Inverse electromagnetic scattering models for sea ice

Inverse scattering algorithms for reconstructing the physical properties of sea ice from scattered electromagnetic field data are presented. The development of these algorithms has advanced the theory of remote sensing, particularly in the microwave region, and has the potential to form the basis for a new generation of techniques for recovering sea ice properties, such as ice thickness, a parameter of geophysical and climatological importance. Moreover, the analysis underlying the algorithms has led to significant advances in the mathematical theory of inverse problems. In particular, the principal results include the following. (1) Inverse algorithms for reconstructing the complex permittivity in the Helmholtz equation in one and higher dimensions, based on layer stripping and nonlinear optimization, have been obtained and successfully applied to a (lossless) laboratory system. In one dimension, causality has been imposed to obtain stability of the solution and layer thicknesses can be obtained from the recovered dielectric profile, or directly from the reflection data through a nonlinear generalization of the Paley-Wiener theorem in Fourier analysis. (2) When the wavelength is much larger than the microstructural scale, the above algorithms reconstruct a profile of the effective complex permittivity of the sea ice, a composite of pure ice with random brine and air inclusions. A theory of inverse homogenization has been developed, which in this quasistatic regime, further inverts the reconstructed permittivities for microstructural information beyond the resolution of the wave. Rigorous bounds on brine volume and inclusion separation for a given value of the effective complex permittivity have been obtained as well as an accurate algorithm for reconstructing the brine volume from a set of values. (3) Inverse algorithms designed to recover sea ice thickness have been developed. A coupled radiative transfer-thermodynamic sea ice inverse model has accurately reconstructed the growth of a thin, artificial sea ice sheet from time-series electromagnetic scattering data