A study of scattering from snow embedded with non-spherical shapes of scatterers with relaxed hierarchical equivalent source algorithm (rhesa)
01 Jan 2017-Progress in Electromagnetics Research M (The Electromagnetics Academy)-Vol. 61, pp 51-60
TL;DR: In this paper, a theoretical model based on radiative transfer formulation that utilizes computational electromagnetics in the modelling of scattering from arbitrary shape of scatterers was presented, and the effect of shape on scattering mechanisms and total backscattering coefficient was also studied.
Abstract: 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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01 Jan 2007
TL;DR: In this paper, 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.
Abstract: 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.
21 citations
01 Dec 2019
TL;DR: In this article, optical models of semitransparent glacier cover (with scattering and absorbing snow and ice layers) depending on their physical structure are presented, and theoretical estimates of the subsurface temperature distributions with positive (negative) gradient in active upper layer of the glacier at combine heat exchange are offered for developed optical models.
Abstract: 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.
2 citations
TL;DR: In this paper , the backscattering cross section of cylindrical and elliptical disk-shaped scatterers was investigated using a new numerical solution method called the relaxed hierarchical equivalent source algorithm (RHESA).
Abstract: 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.
1 citations
11 Jul 2021
TL;DR: In this article, 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).
Abstract: 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.
1 citations
References
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Book•
10 Jun 2002
TL;DR: In this paper, the basic theory of Electromagnetic Scattering, Absorption, and Emission was presented, and the T-matrix method and Lorenz-Mie theory were used to calculate and measure the scattering and absorption properties of small particles.
Abstract: Preface Acknowledgements Part I. Basic Theory of Electromagnetic Scattering, Absorption, and Emission: 1. Polarization characteristics of electromagnetic radiation 2. Scattering, absorption, and emission of electromagnetic radiation by an arbitrary finite particle 3. Scattering, absorption and emission by collections of independent particles 4. Scattering matrix and macroscopically isotropic and mirror-symmetric scattering media Part II. Calculation and Measurement of Scattering and Absorption Characteristics of Small Particles: 5. T-matrix method and Lorenz-Mie theory 6. Miscellaneous exact techniques 7. Approximations 8. Measurement techniques Part III. Scattering and Absorption Properties of Small Particles and Illustrative Applications: 9. Scattering and absorption properties of spherical particles 10. Scattering and absorption properties of nonspherical particles Appendices References Index.
1,816 citations
"A study of scattering from snow emb..." refers methods in this paper
...As the shape of the particle selected for the simulations are all having an axis of symmetry, we can reduce the phase matrix to a simpler form [22] with faster computation....
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Book•
28 Feb 1994
TL;DR: First-order radiative transfer solution passive sensing formulation of the surface scattering problem surface model and special cases ranges validity of the IEM model matrix doubling formulations for scattering and emission scattering and emissions models for snow and sea ice comparisons of model predictions with backscattering and emission measurements from snow and ice.
Abstract: First-order radiative transfer solution first-order radiative transfer solution passive sensing formulation of the surface scattering problem surface model and special cases ranges validity of the IEM model matrix doubling formulations for scattering and emission scattering and emissions models for snow and sea ice comparisons of model predictions with backscattering and emission measurements from snow and ice.
1,334 citations
"A study of scattering from snow emb..." refers background in this paper
...where 〈|Ψ|(2)〉n is the dense medium phase correction factor that considers the coherency effect of closely spaced scatterers [8], and S is the Stokes matrix as shown below [4]:...
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Book•
26 Aug 2021
TL;DR: In this article, the Fast Multipole Method (FMM) was used to solve the problem of two-dimensional problems with three-dimensional surfaces, and the Matrix-Vector Product Addition Theorem (MVPIT) was applied to solve it.
Abstract: PREFACE Computational Electromagnetics Computational Electromagnetics Algorithms A Brief Review of Electromagnetics Maxwell's Equations Electromagnetic Boundary Conditions Formulations for Radiation Vector Potentials Near and Far Fields Equivalent Problems Surface Integral Equations The Method of Moments Electrostatic Problems The Method of Moments Common Two-Dimensional Basis Functions Solution of Matrix Equations Thin Wires Thin Wire Approximation Thin Wire Excitations Solving Hallen's Equation Solving Pocklington's Equation Thin Wires of Arbitrary Shape Examples two-dimensional Problems Two-Dimensional EFIE Two-Dimensional MFIE Examples Bodies of Revolution BOR Surface Descriptions Surface Current Expansion on a BOR EFIE for a Conducting BOR MFIE for a Conducting BOR Notes on Software Implementation Examples three-dimensional Problems Representation of Three-Dimensional Surfaces Surface Currents on a Triangle EFIE for Three-Dimensional Conducting Surfaces MFIE for Three-Dimensional Conducting Surfaces Notes on Software Implementation Considerations for Modeling with Triangles Examples The Fast Multipole Method The Matrix-Vector Product Addition Theorem FMM Matrix Elements One-Level Fast Multipole Algorithm Multilevel Fast Multipole Algorithm Notes on Software Implementation Preconditioning Examples Integration One-Dimensional Integration Integration over Triangles INDEX References appear at the end of each chapter.
813 citations
Additional excerpts
...The emergence and use of Method of Moments (MoM) [16] allow the electromagnetics integral equations to be converted into a matrix-form linear equations that a powerful computer can solve it approximately....
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TL;DR: A multilevel algorithm is applied to the solution of an integral equation using the conjugate gradient method and shows that the complexity of a matrix-vector multiplication is proportional to N (log(N))2.
Abstract: In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix-vector multiplication, requiring O(N2) floating-point operations. The fast multipole method (FMM) reduced the operation to O(N15). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix-vector multiplication is proportional to N (log(N))2. © 1994 John Wiley & Sons, Inc.
303 citations
"A study of scattering from snow emb..." refers methods in this paper
...More and more numerical algorithms have been successfully applied with MoM and the computational speed has been improved through methods such as equivalence principle algorithm (EPA) [17, 18], relaxed hierarchical equivalent source algorithm (RHESA) [19], multilevel fast multipole algorithm (MLFMA) [20] and finite-difference timedomain method (FDTDM) [21]....
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TL;DR: A domain decomposition scheme based on the equivalence principle, similar to Huygens' principle, for integral equation solvers and the method of moments is introduced, and the solution is shown to be accurate.
Abstract: A domain decomposition scheme based on the equivalence principle, similar to Huygens' principle, for integral equation solvers and the method of moments is introduced. The equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume. It also allows the dissociation of the solution of one region from that of another region. In this manner, problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns. It can aid in parallel algorithms, reusability of solutions, as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed. The challenge arises when an equivalence surface intercepts a current-carrying conductor, because the breakup of the current into separate pieces gives rise to charge singularity. A junction basis can be used to mitigate this singularity. However, a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces. Using this scheme, the current continuity is conserved and the singularity of the charges is avoided. The solution is shown to be accurate
191 citations
"A study of scattering from snow emb..." refers methods in this paper
...EPA can reduce the unknowns and decompose one whole solution into several subproblems based on domain decomposition method (DDM) [17]....
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...RHESA is a newly implemented numerical solution based on EPA foundation....
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...To eliminate the problem of singularities faced in EPA, RHESA uses relaxed hierarchical arrangement of spherical equivalence surfaces to avoid interception with internal primary sources....
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...More and more numerical algorithms have been successfully applied with MoM and the computational speed has been improved through methods such as equivalence principle algorithm (EPA) [17, 18], relaxed hierarchical equivalent source algorithm (RHESA) [19], multilevel fast multipole algorithm (MLFMA) [20] and finite-difference timedomain method (FDTDM) [21]....
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...In EPA, the original sources are replaced by electric and magnetic currents on an equivalence surface and these are known as equivalent source....
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