenuation of Radio Waves due to Snowfall,” Electron. Commun. Jpn. 54-B, 27 (1971).

A. Nishitsuji, “Method of Calculation of Radio-Wave Attenuation in Snowfall,” Electron. Commun. Jpn. 54-B, 74 (1971).

Oguchi, T.

T. Oguchi, “Electromagnetic Wave Propagation and Scattering in Rain and Other Hydrometeors,” Proc. IEEE 71, 1029 (1983).
[CrossRef]

Polder, D.

D. Polder, J. H. Van Santen, “The Effective Permeability of Mixtures of Solids,” Physica XII, 237 (1946).

Pounder, E. R.

E. R. Pounder, The Physics of Ice (Pergamon, New York, 1965).

Ray, P. S.

Taylor, L. S.

L. S. Taylor, “Dielectric Properties of Mixtures,” IEEE Trans. Antennas Propag. AP-13, 943 (1965).
[CrossRef]

Van Santen, J. H.

D. Polder, J. H. Van Santen, “The Effective Permeability of Mixtures of Solids,” Physica XII, 237 (1946).

Appl. Opt.

Bell Syst. Tech. J.

T. S. Chu, “Rain-Induced Cross-Polarization at Centimeter and Millimeter Wavelengths,” Bell Syst. Tech. J. 53, 1557 (1974).

Electron. Commun. Jpn.

A. Nishitsuji, “Method of Calculation of Radio-Wave Attenuation in Snowfall,” Electron. Commun. Jpn. 54-B, 74 (1971).

A. Nishitsuji, M. Hirayama, “Anomalous Attenuation of Radio Waves due to Snowfall,” Electron. Commun. Jpn. 54-B, 27 (1971).

IEEE Trans. Antennas Propag.

L. S. Taylor, “Dielectric Properties of Mixtures,” IEEE Trans. Antennas Propag. AP-13, 943 (1965).
[CrossRef]

J. Appl. Phys.

W. A. Cumming, “The Dielectric Properties of Ice and Snow at 3.2 cm,” J. Appl. Phys. 23, 768 (1952).
[CrossRef]

W. I. Linlor, “Permittivity and Attenuation of Wet Snow Between 4 and 12 GHz,” J. Appl. Phys. 51, 2811 (1980).
[CrossRef]

J. Chem. Phys.

K. S. Cole, R. H. Cole, “Dispersion and Absorption in Dielectrics,” J. Chem. Phys. 9, 341 (1941).
[CrossRef]

J. Glaciol.

S. Evans, “Dielectric Properties of Ice and Snow—a Review,” J. Glaciol. 15, 773 (1965).

Physica

D. Polder, J. H. Van Santen, “The Effective Permeability of Mixtures of Solids,” Physica XII, 237 (1946).

Proc. IEEE

T. Oguchi, “Electromagnetic Wave Propagation and Scattering in Rain and Other Hydrometeors,” Proc. IEEE 71, 1029 (1983).
[CrossRef]

Other

E. R. Pounder, The Physics of Ice (Pergamon, New York, 1965).

P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974).

P. Debye, Polar Molecules (Dover, New York, 1929).

W. I. Linlor, Advanced Concepts and Techniques in Resources (National Academy of Sciences, Washington D.C., 1974), p. 720.

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Figures (2)

Fig. 1
Fig. 1

Variation of n′ with frequency at 0°C.

Fig. 2
Fig. 2

Variation of n″ with frequency at 0°C.

Tables (4)

Tables Icon

Table I Refractive index of Water at Temperatures of 20 and 0°C

Tables Icon

Table II Refractive Index of Ice at Temperatures of 0 and −5°C

Tables Icon

Table III Classification of Snowfall

Tables Icon

Table IV Refractive Index of Snow at 0°C Temperature

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

= + i
N = n + i n
N = .
= + 0 1 i ( λ s λ ) = + i .
= + 0 1 + ( λ s λ ) 2 ,
= ( 0 ) ( λ s λ ) 1 + ( λ s λ ) 2 ,
= + ( 0 ) [ 1 + ( λ s λ ) 1 α sin ( α π 2 ) ] 1 + 2 ( λ s λ ) 1 α sin ( α π 2 ) + ( λ s λ ) 2 ( 1 α ) ,
= ( 0 ) ( λ s λ ) 1 α cos ( α π 2 ) 1 + 2 ( λ s λ ) 1 α sin ( α π 2 ) + ( λ s λ ) 2 ( 1 α ) + σ λ σ 0 ,
= 5.27137 + 0.0216474 T 0.00131198 T 2 ,
α = 0.069265 16.8129 T + 273 ,
λ s = 3.3836 × 10 4 exp ( 2513.98 T + 273 ) ,
σ = 1.25664 × 10 9 ,
0 = 78.54 [ 1.0 4.579 × 10 3 ( T 25.0 ) + 1.19 × 10 5 ( T 25.0 ) 2 2.8 × 10 8 ( T 25.0 ) 3 ] ,
= 3.168 ,
α = 0.288 + 0.0052 T + 0.00023 T 2 ,
λ s = 9.990288 × 10 4 exp [ 1.32 × 10 4 ( T + 273 ) × 1.9869 ] ,
σ = 1.26 exp [ 1.25 × 10 4 ( T + 273 ) × 1.9869 ] ,
0 = 203.168 + 2.5 T + 0.15 T 2 ,
M s K s ρ s = M i K i ρ i = M w K w ρ w = M a K a ρ a ,
K = N 2 1 N 2 + U = 1 + U .
s 1 s + U = P i i 1 i + U + P w w 1 w + U + P a a 1 a + U ,
P i + P w + P a = 1 .
P i = P w P w 0.92 .
s 1 s + U = W w 1 w + U + ( W W ) 0.92 i 1 i + U .
s = 1 + β U 1 β .

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