This study is concerned with the development of a model to describe microwave emission from dry snow cover. The model is based on the radiative transfer and the strong fluctuation theory. In the model, a spherical symmetric correlation function with an exponential form is used to describe the random permittivity fluctuations. The phase matrix and extinction coefficient of snowpack for a spherical symmetric correlation function are obtained by employing the strong fluctuation theory. The vector radiative transfer equation for a layer of a random medium is solved by using Gaussian quadrature and eigen analysis. Comparisons with brightness temperature data at 5, 10.7, 18, 37 GHz are made. It is shown that the model fits the experimental data by using physical parameters of the dry snow as obtained from ground truth measurements.
1. Ulaby, F., R. Moore, and A. Fung, Microwave Remote Sensing, Vol. III, Artech House, Inc., Norwood, MA, 1986.
2. Fung, A. K., Microwave Scattering and Emission Models and Their Applications, Artech House, 1994.
3. Tsang, L., J. A. Kong, and R. T. Shin, Theory of Remote Sensing, Wiley Series in Remote Sensing, J. A. Kong (ed.), New York, 1985.
4. Tsang, L. and J. A. Kong, "Scattering of electromagnetic waves for random media with strong permittivity fluctuations," Radio Sci., Vol. 16, 303-320, 1981. doi:10.1029/RS016i003p00303
5. Tsang, L., J. A. Kong, and R. W. Newton, "Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture," IEEE Trans. on Antennas and Propagation, Vol. 30, No. 2, 292-302, 1982. doi:10.1109/TAP.1982.1142774
6. Stogryn, A., "The bilocal approximation for the effective dielectric constant of an isotropic random medium," IEEE Trans. on Antennas and Propagation, Vol. 32, No. 5, 517-520, 1984. doi:10.1109/TAP.1984.1143344
7. Jin, Y. Q., "The radiative transfer equation for strongly-fluctuation continuous random media," J. Quant. Spectrosc. Radiat. Transfer, Vol. 42, 529-537, 1989. doi:10.1016/0022-4073(89)90043-5
8. Nghiem, S. V., R. Kwok, J. A. Kong, and R. T. Shin, "A model with ellipsoidal scatters for polarimetric remote sensing of anisotropic layered media," Radio Sci., Vol. 28, 687-703, 1993. doi:10.1029/93RS01605
9. Nghiem, S. V., R. Kwok, S. H. Yueh, J. A. Kong, C. C. Hsu, M. A. Tassoudji, and R. T. Shin, "Polarimetric scattering from layered media with multiple species of scatterers," Radio Sci., Vol. 30, 835-852, 1995. doi:10.1029/95RS01247
10. Nghiem, S. V., R. Kwok, J. A. Kong, R. T. Shin, S. A. Arcone, and A. J. Gow, "An electrotheromdynamic model with distributed properties for effective permittivity of sea ice," Radio Sci., Vol. 31, 297-311, 1996. doi:10.1029/95RS03429
11. Yueh, S. H. and J. A. Kong, "Scattering from random oriented scatters with strong permittivity fluctuations," J. Electrom. Waves and Appl., Vol. 4, 983-1004, 1990. doi:10.1163/156939390X00717
12. Wang, H., J. Pulliainen, and M. Hallikainen, "Effective permittivity of dry snow in the 18 to 90 GHz range," J. Electrom. Waves and Appl., Vol. 13, 1391-1392, 1999 for abstract; Progress in Electromagnetics Research, PIER 24, 119–133, 1999 for the complete text.
13. Tsang, L. and J. A. Kong, "Thermal microwave emission from a three-layer random medium with three-dimensional variations," IEEE Trans. Geosci. Remote Sensing, Vol. 18, No. 2, 212-216, 1980. doi:10.1109/TGRS.1980.350275
14. Kong, J. A., R. Shin, J. Shiue, and L. Tsang, "Theory and experiment for passive microwave remote sensing of snowpacks," J. Geophys. Res., Vol. 48, No. B10, 5669-5673, 1979. doi:10.1029/JB084iB10p05669
15. Hallikainen, M., F. Ulaby, and T. Van Deventer, "Extinction behaviour of dry snow in the 18- to 90-GHz range," IEEE Trans. Geosci. Remote Sensing, Vol. 25, No. 6, 737-745, 1987. doi:10.1109/TGRS.1987.289743
16. Hufford, G., "A model for the complex permittivity of ice at frequencies below 1 THz," International Journal of Infrared and Millimeter Waves, Vol. 12, No. 7, 677-682, 1991. doi:10.1007/BF01008898
17. Matzler, C. and U. Wegm¨uller, "Dielectric properties of freshwater ice at microwave frequencies," J. Phys. D: Appl. Phys., Vol. 20, 1623-1630, 1987. doi:10.1088/0022-3727/20/12/013
18. Wang, H., J. Pulliainen, and M. Hallikainen, "Extinction behaviour of dry snow at microwave range up to 90 GHz by using strong fluctuation theory," 1998 IEEE International Geoscience and Remote Sensing Symposium Proceedings, 42-44, Seattle, WA, USA, June 6–10, 1998.
19. Hallikainen, M., F. Ulaby, M. Dobson, M. El-Rayes, and L. Wu, "Microwave dielectric behaviour of wet soil — Part I: Empirical equations and experimental observations," IEEE Trans. on Geosci. Remote Sensing, Vol. 23, No. 1, 25-34, 1985. doi:10.1109/TGRS.1985.289497
20. Oberhettinger, F., Fourier Transforms of Distributions and Their Inverses, A Collection of Tables, Academic Press, Inc., New York, 1973.
21. Wang, H., J. Pulliainen, and M. Hallikainen, "Correlation functions and correlation lengths for dry snow," J. Electrom. Waves and Appl., Vol. 12, 1337-1347, 1998. doi:10.1163/156939398X01420