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

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure

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

Simulation of the Microwave Emission of Multi-layered Snowpacks Using the Dense Media Radiative Transfer Theory: the DMRT-ML Model

DMRT-ML is a physically based numerical model designed to compute the thermal microwave emission of a given snowpack. Its main application is the simulation of brightness temperatures at frequencies in the range 1-200 GHz similar to those acquired routinely by spacebased microwave radiometers. The model is based on the Dense Media Radiative Transfer (DMRT) theory for the computation of the snow scattering and extinction coefficients and on the Discrete Ordinate Method (DISORT) to numerically solve the radiative transfer equation. The snowpack is modeled as a stack of multiple horizontal snow layers and an optional underlying interface representing the soil or the bottom ice. The model handles both dry and wet snow conditions. Such a general design allows the model to account for a wide range of snow conditions. Hitherto, the model has been used to simulate the thermal emission of the deep firn on ice sheets, shallow snowpacks overlying soil in Arctic and Alpine regions, and overlying ice on the large icesheet margins and glaciers. DMRT-ML has thus been validated in three very different conditions: Antarctica, Barnes Ice Cap (Canada) and Canadian tundra. It has been recently used in conjunction with inverse methods to retrieve snow grain size from remote sensing data. The model is written in Fortran90 and available to the snow remote sensing community as an open-source software. A convenient user interface is provided in Python

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

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

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

Investigation of radar backscattering from second-year sea ice

The scattering properties of second-year ice were studied in an experiment at Mould Bay in April 1983. Radar backscattering measurements were made at frequencies of 5.2, 9.6, 13.6, and 16.6 GHz for vertical polarization, horizontal polarization and cross polarizations, with incidence angles ranging from 15 to 70 deg. The results indicate that the second-year ice scattering characteristics were different from first-year ice and also different from multiyear ice. The fading properties of radar signals were studied and compared with experimental data. The influence of snow cover on sea ice can be evaluated by accounting for the increase in the number of independent samples from snow volume with respect to that for bare ice surface. A technique for calculating the snow depth was established by this principle and a reasonable agreement has been observed. It appears that this is a usable way to measure depth in snow or other snow-like media using radar

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