Son V. Nghiem

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.

Forward electromagnetic scattering models for sea ice

Recent advances in forward modeling of the electromagnetic scattering properties of sea ice are presented. In particular, the principal results include the following: (1) approximate calculations of electromagnetic scattering from multilayer random media with rough interfaces, based on the distorted Born approximation and radiative transfer (RT) theory; (2) comprehensive theory of the effective complex permittivity of sea ice based on rigorous bounds in the quasi-static case and strong fluctuation theory in the weakly scattering regime; (3) rigorous analysis of the Helmholtz equation and its solutions for idealized sea ice models, which has led in the one dimensional (1D) case to nonlinear generalizations of classical theorems in Fourier analysis. The forward models considered incorporate many detailed features of the sea ice system and compare well with experimental data. The results have advanced the general theory of scattering of electromagnetic waves from complex media as well as homogenization theory, which relates bulk properties of composite media to their microstructural characteristics. Furthermore, the results have direct application to microwave remote sensing and serve as the basis for inverse algorithms for reconstructing the physical properties of sea ice from scattering data.

A broad spectral, interdisciplinary investigation of the electromagnetic properties of sea ice

This paper highlights the interrelationship of research completed by a team of investigators and presented in the several individual papers comprising this Special Section on the Office of Naval Research (ONR), Arlington, VA, Sponsored Sea Ice Electromagnetics Accelerated Research Initiative (ARI). The objectives of the initiative were the following: (1) understand the mechanisms and processes that link the morphological and physical properties of sea ice to its electromagnetic (EM) characteristics; (2) develop and verify predictive models for the interaction of visible, infrared, and microwave radiation with sea ice; (3) develop and verify inverse scattering techniques applicable to problems involving the interaction of EM radiation with sea ice. Guiding principles for the program were that all EM data be taken with concurrent physical property data (salinity, density, roughness, etc.) and that broad spectral data be acquired in as nearly a simultaneous fashion as possible. Over 30 investigators participated in laboratory, field, and modeling studies that spanned the EM spectrum from radio to ultraviolet wavelengths. An interdisciplinary approach that brought together sea ice physicists, remote-sensing experts (in fill measurements), and forward and inverse modelers (primarily mathematicians and EM theorists) was a hallmark of the program. Along with describing results from experiments and modeling efforts, possible paradigms for using broad spectral data in developing algorithms for analyzing remote-sensing data in terms of ice concentration, age, type, and possibly thickness are briefly discussed.