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

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

Fast Numerical Algorithms for 3-D Scattering from PEC and Dielectric Random Rough Surfaces in Microwave Remote Sensing

abstract: We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin’s procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N^2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

A 3-D Full-Wave Model to Study the Impact of Soybean Components and Structure on L-Band Backscatter

Microwave remote sensing offers a powerful tool for monitoring the growth of short, dense vegetation like soybean. As the plants mature, changes in their biomass and 3-D structure impact the electromagnetic (EM) backscatter signal. This backscatter information holds valuable insights into crop health and yield, prompting the need for a comprehensive understanding of how structural and biophysical properties of soybeans as well as soil characteristics contribute to the overall backscatter signature. In this study, a full-wave model is developed for simulating L-band backscatter from soybean fields. Leveraging the ANSYS High-Frequency Structure Simulator (HFSS) framework, the model solves for the scattering of EM waves from realistic 3-D structural models of soybean, explicitly incorporating the interplant scattering effects. The model estimates of backscatter match well with the field observations from the SMAPVEX16-MicroWEX and SMAPVEX12, with average differences of 1-2 dB for co-pol and less than 4 dB for cross-pol. Furthermore, the model effectively replicates the temporal dynamics of crop backscatter throughout the growing season. The HFSS analysis revealed that the stems and pods are the primary contributors to HH-pol backscatter, while the branches contribute to VV-pol, and leaves impact the cross-pol signatures. In addition, a sensitivity study with 3-D bare soil surface resulted in an average variation of 8 dB in co- and cross-pol, even when the root mean square height and correlation length were held constant

Combined Radar-Radiometer Surface Soil Moisture and Roughness Estimation

A robust physics-based combined radar-radiometer, or Active-Passive, surface soil moisture and roughness estimation methodology is presented. Soil moisture and roughness retrieval is performed via optimization, i.e., minimization, of a joint objective function which constrains similar resolution radar and radiometer observations simultaneously. A data-driven and noise-dependent regularization term has also been developed to automatically regularize and balance corresponding radar and radiometer contributions to achieve optimal soil moisture retrievals. It is shown that in order to compensate for measurement and observation noise, as well as forward model inaccuracies, in combined radar-radiometer estimation surface roughness can be considered a free parameter. Extensive Monte-Carlo numerical simulations and assessment using field data have been performed to both evaluate the algorithms performance and to demonstrate soil moisture estimation. Unbiased root mean squared errors (RMSE) range from 0.18 to 0.03 cm3cm3 for two different land cover types of corn and soybean. In summary, in the context of soil moisture retrieval, the importance of consistent forward emission and scattering development is discussed and presented

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

High-Resolution Soil-Moisture Maps Over Landslide Regions in Northern California Grassland Derived From SAR Backscattering Coefficients

Slow-moving landslides are destabilized by accumulated precipitation and consequent soil moisture. Yet, the continuous high-resolution soil-moisture measurements needed to aid the understanding of landslide processes are generally absent in steep terrain. Here, we produce soil-moisture time-series maps for a seasonally active grassland landslide in the northern California coast ranges, USA, using backscattering coefficients from NASA's uninhabited aerial vehicle synthetic aperture radar at 6-m resolution. A physically based radar scattering model is used to retrieve the near-surface (5-cm depth) soil moisture for the landslide. Both forward modeling (backscattering estimation) and the retrieval (soil-moisture validation) show good agreement. The root-mean-square errors (RMSE) for vertical transmit vertical receive (VV) and horizontal transmit horizontal receive (HH) polarizations in forward model comparison are 1.93 dB and 1.88 dB, respectively. The soil-moisture retrieval shows unbiased RMSE of 0.054 m³/m³. Our successful retrieval benefits from the surface and double-bounce scattering, which is common in grasslands. The retrieved maps show saturated wetness conditions within the active landslide boundaries. We also performed sensitivity tests for incidence angle and found that the retrieval is weakly dependent on the angle, especially while using copolarized HH and VV together. Using the two copolarized inputs, the retrieval is also not sensitive to the change of orientation angles of grass cylinders. The physical model inversion presented here can be generally applied for soil-moisture retrieval in areas with the same vegetation cover types in California

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