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The interaction of microwaves with sea ice

  • Kenneth M. Golden
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 96)

Abstract

The sea ice pack in the polar regions plays a fundamental role in global climate as the boundary layer separating the ocean and atmosphere in these regions. Due to its vast extent, the physical properties of the sea ice pack are often studied via electromagnetic remote sensing from satellites and airplanes, in the microwave regime. In this work we give an overview of ongoing investigations of the interaction of microwaves with sea ice. This interaction is particularly interesting in the case of sea ice, which is a composite of pure ice with random brine and air inclusions, whose geometry can depend dramatically on temperature. These investigations include finding a series of bounds on the effective complex permittivity ε* of sea ice, under constraints on the microgeometry, such as fixed brine volume. In particular, we describe some rather tight bounds on ε* which incorporate the geometrical constraint that for temperatures colder than the percolation threshold, Tc ≈ –5°C, the brine phase is contained in separated inclusions. These bounds fit actual data on ε* at 4.75 GHz quite closely. We also describe how this series of bounds, which are derived in the quasistatic limit, break down when compared with data taken in the 26.5–40.0 GHz range. Finally, we briefly discuss some preliminary results of backscatter experiments we conducted at C band (5.3 GHz) on first year sea ice in the Weddell Sea, Antarctica, during the austral winter of 1994.

Key words

microwaves complex permittivity sea ice matrix-particle composites 

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References

  1. [1]
    J. Addison, Electrical properties of saline ice, J. Appl. Phys., 40: 3105–3114, 1969.CrossRefGoogle Scholar
  2. [2]
    S.A. Arcone, A.J Gow, and S. McGrew, Structure and dielectric properties at 4.8 and 9.5 GHz of saline ice, J. Geophys. Res., 91 (C12): 14281–14303, 1986.CrossRefGoogle Scholar
  3. [3]
    D.J. Bergman, The dielectric constant of a composite material-A problem in classical physics, Phys. Rep. C, 43:377–407, 1978.MathSciNetCrossRefGoogle Scholar
  4. [4]
    D.J. Bergman, Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of a two-component composite material, Phys. Rev. Lett., 44:1285, 1980.CrossRefGoogle Scholar
  5. [5]
    D.J. Bergman, Rigorous bounds for the complex dielectric constant of a two-component composite, Ann. Phys., 138:78, 1982.MathSciNetGoogle Scholar
  6. [6]
    O. Bruno, The effective conductivity of strongly heterogeneous composites, Proc. R. Soc. London A, 433: 353–381, 1991.MathSciNetCrossRefGoogle Scholar
  7. [7]
    O. Bruno, Effective moduli of strongly heterogeneous composites,In G. Bouchitté, G. Butazzo, and P. Suquet, editors, Calculus of Variations, Homogenization and Continuum Mechanics, pages 99–115, World Scientific Publishing Co., Singapore, 1994.Google Scholar
  8. [8]
    E. Cherkaeva and K.M. Golden, Inverse bounds on the brine volume of sea ice from complex permittivity data, In preparation.Google Scholar
  9. [9]
    G.F.N. Cox and W.F. Weeks, Equations for determining the gas and brine volumes in sea-ice samples, J. Glaciology, 29: 306–316, 1983.Google Scholar
  10. [10]
    G. Frankenstein and R. Garner, Equations for determining the brine volume of sea ice from -0.5° to -22.9° C, J. Glaciology, 6 (48): 943–944, 1967.Google Scholar
  11. [11]
    K. Golden, Bounds on the complex permittivity of a multicomponent material, J. Mech. Phys. Solids,34(4):333–358, 1986.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    K. Golden, Bounds on the complex permittivity of sea ice, J. Geophys. Res. (Oceans), 100(C7):13,699–13,711, 1995.CrossRefGoogle Scholar
  13. [13]
    K. Golden and G. Papanicolaou, Bounds for effective parameters of hetero geneous media by analytic continuation, Comm. Math. Phys., 90: 473–491, 1983.MathSciNetCrossRefGoogle Scholar
  14. [14]
    K.M. Golden and S.F. Ackley, Modeling of anisotropic electromagnetic reflection from sea ice, J. Geophys. Res., 86 (C9): 8107–8116, 1981.CrossRefGoogle Scholar
  15. [15]
    Z. Hashin and S. Shtrikman, A variational approach to the theory of effective magnetic permeability of multiphase materials, J. Appl. Phys., 33: 3125–3131, 1962.zbMATHCrossRefGoogle Scholar
  16. [16]
    P. Hoekstra and P. Capillino, Dielectric properties of se a and sodium chloride ice at UHF and microwave frequencies, J. Geophys. Res., 76: 4922–4931, 1971.CrossRefGoogle Scholar
  17. [17]
    A.R. Hosseinmostafa, V.I. Lytle, K.C. Jezek, S.P. Gogineni, S.F. Ackley, and R.K. Moore, Comparison of radar backscatter from Antarctic and Arctic se a ice, J. Eleciromagnetic Appl., 9: 421–438, 1995.Google Scholar
  18. [18]
    V.I. Lytle and K.M. Golden, Microwave backscatter measurements from frist year pack ice in the eastern Weddell Sea, Antarctic Journal of ihe U.S., 30: 125–127, 1995.Google Scholar
  19. [19]
    C. Mätzler and U. Wegmüller, Dielectric properties of fresh-water ice at microwave frequencies, J. Phys. D: Appl. Phys., 20: 1623–1630, 1987.CrossRefGoogle Scholar
  20. [20]
    G.W. Milton, Bounds on the complex dielectric constant of a composite material, Appl. Phys. Lett., 37:300–302, 1980.CrossRefGoogle Scholar
  21. [21]
    R. Sawicz and K. Golden, Bounds on the complexpermittivity of matrix-particle composites, J. Appl. Phys., 78: 7240–7246, 1995.CrossRefGoogle Scholar
  22. [22]
    R.A. Shuchman and R.G.Onstott, Remote sensing of the polar oceans, In W. O. Smith, editor, Polar Oceanography, Part A, Physical Science, pages 123–169, Academic Press, New York, USA, 1990.Google Scholar
  23. [23]
    A.H. Slhvola and J.A. Kong, Effective permittivity of dielectric mixtures, IEEE Trans. Geosci. Remote Sensing, 26 (4): 420–429, 1988.CrossRefGoogle Scholar
  24. [24]
    A. Stogryn, An analysis of the tensor dielectric constant of se a ice at microwave frequencies, IEEE Trans. Geosci. Remote Sensing, GE-25(2):147–158, 1985.CrossRefGoogle Scholar
  25. [25]
    A. Stogryn and G. J. Desargant, The dielectric properties of brine in sea ice at microwave frequencies, IEEE Trans. Ant. Prop., AP-33(5):523–532, 1985.CrossRefGoogle Scholar
  26. [26]
    W.R. Tinga, A.G. Voss, and D.F. Blossey, Generalizedapproach to multiphase dielectric mixture theory, J. Appl. Phys., 44 (9): 3897–3902, 1973.CrossRefGoogle Scholar
  27. [27]
    M.R. Vant, R.O. Ramseier, and V. Marios, The complex-dielectric constant of sea ice at frequencies in the range 0.1–40 GHz, J. Appl. Phys., 49 (3): 1264–1280, 1978.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Kenneth M. Golden
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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