Scattering of Ocean Surfaces in Microwave Remote Sensing by Numerical Solutions of Maxwell Equations

Sea-surface scattering has long been studied using various analytical methods. These analytical methods include the two scale method (TSM), the small-slope approximation (SSA), the small-perturbation method (SPM), the Advanced Integral Equation Method (AIEM), and the Geometrical/Physical Optics (GO/PO) method. These analytical methods rely on making approximations and assumptions in the modelling process. Some of these assumptions undermine their applicability in a wide range of situations. The input for analytical methods are usually the ocean spectrum. In real implementations, there are 2 sources of uncertainty in such approaches: (1) the analytical methods have a limited range of applicability to the surface scattering problem; the approximations made in these methods are questionable and (2) the various ocean spectra are another source of uncertainty. We earlier applied a numerical method in 3-dimensions (NMM3D) to the scattering problem of soil surfaces. Through comparison with measured data, we established the accuracy and applicability of NMM3D. We see a drastic increase of ocean remote sensing applications in recent years. It is thus feasible to extend NMM3D to the sea-surface scattering problem. Compared to soil, sea water has a much higher permittivity, e.g., 75+61i at L-band. The large permittivity dictates the need for using a much denser mesh for the sea surface. In addition, the root mean square (rms) height of the sea surface is large under moderate to high ocean wind speeds, which requires a large simulation area to account for the influence of long scale wave like gravity waves. Compared to the two-scale model commonly used for the ocean scattering problem, NMM3D does not need an ad-hoc split wavenumber in the ocean spectrum. Combined with a fast computational algorithm, it was shown that NMM3D can produce accurate results compared to measured data like the Aquarius missions. TSM could also match well with Aquarius provided with a pre-selected splitting wavenumber. But it was observed that the result of TSM changes with different splitting wavenumbers. It is seen that TSM is fairly heuristic while NMM3D can serve as an exact method for the scattering problem. On the other hand, through our study of NMM3D, we found that with a fine grid, the final impedance matrix converges slowly and also it becomes hard to perform simulations for a large surface. This has provoked us to (1) solve low convergence problem for a dense mesh and (2) resolve difficulties in simulations of large surfaces. Inspired by the existing impedance boundary condition (IBC) method, we proposed a neighborhood impedance boundary condition (NIBC) method to solve the slow convergence problem caused by the dense grid. Different from IBC where the surface electric field and the surface magnetic field are related locally, NIBC relates the surface electric field to the magnetic field within a preselected bandwidth BW. Through numerical simulations, we found that the condition number can be reduced using NIBC. Errors of NIBC are controllable through changing BW. We applied NIBC to various wind speeds and surface types and found NIBC to be quite accurate when surface currents only suffer an error norm of less than 1%.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145797/1/qiaot_1.pd

Vegetation/Forest Effects in Microwave Remote Sensing of Soil Moisture

This thesis includes (1) the distorted Born approximation (DBA) and an improved coherent model for vegetation-covered surfaces at L-band for data-cube based soil moisture retrieval; (2) a unified approach for combined active and passive remote sensing of vegetation-covered surfaces with the same input physical parameters; (3) Numerical Maxwell Model in 3D (NMM3D) simulations of a vegetation canopy comprising randomly distributed dielectric cylinders; and (4) a hybrid method based on the generalized T matrix of single objects and Foldy-Lax equations for NMM3D full-wave simulations of the realistic vegetation/forest with vector spherical, spheroidal and cylindrical wave expansoins. The main contributions and novelty of this thesis are NMM3D full-wave simulations of vegetation/forest canopy using the generalized T matrix of the single object and Foldy-Lax equations of multiple scattering among many objects. Before this work, the large-scale full-wave simulations of vegetation/forst such as many tree trunks were deemed very difficult. The NMM3D full-wave simulation results showed that the results of past models significantly overestimate attenuation in a vegetation/forest canopy. The NMM3D full-wave models predict transmissions that are several times greater than that of past models. A much greater microwave transmission means the microwave can better penetrate a vegetation/forest canopy and thus it can be used to retrieve soil moisture. The thesis starts with the DBA to compute the backscattering coefficients for various kinds of vegetation-covered surfaces such as pasture, wheat and canola fields. For the soybean fields, an improved coherent branching model is used. The novel feature of the analytic coherent model consists of conditional probability functions to eliminate the overlapping effects of branches in the former branching models. In order to make use of complex physical models for real time retrieval for satellite missions, the outputs of the physical model are provided as lookup-tables (data-cubes). By inverting the lookup-tables, time-series retrieval of soil moisture is performed. Next, the DBA is extended to calculate the bistatic scattering coefficients. Emissivities are calculated by integrating the bistatic scattering coefficients over the hemispherical solid angle. The backscattering coefficients and emissivities calculated using this approach form a consistent model for combined active and passive microwave remote sensing. In the analytical physical models mentioned above, as well as in another commonly used approach of the radiative transfer equation (RTE), the attenuation of the wave is accounted for by the attenuation rate per unit distance, which originates from the concept of an “effective medium”. Such a model is unsuitable for a vegetation canopy. Because of these issues, NMM3D full-wave simulations of vegetation are pursued. Firstly, the scattering of a vegetation canopy consisting of cylindrical scatterers is calculated. The approach for solving Maxwell’s equations is based on the Foldy-Lax multiple scattering equations (FL) combined with the body of revolution (BOR). For a layer of extended-cylinders distributed in clusters, the NMM3D simulations at C-band show very different results from DBA/RTE. The method FL-BOR is limited for rotationally symmetric objects such as cylinders and circular disks. To perform NMM3D full-wave simulations for realistic vegetation/forests, a hybrid method is used, which is a hybrid of the off-the-shelf techniques and newly developed techniques. The newly developed techniques are the three key steps of the hybrid method: (1) extracting the generalized T matrix of each single object using vector spheroidal/cylindrical waves, (2) vector wave transformations, and (3) solving FL for all the objects.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153347/1/huanght_1.pd

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with/without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational e±ciency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91459/1/xduan_1.pd

Accelerated integral equation techniques for solving EM wave propagation and scattering problems

This dissertation focuses on the development of the robust, efficient and accurate numerical methods of EM wave propagation and scattering from urban, rural areas and random rough surfaces. There are four main contributions of this dissertation. - The Improved Tabulated Interaction Method (ITIM) is proposed to compute EM wave propagation over lossy terrain profiles using a coupled surface integral equation formulation. The ITIM uses a common set of basis functions in conjunction with a simple matching technique to compress the original system to a reduced system containing considerably smaller number of unknowns and therefore provide a very efficient and accurate method. - Initial efforts in using the full-wave method to compute EM wave propagation over urban areas. The un-accelerated full-wave method has a massive computational burden. In order to reduce the computational complexity, Generalized Forward Backward Method (GFBM) is applied (note that the conventional Forward Backward Method diverges in this scenario). - The Improved Forward Backward Method with Spectral Acceleration (FBM-SA) is proposed to solve the problem of 2D wave scattering from random lossy rough surfaces. - An efficient and accurate iterative method is proposed for computing the 3D wave scattering from 2D dielectric random rough surfaces. The proposed method referred to as the Block Forward Backward Method improves the convergence of the 3D FBM, makes it converge for the case of 2D dielectric surfaces. In addition the Spectral Acceleration is also modified and combined with the BFBM to reduce the computational complexity of the proposed method

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137141/1/srtan_1.pd

Electromagnetic Modeling for Radar Remote Sensing of Snow-Covered Terrain

This thesis investigates the radar remote sensing of snow-covered terrain for estimation of snow equivalent water on global scale. The importance and impact of this research stems from the fact that water from snowmelt is the major source of water for inland cities and agriculture during summer. This effort is focused on developing a physics-based model for snow and a fully coherent polarimetric scattering model for snow above ground. Both the physical model and the forward polarimetric scattering model present a significant improvement compared to the existing models for snowpack. Computer-generated snow media are constructed using 3-D spatial exponential correlation functions, along with Lineal-Path functions that serve to preserve the connectivity of the snow particles. A fully-coherent model is presented through the use of the Statistical S-matrix Wave Propagation in Spectral-Domain (SSWaP-SD) technique. The SSWaP-SD depends on the discretization of the medium into thin slabs. Several realizations of a thin snow slab are solved numerically to form the statistics of the scattering matrix representing such a thin snow layer. For each thin slab of the snow-pack, a corresponding polarimetric N-port (representing different directions of scattering) S-matrix is generated. These S-matrices are cascaded using the SSWaP-SD method to calculate the total forward and backward bistatic scattered fields in a fully coherent way. The SSWaP-SD, in conjunction with a Method of Moments (MoM) code based on the Discrete-Dipole Approximation (DDA), is chosen to leverage both the time-efficient computations of the DDA and the full-coherency of the SSWaP-SD method, simultaneously. In addition to the MoM-DDA, a Finite Element Method (FEM) based on commercial software is used for cross-comparison and validation. The simulation results of the backscattering from an arbitrary thick snow layer are presented and validated with measurements. The underlying rough ground surface response is then estimated through both an analytical technique based on the Physical Optics (PO) method and a numerical solver based on MoM using a commercial full-wave solver. Finally, the complete response is then calculated by cascading the S-matrices representing the snow and the rough surface responses. The simulation results of the backscattering are presented using a Monte-Carlo process, which show very good agreement with measurements.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167972/1/mzaky_1.pd

Modeling microwave emission from snow covered soil

Il ciclo idrologico rappresenta l’insieme di tutti i fenomeni legati alla circolazione e alla conservazione dell’acqua sulla Terra. Il monitoraggio su scala globale dei fattori che concorrono a produrre e modificare tale ciclo (umidità del terreno, copertura vegetale, estensione e caratteristiche del manto nevoso) risulta di estrema importanza per lo studio del clima e dei cambiamenti globali. Inoltre, l’osservazione sistematica di queste grandezze è importante per prevedere condizioni di rischio da alluvioni, frane e valanghe come pure fare stime delle risorse idriche. In questo contesto Il telerilevamento da satellite gioca un ruolo fondamentale per le sue caratteristiche di osservazioni continuative di tutto globo terrestre. I sensori a microonde permettono poi di effettuare misure indipendentemente dall’illuminazione solare e anche in condizioni meteorologiche avverse. I processi idrologici, ed in particolare quelli della criosfera (la porzione di superficie terrestre in cui l’acqua è presente in forma solida), sono fra quelli che meglio si possono investigare analizzando la radiazione elettromagnetica emessa o diffusa. Mediante l’utilizzo di modelli elettromagnetici che permettono di simulare l’emissione e lo scattering da superfici naturali è possibile interpretare le misure elettromagnetiche ed effettuare l’estrazione di quelle grandezze che caratterizzano i suoli e la loro copertura. In questo lavoro di dottorato si è affrontato il problema della modellistica a microonde dei terreni coperti da neve, sia asciutta che umida. Dopo aver preso in considerazione i modelli analitici maggiormente utilizzati per simulare diffusione ed emissione a microonde dei suoli nudi e coperti da neve si è proceduto allo sviluppo e implementazione di due modelli di emissività. Il primo, basato sulla teoria delle fluttuazioni forti, è atto a descrivere il comportamento di un manto nevoso umido. Il secondo, basato sull’accoppiamento del modello di scattering superficiale AIEM (Advanced Integral Equation Method) con la teoria del trasferimento radiativo nei mezzi densi, è volto allo studio di uno strato di neve asciutta sovrastante un suolo rugoso. Tali modelli tengono conto degli effetti coerenti presenti nell’emissione del manto nevoso e non inclusi nella teoria del trasporto radiativo classico. Entrambi i codici sono stati validati con datasets numerici e sperimentali in parte derivati da archivi ed in parte ottenuti nel contesto di questo lavoro che ha previsto quindi anche una fase sperimentale. Quest’ultima è stata condotta con misure radiometriche multifrequenza su un’area di test situata sulle Alpi orientali. Le simulazioni ottenute con questi modelli e le conseguenti analisi hanno permesso di individuare la sensibilità della temperatura di brillanza ai parametri di interesse (spessore, equivalente in acqua e umidità del manto nevoso) in funzione di diverse configurazioni osservative (frequenza, polarizzazione ed angolo di incidenza). Questo ha consentito di migliorare la comprensione dei meccanismi di emissione dalle superfici innevate e di individuare le migliori condizioni osservative per un sistema di telerilevamento terrestre

Review Article: Global Monitoring of Snow Water Equivalent Using High-Frequency Radar Remote Sensing

Seasonal snow cover is the largest single component of the cryosphere in areal extent, covering an average of 46 × 106 km2 of Earth\u27s surface (31 % of the land area) each year, and is thus an important expression and driver of the Earth\u27s climate. In recent years, Northern Hemisphere spring snow cover has been declining at about the same rate (∼ −13 % per decade) as Arctic summer sea ice. More than one-sixth of the world\u27s population relies on seasonal snowpack and glaciers for a water supply that is likely to decrease this century. Snow is also a critical component of Earth\u27s cold regions\u27 ecosystems, in which wildlife, vegetation, and snow are strongly interconnected. Snow water equivalent (SWE) describes the quantity of water stored as snow on the land surface and is of fundamental importance to water, energy, and geochemical cycles. Quality global SWE estimates are lacking. Given the vast seasonal extent combined with the spatially variable nature of snow distribution at regional and local scales, surface observations are not able to provide sufficient SWE information. Satellite observations presently cannot provide SWE information at the spatial and temporal resolutions required to address science and high-socio-economic-value applications such as water resource management and streamflow forecasting. In this paper, we review the potential contribution of X- and Ku-band synthetic aperture radar (SAR) for global monitoring of SWE. SAR can image the surface during both day and night regardless of cloud cover, allowing high-frequency revisit at high spatial resolution as demonstrated by missions such as Sentinel-1. The physical basis for estimating SWE from X- and Ku-band radar measurements at local scales is volume scattering by millimeter-scale snow grains. Inference of global snow properties from SAR requires an interdisciplinary approach based on field observations of snow microstructure, physical snow modeling, electromagnetic theory, and retrieval strategies over a range of scales. New field measurement capabilities have enabled significant advances in understanding snow microstructure such as grain size, density, and layering. We describe radar interactions with snow-covered landscapes, the small but rapidly growing number of field datasets used to evaluate retrieval algorithms, the characterization of snowpack properties using radar measurements, and the refinement of retrieval algorithms via synergy with other microwave remote sensing approaches. This review serves to inform the broader snow research, monitoring, and application communities on progress made in recent decades and sets the stage for a new era in SWE remote sensing from SAR measurements

Microwave Radiometry at Frequencies From 500 to 1400 MHz: An Emerging Technology for Earth Observations

icrowave radiometry has provided valuable spaceborne observations of Earth’s geophysical properties for decades. The recent SMOS, Aquarius, and SMAP satellites have demonstrated the value of measurements at 1400 MHz for observ- ing surface soil moisture, sea surface salinity, sea ice thickness, soil freeze/thaw state, and other geophysical variables. However, the information obtained is limited by penetration through the subsur- face at 1400 MHz and by a reduced sensitivity to surface salinity in cold or wind-roughened waters. Recent airborne experiments have shown the potential of brightness temperature measurements from 500–1400 MHz to address these limitations by enabling sensing of soil moisture and sea ice thickness to greater depths, sensing of temperature deep within ice sheets, improved sensing of sea salinity in cold waters, and enhanced sensitivity to soil moisture under veg- etation canopies. However, the absence of significant spectrum re- served for passive microwave measurements in the 500–1400 MHz band requires both an opportunistic sensing strategy and systems for reducing the impact of radio-frequency interference. Here, we summarize the potential advantages and applications of 500–1400 MHz microwave radiometry for Earth observation and review recent experiments and demonstrations of these concepts. We also describe the remaining questions and challenges to be addressed in advancing to future spaceborne operation of this technology along with recommendations for future research activities