The Ultra-Wideband Software defined microwave radiometer (UWBRAD) was developed to probe internal ice sheet temperatures using 0.5-2 GHz microwave radiometry. The airborne brightness temperature data of UWBRAD show a significant reduction due to reflections of surface layering of density fluctuations making difficult the retrieval of subsurface temperature in the kilometer range of depth. Such reflections can be measured by the ultra-wideband radar in the same frequency range suggesting a combined active and passive remote sensing of polar ice sheets. In this paper, we develop a coherent reflectivity model for both ice sheet thermal emission and backscattering. Maxwell equations are used to calculate the coherent reflections from the cap layers, and the WKB approximation is used to calculate the transmission for the slowly varying profile below the cap layers. Results are then shown to demonstrate the use of radar measurements to compensate reflection effects on brightness temperatures. It is shown that the reflections corrected brightness temperature is directly related to the physical temperature and absorption profile making possible the retrieval of subsurface temperature profile with multi-frequency measurements
2. Meier, W., G. Hovelsrud, B. van Oort, J. Key, K. Kovacs, C. Michel, C. Hass, M. Granskog, S. Gerland, D. Perovich, A. Makshtas, and J. Reist, "Arctic sea ice in transformation: A review of recent observed changes and impacts on biology and human activity," Rev. Geophys., Vol. 52, 185-217, 2014.
3. Rignot, E., I. Velicogna, M. R. van den Broeke, A. Monaghan, and J. Lenaerts, "Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise," Geophys. Res. Lett., Vol. 38, L05503, 2011.
4. Alley, R. B., P. U. Clark, P. Huybrechts, and I. Joughin, "Ice-sheet and sea-level changes," Science, Vol. 310, No. 5747, 456-460, 2005.
5. Jacob, T., J. Wahr, W. T. Pfeffer, and S. Swenson, "Recent contributions of glaciers and ice caps to sea level rise," Nature, Vol. 482, No. 7386, 514, 2012.
6. Hock, R., M. de Woul, V. Radic, and M. Dyurgerov, "Mountain glaciers and ice caps around Antarctica make a large sealevel rise contribution," Geophysical Research Letters, Vol. 36, L07501, 2012.
7. Zwally, H. J., M. B. Giovinetto, J. Li, H. G. Cornejo, M. A. Beckley, A. C. Brenner, and D. Yi, "Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992–2002," Journal of Glaciology, Vol. 51, No. 175, 509-527, 2005.
8. Matsuoka, K., R. C. Hindmarsh, G. Moholdt, M. J. Bentley, H. D. Pritchard, J. Brown, and T. Hattermann, "Antarctic ice rises and rumples: Their properties and significance for ice-sheet dynamics and evolution," Earth-Science Reviews, Vol. 150, 724-745, 2015.
9. Gagliardini, O., G. Durand, T. Zwinger, R. C. A. Hindmarsh, and E. Le Meur, "Coupling of iceshelf melting and buttressing is a key process in ice-sheets dynamics," Geophysical Research Letters, Vol. 37, L14501, 2010.
10. Matelli, E. and C. Schoof, "Thermally-activated sliding in ice sheet flow," American Geophysical Union, Fall Meeting 2018, 2018.
11. Mantelli, E. and C. Schoof, "Ice sheet dynamics with temperature-dependent sliding," Geophysical Research Abstracts, Vol. 21, EGU2019-10993-5, 2019.
12. Hill, B., et al., "Using radio-wave attenuation to constrain ice temperature in regions of fast flow," American Geophysical Union, Fall Meeting 2018, 2018.
13. Winebrenner, D. P., S. Tyler, and J. Selker, "Diagnosis of glacier and ice bed dynamics by means of Raman distributed temperature sensing and melt-probe deployment," American Geophysical Union, Fall Meeting 2018, 2018.
14. Forster, R. R., et al., "Extensive liquid meltwater storage in firn within the Greenland ice sheet," Nat. Geosci., Vol. 7, 95-98, 2014.
15. Miller, O., D. K. Solomon, C. Miege, L. S. Koenig, R. R. Forster, L. N. Montgomery, N. Schmerr, S. R. M. Ligtenberg, A. Legchenko, and L. Brucker, "Hydraulic conductivity of a Firn Aquifer in Southeast Greenland," Front. Earth Sci., Vol. 5, No. 38, 2017.
16. Andrews, M. J., et al., "The ultrawideband software-defined microwave radiometer: Instrument description and initial campaign results," IEEE Trans. Geosci. Remote. Sens., Vol. 56, No. 10, 5923-5935, Oct. 2018.
17. Johnson, J., K. Jezek, M. Andrews, M. Durand, Y. Duan, C. Yardim, A. Bringer, G. Macelloni, M. Brogioni, S. Tan, and L. Tsang, "Measurement of ice sheet internal temperature profiles with ultrawidebandmicrowave radiometry," American Geophysical Union, Fall Meeting 2018, 2018.
18. Yardim, C., J. T. Johnson, K. C. Jezek, M. Andrews, M. Durand, Y. Duan, S. Tan, L. Tsang, M. Brogioni, G. Macelloni, and A. Bringer, "Greenland ice sheet subsurface temperature estimation using ultra-wideband microwave radiometry," IEEE Trans. Geosc. Rem. Sens., 2019.
19. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves: Theories and Applications, Vol. 1, 203-217, Ch. 5, Wiley, Hoboken, NJ, USA, 2000.
20. Rytov, S. M., Theory of Electromagnetic Radiation and Fluctuations, Publishing House, Academy of Science, USSR, 1953.
21. Tan, S., et al., "Physical models of layered polar firn brightness temperatures from 0.5 to 2 GHz," IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., Vol. 8, No. 7, 3681-3691, Jul. 2015.
22. Tan, S., L. Tsang, H. Xu, J. T. Johnson, K. C. Jezek, C. Yardim, M. Durand, and Y. Duan, "A partially coherent approach for modelong polar ice sheet 0.5–2 GHz thermal emission," IEEE Trans. Geosc. Rem. Sens., 2019.
23. Van der Veen, J., Fundamentals of Glacier Dynamics, A. A. Balkema, 462, Rotterdam, The Netherlands, 1999.
24. Matzler, C. and A. Wiesmann, "Extension of the microwave emission model of layered snowpacks to coarse-grained snow," Remote Sens. Environ., Vol. 70, 317-325, 1999.
25. Matzler, C., "Microwave permittivity of dry snow," IEEE Trans. Geosci. Remote. Sens., Vol. 34, No. 2, 573-581, Mar. 1996.
26. Tiuri, M. E., A. H. Sihvola, E. G. Nyfors, and M. T. Hallikainen, "The complex dielectric constant of snow at microwave frequencies," IEEE J. Oceanic Eng., Vol. 9, No. 5, 377-382, Dec. 1984.