The physical characteristics of air inclusions embedded in the ice covers of the Saint Francois River (Quebec, Canada) and the Athabasca River (Alberta, Canada) are studied because of the importance of such inclusions to the analysis and interpretation of Synthetic Aperture Radar satellite images used to characterize river ice. Studies of ice cores sampled from these two rivers show that the concentration of air inclusions in the ice cover is highly dependent on both the ice type as well as the rate of freezing. When this rate is slow, the ice cover will have few air inclusions. However, when it is rapid and sustained in duration, the amount and cross sectional diameter of these inclusions increase. Air inclusions in the snow ice were found to be spherical and ranging in size from just a few millimetres up to about a centimetre. Generally, air inclusions formed in the sampled columnar ice were sparse and either spherical or tubular in shape. Air inclusions in the frazil ice were found to present a different structure from those formed in the other ice types. In most cases, their shape were irregular and their distribution was inhomogeneous. The study of these inclusions under a microscope showed them to have angular boundaries with a whitish appearance. These results will be valuable to the development of radar backscatter analysis algorithms for river ice characterization.

Physical characterization of air inclusions in river ice for the purpose of a backscatter model

Optical models of semitransparent glacier cover (with scattering and absorbing snow and ice layers) depending on their physical structure are presented in this study. At absorption indices (~ 1 m−1) and the scattering ones (~ 10–1000 m−1) for transparent ice and inhomogeneous snow, their albedo changed accordingly from ~30% to ~98%. For the first time, theoretical estimates of the subsurface temperature distributions with positive (negative) gradient in active upper layer of the glacier at combine heat exchange were offered for developed optical models of snow and ice covers. The formation of internal radiant overheating was discussed.

Radiant Overheating of Semitransparent Glacier Cover

The backscattering cross section of cylindrical and elliptical disk-shaped scatterers was investigated in this study, utilising a new numerical solution method called the relaxed hierarchical equivalent source algorithm (RHESA). The results were compared with the backscattering cross section of similar cases, using analytical method validation from literature. The objective of this research was to look into the possibility of replacing analytical methods with the RHESA in volume scattering calculations, and integrating it into modelling the backscattering of layers of dense media for microwave remote sensing in vegetation; as RHESA provides the freedom to model any shape of scatterer, as opposed to the limited shapes available of scatterers in analytical method models. The results demonstrated a good match, indicating that the RHESA may be a good fit for modelling more complicated media, such as vegetation, in future studies.

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Backscattering Analysis Utilizing Relaxed Hierarchical Equivalent Source Algorithm (RHESA) for Scatterers in Vegetation Medium

Active microwave remote sensing is essential to monitor the conditions of the environment by analyzing the microwave returns from the earth terrain. Various Computational Electromagnetics (CEM) techniques are implemented to study the backscattering coefficient of numerous earth terrains such as vegetation and snow medium. In this paper, a theoretical model based on second order radiative transfer equation is investigated by incorporating two computational methods which are known as coupled Finite Element Method (FEM) and Method of Moment (MoM), and Relaxed Hierarchical Equivalent Source Algorithm (RHESA). These theoretical models consider three shapes of scatterers which can be used to represent the ice particles of snow medium. These mentioned shapes are sphere, droxtal and hexagonal column. These methods are used to investigate the effect of various incident angles and frequencies on the backscattering mechanism. These results are compared with analytical Mie solution and ground truth measurement to analyze and verify the model.

Model Computation with Second-Order Radiative Transfer Equation for Snow Medium Using Coupled Finite Element Method and Method of Moment and Relaxed Hierarchical Equivalent Source Algorithm

This paper analyses the backscattering cross section of a cylinder both using traditional method model and a new numerical solution model, namely Relaxed Hierarchical Equivalent Source Algorithm (RHESA). The purpose of this study is to investigate the prospect of incorporating numerical solution model into volume scattering calculation, to be applied into microwave remote sensing in vegetation area. Results show a good match, suggesting that RHESA may be suitable to be used to model the more complex nature of vegetation medium.

No. 3 Backscattering Analysis of Cylinder Shaped Scatterer in Vegetation Medium: Comparison Between Theories

Remote sensing has been used widely in studying the earth terrain such as snow or sea ice due to its fast, convenient and long-term monitoring capabilities. SAR images acquired could be used to analyze the condition of snow, snow water equivalent (SWE), surface roughness and others. Theoretical models have also been developed to understand how microwave interacts with the snow medium and the scatterers embedded inside the medium. Conventionally, spherical shape of scatterers is commonly used to represent the ice particles embedded inside snow where the actual shape of scatterers can vary. This paper is to present a theoretical model based on radiative transfer formulation that utilizes computational electromagnetics in the modelling of scattering from arbitrary shape of scatterers. The paper also studies the effect of scatterer shape on scattering mechanisms and total backscattering coefficient. Numerical solution of Relaxed Hierarchical Equivalent Source Algorithm (RHESA) was integrated with existing radiative transfer theoretical model to simulate a layer of random discrete snow medium. Several shapes of scatterers were simulated, and theoretical simulation were compared with ground truth measurement data with promising results.

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A study of scattering from snow embedded with non-spherical shapes of scatterers with relaxed hierarchical equivalent source algorithm (rhesa)

This paper is to present a new numerical method which can be used in computational electromagnetics in microwave remote sensing of random discrete medium embedded with irregular shape of scatterers. Current Radiative Transfer (RT) theoretical modeling is normally used to simulate wave propagation in the medium and wave scattering by basic shapes of scatterers, e.g., cylinder, disk, needle or sphere where the scattering of those scatterers was normally derived analytically with some assumption and approximation. To simulate the total backscattering coefficient from a layer of random medium, traditionally it was quite common that Mie phase matrix was used to compute the scattered fields of the scatterers which were approximated to be spherical shape. This has limited the extension of current theoretical model to be used to compute cases where irregular shape of scatterers are found embedded in the medium where many of the scatterers in real world are normally irregular or of complex shapes. As computational electromagnetics (CEM) becomes important in current modern engineering field, this provides an approach to model the scattering of such scatterers using CEM. In this paper, the Hierarchical Equivalent Source Algorithm (HESA) is used to compute scattered fields based on hierarchically structured equivalence sources residing within relaxed spherical equivalence surfaces. The 3D scatterer model used in HESA can be created using a 3D modeling software. After the 3D scatterer model is divided into smaller groups and each group is enclosed with a spherical equivalence surface, the scattered fields can be computed by equivalence source residing on smooth spherical equivalence surface through integral formulations. By incorporating HESA method into the current RT theoretical modeling, this can provide the improved theoretical model the capability to compute scattering of irregular or non-basic shape of scatterers embedded within the medium. The simulated scattering coefficient and extinction coefficient results from the newly implemented HESA based theoretical model were compared with those of current RT theoretical model and it was found that both results agreed with each other. The new model is then ready to be applied to simulate backscattering from a layer of earth medium for further theoretical analysis.

A study of scattering from a layer of random discrete medium with Hierarchical Equivalent Source Algorithm (HESA)

It is common that spherical scatterers are used to represent air bubbles or brine inclusions embedded in the snow or sea ice layer. This physical configuration is then solved using radiative transfer theory to obtain backscattering coefficient from the snow or sea ice layer. With the advent of new techniques in computational electromagnetics, the typical theoretical model of single layer of snow or sea ice can be easily extended to consider types of scatterers which are of other shapes or irregular shapes. A computational electromagnetic method based on equivalence principle algorithm can be incorporated into existing theoretical model to calculate the backscattering coefficient of layers using radiative transfer theory. Averaging over different orientation angles of the scatterers in the medium is also needed in the calculation of phase matric and extinction matrix of scatterers when the scatterers are no longer limited in spherical shape. Theoretical analysis of the developed model is presented for this extension work.

Chan-Fai Lum

Papers

A study of scattering from snow embedded with non-spherical shapes of scatterers with relaxed hierarchical equivalent source algorithm (rhesa)

A study of scattering from a layer of random discrete medium with Hierarchical Equivalent Source Algorithm (HESA)

A study of single scattering of scatterer at various orientation angles with equivalence principle algorithm