To better understand the interactions of satellite C-band radar with the soil-snow-vegetation continuum in a spatio-temporal context and to provide a novel approach for snow depth retrieval from Sentinel-1 observations, a coupled radiative transfer model was developed. This model combines a snow, soil and vegetation radiative transfer model to simulate the Sentinel-1 observations over the Alps, and can be inversed to obtain estimates of snow depth. Performance will be assessed at 1 km spatial resolution for the winter of 2017-2018, across a wide range of elevations, local incidence angles and total accumulated snow, using several performance measures (Pearson correlation and MAE).

We reported on the progress of fast hybrid method (FHM) for full- wave simulations of propagation of L-band microwaves in forested environment. For L band, previously we performed full wave simulations of realistic trees initially at 8 meters [1], followed by 13 meters [2]. The progress in this work is at comparisons of the electromagnetic model simulations with SMAPVEX19-22 data: 1) The height of the trees have been extended to 17 meters with the multiple scattering effects of 91 trees in the spatial domain with simulated transmissivity at 0.57 2) the spatial patterns of electric field distribution are simulated with electric field as high as 1.6 that of the incident wave corresponding to 2.56 times the Poynying of the incident waves, and the patterns exhibits gaps and shadows 3) the effects of clustering of trees with gaps show different results from that of uniformly positioned trees and 4) tree structures are varied with examples of trees with two trunks branching out from the main trunk, and the case of tapering trunk radius.

Recent updates in the use of 0.5-2 GHz microwave radiometry for remotely sensing Earth’s cryosphere are reported. These updates concern measurements and modeling of the spectral properties of brightness temperatures for geophysical regions such as ice sheets, sea ice, ice shelves, and others. The results are intended to support the continued development of 0.5-2 GHz passive microwave mission concepts for future deployment in space.

In this paper we describe the development and motivation behind the development of a NASA-sponsored airborne instrument, SNOWWI (Snow Water-equivalent Wide Swath Interferometer) that is being developed for exploring the volume scattering and penetration depth characteristics of the snowpack at three different frequencies (5.4 GHz, C-band; 13.64 GHz known as Ku-low; 17.24 GHz known as Ku-high). The system, as it is being constructed is able to receive co- and cross-polarized (VV and VH) returns in an interferometric configuration. By implementing these components of the radar signature on the same platform, we will be able to explore the relationship between snow depth, density and snow water equivalent on the overall radar signature. This work is being done in conjunction with a strong modeling component being led by the University of Michigan, a ground campaign component supported by Boise State University and the US Army Corps of Engineers Cold Regions Research and Engineering Laboratory (CRREL), and a spaceborne concept development being led by Capella Space.

This article presents the first results of the newly conceived airborne Synthetic Aperture Radar system, SNOWWI.SNOWWI is a dual Ku- and C-Band interferometric and dualpolarized (VV and VH) system operating at 13.64 GHz, 17.24 GHz, and 5.39 GHz. The system aims to deliver snowpack observations to quantify Snow Depth (SD) and Snow Water Equivalent (SWE), which have been included as Targeted Observables in the National Academies’ 2017 Decadal Strategy for Earth Observation from Space. This manuscript includes results from the system’s first deployment in Grand Mesa, CO, in January and March 2024.

Ice shelves are important parts of the cryosphere that influence ice sheet dynamics and mass loss. The internal temperatures of ice shelves are currently known only from a few borehole sites or from glaciological models. Microwave radiometry in the 0.4–2.5 GHz range is capable of receiving thermal emissions from deep within an ice shelf and thereby providing information on internal temperatures. This letter reports modeling studies of the brightness temperature of the Ross Ice Shelf (RIS) from 0.4 to 2.5 GHz that provide insight into the potential of microwave radiometers for measuring ice shelf internal properties.

Full-wave simulations of the effective permittivity of firn aquifer and wet snow at L-band are reported. The Monte Carlo simulations are carried out for bicontinuous media embedded in a sphere, and the scattering cross section and absorption cross section are calculated. By averaging over realizations, the effective permittivity is extracted by comparing it with Mie solutions. The simulations are validated by using three numerical methods of 3-D solutions of Maxwell equations: finite difference frequency domain (FDFD), finite element method (FEM), and the discrete dipole approximation (DDA). Full-wave simulation results are compared with those from the classical Maxwell–Garnett and Polder–van Santen mixing formulas. The results show large differences from mixing formulas when there are large permittivity contrasts between the background medium and the scatterers, which are scenarios in aquifer and wet snow. The significance of these results is examined for the L-band microwave remote sensing of terrestrial wet snow and aquifer in polar regions.

To quantify the forest effects on P-band radar remote sensing, this paper utilizes the fast hybrid method (FHM) combining fast multiple scattering theory (FMST) and a numerical electromagnetic solution. Considering estimation of the domain area, the required number of trees for P-band signal analysis is 121. For the efficient scattering solutions of a large number of trees, the FHM uses the triple FFT applied to the Foldy-Lax equation where two FFTs are applied to a 2-D spatial domain and one FFT to the order of cylindrical waves corresponding to translation addition theorem. This speeds up calculation of a translation addition matrix multiplied by a column vector. The accuracy of FHM is validated by FEKO using 25 trees, showing excellent agreement. Also, FHM provides faster solutions than commercial software. Using dielectric constants of winter and summer conditions, forest effects in P-band signals are validated by calculating transmissivity.

In studying the mass balance of polar ice sheets, the fluctuation of the firn density near the surface is a major uncertainty. Temporal knowledge of firn densities are used to interpret elevation change measured by altimeters in terms of ice mass change. In this paper, we use microwave radiometer from 0.5GHz to 2Ghz and radar datasets to infer firn density fluctuations. We examine data collected from four sites in the accumulation zone of Greenland (including those that experience significant melt and refreeze events), the FA-13 site on the south east coast of Greenland where firn aquifers are present, and DOME-C in Antarctica where the firn is believed to experience minimal melt effects. The Community Firn Model is used as a reference for the four locations in Greenland. UWBRAD, SMOS, and SMAP brightness temperature data and Snow radar echograms are used in the analysis. A radiative transfer model is used to account for the effects of firn density fluctuation and refrozen layers observed in the radar echograms in the accumulation zone in Greenland. The density fluctuation is treated as a 3D variation accounting for both vertical and horizontal density changes. Results over the Greenland accumulation zone show that the dynamic range of brightness temperature is correlated with the number of peaks in the radar echograms. Forward modelling results show a consistency of the input density parameters with the Community Firn Model when a good match between modeled and measured TB is achieved, and forward modeled multi-angle results also are in good agreement with SMOS observations. SMAP data at the FA- 13 site is also shown to be interpretable using the forward model. This work provides a combined active and passive method for the remote sensing of firn densities.

Snow water equivalent (SWE) is an important characteristic of a terrestrial hydrological cycle that needs to be retrieved in any global snow satellite mission. Many retrieval algorithms have been proposed based on microwave backscattering of snow packs. And X and Ku bands have been a focus on many of these past and future missions. In this paper we analyse the airborne X(9.6 GHz) and Ku (17.2 GHz) band data of the SnowSAR 2017 campaign and the University of Massachusetts InSAR Ku (13.3 GHz) band data using the bi-continuous dense media radiative transfer (DMRT) model. In-situ measurements of density, temperature and specific surface area (SSA) from the snow pits are used as physical parameters and are used in estimating the numerical parameters ($\zeta$) and$b$which characterizes the model. The background effects such as rough surface scattering are also removed from the airborne data and only the volume scattering is analyzed. Overcoming limitations in other models such as the sticky sphere model, the bi-continuous media model gives a more realistic representation of snow microstructure and has a weaker frequency dependence.

In this paper, the Numerical Maxwell Model of 3D (NMM3D) full-wave simulation is performed over a corn field using a hybrid method to study the vegetation effect on the microwave. The commercial software of FEKO is used to extract T-matrix of single corn in the first step. Then the calculated T-matrix is combined with Wave Multiple Scattering Theory (W-MST) in the second step to consider the multiple scattering among different plants. The hybrid method is validated with HFSS by solving scattering from 2 corns. A corn field of 25 corn is simulated using the hybrid method and the transmission is calculated and compared with those obtained from the classical radiative transfer model.

The density profile of a polar ice sheet is an important parameter for the estimation of ice mass balance. Wave reflections caused by density variations are also a key uncertainty in the retrieval of ice sheet temperature profiles in Ultra-Wide band radiometry. In this paper, we examine different firn density profile models and analyze the subsurface reflections they cause using an analytical partially coherent approach. We also examine firn density profiles obtained from borehole measurements, from past UWBRAD modeling studies, from a community firn model, and from snow radar echo measurements. In previous studies, the ice sheet has been model as a 1D random medium with density variations in depth. However, horizontal density variations also exist, so that the ice sheet is a 3D random medium. Analyses using the partially coherent model show that in the presence of horizontal fluctuations, contributions from short scale variations vanish as the horizontal correlation length decreases due to the diffraction of waves.

In this paper, an Analytical Kirchhoff Solution (AKS) and Numerical Kirchhoff approach (NKA) are used to study coherent and incoherent land surface near specular scattering at L and P bands. The AKS model includes both coherent and incoherent waves, and includes the effects of topographic slopes and elevations. The land profile is modelled as a summation of three scales of surface roughness corresponding to “microwave”, “fine topography”, and “coarse topography”, where the microwave roughness and fine topography are treated as random processes while the coarse topography is deterministic. An airborne lidar survey performed over the San Luis Valley, CO is used to obtain surface roughness information for the simulation results of$\mathrm{P}$and L-band scattering. Results using the lidar surface data show that coherent reflection can dominate returns from a 5 km by 5 km area at P band, while incoherent scattering dominates L band returns in the same scenario.

Stratification in terrestrial snow is a key factor in the retrieval of snow water equivalence (SWE) due to the different snow volume fractions and particle sizes. In studying the layered structure of snow, radar tomography has been used and multiple ground based experiments are performed. The conventional back projection method has been used to construct the image based on radar measurements at different incident angles and frequencies. However, the conventional back projection method based on Born's approximation would show deformation in the final snow image. In this paper, we use the asymmetrical distorted Born's approximation to correct the deformation in the image.

Backscattering from rough soil surface has important applications to the remote sensing of soil moisture and snow water equivalent (SWE), To extend simulations to Ku-band, we have performed full wave simulations up tokh=15. Results are simulated for various profiles and show that the scattering at C-, X-, and Ku-bands is influenced by both scales of centimeters roughness and millimeter roughness. Comparisons are made between constant ratios rough surface and constant correlation length rough surfaces. The results are illustrated for both VV and HH polarizations. Simulation results are in good agreement with X band measurement data as a function of incidence angle. An illustration is used to show how the results can be used for theoretical models of rough surface scattering in remote sensing of snow water equivalent.

A comparison of three different electromagnetic scattering models for land surface delay-Doppler maps (DDMs) obtained from global navigation satellite system reflectometry (GNSS-R) along a Cyclone Global Navigation Satellite System (CYGNSS) track in the San Luis Valley, Colorado, USA, is presented. The three models are the analytical Kirchhoff solutions (AKS), the Soil And VEgetation Reflection Simulator (SAVERS), and the improved geometrical optics with topography (IGOT). Common inputs to the three models were defined by using field samples of soil moisture and texture, soil surface roughness measurements, and a digital elevation model (DEM). The resulting peak reflectivity profiles of the models and the CYGNSS data all had a range of 10 dB along the selected track, mainly due to the influence of topography. The reflectivities obtained from all three models agreed with one another to within 2.4 dB along the full length of the track. The models also showed general agreement with the corresponding CYGNSS data, although the modeled profiles were higher than CYGNSS Science Data Record Version 3.1 by an average of 5 dB and also smoother. Additional characterization of fine-scale surface roughness is identified as an area for future work to improve model fidelity. An intercomparison of DDM structure for three selected acquisitions is also provided.

Although ice sheet internal temperature is a first-order control on glacier dynamics, relatively few in situ borehole temperature profiles exist. The ultra-wideband software-defined microwave radiometer (UWBRAD) was designed to estimate internal ice sheet temperature (Ti) by measuring microwave brightness temperatures (Tb) from 0.5 GHz to 2 GHz. The retrieval ofTifromTbis not straightforward, however, due in part to the complicating effects of ice density fluctuations onTb. In this paper, we report a simulation study to assess the feasibility of realizing three science goals: the retrieval of a)Tiat 10 m depth to within 1 K; b) vertically-averagedTito within 1 K; and c) the verticalTiprofile to within 1 K RMSE. Two analyses along the Greenland ice divide are presented. First, we assess the ideal UWBRADTiretrieval precision via the Cramér-Rao Lower Bound (CRLB). Second, we perform a “Virtual Experiment” (VE) using synthetic UWBRAD observations. Both the CRLB and VE analyses indicate that the science goals are achievable with the caveats that ice thickness and UWBRADTbprecision impact performance. Assuming a UWBRADTbprecision of 0.5 K, and for places where ice sheet thickness is less than 3 km, all science goals can be achieved. The results of the study provide a strong indication of the potential of UWBRAD to provide valuable Greenland ice temperature profile information to the scientific community.

Ice sheet subsurface temperature is important for understanding glacier dynamics, yet existing methods to obtain the temperature of the ice sheet column are limited toin situsources at present. The ultrawideband software-defined microwave radiometer (UWBRAD) has been developed to investigate the remote sensing of ice sheet internal temperatures. UWBRAD measures brightness temperature spectra from 0.5 to 2 GHz using 12 subchannels and employs a sophisticated algorithm for detection and mitigation of radio frequency interference (RFI). The instrument was deployed during a flight over northwestern Greenland in September 2017 and acquired the first wideband low-frequency brightness temperature spectra over the ice sheet and coastal regions. The results reveal strong spatial and spectral variations that correlate well with internal ice sheet temperature information. In this article, the section of the flight path ranging from the Camp Century to NEEM to NGRIP boreholes is used for subsurface temperature estimation. A “partially coherent” forward model is applied along with a Robin model for the temperature profile and a two-scale model of ice sheet density variations to describe measured brightness temperatures. Using this model, vertical temperature profiles are retrieved along the flight path using a sequential Bayesian estimator; borehole measurements at the three campsites are used to obtain Bayesian priors. The retrieved temperature profiles show reasonable behaviors and demonstrate the potential of ultrawideband microwave radiometry for remotely sensing internal ice sheet temperatures.

A comparison of three different electromagnetic scattering models for delay-Doppler maps (DDMs) of global navigation satellite system reflectometry (GNSS-R) from land is performed along a Cyclone Global Navigation Satellite System (CYGNSS) track over a validation site in the San Luis Valley, Colorado, USA. The peak reflectivity profiles of all three models and of the corresponding CYGNSS data are found to be in general agreement and are strongly influenced by topography. An intercomparison of DDM structure for one acquisition is also included. Efforts to refine the model results using a high resolution lidar survey are ongoing.

To investigate the feasibility of using multi-frequency to further improve the soil moisture retrieval, the recently developed hybrid method is used to perform full-wave simulations of a wheat field at three different frequencies of L-, S-, and C-bands. In the hybrid method, the multiple scattering within a single wheat plant is first captured using the T-matrix based on the full-wave solutions of HFSS. In the second step, the scatterings among different plants are considered using the Foldy-Lax equations of multiple scattering theory (MST). The transmission of microwaves through wheat field at the L-, S- and C-bands are calculated using the hybrid method. Results show that: (1) the transmission obtained from the full-wave simulations is much larger than those computed from the radiative transfer equations (RTE) model, (2) the hybrid method transmission has a weaker frequency dependence than those of the RTE, and (3) the attenuation caused by the vegetation layer would saturate with an increase in frequency.

In this paper we present processing and analysis results of an airborne Ku-band InSAR, constructed at the University of Massachusetts, and flown on a Cessna 208 Caravan over the Trail Valley Creek region in Canada's Northwest Territories during the 2018–19 snow season. In this paper, we describe the Ku-band InSAR, provide some intermediate results and discuss on how these data can be used for furthering the science in the remote sensing of snow.

The capability of Sentinel 1 C band radar observations for mapping snow depth or snow water equivalent (SWE) has been demonstrated recently. However, theoretical models of C band radar signatures for snow retrieval are still lacking. In this paper, we study the volume scattering of snowpack and the surface scattering from the snow/soil interface. The snowpack is computer generated including dense ice aggregates. The volume scattering is calculated by the dense media radiative transfer (DMRT) model and the surface scattering is computed with the Oh model. With well characterized surface scattering, surface scattering contributions can be subtracted from radar observations to enhance sensitivity of volume scattering to SWE. The study will help improve C band SWE retrieval and provide the theoretical basis for retrieval algorithms.

Electromagnetic scattering and emission from 1-D rough surfaces with multiple elevations are studied using full-wave simulations. Both the root-mean-square (rms) heights and the surface length are large compared to the wavelength. A novel multilevel steepest decent-sparse matrix canonical grid (MLSD-SMCG) method is proposed to address limitations in the original SMCG. The uniform Nystrom method and neighborhood impedance boundary condition (NIBC) are also incorporated in solving the dual surface integral equations (SIEs) of the method of moments (MoM). Simulation results are illustrated at L-band for soil and ocean surfaces. The surface rms heights and lengths are up to 1.43 and 243.8 m corresponding to 6 and 1024 wavelengths at 1.26 GHz, respectively. For ocean surfaces, the wind speeds up to 20 m/s are considered, and the entire spectrum is included to capture all relevant surface length scales. Numerical results indicate the proposed approach is computationally efficient and accurate. Energy conservation checks in simulations are at $10^{-4}$ for ocean scattering and emission. Also, the effects of wind-driven roughness on ocean emissivity are further investigated using the proposed approach in terms of wind speed and observation angle for both polarizations.

The Ultra-Wideband Software Defined Microwave Radiometer (UWBRAD) is a wideband radiometer operating from 0.5 to 2 GHz for remote sensing of polar ice sheet temperature profiles. Small-scale (cm to m) fluctuations in firn density in the upper portion of the ice sheet significantly impact observed brightness temperatures. Previously, a fully coherent model based on solving Maxwell’s equations for thousands of layers throughout the entire ice sheet was developed. Density profiles in the model are described as the sum of a smooth average density profile with a spatially correlated random process that represents density fluctuations. In this article, we develop a “partially coherent” implementation of the coherent model that captures the impact of variations in ice density on predicted brightness temperatures while improving computational efficiency. The partially coherent model divides the ice sheet into blocks. Within each block, the coherent model is applied to take into account coherence among the contributions of closely spaced layers. A Monte Carlo procedure is used to calculate the average block reflection and transmission parameters. Between adjacent blocks, interactions are assumed to be incoherent, and the radiative transfer theory is used to incoherently cascade block parameters. Results of the partially coherent model are in good agreement with the fully coherent model and also with Soil Moisture Ocean Salinity (SMOS) and UWBRAD brightness temperature observations.

Accurate calculations of electromagnetic scattering and emission from ocean surfaces with large sizes and root-mean-square (RMS) heights are still a challenge for the fullwave numerical methods. The widely used sparse matrix canonical grid (SMCG) method is only efficient for small and moderate roughness surfaces. This is because of the limitation of approximations in the far-field expressions using Taylor series expansion. In this paper, a novel multilevel steepest decent-sparse matrix canonical grid (MLSD-SMCG) method is proposed to address this issue. The proposed approach is implemented with the method of moment (MoM) in solving the dual surface integral equations (SIEs). Simulation results are illustrated at L-band for ocean surfaces with wind speed up to 20 m/s. The entire spectra are involved to capture all scales of waves in simulations. Thus the surface root-mean-square (RMS) heights and lengths are up to 3.82 and 1024 wavelengths of 1.26 GHz, respectively. Numerical results indicate the proposed approach is computationally efficient and accurate. Energies in simulations are conserved to the order of 10-4for ocean scattering and emission at various wind speeds.

The vegetation layer effects play an important role on microwave remote sensing of soil moisture. The classical Radiative Transfer Equation (RTE) and Distorted Born Approximation (DBA) model assume that the position of scatterers in vegetation is statistically homogeneous in 3D space. Such assumptions are incorrect because the scatterers in vegetation are in clusters and also in the form of extended cylinders. In this paper, we develop a new hybrid method that makes the Numerical Maxwell Model of 3D (NMM3D) full-wave simulation possible for vegetation. A geometry setup is introduced to account for the gap effects and vegetation structure. The T-matrix of a single plant composed of multiple cylinders in a cluster is extracted using Huygen's principle and the vector cylindrical wave (VCW) expansions. Foldy-Lax multiple scattering (FL) equations are used to solve for the transmissivity of the vegetation layer. The convergence and accuracy of the hybrid method are verified using Ansys High Frequency Structure Simulator (HFSS). Transmission through wheat is calculated using the hybrid method and compared with those of RTE/DBA.

Recently, the Synthetic Aperture Radar(SAR) Tomography (TomoSAR) has been used in monitoring the snowpack from X-band to Ku-band. This technique provides unique access to the structure of the imaged scene, and in the case of snowpack, it enables the separation of multiple snow layers as well as the detection of and compensation for soil and vegetation layers. The addition of polarimetric capabilities brings in the ability to detect spatially varying shapes, sizes, and permittivities, to decompose the backscattered signal into volumetric and surface scattering components, and to distinguish between snow, soil, and vegetation. There are a few ground-based field experiments that demonstrate the focused image recover the layering structure of the snowpack with different densities. To better understand the measurement, this paper aims to provide physical-based forward modeling to reconstruct the TomoSAR images with realistic snow profiles. Without loss of generality, we perform the analysis on a two-layer snowpack.

In this paper, we study the scattering of land surfaces for the Global Navigation Satellite System Reflectometry (GNSS-R) land applications. Topography slopes are introduced to improve the physical patch model. The entire area within the footprint is divided into patches. Each patch is on a slope with elevation. Simulation results have shown that for small rms height, the received power to transmitted power ratio, Pr/Pt is smaller than the coherent model and the patch model with only elevation effects but greater than the incoherent model. The delay-doppler maps are also simulated based on the patch model.

Previous experiments showed that the frequency dependence of snow volume scattering from 18 to 90GHz is power of 2.8, which is much weaker than the power of 4 of Rayleigh scattering. Recently monitoring snow using existing satellites (such as Sentinel-1, COSMO-SkyMed and QuickScat) have been widely studied. The radar signatures from C to Ku band are important for active remote sensing of snow. In this paper, we study the snow aggregation effects and its frequency dependence of volume scattering from C to Ku band (4-18GHz) with the bicontinuous model. The bicontinuous media model is applied to model the snow microstructure with aggregates. The integral equation of snow scattering volume is derived based on the Born approximation which then leads to the scattering coefficients. Scattering coefficients of snow are computed from C to Ku band giving a frequency dependence of ~2.6 power, weaker than that of Rayleigh scattering because of the aggregation effects. In addition, results are also in good agreement with the full wave numerical solutions from X to Ku band.

We use full-wave simulations of rough surfaces to calculate the emissivities of a polar ocean between 0.5 GHz and 2 GHz for applications in ocean salinity. High accuracy is required because the emissivity variations between flat and rough surfaces are at the order of magnitude of 10-3. In addition, the changes of emissivity due to salinity change are only about 4.2 × 10-4/psu to 2.6 × 10-3/psu for 0.5-2 GHz over the polar region. An enhanced method is proposed by combining neighborhood impedance boundary condition (NIBC), Nystrom, and sparse matrix canonical grid (SMCG) to solve the dual surface integral equations (SIEs) using the method of moments (MoM). To simulate large-scale ocean waves using a complete ocean spectrum, the surface root-mean-square (RMS) heights are up to 22.5 cm corresponding to 1.5 times wavelength of 2 GHz. Thus, the surface lengths used are up to 333 wavelengths to account for the large RMS height. Simulation results are illustrated for 0.5-2 GHz. We show that the energy conservations are obeyed to 10-4. The effects of roughness and salinity on broadband polar ocean emissivity are studied with the proposed approach. Numerical simulations show that the sensitivity to salinity is still preserved in spite of roughness.

In passive microwave remote sensing, the change of ocean emissivity is very small due to the roughness and salinity change, particularly for the polar region. This puts forward a strict requirement of the simulation accuracy. The ultra-wideband software-defined microwave radiometer (UWBRAD) is developed to measure the ocean salinity over polar region using wide-frequency microwave from 0.5 GHz to 2 GHz. In this paper, in order to meet the high accuracy requirement for sea surface salinity detection with UWBRAD, the Nystrom method is used in solving surface integral equations with moment method (MoM). A neighborhood impedance boundary condition (NIBC) technique is also applied to solve the matrix equation efficiently. Moreover, to save the memory and further accelerate the calculation speed, the sparse matrix canonical grid (SMCG) method is firstly combined with Nystrom/NIBC. Simulation results are illustrated for 0.5-2 GHz and show that emissivities using Nystrom/NIBC combined with SMCG are accurate to the magnitude of 10-4, which meet the accuracy requirement of retrieving polar ocean salinity within 0.2 psu.

The transmission through vegetation/forest canopy is important for remote sensing of soil moisture. The commonly used vegetation models are distorted Born Approximation (DBA) and Radiative Transfer Equation (RTE). We recently developed Numerical Maxwell Model of 3D (NMM3D) full wave simulations of vegetation/forests. The results of NMM3D show much larger transmission than that of RTE/DBA. A much larger transmission of NMM3D means microwave emission from soil can reach the radiometer, which is different from the conclusion for microwave remote sensing of soil moisture based on RTE and DBA. In this paper, we implement NMM3D based on the scattered field formulation of Foldy-Lax multiple scattering equations (FL). The novelty of this method is that the 3D cylindrical vector wave expansions are used in FL. The correctness of the method is verified. We implement the method on parallel computation using a large number of tall cylinders.

Arctic and Antarctic sea ice covers are in a sharp contrast in terms of characteristics, distributions, and processes with a drastic decrease in the Arctic versus the opposite increase in the Antarctic in a changing climate. In quantifying polar sea ice differences to address the contrasted sea ice behaviors, two key parameters are sea ice thickness and melt pond fraction, which remain challenging to measure extensively in time and in space with a sustainable approach. Here, we present a new paradigm for such measurements using bistatic radar reflectometry, thanks to developments of low-cost receivers to acquire reflected signals from numerous existing transmitter systems operated at multiple frequencies to be replenished and sustained indefinitely into the future. For sea ice thickness measurement to determine ice volume, reflected signals likely come from the bottom ice-water interface avoiding large errors inherent in current altimetry techniques due to uncertainty in free-board height and snow cover. Regarding melt pond faction on sea ice to estimate albedo and insolation, the bistatic reflection can be dominated by melt pond water with permittivity that is one order of magnitude larger compared to that of snow or ice. These are examined by a combination of numerical Kirchhoff (KA) simulator and Numerical Maxwell Model of 3D simulations (NMM3D) to preserve phase and amplitude information and thereby account for both coherent and incoherent effects. Physical insights from the rigorous theory for bistatic radar reflectometry will be valuable to develop future satellite missions to resolve cryospheric science issues concerning the polar sea ice differences.

The concept of wideband autocorrelation radiometry has recently been proposed and applied for the remote sensing of snow and lake ice. Such instruments measure the microwave emission from a scene of snow and ice over a wide and low frequency band where volume scattering within the snow/ice layer is negligible. Experiments have demonstrated that such wideband brightness temperature spectra can show oscillatory features. These features arise from coherent interference among the direct upward emission and its replicas from multiple reflections, are related to the layer thickness of snow or ice, and can be affected by interface roughness or any above snow vegetation canopy. The latter is therefore an important factor affecting the application of wideband autocorrelation radiometry in terrestrial snow remote sensing. In this paper, we analyze the effects of an above snow vegetation layer on brightness temperature spectra, particularly the possible decay of wave coherence arising from volume scattering in the vegetation canopy. In our analysis, the snow layer is assumed to be flat, and its upward emission and surface reflectivities are modeled by a fully coherent model, while the volume scattering from the vegetation layer is described by an incoherent radiative transfer model. The solution to the radiative transfer equation is obtained through an interative approach accounting for multiple scattering effects. The angular and polarization coupling arising from volume scattering and the emission contributed by the vegetation layer all cause smoothing of oscillatory patterns in the observed brightness temperature spectra.

Traditionally, a snow stratigraphy is characterized through a snow pit study. It only represents a snapshot view of the snow vertical properties and cannot capture the continually evolving snow process. This type of study is also destructive and time-consuming. Recent studies show that by using multi-baseline SAR configuration, the tomographic processing can provide the vertical image of the snowpack and monitor temporal variability. In this study, the full wave solution of the forward model will be used to reconstruct the tomograms and relate snow properties with the images.

The Global Navigation Satellite System Reflectometry (GNSS-R) for land applications have attracted considerable attention. Prior models include the coherent model and incoherent models. There are big differences between these two models. In this paper, we propose a patch model with NMM3D (Numerical Maxwell model of 3D simulations). The models take effects of multiple elevations of land surfaces into account. Results are compared with 1) coherent model, 2) incoherent model, and (3) numerical Kirchhoff simulator (KA simulator). Results of the patch model are consistent with those of KA simulator and have many dB difference with coherent and incoherent model.

An ultrawideband radiometer was used to measure microwave brightness temperature spectra over Arctic sea ice in the Lincoln Sea near the north coast of Greenland. Spectra over the range of 0.5-2 GHz were compared to thermal infrared images collected during the airborne campaign and also compared to nearly concurrent Sentinel-1 C-band synthetic aperture radar (SAR) data. Based on those comparisons, spectral signatures were associated with thick multiyear ice and thin ice. A radiative transfer (RT) model consisting of a homogeneous slab of sea ice bounded by sea water and air was then used to invert the spectra for sea ice thickness and salinity. Inferred thicknesses were consistent with ice thickness climatology for ice floes in the Lincoln Sea. Salinities are higher than expected which may be a consequence of neglecting surface and volume scattering contributions in the models.

In this paper we introduce an approach to enhance the precision of the vegetation parameterization in soil moisture retrieval using passive microwave observations. We present an algorithm that utilizes conventionally defined scattering (S) parameters to represent the propagation of the electromagnetic radiation through the vegetation layer over soil. The S-parameters can be determined with full wave simulations of 3-D Maxwell Equations enabled by recent advances in numerical simulation techniques. Traditional retrieval algorithms have relied on approximation of the radiative transfer equation in order to find simple parameterization for the equation. This results in added uncertainty when the attenuation and scattering within the vegetation layer increases. The presented method provides a way to model the radiative transfer accurately while preserving a reasonable complexity and number of parameters in the algorithm. The results show that the presented method improves the brightness temperature modelling accuracy significantly when vegetation water content reaches about 5 kg/m2, depending on the scattering properties of the vegetation type.

In this paper, we develop a hybrid method combining T matrix of single objects and Fold-Lax multiple scattering theory (FL), for full wave simulations of vegetation/trees. The hybrid method of solving the Maxwell equations consist of off-the-shelf technique for single objects (e.g. HFSS) and newly developed techniques. The newly developed techniques are the three key steps of the hybrid method: (1) extracting the T matrix of each single object, (2) numerical wave transformations and (3) solving the coupled wave interaction equations (i.e. FL) for all the objects. For step (1), we extract the T matrix of a single object by numerical integration with the use of HFSS which is a 3D full-wave electromagnetic field simulation tool. The method of T matrix extraction from HFSS is verified by comparison with the analytical solution of a sphere. The method is applicable to find the T matrix for complicated object where the analytical solution is not available. Then, the wave transformations are performed based on the translation addition theorem. Numerical methods of calculating the transformation coefficients are developed. Finally, the wave interactions among the single objects are accounted for by FL. The results of the hybrid method agree with those of the HFSS brute force method. In comparison, the hybrid method is much more efficient than HFSS for vegetation scattering and applicable to large problems such as full wave simulations of a tree.

The Ultra-Wideband Software Defined Microwave Radiometer (UWBRAD) measures scene brightness temperatures from 0.5-2 GHz. UWBRAD was deployed in a September 2017 airborne campaign in Greenland, and observed brightness temperatures of the ice sheet as well as sea ice, the ocean surface, and land regions during the transit to and from Calgary, Canada (the aircraft base of operations). This presentation will review the campaign and datasets collected. Spectral features of thermal emissions from the ice sheet and other geophysical regions are also examined to obtain insight into the utility of 0.5-2 GHz thermal emission measurements for remote sensing applications.

Earth's cold regions are key elements of the planet's climate system: they have strong feedbacks with global change and they have a direct impact on human activities. Despite their importance, at present they are not adequately monitored by state-of-the-art instruments. In order to fill this gap, a dedicated spaceborne mission called Cryorad has been proposed in the framework of the ESA Earth Explorer 10 call. The mission would comprise a 0.4-2 GHz nadir-looking radiometer installed on a polar-orbit satellite. Scientific and technical studies are underway, as well as experimental campaigns in Greenland and Antarctica.

This paper shows results from a proof-of-concept tower experiment that computed phase from a reflected P-band signal. The change in phase of the reflected signal is related to SWE for dry snow and snow depth for wet snow and the rate of change of phase is directly correlated to frequency of observation. The effect of vegetation was also evaluated by using measurements from two towers: one with no vegetation and one surrounded by small trees with heights of up to 3 meters. The phase measurement from the two sites had excellent correlation of 0.99 during the accumulation phase. The correlation between SWE and phase measurement was found to be between 0.95 and 0.98 during the accumulation phase. During the melt phase, negative correlation between 0.68 and 0.80 was found between snow depth and phase measurement.

We apply the analytical fully coherent model to bicontinuous media for applications in microwave remote sensing of snow cover. In our model, snow is represented by bicontinuous media which is generated by a Gaussian random process. The statistical moments and correlation functions of bicontinuous media can be calculated. With the correlation functions, we apply the strong permittivity fluctuation (SPF) theory to derive the analytical solutions for calculation of scattering properties and effective permittivity of bicontinuous meida. The SPF theory is under the bilocal approximation. Effective permittivity and extinction coefficient from the analytical solutions are compared with those of the numerical solution of Maxwell's equation in 3D (NMM3D). The real part of effective permittivity of SPF is also compared with solutions of Maxwell-Garnett formula.

A time series multi-angular method was presented towards combining space-borne radar data acquired from both descending and ascending orbits with different observation modes in soil moisture retrieval. Inherit from multi-temporal based retrieval methods, the method assumes time-invariant roughness and vegetation, but not requires incidence angle normalization. The numerical Maxwell model of three-dimensional simulations and distorted Born approximation (NMM3D-DBA) were used to build a set of multi-angular data cubes (3 dimension look up table). Genetic algorithm (GA) was used to minimize the difference between data cubes and radar observations with the constraint of drying down soil moisture. Evaluation based on the fifth Soil Moisture Active Passive Experiment (SMAPEx-5) dataset shows an overall root mean square error (RMSE) of 0.07 cm3/cm3at the 50-m pixel scale.

An ultra-wideband radiometer has been developed to measure subsurface properties of the cryosphere including ice sheets and sea ice. The radiometer measures brightness temperature spectra from 0.5 to 2 GHz using 12 channels, each of which measures scene brightness temperatures over an ~88-MHz bandwidth resolved into 0.24-MHz intervals. The instrument was flown over northwestern Greenland in September 2016 and acquired the first, wideband, low-frequency brightness temperature spectra over the ice sheet and coastal region. The results reveal strong spatial and spectral variations that correlate well with the physical properties of the surface encountered along the flight path, which started over ocean, then passed the rock near the coast, and then up onto the ablation, wet, percolation, and dry snow zones of the interior ice sheet. In particular, strong spectral responses in percolation and dry snow zones are observed and plausibly explained by varying the distribution of horizontal density layers and isolated icy bodies in the upper portion of the firn. The success of the airborne deployment of the instrument and subsequent implementation of algorithms to limit radio frequency interference in unprotected bands is motivating continued airborne investigations as well as stimulating research into the feasibility of a spaceborne instrument.

Radar scattering from ocean surfaces is investigated by 3-D numerical solution of Maxwell's equations [numerical Maxwell's model in 3-D (NMM3D)] using the ocean surface profiles stochastically generated from a 3-D Durden-Vesecky ocean spectrum. The surface integral equations (SIEs) are formulated for dielectric surfaces using Green's functions of the air and the ocean permittivities with the surface tangential electric and magnetic fields as the unknowns. In solving the SIEs using the method of moment, a fast matrix solver of the sparse matrix canonical grid is used in conjunction with Rao-Wilton-Glisson basis functions. The computation has been implemented on a high-performance parallel computing cluster for problems with up to six million surface unknowns. Unlike the two-scale model (TSM) approximation, NMM3D does not require division of the surface spectrum into large- and small-scale ocean waves. The results of backscattering simulations are compared to Aquarius satellite radar measurements for wind speeds of 5, 8, and 10 m/s and for incidence angles of 29°, 39°, and 46°. The results show that NMM3D ocean backscattering solutions at L-band are in good agreement with Aquarius satellite radar data for co-polarized VV, HH, and cross-polarized VH returns as well as for the VV/HH ratio. The azimuthal dependence of L-band backscatter is also assessed. Finally, NMM3D results are compared to TSM solutions and are shown to lie close to Aquarius data in observed VV/HH ratio, and their azimuthal dependencies.

In this paper, we develop a radar snow water equivalent (SWE) retrieval algorithm based on a parameterized forward model of bicontinuous dense media radiative transfer (Bic-DMRT). The algorithm is based on retrieving the absorption loss of the snowpack which is directly proportional to the SWE. In the algorithm, Bic-DMRT is first applied to generate a lookup table (LUT) of snowpack backscattering at X- and Ku-band. Regression training is applied to the LUT to transform the dual-frequency backscatter into functions of two parameters: the scattering albedo at X-band and SWE. The background scattering is subtracted from the SnowSAR data to give the volume scattering of snow. Classification of SnowSAR data is applied to provide a priori information. Based on the obtained volume scattering and the priori information, a cost function is established to find SWE. Performance of the retrieval algorithm was tested using three sets of airborne SnowSAR data acquired over mixed areas in Finland and open tundra landscape in Canada. It is shown that the retrieval algorithm has a root-mean-square error below 30 mm of SWE and a correlation coefficient above 0.64.

The Ultra-Wideband Microwave Radiometer is a novel pseudo-correlation radiometer design measuring scene brightness temperatures from 0.5-2 GHz created under NASA's Instrument Incubator Program. This document analyzes the design and operation of the radiometer, the accuracy and stability of the brightness temperatures it produces, and presents initial results from a field campaign conducted in Greenland in September 2016.

We study the scattering of a vegetation canopy consisting of a large number of thin cylindrical scatterers using Numerical Maxwell Model in 3D Simulations (NMM3D). The full wave approach for solving Maxwell equations is based on the Foldy-Lax multiple scattering equations (FL) combined with the Method of Moments for bodies of revolution (BOR). The accuracy of the method FL-BOR is first validated by comparing with the results from the commercial software HFSS for the two and five cylinders' cases. Next, the transmission through a vegetation canopy of cylindrical scatterers is calculated using Monte Carlo simulation where the cylinders, as many as 500, are generated in each realization and the scattering is solved by FL-BOR with exact solutions of the matrix equation. The results of transmission at C-band are compared with those from the distorted Born approximation (DBA) where the attenuation rate {κe}is computed using Foldy's approximation. In NMM3D simulations, the transmission is calculated without the need of defining or calculating the attenuation rate. Two cases are studied: (a) short cylinders where the cylinder lengths are much smaller than the layer thickness and are randomly distributed in 3D in the vegetation layer, and (b) long cylinders where the cylinder lengths are the same as the thickness of the vegetation layer. Case (b) represents several vegetation types and also part of other vegetation types. The results of case (b) show there are significant differences of transmission, as much as 6 dB, from that of DBA.

We applied the Numerical Maxwell Model in 3 Dimensions (NMM3D) to radar scattering from ocean surfaces at L band. The formulation is based on the PMCHWT surface integral equation which uses separate Green's functions for air and ocean permittivities. The Sparse Matrix Canonical Grid (SMCG) is used to compute Method of Moments (MoM) solutions in conjunction with Rao-Wilton-Glisson (RWG) basis functions with the surface electric field and surface magnetic field as the unknowns. Surface sizes used are up to 64 wavelengths by 64 wavelengths. Isotropic sea surfaces simulated using the Durden-Vesecky spectrum are studied for wind speeds ranging from 5 m/s to 10 m/s and incidence angles varying from 29° to 46°. Backscattering from NMM3D and composite two-scale model computations are compared with Aquarius satellite scatterometer estimates. Unlike the two-scale model, NMM3D does not impose separation between large scale roughness and small scale roughness elements. Results show that, in spite of using just the isotropic DV spectrum, NMM3D are in measurably better agreement with data than the composite surface model for co-polarized returns as well as the polarization ratio.

Effect of roughness on forward physical model for Brightness Temperature of Antarctic ice sheets is presented. The Antarctic ice sheet which is characterized by layers of ice with permittivity fluctuations in addition to random rough interfaces. In order to investigate effect of roughness on brightness temperature, we only consider top 20 layers of ice sheets rough and all other layers with flat interfaces. The comparison between the results of the model and ESA's soil moisture ocean salinity (SMOS) brightness temperature show that the influence of roughness can significantly increase horizontally polarized thermal emission while leaving vertically polarized emissions relatively unaffected.

A fully coherent snowpack scattering and emission model is developed by numerically solving Maxwell's equations over the entire snowpack on a bottom half-space. The scattering matrix of the snowpack is directly obtained including both amplitude and phase. Both bistatic scattering coefficients and brightness temperatures of the snowpack are derived from full wave simulations. Simulation results demonstrate backscattering enhancement effects and coherent thin layer effects. The model is applied to study microwave signatures of the Arctic sea ice where the snow cover thickness has rapidly decreased. Microwave signatures are important in classification of sea-ice types and in quantitative characterization of snow cover properties. Both have strong impacts on the thermodynamics of sea ice. In the fully coherent model, a half-space dyadic Green's function is used in the volume integral equation to represent the effects of the underlying sea ice. Discrete dipole approximation is used to solve the volume integral equations, where parallel fast Fourier transform technique is utilized to accelerate the matrix-vector multiplications. The snowpack is represented as a bicontinuous medium. Periodic boundary conditions are applied in the two horizontal dimensions to simulate an infinite lateral extent of the snowpack.

We have been engaged in Numerical Solutions of Maxwell equations (NMM3D) for more than fifteen years [1-2]. In this paper, we report on the recent progress of NMM3D on random rough surfaces and discrete random media and their applications in active and passive microwave remote sensing. The random rough surface models were applied to soil surfaces and ocean surfaces. The discrete random media models were applied to snow and vegetation. We describe the numerical methodologies and the simulation results. Comparisons are also made with experimental measurements.

We validate an absorption based radar retrieval algorithm of snow water equivalent (SWE) using X- and Ku-band backscatter with airborne SAR data. The bicontinuous dense media radiative transfer (Bic-DMRT) model is first applied to generate a look-up table of snow properties against backscattering at X- and Ku-bands. In the retrieval algorithm, the background scattering is subtracted from the total scattering giving the volume scattering of snow. With the look-up table, we generate regression equations between multiple and single scattering and correlations between the scattering albedo and optical thickness at the two bands. With these relationships and the volume scattering of the snowpack, the best solution for the radar observation is found using a priori constrained least-squares cost function. Next, the absorption loss of the snowpack is derived from the solution, which is directly proportional to the SWE. We have applied the algorithm to airborne SAR observations from Finland and Canada. The retrieval algorithm is shown to be effective, achieving root mean square error (RMSE) of ~19 mm for both SnowSAR data, which is smaller than the 20mm RMSE requirement of SCLP.

The second-order small perturbation method is applied to investigate brightness temperature corrections caused by the rough interfaces of a two-layer medium. The spectral weighting functions of the two rough interfaces are extracted from the solution, and their properties examined. It is found that the functions are identical for the two interfaces as the spectral variable approaches zero, indicating an identical weighting of the surface height variance on each interface and an additive effect on the brightness temperature at nadir. Sample results for some realistic scenarios show that surface roughness in a two-layer medium can increase or decrease the observed brightness temperature at shallower angles, and in the case of a wideband measurement, can shift the interference pattern in frequency.

This paper evaluates the retrieval of soil moisture in the top 5-cm layer at 3-km spatial resolution using L-band dual-copolarized Soil Moisture Active-Passive (SMAP) synthetic aperture radar (SAR) data that mapped the globe every three days from mid-April to early July, 2015. Surface soil moisture retrievals using radar observations have been challenging in the past due to complicating factors of surface roughness and vegetation scattering. Here, physically based forward models of radar scattering for individual vegetation types are inverted using a time-series approach to retrieve soil moisture while correcting for the effects of static roughness and dynamic vegetation. Compared with the past studies in homogeneous field scales, this paper performs a stringent test with the satellite data in the presence of terrain slope, subpixel heterogeneity, and vegetation growth. The retrieval process also addresses any deficiencies in the forward model by removing any time-averaged bias between model and observations and by adjusting the strength of vegetation contributions. The retrievals are assessed at 14 core validation sites representing a wide range of global soil and vegetation conditions over grass, pasture, shrub, woody savanna, corn, wheat, and soybean fields. The predictions of the forward models used agree with SMAP measurements to within 0.5 dB unbiased-root-mean-square error (ubRMSE) and −0.05 dB (bias) for both copolarizations. Soil moisture retrievals have an accuracy of 0.052 m3/m3ubRMSE, −0.015 m3/m3bias, and a correlation of 0.50, compared toin situmeasurements, thus meeting the accuracy target of 0.06 m3/m3ubRMSE. The successful retrieval demonstrates the feasibility of a physically based time series retrieval with L-band SAR data for characterizing soil moisture over diverse conditions of soil moisture, surface roughness, and vegetation.

Atmospheric ice particles can be rimed and contaminated (e.g., by soot attachments). Previous optical property calculations usually assume rimed particles such as graupel and hailstones to be homogeneous spheres with fixed densities. The relevant dielectric constants are estimated with the effective medium approximation (EMA), although such particles are predominately nonspherical, porous, and contain small interior grains. This paper assesses the effects of nonsphericity, density, and inhomogeneity of graupel and hailstones on their optical properties. The bicontinuous medium approximation (BMA) is employed to simulate the particle internal structure. Conical shapes are compared with spherical and spheroidal shapes to assess the effect of nonsphericity. At frequencies lower than 89 GHz, the optical properties are more sensitive to particle's mass density than to overall particle shape, and the internal structure plays an insignificant role when the particle effective diameter (a quantity involving the particle size distribution) is smaller than approximately 10 mm, and the internal grain size is smaller than 0.2 mm. With a small grain size, the BMA phase function converges to the EMA phase function with an effective refractive index calculated with the Bruggeman formulation. Simulated top of atmosphere radiances at three microwave frequencies, 18.7, 36.5, and 89 GHz, are quite sensitive to ice particle effective diameter between 1 and 5 mm, ice fraction between 0.1 and 0.9, and ice water path between 1 and 5 kg/m2. Thus, these frequencies are suitable for retrieving the microphysical properties.

The distorted Born approximation (DBA) combined with the numerical solutions of Maxwell equations (NMM3D) has been used for the radar backscattering model for NASA's Soil Moisture Active Passive (SMAP) mission. The models for vegetated surfaces such as wheat, grass, soybean and corn have been validated with the Soil Moisture Active Passive Validation Experiment 2012 (SMAPVEX12) data. In this paper we report progress on development of a consistent model for combined active and passive microwave remote sensing of vegetated surfaces by using the same approach to obtain backscatter and emissivity. The active model DBA/NMM3D is extended to calculate bistatic scattering for each of the three scattering mechanisms: volume, double bounce and surface scattering. Then emissivity is obtained by integration of the bistatic scattering. An advantage of this combined active and passive model is that the same physical parameters of vegetation and soil surfaces are used in both the active model and the passive model. The β parameter that relates backscattering to emissivity is also derived for various vegetated surfaces.

The Ultra-wideband Software Defined Radiometer (UWBRAD) for ice sheet internal temperature sensing is designed to provide observations of ice sheet brightness temperatures from 500-2000 MHz. This presentation reports on current status of the instrument development, experimental results obtained to date, and plans for a September 2016 airborne deployment over Greenland.

Surface soil moisture was retrieved globally by systematically correcting for the effects of vegetation and soil surface roughness. The retrieval is enabled by employing physical-models of radar forward scattering for individual vegetation types to account for vegetation scattering and absorption, and by constraining the surface roughness effect using time-series observations. The L-band SMAP multi-polarized (HH/VV/HV) σ° data acquired globally every three days were used from mid-April to early July, 2015. Assessment was conducted over 13 rigorously-chosen core validation sites covering a wide range of biomass types, biomass amount, and soil conditions. The soil moisture retrieval reached an accuracy of 0.06 m3/m3RMSE, a bias of 0.003 m3/m3, and a correlation of 0.56. The successful retrieval demonstrates that the physically-based retrieval method is capable of characterizing soil moisture over diverse conditions of soil moisture, surface roughness, and vegetation on a global scale.

In vegetated surface scattering, the physical values of optical thickness and scattering albedo both increase with frequency. At C-band, because of the attenuation due to large optical thickness, the distorted Born approximation gives negligible values for the surface scattering term and double bounce term. Because of the smallness of these two terms, the distorted Born approximation gives results independent of soil moisture. Physically, because the albedo is significant such as between 0.5 and 0.9, the radiative energy does not dissipate with the optical thickness, but go through multiple scattering within the vegetation layer. In this paper, we use vector radiative transfer theory to study the multiple scattering effects. We also study the transmission of the incident wave For rough surface scattering at C-band, due to increasing incoherent bistatic scattering from rough surface and the attenuation of coherent reflection, rough surface boundary condition will be applied to consider all scattered energy in rough surface scattering and the radiative energy interaction with the vegetation layer.

We study the accuracies of numerical simulations of scattering by random rough surfaces in 2D based on the Nystrom method. The method is shown to be accurate for a large range of permittivities as well as for large roughness and fine scale roughness. We compared Nystrom method with impedance boundary conditions (IBC) method using both parameters of soil surfaces and ocean surfaces. In some cases, we found more than 10K difference of brightness temperature between Nystrom method and IBC. For cases of roughness of large rms height, we also found more than 3dB difference between Nystrom method and IBC. Energy conservation is obeyed within 0.1% for the Nystrom method. We are performing simulations on various surface profiles and permittivities for soil and ocean surfaces using Nystrom method.

We apply computer generation of anisotropic bicontinuous media with different vertical and horizontal correlation functions. We then use NMM3D (Numerical solutions of Maxwell equations in 3-Dimensions) to calculate the uniaxial effective permittivities and the effective propagation constants of V and H polarizations. The co-polarization phase differences (CPD) between VV and HH backscattered signal are derived. The CPD has recently been applied to the retrieval of snow water equivalent (SWE) and snow depth. The NMM3D simulation results are also compared with the results from that of the strong permittivity fluctuations (SPF) in the low frequency limit.

Snowpack consists of ice grains that are densely packed in the wavelength scale at microwave frequencies so that the coherent microwave interactions among the ice grains are important in microwave signatures. We have used Numerical Maxwell Model of 3D simulations (NMM3D) of random media / discrete scatterer to study such interactions. In the partial coherent model of Dense Media Radiative Transfer (DMRT), we use NMM3D to calculate the effective propagation constants, the extinction coefficients and the phase matrices. These are then used in radiative transfer equations to calculate the emission and backscattering signatures. In the fully coherent model, we use NMM3D to calculate the bistatic scattering and emissivity for a layer of snow pack over the ground. Using the fully coherent approach, we calculate the complex scattering amplitudes from the snowpack, including both magnitude and phase. In microstructure characterization of snow, we have used 2 models a) densely packed scatters of sticky particles or multiple sizes, and b) computer generated bicontinuous media. Both models can be characterized by correlation functions. In this paper, we also describe the recent simulated results for tomography and co-polarization phase differences of anisotropic dense media.

A partially coherent low frequency microwave emission model for polar ice sheet is developed to operate from 0.5GHz to 2.0GHz predicting brightness temperatures. The emission from polar ice sheet over the wide frequency band is shown to be correlated with its temperature profile and affected by its density fluctuations. The density fluctuations creating weakly reflective internal interfaces cause the decay of wave coherence so that the ice sheet can be divided into blocks. The coherent wave interaction are accounted for within the block by full wave simulations while inter-block wave interaction are taken incoherently by cascading boundary conditions in radiative transfer. The layer thickness / correlation length of the density fluctuation cause distinct frequency spectrum of the brightness temperature. The air/ snow interface and intermediate snow layer interfaces are rough causing angular coupling and polarization coupling in microwave emissions, and affect the angular patterns of the brightness temperature.. We apply the small perturbation method to study the roughness effects of multiple interfaces. Results of vertical and horizontal emissivities are illustrated as a function of observation angles.

In this letter, we generate anisotropic bicontinuous media with different vertical and horizontal correlation functions. With the computer-generated bicontinuous medium, we then use numerical solutions of Maxwell equations in 3-dimensions (NMM3D) to calculate the anisotropic effective permittivities and the effective propagation constants of V and H polarizations. The copolarization phase difference (CPD) of VV and HH is then derived. The CPDs have recently been applied to the retrieval of snow water equivalent, snow depth, and anisotropy. The NMM3D simulation results are also compared with the results of the strong permittivity fluctuations in the low frequency limit and compared against the Maxwell-Garnett mixing formula.

Comparison studies are made between the QCA-Mie model and the bicontinuous model in microwave scattering from terrestrial snow. Both the scattering properties and the medium characterization are compared. For QCA, we use the multisize and the sticky particle models. For the bicontinuous model, we use the probability distribution function for the wavenumber. We compare the scattering rate and the angular distribution of scattering using the mean cosine of scattering and show that the two models have similar properties. In medium characterization, we use the pair distribution functions used in QCA to derive the correlation functions. We show that both the Percus-Yevick pair functions and the bicontinuous model have tails in the correlation functions that are distinctly different from the traditional exponential correlation functions. The methodologies of using ground measurements of grain size distributions and correlation functions to obtain model parameters are addressed.

We extend the 3-D numerical method of Maxwell's equation (NMM3D) for rough soil surface scattering from L-band to C-, X-, and Ku-bands. We illustrate the results for copolarization, cross-polarization, and polarization ratio (HH/VV). Copolarized and cross-polarized backscattering coefficients from NMM3D are analyzed for frequency dependence, incident angle dependence, and soil moisture dependence. We also cross compare results from analytical and empirical models. The 16 × 16 squared wavelength (λ2) of rough surface is applied for NMM3D using 256 processors on NSF Extreme Science and Engineering Discovery Environment clusters. Polarization ratio, HH/VV, is studied to address the feature of dependence on frequency for same fields (same physical parameters for the model). HH/VV is shown useful to provide additional information to study land surface. Results from NMM3D are also validated with POLARSCAT measurement data-1. NMM3D shows good agreement with data and better performance while considering copolarization, cross-polarization, and polarization ratio (HH/VV) together. The key advancement in computation efficiency in this paper is the implementation of a physically based near-field precondition algorithm in NMM3D to accelerate parallel computation. With precondition, the computation time is faster by ten times for larger root-mean-square height.

Scattering matrices (SVV, SHH, SVH, SHV) are calculated from numerical 3D solutions of Maxwell equations (NMM3D). Using the simulated scattering matrices, we compute the polarimetric speckle and the coherency matrix for Pol-SAR applications. Results from NMM3D are examined by the comparison with theoretical distributions, including amplitude, phase difference, and amplitude ratio. Surface roughness dependence with entropy, anisotropy, and alpha angle from the ensemble average of coherency matrix is also studied. In this paper, we calculate polarimetric statistics of rough surface at C-band (5.4GHz) with 40 degree incidence. In addition, we study complete polarimetry of vegetated surface using distorted born approximation with surface scattering from NMM3D. Numerical Maxwell Method in 3D (NMM3D) with near field precondition was applied.

We investigate the degree to which ultrahigh frequency radio emission can be used to estimate subsurface physical temperature in the polar ice sheets. We combine electromagnetic emission forward models with plausible models of depth-dependent physical properties in the ice sheet. Temperature models are parameterized with variables including accumulation rate, geothermal heat flux, and surface temperature. Scattering is parameterized using empirical observations of grain growth combined with measured densities. Electromagnetic absorption is modeled using dielectric dispersion processes and semiempirical models based on observations. Our models illustrate that information about East Antarctic ice sheet temperature from near the surface to near the base can be gleaned from ultrawideband radiometer data. Based on our modeling study, we illustrate an instrument concept to measure ice sheet temperature profiles comprising a novel ultrawideband radiometer.

Many quantities describing ice sheet dynamics can be measured via remote sensing. However, subsurface ice sheet temperature, a very important parameter which determines in part internal deformation and ice flow, is not currently measured remotely. Direct knowledge is available only through measurements from a small number of boreholes. This paper presents the concept of utilizing microwave radiometry in the 0.5–2GHz frequency band to probe subsurface ice sheet temperatures. Ice sheet geophysical properties and the resulting microwave emission are reviewed, and an initial retrieval algorithm for subsurface ice sheet temperatures is described. Finally an ultrawideband radiometer design to realize the proposed measurements is summarized.

We use the coherent model for L band radar remote sensing of soya bean fields. Analytic methods and Monte Carlo simulations are used. The novel feature of the analytic model consists of introducing mutual exclusion functions to eliminate the overlap effects of branches in the former branching model. To validate the new results, Monte Caro simulations are also used by generating samples of soya bean fields and calculating the scattered field for each sample. The Monte Carlo simulations are in good agreement with proposed analytic model. Backscattering coefficients are illustrated for a variety of scenarios with varying VWC and soil moisture conditions. The results show that HH are significantly different based on the coherent model versus that of the distorted Born approximation or first order radiative transfer model. The results are compared with experimental data measured at SMAPVEX 12 field campaign in both the absolute values of backscattering as well as the polarization ratio between VV and HH.

We have performed simulations of random rough surface scattering using 3-D numerical solution of Maxwell equations (NMM3D) using surface size up to 32 × 32 squared wavelengths. The rough surfaces are characterized by exponential correlation functions. The simulation results of crossand copolarization backscattering coefficients were in good agreement with experimental measurements of bare soils at L-band. Because in numerical solutions of Maxwell equations the electric fields of the scattered wave are calculated for each realization, scattering matrices can be simulated by NMM3D, and such simulations are performed in this paper. For a given RMS height, correlation length, soil permittivity, and incident angle, we calculated the radar scattering matrix up to 958 independent realizations. For each realization, the components of the scattering matrix, namely, SHH, SVV, SHV, and SVH, are calculated. Using the simulated scattering matrices, we calculate the polarimetric speckle statistics (amplitude and phase difference), followed by a comparison with theoretical distributions. For fully developed speckle from the homogeneous rough surface, the results are examined and validated to ensure the simulated data quality as far as polarimetric properties are concerned. By taking ensemble averages, we calculate the coherency matrix from which the eigenvalues, entropy, anisotropy, and alpha angle in coherent target decomposition are then calculated. In particular, characterization of polarimetric descriptors for rough surface is presented. Issues of scattering symmetry characteristics are also discussed.

Physical models for radar backscattering coefficients are developed for the global land surface at L-band (1.26 GHz) and 40°incidence angle to apply to the soil moisture retrieval from the upcoming soil moisture active passive mission data. The simulation of land surface classes includes 12 vegetation types defined by the International Geosphere-Biosphere Programme scheme, and four major crops (wheat, corn, rice, and soybean). Backscattering coefficients for four polarizations (HH/VV/HV/350611873VH) are produced. In the physical models, three terms are considered within the framework of distorted Born approximation: surface scattering, double-bounce volume-surface interaction, and volume scattering. Numerical solutions of Maxwell equations as well as theoretical models are used for surface scattering, double-bounce reflectivity, and volume scattering of a single scatterer. To facilitate fast, real-time, and accurate inversion of soil moisture, the outputs of physical model are provided as lookup tables (with three axes; therefore called datacube). The three axes are the real part of the dielectric constant of soil, soil surface root mean square (RMS) height, and vegetation water content (VWC), each of, which covers the wide range of natural conditions. Datacubes for most of the classes are simulated using input parameters from in situ and airborne observations. This simulation results are found accurate to the co-pol RMS errors of to 3.4 dB (six woody vegetation types), 1.8 dB (grass), and 2.9 dB (corn) when compared with airborne data. Validated with independent spaceborne phased array type L-band synthetic aperture radars and field-based radar data, the datacube errors for the co-pols are within 3.4 dB (woody savanna and shrub) and 1.5 dB (bare surface). Assessed with spaceborne Aquarius scatterometer data, the mean differences range from ~ 1.5 to 2 dB. The datacubes allow direct inversion of sophisticated forward models without empirical parameters or formulae. This capability is evaluated using the time-series inversion algorithm over grass fields.

A compact polarimetric (CP) radar system requires fewer measurements than a fully polarimetric (FP) system, thus allowing added flexibility in radar system design. Previous studies have shown the potential of using compact polarimetry for radar remote sensing of soil moisture. This paper extends previous studies by considering a time series data cube retrieval algorithm and measurements in the presence of vegetation. Vegetation information is assumed to be provided by an ancillary data source in the retrieval process. The performance of an algorithm for reconstructing FP information from CP measurements of vegetated soil surfaces is also examined. The results of the study show that only a modest degradation in soil moisture retrieval performance occurs when compact-pol measurements are used in place of full-pol data.

Active and passive microwave remote sensing has been used for monitoring the soil moisture and snow water equivalent. In the interactions of microwaves with bare soil, the effects are determined by scattering of electromagnetic waves by random rough surfaces. In the interactions of microwaves with terrestrial snow, the effects are determined by volume scattering of dense media characterized by densely packed particles. In this paper, we review the electromagnetic full-wave simulations that we have conducted for such problems. In volume scattering problems, one needs many densely packed scatterers in a random medium sample to simulate the physical solutions. In random rough surface scattering problems, one needs many valleys and peaks in the sample surface. In random media and rough surface problems, the geometric characterizations of the media and computer generations of statistical samples of the media are also challenges besides electromagnetic computations. In the scattering of waves by soil surfaces, we consider the soil to be a lossy dielectric medium. The random rough surface is characterized by Gaussian random processes with exponential correlation functions. Surfaces of exponential correlation functions have fine-scale structures that cause significant radar backscattering in active microwave remote sensing. Fine-scale features also cause increase in emission in passive microwave remote sensing. We apply Monte Carlo simulations of solving full 3-D Maxwell's equations for such a problem. A hybrid UV/PBTG/SMCG method is developed to accelerate method of moment solutions. The results are illustrated for coherent waves and incoherent waves. We also illustrate bistatic scattering, backscattering, and emissivity which are signatures measured in microwave remote sensing. For the case of scattering by terrestrial snow, snow is a dense medium with densely packed ice grains. We have used two models: densely packed particles and bicontinuous media. For the case of densely packed particles, we used the Metropolis shuffling method to simulate the positions of particles. The particles are also allowed to have adhesive properties. The Foldy–Lax equations of multiple scattering are used to study scattering from the densely packed spherical particles. The results are illustrated for the coherent waves and incoherent waves. For the case of bicontinuous media, the method developed by Cahn is applied to construct the interfaces from a large number of stochastic sinusoidal waves with random phases and directions. The volume scattering problem is then solved by using CGS–FFT. We illustrate the results of frequency and polarization dependence of such dense media scattering.

The development of bi-continuous scattering model greatly enhanced the ability to model the snow scattering characteristics based on microstructure with most similarity to real snowpack. In this study, snow section images of snow microstructure were used to study the scattering characteristics of snow by using the reconstructed snow 3D microstructure. The equivalent grain size of the continuous random structure is derived by using stereological method. By combining with dense media radiative transfer equations, the snow backscattering is simulated. The polarimetric and frequency characteristics were studied.

A hybrid UV/PBTG/SMCG method is developed to accelerate the solution of NMM3D for 3-D electromagnetic wave scattering by random rough soil surfaces. It takes only 1.5 min using 16 processors on a cluster of NSF TeraGrid to compute 3-D solution of Maxwell equations of 8 by 8 square wavelengths. With the improved computational efficiency, we computed results using areas up to 32 by 32 square wavelengths. With the larger surface area, we were able to compute cases with larger rms heights up to 8 cm at SMAP radar frequency of 1.26 GHz that corresponds to kh = 2.28. New results computed include the cross-polarization. The five tests on the accuracy of results were performed: convergence with realizations, convergence with discrete samplings, convergence with sample surface sizes, energy conservation for each realization, and reciprocity for each realization. The numerical results show that for a single realization VH = HV within 0.5 dB in the backscattering direction showing that reciprocity is obeyed. Results were compared with experimental data, and both co-polarization and cross-polarization were in good agreements with experimental data.

A time-series algorithm is proposed to retrieve bare surface soil moisture and rms height using two copolarized (HH and VV) L-band backscattering coefficients (σ0). The retrieval approach inverts a forward model for radar scattering from an isotropic bare surface. Because real-time inversion of a complex forward model is often computationally impractical, the inversion is implemented using a precomputed lookup table representation of σ0obtained from numerical Maxwell model in 3-D simulations. The retrieval process assumes that surface roughness properties are constant during the time-series interval, so that only a single rms height estimate is produced for the entire time series. The use of this rms height estimate as a constraint simplifies the associated soil moisture retrievals at each time step. A Monte-Carlo simulation of this algorithm with 0.7 dB radar measurement error (1-sigma) shows that retrievals using six time steps outperform a “snapshot” method (which retrieves rms height and soil moisture at each time step) by a factor of about two in rms soil moisture error. A second study using measured data having 6 to 11 time steps shows an rms error of 0.044 cm3/cm3for soil moisture with a correlation coefficient of 0.89 between retrieved and in situ data. Surface rms height estimates are also found accurate to 10 to 30% of in situ measurements. It is also shown that retrieval performance is not sensitive to errors in knowledge of the surface roughness correlation length for most of the bare surface conditions examined.

Snow dunes on Greenland ice sheets are featured as Sastrugi surfaces, which have large heights at microwave remote sensing frequencies. They can also have large slopes. For this type of surfaces over multilayered snow structure, WindSat passive microwave polarimetric signatures have exhibited interesting polarimetric and angular signatures. In this paper, we study conical electromagnetic diffraction from Sastrugi surface that are modeled as ridged surfaces with random widths of the ridges. Then a surface integral equation with conical incident wave at a nonzero azimuthal angle is used to solve the surface fields. The surface integral equation is solved by method of moments (MoM). Because of the large rms heights of 7 wavelengths, there are more than 29,000 surface unknowns. Numerical results of the bistatic transmission coefficients from air to snow and from snow to air are studied. The effects of transmission beyond the critical angles are studied. The rough surface bistatic scattering properties are then incorporated in radiative transfer equations for 4 Stokes parameters of passive microwave wave remote sensing in layered snow, which is ready for the calculation of overall reflectivity and emissivity for 4 Stokes parameters.

A radar-based time-series algorithm is evaluated for retrieving soil moisture (from the surface down to 5 cm depth) and roughness using two co-polarized (HH and VV) backscatter cross-section measurements (σ0). The retrieval approach inverts a forward model for radar scattering from a bare surface using a pre-computed lookup-table representation of σ0obtained from Numerical Maxwell Model in 3D simulations. The retrieval process assumes that surface roughness properties are constant during the time series interval, so that only a single rms height estimate is produced for the entire time series. A study using measured data having 6 to 11 time-steps shows an rms error of 0.044 cm3/cm3for soil moisture with a correlation coefficient of 0.89 between retrieved and in-situ data. Surface rms height estimates are also found accurate to 10 to 30% of in-situ measurements. It is also shown that retrieval performance is not sensitive to errors in knowledge of the surface roughness correlation length for most of the bare surface conditions examined.

In this paper, we used NMM3D (Numerical Maxwell Model of 3 Dimensional simulations) to study the full wave 3 dimensional scattering of random soil surfaces. In 3D simulations, the height function z=f(x,y) of the rough surfaces vary in both two horizontal directions. Several hundreds of cases are simulated by varying incident angles, surface roughness and soil permittivities. The incident angles vary from 20° to 50°. The coherent/incoherent bistatic coefficients, backscattering coefficients, and emissivities are computed. The results are compared with empirical models and analytical methods. The backscattering coefficients are compared with measurement data and are found to be in good agreement. Based on the several hundreds of computed case, interpolation tables are made for the full range of parameters that can be directly applied to L band active and passive microwave remote sensing of soil moisture, such as the SMAP Mission and the SMOS Mission.

In this study, we develop a combined active/passive technique to estimate surface soil moisture with the focus on the short vegetated surfaces. We first simulated a database for both active and passive signals under SMAP's sensor configurations using the radiative transfer model with a wide range of conditions for surface soil moisture, roughness and vegetation properties that we considered as the random orientated disks and cylinders. Using this database, we developed 1) the techniques to estimate surface backscattering and emission components and 2) the technique to estimate soil moisture with the estimated surface backscattering and emission components. We will demonstrate these techniques with the model simulated data and its validation with the airborne PALS image data from the soil moisture SGP'99 and SMEX'02 experiments.

The Soil Moisture Active Passive (SMAP) mission is one of the first Earth observation satellites being developed by NASA in response to the National Research Council's Decadal Survey. SMAP will make global measurements of the soil moisture present at the Earth's land surface and will distinguish frozen from thawed land surfaces. Direct observations of soil moisture and freeze/thaw state from space will allow significantly improved estimates of water, energy, and carbon transfers between the land and the atmosphere. The accuracy of numerical models of the atmosphere used in weather prediction and climate projections are critically dependent on the correct characterization of these transfers. Soil moisture measurements are also directly applicable to flood assessment and drought monitoring. SMAP observations can help monitor these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing will also reduce a major uncertainty in quantifying the global carbon balance by helping to resolve an apparent missing carbon sink on land over the boreal latitudes. The SMAP mission concept will utilize L-band radar and radiometer instruments sharing a rotating 6-m mesh reflector antenna to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these observations with advanced modeling and data assimilation to provide deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP is scheduled for launch in the 2014-2015 time frame.

This special issue covers recent and future Earth observing satellites including the purpose of each mission, technology of the measurements, modeling of the physics and data, image and signal processing.

For electromagnetic (EM) scattering by dense media, the traditional approach is to use particles of spheres or ellipsoids that are densely and randomly packed in a background medium. The particles have discrete permittivities that are different from the background medium. The dense-medium model has been applied to the microwave remote sensing of terrestrial snow. In this paper, we propose a different approach of using a bicontinuous medium with discrete permittivities and study the EM scattering properties using analytical and numerical methods. The bicontinuous medium is a continuous representation of interfaces between inhomogeneities within the medium. Discrete permittivities are then assigned to the inhomogeneities of the structure. The analytical approach is based on the Born approximation using the derived analytical correlation functions. The numerical method is based on the numerical Maxwell model of 3-D (NMM3D) approach. In particular, the discrete-dipole approximation and the conjugate gradient-squared method accelerated by the fast Fourier transform technique are used in solving the volume integral equation. Scattering results of analytical and numerical approaches are compared. Numerical results are illustrated using parameters in microwave remote sensing of terrestrial snow. In the NMM3D simulations, three kinds of convergence tests are conducted, viz., convergence with respect to the discretization size, convergence with respect to the sample size, and convergence with respect to the number of realization. The NMM3D results indicate that the scattering by the bicontinuous medium with a broader size distribution has a weaker frequency dependence than that by the medium with a more narrow size distribution. The frequency-dependence power law index can be lower than two, which is very much lower than the power of four in Rayleigh scattering. The NMM3D results also exhibit fairly large cross-polarization returns which account for the local nonisotropic microstructures of bicontinuous media, although the medium is statistically isotropic.

We used Numerical Maxwell Model in 3-D Simulations (NMM3D) to study the backscattering coefficients, coherent reflectivities, and emissivities of soil surfaces using Gaussian random rough surfaces with exponential correlation functions. The surface area used is 8 by 8 square wavelengths. A total of close to 200 cases are computed by varying rms height, correlation length, and soil permittivity. We consider a 40° incidence angle. For each case, 15 realizations of rough surface profiles are generated, and 30 solutions of Maxwell equations are computed because of two polarizations. The method for solving the Maxwell equations is based on the Method of Moments (MoM) with Rao-Wilton-Glisson (RWG) basis functions. The solutions are accelerated by the sparse matrix canonical grid method implemented on parallel computing. The rms height varies up to 0.126 wavelength. The results are compared with the Dubois formulation, Small Perturbation Method (SPM), Kirchhoff Approximation (KA), and Advanced Integral Equation Model (AIEM). The NMM3D results are also compared with VV and HH backscatter data of soil surfaces where ground truth rms heights and correlation lengths were both measured. Good agreement is found between the NMM3D results and experimental measurement data. Based on the computed cases, interpolation tables are derived that can be directly applied to L-band active and passive microwave remote sensing of soil moisture, such as for the upcoming Soil Moisture Active and Passive (SMAP) mission.

In this paper, we study the electromagnetic scattering properties of 2-D rough surface with large slope and large height. The ridges on the surface have heights of about 20cm. In microwave remote sensing of land, these heights are larger than wavelength. By using a tapered incident wave, the surface fields are solved by using numerical solution of Maxwell equations. Method of Moment (MOM) is used to solve the surface integral equations and rooftop basis function and Galerkin's method are used. The bistatic reflection and transmission are then calculated from the surface fields. Then the reflectivity from sastrugi over layered snow is calculated by solving multilayer radiative transfer (RT) equation with bistatic reflection and transmission coefficients as the boundary condition. We compare the electromagnetic scattering properties between Sastrugi rough surface and smooth surface. We show in this paper that for the sastrugi case, transmission angle can be larger than incident angle when incident from air to snow. This results in total internal reflection when the second layer of snow beneath sastrugi has a smaller permissivity and larger reflectivity than smooth surface.

In this paper, we considered a physical-based model which use numerical solution of Maxwell Equations in three-dimensional simulations and apply into Dense Media Radiative Theory (DMRT). The model is validated in two specific dataset from the second Cold Land Processes Experiment (CLPX II) at Alaska and Colorado. The data were all obtain by the Ku-band (13.95 GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). Snow is a densely packed media. To take into account the collective scattering and incoherent scattering, analytical Quasi-Crystalline Approximation (QCA) and Numerical Maxwell Equation Method of 3-D simulation (NMM3D) are used to calculate the extinction coefficient and phase matrix. DMRT equations were solved by iterative solution up to 2ndorder for the case of small optical thickness and full multiple scattering solution by decomposing the diffuse intensities into Fourier series was used when optical thickness exceed unity. It was shown that the model predictions agree with the field experiment not only co-polarization but also cross-polarization. For Alaska region, the input snow structure data was obtain by the in situ ground observations, while for Colorado region, we combined the VIC model to get the snow profile.

In this paper, we model the backscattering coefficients of multi-layer dry snowpacks, based on Dense Media Radiative Transfer theory (DMRT) with the Quasicrystalline Approximation (QCA). The DMRT model accounts for adhesive aggregate effects, which leads to dense media Mie scattering by using a Sticky particle model. The same set of DMRT equations are used for modeling both active and passive remote sensing. The model is validated by using the Cold-Land Processes Field Experiment CLPX ground based polarimetric scatterometry observation at local-scale observation site (LSOS) and airborne polarimetric Ku-band scatterometer (POLSCAT) data at Fool-Creek, Fraser. The snow density profiles are from ground observation and grain sizes are fitting parameters. It shows that the co-polarization simulations are in good agreement with the data, the cross-polarization simulations are around 2 dB lower than ground based observation and 5 dB lower than airborne observation. With the same set of multi-layer snowpack profile, the QCA/DMRT model matched co-polarization backscattering coefficients and all 4 channels of brightness temperature observations simultaneously at LSOS. The cross-polarization simulation can be improved by 3-dimensional numerical solutions of Maxwell equations (NMM3D). Study at Fool-Creek shows that NMM3D/DMRT simulations can match both co-polarization and cross-polarization observations simultaneously.

In this paper, we report on the polarimetric active and passive microwave remote signatures for exponential correlation function surfaces. Applications are in soil moisture problems at the frequencies L, C and X band. We use the same physical parameters of rms heights and correlation lengths at the three frequencies. Results for 2D case with rms height up to 2 wavelengths at X band are shown. The hybrid UV-SMCG method for RWG basis is also used to accelerate MoM solution. Comparisons are made with SPM, KA and AIEM predictions. We also compare backscattering between horizontal and vertical polarization cases at different rms heights with exponential correlation. At small rms height, the backscattering for vertical polarization case is larger than that for horizontal polarization case. On the other hand, at large rms height, the backscattering for horizontal polarization case is larger.

Rough surface scattering effects are important problem for solving emission in microwave remote sensing. Stochastically the surface length should be infinite to simulate random rough surface scattering which is possible for analytical method but not for numerical method. Generally there are two approximations to simulate real life: the tapered wave method and periodic boundary condition. Both are valid for random rough surface scattering if convergence is shown with increase of surface length for the tapered wave and if the period is large enough for periodic boundary condition. In this paper we compare the results for the four Stokes parameters between periodic boundary conditions and the tapered wave approach.

A model for the microwave emissions of multilayer dry snowpacks, based on dense media radiative transfer (DMRT) theory with the quasicrystalline approximation (QCA), provides more accurate results when compared to emissions determined by a homogeneous snowpack and other scattering models. The DMRT model accounts for adhesive aggregate effects, which leads to dense media Mie scattering by using a sticky particle model. With the multilayer model, we examined both the frequency and polarization dependence of brightness temperatures (Tb's) from representative snowpacks and compared them to results from a single-layer model and found that the multilayer model predicts higher polarization differences, twice as much, and weaker frequency dependence. We also studied the temporal evolution of Tb from multilayer snowpacks. The difference between Tb's at 18.7 and 36.5 GHz can be 5 K lower than the single-layer model prediction in this paper. By using the snowpack observations from the Cold Land Processes Field Experiment as input for both multi- and single-layer models, it shows that the multilayer Tb's are in better agreement with the data than the single-layer model. With one set of physical parameters, the multilayer QCA/DMRT model matched all four channels of Tb observations simultaneously, whereas the single-layer model could only reproduce vertically polarized Tb's. Also, the polarization difference and frequency dependence were accurately matched by the multilayer model using the same set of physical parameters. Hence, algorithms for the retrieval of snowpack depth or water equivalent should be based on multilayer scattering models to achieve greater accuracy.

The Dense Media Radiative Transfer theory (DMRT) of Quasicrystalline Approximation of Mie scattering by sticky particles is used to study the multiple scattering effects in layered snow in microwave remote sensing. Results are illustrated for various snow profile characteristics. Polarization differences and frequency dependences of multilayer snow model are significantly different from that of the single-layer snow model. Comparisons are also made with CLPX data using snow parameters as given by the VIC model.

In microwave remote sensing of land surfaces, the surfaces with exponential correlation functions have become a common choice in recent years. The use of Gaussian correlation function is not appropriate for land surfaces because the computed backscattering coefficients are many decibels below that of measurements. However, the numerical simulations of Maxwell equations were performed using Gaussian correlation functions. In the past, regimes of validity were established for analytic methods using numerical 2-D simulations. However, these past efforts of numerical tests to establish regimes of validity were for Gaussian correlation functions. The conclusions of these past numerical tests are not valid for exponential correlation functions. In this paper, we report on the polarimetric active and passive microwave remote signatures for exponential correlation function surfaces. Comparisons are made with analytic theory such as small perturbation method (SPM), Kirchhoff approximation (KA) and Advanced Integral Equation Model (AIEM). We particularly emphasize on the case of moderate rms heights of the order of 1 wavelength. This is particularly important for X band scattering from land surfaces. Numerical results are illustrated for bistatic scattering and emissivities as functions of frequencies, incidence and scattering angles and polarization for cases of interests in microwave remote sensing. We also compare backscattering between horizontal and vertical polarization cases at different rms heights with exponential correlation function. At small rms height or small slope, the backscattering for vertical polarization case is larger than that for horizontal polarization case. On the other hand, at large rms height or large slope, the backscattering for horizontal polarization case is larger.

The rough surfaces in Greenland are exhibited as sastrugi. The roughness heights are less than 8 cm for much of the year except in late winter and spring, when they increase to 25 cm or less. Roughness profiles were also related to snow and firn ventilation. WindSat, launched in January 2003, was the first spaceborne polarimetric radiometer to measure all 4 elements of Stokes vector, viz., the vertical polarized brightness temperatures, the horizontal polarized brightness temperatures, and the real and imaginary part of the cross-correlations of the vertical and horizontal polarizations. It was shown by Tsang (1984, 1990) that azimuthal asymmetry will create nonzero third and fourth Stokes parameter in passive microwave remote sensing. Thus the third and fourth Stokes parameters contain information of the azimuthal structure. Usually the third and fourth Stokes parameters are quite small between 0.5 K to 1 K over land and less than plusmn2.5 K over ocean. However, measurements of third and Stokes parameters over Greenland show surprising values of 10 K for the third Stokes parameter and between -10 K and 20 K for the fourth Stokes parameter. In this paper, we use physically based electromagnetic model to study the passive polarimetric remote sensing of snow in Greenland by consider the scattering and emission from a random rough surface over multi-layered media. We consider the random rough surface varied in only one horizontal direction so that azimuthal asymmetry exists in the 3-D problem. Dyadic Green's functions of multilayered medium (Tsang et al., 2000) is used to formulate the surface integral equation so that the polarization dependence of emission and scattering is accounted for systematically. The surface integral equations are solved by using the method of moments in conjunction with fast numerical algorithms such as the multilevel UV method. Numerical results of brightness temperatures are illustrated for all four Stokes parameters to demonstrate the signatures of sastrugi in passive microwave remote sensing. To account for the large third and fourth Stokes parameters, we also consider the case of anisotropic scatterers in volume scattering. Full multiple volume scattering are studied with numerical solutions of the radiative transfer equations for non-spherical scatterers with preferred orientation.

Dense media radiative transfer (DMRT) theory is used to study the multiple-scattering effects in active microwave remote sensing. Simplified DMRT phase matrices are obtained in the 1-2 frame. The simplified expressions facilitate solutions of the DMRT equations and comparisons with other phase matrices. First-order, second-order, and full multiple-scattering solutions of the DMRT equations are obtained. To solve the DMRT equation, we decompose the diffuse intensities into Fourier series in the azimuthal direction. Each harmonic is solved by the eigen-quadrature approach. The model is applied to the active microwave remote sensing of terrestrial snow. Full multiple-scattering effects are important as the optical thickness for snow at frequencies above 10 GHz often exceed unity. The results are illustrated as a function of frequency, incidence angle, and snow depth. The results show that cross polarization for the case of densely packed spheres can be significant and can be merely 6 to 8 dB below copolarization. The magnitudes of the cross polarization are consistent with the experimental observations. The results show that the active 13.5-GHz backscattering coefficients still have significant sensitivity to snow thickness even for snow thickness exceeding 1 m

Bistatic scattering and emissivities of surfaces with exponential correlation functions are studied numerically for 2-D geometries in a numerical Maxwell model with 2-D simulations. Surfaces with exponential correlation functions are important for the active and passive microwave remote sensing of land surfaces. Because of the fine-scale features with large slopes of such surfaces, numerical accuracy, which is particularly important for the calculation of emissivity in passive remote sensing, is ensured by a variety of procedures in this paper. The rooftop function and Galerkin's method with numerical integration of near-field impedance matrix elements are used. Cubic spline interpolation is employed to connect knots on random rough surfaces. Numerical accuracy convergence tests are performed for numerical solutions of Maxwell equations by varying the number of points from 13 to 103 points per wavelength in the dielectric medium corresponding to 50-400 points per free wavelength. Surface lengths of up to 100 and 200 free wavelengths and root mean square heights of up to 0.4 and 0.8 free wavelengths, respectively, are used at 5 and 10 GHz to capture all the essential features. Because of the large number of surface unknowns (up to 80 000), the multilevel UV method is further used to accelerate the matrix equation solver. Numerical results are illustrated for both bistatic scattering and emissivities as functions of frequencies and incidence and scattering angles for cases of interests in microwave remote sensing. Comparisons are made with the second-order small perturbation method and Kirchhoff's approximation to reestablish the regimes of validity of these methods

Dense media radiative transfer theory (DMRT) is used to study the multiple scattering effects in active microwave remote sensing. To solve the dense media radiative transfer equation, we decompose the diffuse intensities into Fourier series in the azimuthal direction. Each harmonic is solved by the eigen-quadrature approach. The solution includes full multiple scattering effects within DMRT. Comparisons are made with the first order and the second order solutions. The model is applied to active microwave remote sensing of terrestrial snow. Full multiple scattering effects are important as the optical thickness for snow often exceed unity. The results are illustrated as a function of frequency, incidence angle and snow depth. The results show that cross polarization can be significant and can be only 6 to 8 dB below co-polarization, a result that is consistent with experimental observations. Also we note that even at snow depth of more than one meter, the active 13.5 GHz backscattering coefficients still have significant sensitivity to snow thickness.

This paper proposes improvements in the row and column samplings of the multilevel QR factorization method known as IES/sup 3/, a fast integral equation solver previously proposed for efficient three-dimensional (3-D) parameter extraction. First, a rigorous Gram-Schmidt row sampling is developed to replace the row sampling algorithm in IES/sup 3/, leading to a more stable algorithm. Second, to further enhance the efficiency of column sampling, a new scheme based on the idea of locating the interpolation points is presented. Error analyses indicate that the proposed schemes have higher accuracies than the original sampling in IES/sup 3/, especially when the number of sampled points is small. The IES/sup 3/ that uses one of these improved algorithms is called improved multilevel matrix QR factorization (IMLMQRF). These IMLMQRFs are applied in the magnetoquasistatic analysis of printed circuits on multilayered lossy medium for extractions of inductances and resistances. The frequency dependency of such parameters is also illustrated.

A microwave model for remote sensing of snow based on dense media radiative transfer theory with random rough surface boundary conditions is developed. Both volume scattering and rough surface scattering effects are treated by numerical Maxwell model of 3D simulations (NMM3D). Detailedly, the volume scattering model is based on dense media radiative transfer (DMRT) theory by using Monte Carlo (MC) simulations of the three-dimensional solutions of Maxwell's equations for densely distributed sticky particles. The rough surface scattering is modeled by the numerical Maxwell model of 3D simulations (NMM3D), which is accelerated by sparse matrix canonical grid method (SMCG). The bistatic scattering coefficients and emissivity of rough surfaces are utilized as the boundary conditions for the DMRT. Full multiple scattering solutions are calculated by solving the DMRT numerically. The results for a layer of dry snow over a rough ground at 18.7 GHz and 38.5GHz are illustrated.

In this paper, a new multilevel Green's function interpolation method (MLGFIM) is presented to solve integral equations for large-scale electrostatic problems. In MLGFIM, the problem domain is first divided into multilevel cubes. Next, the peer-level Green's function interpolation technique is employed, and then, a new lower-to-upper-level Green's function interpolation technique is devised. They are used with the multilevel discretization to speed up the matrix-vector multiplications in the iterative solution in which a computational complexity of O(N) is achieved. The MLGFIM is used to extract the capacitances encountered in radio frequency integrated circuits (RFICs) and microelectromechanical systems. Moreover, to demonstrate its efficiency both in simulation speed and memory storage requirement, MLGFIM is compared with FastCap for free space problems and applied to extract capacitances from multilayered structures. For problems with 375,000 unknowns, the proposed method only requires 343 MB of computer memory.

The microwave signatures of a layer of dry snow overlying ground with a rough surface are computed. We use dense medium radiative transfer (DMRT) theory with Quasicrystalline approximation (QCA) for densely distributed sticky moderate size particles to calculate the volume scattering in snow. The rough surface scattering and emission are modeled by the Numerical Maxwell Model of 3D simulations (NMM3D), which is accelerated by fast computation method known as with Sparse-Matrix Canonical Grid method (SMCG). The bistatic scattering coefficients of rough surfaces are used as the boundary conditions for the DMRT. Both active and passive cases are studied.

A UV multilevel partitioning method (UV-MLP) is developed to solve wave scattering by rough surfaces. The method consists of setting up a rank table of transmitting and receiving block size and their separation using fast coarse-coarse sampling. For a specific scattering problem with given geometry, the scattering structure is partitioned into multilevel blocks. By looking up the rank, the impedance matrix for a given transmitting and receiving block is expressed into a product of U and V matrix. In this paper we demonstrate the technique for three cases: a 2D scattering with random rough surface, a 3D scattering problem of random rough surface, and a 2D volume scattering by discrete scatterers. The technique can be applied to the lower order Green's function as well as Green function of higher order partial wave

In the numerical Maxwell-equation model (NMM3D) of rough-surface scattering, we solve Maxwell equations in three dimensions to calculate emissivities for applications in passive microwave remote sensing of soil and ocean surfaces. The difficult cases for soil surfaces are with exponential correlation functions when the surfaces have fine-scale structures of large slopes. The difficulty for ocean surfaces is that because the emissivities are close to that of a flat surface, the emissivities have to be calculated accurately to correctly assess the rough-surface effects. In this paper, the accuracies of emissivity calculations are improved by using Rao-Wilton-Glisson basis functions. We further use sparse matrix canonical method to solve the matrix equation of Poggio-Miller-Chang-Harrington-Wu integral equations. Energy conservation checks are provided for the simulations. Comparisons are made with results from the pulse basis function. Numerical results are illustrated for soil and ocean surfaces respectively with exponential correlation function and ocean spectrum. The emissivities of soil are illustrated at both L- and C-bands and at multiple incidence angles for the same physical roughness parameters. The brightness temperatures for ocean surfaces are illustrated for cases with various wind speeds. We compare results with those from the sparse matrix methods. Comparisons are also made with experimental emissivity measurements of soil surfaces. Parallel computation is also implemented. Lookup tables of emissivities based on NMM3D are provided.

The foam covered ocean surface is treated as densely packed air bubbles coated with thin layers of seawater. Two geometric structures are considered. The first is spherical air bubbles in FCC structure. The second one is Lord Kelvin's tetrakaidecahedron with close to minimal contact surface area. We apply Monte Carlo simulations of solutions of Maxwell's equations to calculate the absorption, scattering and extinction coefficients of each layer at 10.8 GHz and 36.5 GHz. These quantities are then used in dense media radiative transfer theory to calculate the microwave emissivity. Results of emissivities for both horizontal polarization and vertical polarizations at 10.8 GHz and 36.5 GHz are illustrated.

The backscattering coefficients of wet soil surface are studied with the 3-dimensional numerical simulations of Maxwell equations. To improve the accuracy of the simulations, we have recently used the RWG basis functions. Using the simulation results, we study the angular, frequency, and polarimetric dependence of the scattering from different rough surface spectra. The simulation results are compared with the backscattering coefficients at L and C frequency bands and at the multi-incidence angles. The fairly good agreements are observed for the fixed physical surface roughness parameters at two frequency bands.

The snow medium is treated as densely packed sticky ice particles following a size distribution. We apply the quasicrystalline approximation (QCA) dense medium theory to calculate the absorption, scattering and emission of snow at multiple frequencies. The correlation of particle position is taken into account by using the Percus-Yevick approximation that can accommodate particles of multiple sizes. The size distribution is discretized so it can be applied to the Percus-Yevick approximation for the cross pair distribution function of particles with different sizes.

The frequency dependence of scattering by geophysical media at microwave frequencies is an important topic because multifrequency measurements are used in remote sensing applications. In this paper, we study rigorously the frequency dependence of scattering by dense media using Monte Carlo simulations of the three-dimensional solutions of Maxwell's equations. The particle positions are generated by deposition and bonding techniques. The extinction, scattering, and absorption properties of dense media are calculated for dense media of sticky and nonsticky particles. Numerical solutions of Maxwell's equations indicate that the frequency dependence of densely packed sticky small particles are much weaker than that of independent scattering. Numerical results are illustrated using parameters of snow in microwave remote sensing. Comparisons are made with extinction measurements as a function of frequency.

The foam-covered ocean surface is treated as densely packed air bubbles coated with thin layers of seawater. We apply Monte Carlo simulations of solutions of Maxwell's equations to calculate the absorption, scattering, and extinction coefficients at 10.8 and 36.5 GHz. These quantities are then used in dense-media radiative transfer theory to calculate the microwave emissivity. Numerical results of the model are illustrated as a function of foam parameters. Results of emissivities for both horizontal polarization and vertical polarizations at 10.8 and 36.5 GHz are compared with experimental measurements.

This paper presents a model of microwave emissions from rough surfaces. We derive a more complete expression of the single-scattering terms in the integral equation method (IEM) surface scattering model. The complementary components for the scattered fields are rederived, based on the removal of a simplifying assumption in the spectral representation of Green's function. In addition, new but compact expressions for the complementary field coefficients can be obtained after quite lengthy mathematical manipulations. Three-dimensional Monte Carlo simulations of surface emission from Gaussian rough surfaces were used to examine the validity of the model. The results based on the new version (advanced IEM) indicate that significant improvements for emissivity prediction may be obtained for a wide range of roughness scales, in particular in the intermediate roughness regions. It is also shown that the original IEM produces larger errors that lead to tens of Kelvins in brightness temperature, which are unacceptable for passive remote sensing.

This paper presents an algorithm that estimates the spatial distribution and temporal evolution of snow water equivalent and snow depth based on passive remote sensing measurements. It combines the inversion of passive microwave remote sensing measurements via dense media radiative transfer modeling results with snow accumulation and melt model predictions to yield improved estimates of snow depth and snow water equivalent, at a pixel resolution of 5 arc-min. In the inversion, snow grain size evolution is constrained based on pattern matching by using the local snow temperature history. This algorithm is applied to produce spatial snow maps of Upper Rio Grande River basin in Colorado. The simulation results are compared with that of the snow accumulation and melt model and a linear regression method. The quantitative comparison with the ground truth measurements from four Snowpack Telemetry (SNOTEL) sites in the basin shows that this algorithm is able to improve the estimation of snow parameters.

A methodologically simple approach to estimate snow depth from spaceborne microwave instruments is described. The scattering signal observed in multifrequency passive microwave data is used to detect snow cover. Wet snow, frozen ground, precipitation, and other anomalous scattering signals are screened using established methods. The results from two different approaches (a simple time and continentwide static approach and a space and time dynamic approach) to estimating snow depth were compared. The static approach, based on radiative transfer calculations, assumes a temporally constant grain size and density. The dynamic approach assumes that snowpack properties are spatially and temporally dynamic and requires two simple empirical models of density and snowpack grain radius evolution, plus a dense media radiative transfer model based on the quasicrystalline approximation and sticky particle theory. To test the approaches, a four-year record of daily snow depth measurements at 71 meteorological stations plus passive microwave data from the Special Sensor Microwave Imager, land cover data and a digital elevation model were used. In addition, testing was performed for a global dataset of over 1000 World Meteorological Organization meteorological stations recording snow depth during the 2000-2001 winter season. When compared with the snow depth data, the new algorithm had an average error of 23 cm for the one-year dataset and 21 cm for the four-year dataset (131% and 94% relative error, respectively). More importantly, the dynamic algorithm tended to underestimate the snow depth less than the static algorithm. This approach will be developed further and implemented for use with the Advanced Microwave Scanning Radiometer-Earth Observing System aboard Aqua.

The frequency dependence of scattering by geophysical media at microwave frequencies is an important issue because multi-frequency measurements are useful for remote sensing applications. Classically, the independent scattering theory states that if the particles are small, scattering is proportional to the fourth power in 3-D scattering and the third power in 2-D scattering. In this paper, we study rigorously the frequency dependence of scattering by dense media by Monte Carlo simulations of the solutions of both 2- and 3-dimensional Maxwell's equations. The particle positions are generated by deposition and bonding techniques. The sparse-matrix canonical-grid method has been applied to speed up the simulation of scattering by 2D small particles. Numerical solutions of Maxwell's equations indicate that the frequency dependence of densely packed sticky small particles is much weaker than that of independent scattering. The results are illustrated using parameters of snow in microwave remote sensing.

This paper presents an algorithm that estimates the spatial distribution as well as temporal evolution of snow water equivalent and snow depth based on passive remote sensing measurements. It combines the inversion of passive microwave remote sensing measurements with snow accumulation and melt model predictions to yield improved estimates of snow depth and snow water equivalent, at a pixel resolution of 10 km. In the inversion, snow grain size evolution is constrained based on pattern matching by using the local snow temperature history. This algorithm is applied to produce spatial snow map of Upper Rio Grande basin in Colorado. The simulation result of this algorithm is compared with that of snow hydrology model and linear regression method. The comparison with the ground truth measurements from 4 SNOwpack TELemetry (SNOTEL) sites in the basin shows that this algorithm is able to improve the estimates of snow depth and snow water equivalent.

For accurate estimation of global snow depth or snow water equivalent on the Earth's surface using passive microwave instruments, knowledge of the snow pack's physical properties is important. It is known that the bulk snow grain size distribution exerts an important control over the microwave response from snow between 3 mm and 300 mm wavelengths. In the absence of high quality snowpack data at a global scale, we show how the grain size distribution can be estimated using a general empirical model of grain growth. This information is used to parameterize a dense media radiative transfer model (DMRT) to estimate the radiometric response from a snow pack as a function of changing grain size distribution. The DMRT equations are based on the quasi-crystalline approximation (QCA) for densely distributed moderate sized particles in a medium such as a snow pack. The model snow depth estimates from the DMRT are used to calibrate a Special Sensor Microwave Imager (SSM/I) snow depth retrieval algorithm which is based on the brightness temperature difference between 19 and 37 GHz with the SWE. The method is tested using meteorological data from the WMO global network. Results show that using the DMRT model coupled with a grain size model improved estimates of snow depth are obtained.

In this paper, polarimetric microwave emissions from wind-generated foam-covered ocean surfaces are investigated. A dense media radiative transfer model (DMRT) is applied to the foam layer. The effects of boundary roughness are implemented by using the small perturbation method (SPM) describing the bistatic reflection coefficients between foam and ocean. An empirical wavenumber spectrum is used to generate the small-scale wind-generated sea surfaces. The iterative method is employed to solve DMRT equations. The method was applied to simulate results of all four Stokes parameters for 2-dimensional random rough surfaces. The theoretical results of four Stokes brightness temperatures with typical parameters of foam in passive remote sensing at 19 GHz and 37 GHz are illustrated. It is found that, at both frequencies, the first two Stokes parameters are increased with the presence of foam, and the third and fourth parameters, on the contrary, are reduced. The contribution of the foam layer to emission is larger at 37 GHz than at 19 GHz. The azimuth variations of polarimetric brightness temperature are calculated. Emission with various wind speed and foam layer thickness is also studied. Results are compared with the experimental measurements.

The frequency dependence of extinction and scattering by geophysical medium at microwave frequencies is an important scattering topic because multifrequency measurements are used in remote sensing applications. Classical independent scattering theory states that if the particles are small, scattering is proportional to the fourth power in three-dimensional (3D) scattering and the third power in two-dimensional (2D) scattering. In this paper, the authors present Monte Carlo simulation results of dense media scattering. The dense media consists of densely packed small particles. Solutions are based on rigorous methods of generating dense media and subsequent numerical solutions of Maxwell's equation. Numerical simulations indicate that the frequency dependence of densely packed sticky particles is weaker than independent scattering.

Microwave emission of ocean surfaces with full spatial spectrum is studied in this paper. For ocean surfaces with full spectrum, the rms height of roughness can be many wavelengths, and the surface size must be chosen to be larger than the longest scale wave in the spectrum. Due to computer resources, it is not straightforward to conduct numerical simulations of emission from rough surfaces with large rms height and size since a large number of unknowns will be involved. In this paper, the multilevel expansion of the sparse matrix canonical grid (SMCG) method, which is available for surfaces with large rms heights, is used to study the emission of one-dimensional (1-D) ocean surfaces. The computational complexity and the memory requirement are still on the order of O(N log (N)) and O (N), respectively, as in the SMCG method. Ocean surfaces with size 1024 wavelengths (21.9 m at 14 GHz) and spatial spectrum bandwidth between 0.858 rads/m (corresponding to the longest scale of 341.3 wavelengths) and 4691.5 rads/m (corresponding to the shortest scale of 1/16 wavelengths), which is rather wide to be regarded as a full spectrum, are studied. The maximum of the electromagnetic wavenumber-surface rms height product is up to 25.18. The surface is modeled as a lossy dielectric surface with large relative permittivity rather than as a perfectly conducting surface, which is often adopted as an approximation in the active remote sensing of ocean surfaces. A relatively high sampling density is used to ensure accuracy. The effects of the low and high portions of the spectrum on the emissivity are studied numerically. Monte Carlo simulation for ocean surfaces is also performed by exploiting the efficiency of the multilevel expansion method and the use of parallel computing techniques. The convergence of the results with respect to the sampling density is also illustrated.

Soil moisture is an important parameter for hydrological and climatic investigations. Future satellite missions with L-band passive microwave radiometers will significantly increase the capability of monitoring Earth's soil moisture globally. Understanding the effects of surface roughness on microwave emission and developing quantitative bare-surface soil moisture retrieval algorithms is one of the essential components in many applications of geophysical properties in the complex Earth terrain by microwave remote sensing. We explore the use of the integral equation model (IEM) for modeling microwave emission. This model was validated using a three-dimensional Monte Carlo model. The results indicate that the IEM model can be used to simulate the surface emission quite well for a wide range of surface roughness conditions with high confidence. Several important characteristics of the effects of surface roughness on radiometer emission signals at L-band 1.4 GHz that have not been adequately addressed in the current semiempirical surface effective reflectivity models are demonstrated by using IEM-simulated data. Using an IEM-simulated database for a wide range of surface soil moisture and roughness properties, we developed a parameterized surface effective reflectivity model with three typically used correlation functions and an inversion model that puts different weights on the polarization measurements to minimize surface roughness effects and to estimate the surface dielectric properties directly from dual-polarization measurements. The inversion technique was validated with four years (1979-1982) of ground microwave radiometer experiment data over several bare-surface test sites at Beltsville, Maryland. The accuracies in random-mean-square error are within or about 3% for incidence angles from 20/spl deg/ to 50/spl deg/.

This paper describes a snow parameter retrieval algorithm from passive microwave remote sensing measurements. The three components of the retrieval algorithm include a dense media radiative transfer (DMRT) model, which is based on the quasicrystalline approximation (QCA) with the sticky particle assumption, a physically-based snow hydrology model (SHM) that incorporates meteorological and topographical data, and a neural network (NN) for computational efficient inversions. The DMRT model relates physical snow parameters to brightness temperatures. The SHM simulates the mass and heat balance and provides initial guesses for the neural network. The NN is used to speed up the inversion of parameters. The retrieval algorithm can provide speedy parameter retrievals for desired temporal and spatial resolutions, Four channels of brightness temperature measurements: 19V, 19H, 37V, and 37H are used. The algorithm was applied to stations in the northern hemisphere. Two sets of results are shown. For these cases, the authors use ground-truth precipitation data, and estimates of snow water equivalent (SWE) from SHM give good results. For the second set, a weather forecast model is used to provide precipitation inputs for SHM. Additional constraints in grain size and density are used. They show that inversion results compare favorably with ground truth observations.

The effect of the foam covered ocean surface on the passive microwave remote sensing measurements is studied based on the electromagnetic scattering theory. In formulating an electromagnetic scattering model, the authors treat the foam as densely packed sticky air bubbles coated with thin seawater coating. The layer of foam covers the ocean surface that has air bubbles. They then use dense media radiative transfer (DMRT) theory with quasi-crystalline approximation (QCA) for densely distributed sticky moderate size particles to calculate the brightness temperatures of the foam-covered ocean surface. Results are illustrated for 19 GHz and 37 GHz and for both vertical and horizontal polarizations as a function of foam microstructure properties and foam layer thickness. Comparisons are also made with experimental measurements.

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed.

Numerical simulation of passive microwave remote sensing of ocean surfaces has a strict requirement of accuracy. This is because the key output of the simulations is the difference of brightness temperature between a rough surface and a flat surface. Since the difference can be as small as 0.5 K, it is important to simulate the scattering and emission accurately. The authors perform accurate simulations of transverse electric (TE) and transverse magnetic (TM) waves for ocean surfaces with relative permittivity=28.9541/spl plusmn/i36.8430 at 19 GHz. Because ocean permittivity is large, the authors used up to 80 points per free space wavelength. Furthermore, accurate numerical integration is also performed to obtain accurate impedance matrix elements. To ensure accuracy, a matrix equation obtained from the surface integral equation formulation is solved by matrix inversion. Conservation of energy is required to be accurate to a relative error of 0.001, which corresponds to 0.3 K in brightness temperature. Numerical results are illustrated for rough surfaces with Gaussian spectrum and bandlimited ocean spectrum and bandlimited fractal surfaces. The authors show convergence with respect to the density of sampling points and with respect to raising the upper limit of the bandlimited ocean spectrum. Comparisons are also made with results with an impedance boundary condition approximation. Numerical results indicate that fine discretization is required for ocean-like surfaces with fine scale roughness.

Wave scattering from two-dimensional (2-D) random rough surfaces [three-dimensional (3-D) scattering problem] has been previously analyzed using the sparse-matrix/canonical grid (SM/CG) method. The computational complexity and memory requirement of the SM/CG method are O(N log N) per iteration and O(N), respectively, where N is the number of surface unknowns. Furthermore, the SM/CG method is FFT based, which facilitates the implementation on parallel processors. In this paper, we present a cost-effective solution by implementing the SM/CG method on a Beowulf system consisting of PCs (processors) connected by a 100 Base TX Ethernet switch. The workloads of computing the sparse-matrix-vector multiplication corresponding to the near interactions and the fast Fourier transform (FFT) operations corresponding to the far interactions in the SM/CG method can be easily distributed among all the processors. Both perfectly conducting and lossy dielectric surfaces of Gaussian spectrum and ocean spectrum are analyzed thereafter. When possible, speedup factors against a single processor are given. It is shown that the SM/CG method for a single realization of rough surface scattering can be efficiently adapted for parallel implementation. The largest number of surface unknowns solved in this paper is over 1.5 million. On the other hand, a problem of 131072 surface unknowns for a PEC random rough surface of 1024 square wavelengths only requires a CPU time of less than 20 min. We demonstrate that analysis of a large-scale 2-D random rough surface feasible for a single realization and for one incident angle is possible using the low-cost Beowulf system.

The simulations of emissivities from a two-dimensional (2D) wet soil with random rough surfaces are studied with numerical solutions of three-dimensional (3D) Maxwell equations. The wet soils have large permittivity. For media with large permittivities, the surface fields can have large spatial variations on the surface. Thus, a dense discretization of the surface is required to implement the method of moment (MoM) for the surface integral equations. Such a dense discretization is also required to ensure that the emissivity can be calculated to the required accuracy of 0.01 for passive remote sensing applications. It has been shown that the physics-based two-grid method (PBTG) can efficiently compute the accurate surface fields on the dense grid. In this paper, the numerical results are calculated by using the PBTG in conjunction with the sparse-matrix canonical grid method (SMCG). The emissivities are illustrated for random rough surfaces with Gaussian spectrum for different soil moisture conditions. The results are calculated for L- and C-bands using the same physical roughness parameters. The numerical solutions of Maxwell's equations are also compared with the popular H and Q empirical model.

A numerical model for polarimetric thermal emission from penetrable ocean surfaces rough in two directions is presented. The numerical model is based on Monte Carlo simulation with an iterative version of the method of moments (MOM) known as the sparse matrix flat surface iterative approach (SMFSIA), extended to the penetrable surface case through a numerical impedance boundary condition (NIBC) method. Since the small U/sub B/ brightnesses obtained from ocean surfaces (usually less than 1.5 K, or 0.5% of a 300-K physical temperature) require extremely accurate simulations to avoid large errors, a parallel version of the algorithm is developed to allow matrix elements to be integrated accurately and stored. The high accuracy required also limits simulations to near flat surface profiles, so that only high-frequency components of the ocean spectrum are modeled. Variations in nadir polarimetric brightness temperatures with spectrum low- and high-frequency cutoffs show the Bragg (or shortwave) portion of the spectrum to contribute significantly to emission azimuthal signatures, as predicted by the small perturbation or composite surface approximate theories. Quantitative comparisons with approximate methods show perturbation theory to slightly overestimate linear brightness temperatures, but accurately predict their azimuthal variations, while physical optics (PO) significantly underestimates both linear brightness temperatures and their azimuthal variations. Further simulations with the numerical model allow sensitivities to ocean spectrum models to be investigated and demonstrate the importance of an accurate azimuthal description for the ocean spectrum.

Recently, a fast computational technique based on the banded-matrix iterative approach/canonical grid (BMIA/CG) method has been developed for the analysis of random rough surfaces. However, there are situations that the matrix-vector multiplication associated with strong near-field interactions may dominate the CPU and memory storage requirement. In this paper, the wavelet transform method in conjunction with a screening window scheme is used to address these problems. It is noted that the wavelet-transformed matrix for each submatrix is implemented only once for different incident polarizations. Based on the idea of multiresolution analysis, the matrix-vector multiplication in an iterative solver is then efficiently evaluated for its higher sparsity. Numerical simulations are then used to study scattering and emission from the lossy dielectric random rough surfaces. All the four Stokes parameters are calculated in this paper.

An algorithm to incorporate passive microwave remote-sensing measurements within a spatially distributed snow hydrology model to provide estimates of the spatial distribution of snow water equivalent (SWE) as a function of time is implemented. A priori information provided by the snow hydrology model is used to provide initial estimates of snow parameters from brightness temperature measurements. The algorithm is illustrated by applying it to a mountainous region. The passive microwave remote-sensing measurements are 25-km resolution (grid). However, in mountain regions, the spatial variability of SWE over a 25-km grid is large due to topographic influences. On the other hand, the snow hydrology model has built-in topographic information and the capability to estimate SWE at a 1-km resolution. In their work, the snow hydrology SWE estimates are updated and corrected using Special Sensor Microwave/Imager (SSM/I) passive microwave remote-sensing measurements. The method is applied to the Upper Rio Grande River Basin in the mountains of Colorado. The change in prediction of SWE from hydrology modeling with and without updating is compared with measurements from two SNOwpack TELemetry (SNOTEL) sites in and near the basin. The results indicate that the method incorporating the remote-sensing measurements into the hydrology model is able to more closely estimate the temporal evolution of the measured values of SWE as a function of time.

Inverse remote sensing problems are generally ill-posed. In this paper, we propose an approach, which integrates the dense media radiative transfer (DMRT) model, snow hydrology model, neural networks and SSM/I microwave measurements, to infer the snow depth. Four multilayer perceptrons (MLPs) were trained using the data from DMRT model. With the provision of an initial guess from snow hydrology prediction, neural networks effectively invert the snow parameters based on SSM/I measurements. In addition, a prediction neural network is used to achieve adaptive learning rates and a good initial estimate of snow depth for inversion. Result shows that our algorithm can effectively and accurately retrieve snow parameters from these highly nonlinear and many-to-one mappings.

A numerical study of 14-GHz backscattering from ocean-like surfaces, described by a Pierson-Moskowitz spectrum, is presented. Surfaces rough in one and two dimensions are investigated, with Monte Carlo simulations performed efficiently through the use of the canonical-grid expansion in an iterative method of moments. Backscattering cross sections are illustrated for perfectly conducting surfaces at angles from 0 to 60/spl deg/ from normal incidence, and the efficiency of the numerical model enables the composite surface theory to be studied in the microwave frequency range for realistic one-dimensional (1D) surface profiles at low wind speeds (3 m/s). Variations with surface spectrum low-frequency cutoff (ranging over spatial lengths from 21.9 to 4.29 cm) are investigated to obtain an assessment of composite surface model accuracy. The 1D surface results show an increase in hh backscatter returns as surface low-frequency content is increased for incidence angles larger than 30/spl deg/, while /spl nu//spl nu/ returns remain relatively constant, all as predicted by the composite surface model. Similar results are obtained for surfaces rough in two dimensions, although the increased computational complexity allows maximum surface sizes of only 1.37 m to be considered. In addition, cross-polarized cross sections are studied in the two-dimensional (2D) surface case and again found to increase as surface low-frequency content is increased. For both 1D and 2D surfaces, backscattering cross sections within 20/spl deg/ of normal incidence are found to be well matched by both Monte Carlo and analytical physical optics (PO) methods for all low-frequency cutoffs considered, and a comparison of analytical PO and geometrical optics (GO) results indicates an appropriate choice of the cutoff wavenumber in the composite surface model to insure an accurate slope variance for use in GO predictions. This choice of cutoff wavenumber is then applied in the composite surface theory for more realistic ocean spectra and compared with available experimental data.

The authors study a correlation imaging method for the detection of targets embedded in clutter environment. The result is based on Monte Carlo simulations. In the simulations, the targets are embedded in a medium consisting of randomly distributed small scatterers and the scattered fields are calculated. The scattered fields are then used for image processing. The incident and scattered directions are chosen to avoid the "memory effect" of clutter scattering. It has been shown that the correlation function of scattered fields due to clutter is small if the memory effect is avoided. The correlation imaging is to calculate the correlation function with focusing on desired locations, Therefore, it can suppress clutter and have finer resolution. The angular correlation (ACF) imaging is used for circular synthetic aperture radar (SAR) and frequency angular correlation (FACF) imaging is used for linear SAR. Numerical results show improvement over the conventional field imaging.

With the advent of the microwave radiometer, passive remote sensing of clouds and precipitation has become an indispensable tool in a variety of meteorological and oceanographical applications. There is wide interest in the quantitative retrieval of water vapor, cloud liquid, and ice using brightness temperature observations in scientific studies such as Earth's radiation budget and microphysical processes of winter and summer clouds. Emission and scattering characteristics of hydrometeors depend on the frequency of observation. Thus, a multifrequency radiometer has the capability of profiling cloud microphysics. Sensitivities of vapor, liquid, and ice with respect to 20.6, 31.65 and 90 GHz brightness temperatures are studied. For the model studies, the atmosphere is characterized by vapor density and temperature profiles and layers of liquid and ice components. A parameterized radiative transfer model is used to quantify radiation emanating from the atmosphere. It is shown that downwelling scattering of radiation by an ice layer results in enhancement at 90 GHz brightness temperature. Once absorptive components such as vapor and liquid are estimated accurately, then it is shown that the ice water path can be retrieved using ground-based three-channel radiometer observations. In this paper the authors developed two- and three-channel neural network-based inversion models. Success of a neural network-based approach is demonstrated using a simulated time series of vapor, liquid, and ice. Performance of the standard explicit inversion model is compared with an iterative inversion model. In part II of this paper, actual radiometer, and radar field measurements are utilized to show practical applicability of the inverse models.

For pt.I see ibid., vol.35, no.2, p.224-36 (1997). A neural network-based retrieval technique is developed to infer vapor, liquid, and ice columns using two- and three-channel microwave radiometers. Neural network-based inverse scattering methods are capable of merging various data streams in order to retrieve microphysical properties of clouds and precipitation. The method is calibrated using National Oceanic and Atmospheric Administration (NOAA) results in a cloud-free condition. The performance of two- and three-channel neural network-based techniques is verified by independent NOAA estimates. The estimates of vapor and liquid agree with NOAA values. In the presence of ice, the liquid estimates deviated from NOAA's estimates. One of the major contributions of the three-channel radiometer is the estimation of ice in a winter cloud. The three-channel radiometer not only improves estimates of vapor and liquid, but also retrieves the ice column. Passive remote sensing can be ameliorated with the help of active remote sensing methods. The three-channel radiometer is used for estimating columnar contents of vapor, liquid, and ice in a cloud. It is shown that vertical profiles of median size diameter, number concentration, liquid water content, and ice water content can be inferred by combining radar reflectivity and radiometer observations. The combined remote sensor method is applied to Winter Icing and Storms Project (WISP) data to obtain detailed microphysical properties of clouds and precipitation. The authors also derived Z- Ice Water Content (IWC) and Z- Liquid Water Content (LWC) relationships and they are consistent with the earlier results.

The discrimination of the scattered wave from an object buried in shallow ground from that of the rough surface is a difficult task with present ground penetrating radar (GPR) systems. Recently, a new approach for this classical problem has been proposed and its effectiveness has been verified. This new method is based on the angular correlation function (ACF) of the scattered wave observed at two or more different incident and scattered angle combinations. It has been shown that the angular memory signatures of rough surfaces are substantially different from those of typical man-made targets and by choosing the appropriate incident and scattered angles, the surface scattering can be minimized whereas the scattering from the target is almost unchanged. The authors present detailed numerical studies of the ACF of the scattered wave from rough surfaces with and without a buried object. To obtain the ACF, the three averaging methods: realization, frequency and angular averaging, are tested numerically. It is shown that a single random rough surface of moderate extent can exhibit memory effect by using frequency averaging. Frequency averaging with a wide bandwidth is also effective for suppressing fluctuation in ACF and is most useful for practical applications. Numerical simulations indicate that even when the ratio of scattered intensities with and without the buried object is close to unity, the corresponding ratio of ACF magnitude can be more than 10 dB. Thus, using the ACF is superior to using the radar cross section (RCS) in the detection of buried objects.

Electromagnetic wave scattering in dense media, such as snow, depends on the three-dimensional (3D) pair distribution function of particle positions. In snow, two-dimensional (2D) stereological data can be obtained by analyzing planar sections. In this paper the authors calculate the volume 3D pair distribution functions from the 2D stereological data by solving Hanisch's integral equation. They first use Monte Carlo simulations for multisize particles to verify the procedure. Next they apply the procedure to available planar snow sections. A log-normal distribution of particle sizes is assumed for the ice grains in snow. To derive multisize pair functions, a least squares fit is used to recover pair functions for particles with sufficient number density and the hole correction approximation is assumed for the larger particles. A family of 3D pair distribution functions are derived. These are then substituted into dense media scattering theory to calculate scattering. It is found that the computed scattering rates are comparable to those calculated under the Percus-Yevick approximation of pair distribution functions of multiple sizes.

Inverse problems have been often considered ill-posed, i.e., the statement of the problem does not thoroughly constrain the solution space. In this paper the authors take advantage of this lack of information by adding additional informative constraints to the problem solution using Bayesian methodology. Bayesian modeling gains much of its power from its ability to isolate and incorporate causal models as conditional probabilities. As causal models are accurately represented by forward models, the authors convert implicit functional models into data driven forward models represented by neural networks, to be used as engines in a Bayesian modeling setting. Remote sensing problems afford opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. They first apply these Bayesian methods to a synthetic remote sensing problem, showing that the performance is superior to a previously published method of iterative inversion of neural networks. Next, microwave brightness temperatures obtained from the Scanning Multichannel Microwave Radiometer (SMMR) over the African continent are inverted. The values of soil moisture, surface air temperature and vegetation moisture retrieved from the inversion produced contours that agree with the expected trends for that region.>

The inversion of snow parameters from passive microwave remote sensing measurements is performed, using an iterative inversion of a neural network (NN) trained with a dense-media multiple-scattering model. Inversion of four parameters is performed based on five brightness temperatures. The four parameters are mean grain size of ice particles in snow, snow density, snow temperature, and snow depth. Iterative inversion of a data-driven forward NN model is justified on a theoretical and methodological basis. An error analysis is performed, comparing iterative inversion of a forward model with the use of an explicit inverse for the retrieval of independent snow parameters from their corresponding measurements. The NN iterative inversion algorithm is further illustrated by reconstructing a synthetic terrain of snow parameters from their corresponding measurements, inverting all four parameters simultaneously. The reconstructed parameter contours are in good agreement with the original synthetic parameter contours.>

Dense medium radiative transfer theory is applied to a three-layer model consisting of two scattering layers overlying a homogeneous half space with a size distribution of particles in each layer. A model with a distribution of sizes gives quite different results than those obtained from a model with a single size. The size distribution is especially important in the low frequency limit when scattering is strongly dependent on particle size. The size distribution and absorption characteristics also affect the extinction behavior as a function of fractional volume. Theoretical results are also compared with experimental data. The sizes, permittivities, and densities used in the numerical illustrations are typical values for snow.>

The inversion of snow parameters from passive microwave remote sensing measurements is performed with a neural network trained with a dense-media multiple-scattering model. The input-output pairs generated by the scattering model are used to train the neural network. Simultaneous inversion of three parameters, mean-grain size of ice particles in snow, snow density, and snow temperature from five brightness temperatures, is reported. It is shown that the neural network gives good results for simulated data. The absolute percentage errors for mean-grain size of ice particles and snow density are less than 10%, and the absolute error for snow temperature is less than 3 K. The neural network with the trained weighting coefficients of the three-parameter model is also used to invert SSMI data taken over the Antarctic region.>

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. The vector radiative transfer equation contains a general nondiagonal extinction matrix and a phase matrix that are averaged over particle orientations. The nondiagonal extinction matrix accounts for the difference in propagation constants and the difference in attenuation rates between the two characteristic polarisations. The Mueller matrix based on the first-order and second-order multiple scattering solutions of the vector radiative transfer equation is calculated. The copolarized and depolarized returns are also calculated.>