Shurun Tan

Dense Media Radiative Transfer Applied to SnowScat and SnowSAR

The dense media radiative transfer (DMRT) theory is applied to data analysis of recent measurements of multifrequency microwave backscatter from the snow cover on earth. Measurement includes ground-based campaign (SnowScat) and airborne mission (SnowSAR). Both the quasi-crystalline approximation (QCA) model and the bicontinuous model are used for a multilayer snow medium. Two size parameters are used for both models. Grain size and stickiness parameter are used for QCA model. The bicontinuous model has two parameters: the mean wave number 〈ζ〉 and the parameter b. The mean wave number 〈ζ〉 corresponds to the inverse of the grain size, while the b parameter controls the width of the wave number distribution and is related to the clustering property. The bicontinuous model is used to generate the microstructures of snow by computer, and Maxwell equations are solved numerically for each sample of computer-generated structure to calculate the extinction coefficient and the phase matrix. Other geometric descriptors of the bicontinuous medium include correlation functions and specific surface areas, both of which can be calculated from the parameters 〈ζ〉 and b. In making comparisons, we use ground measurements of specific surface area, grain size, densities, and layering of snow cover as input for the theoretical models. The geometric properties and the scattering properties of the bicontinuous model are also compared with past models. In making the multifrequency comparisons, we use the same physical parameters of all three frequencies: 1) X band; 2) Ku bands of 13.3 GHz; and 3) 16.7 GHz. It is emphasized that the DMRT models provide frequency, size, and angular dependence that depart from the classical model of Rayleigh scattering and are in better agreement with experimental observations.

Modeling Both Active and Passive Microwave Remote Sensing of Snow Using Dense Media Radiative Transfer (DMRT) Theory With Multiple Scattering and Backscattering Enhancement

In this paper, we incorporate the cyclical terms in dense media radiative transfer (DMRT) theory to model combined active and passive microwave remote sensing of snow over the same scene. The inclusion of cyclical terms is crucial if the DMRT is used to model both the active and passive contributions with the same model parameters. This is a necessity when setting out on a joint active/passive retrieval. Previously, the DMRT model has been applied to active and passive separately, and in each case with a separate set of model parameters. The traditional DMRT theory only includes the ladder terms of the Feynman diagrams. The cyclical terms are important in multiple volume scattering and volume-surface interactions. This leads to backscattering enhancement which represents itself as a narrow peak centered at backward direction. This effect is of less significance in passive remote sensing since emissivity is relating to the angular integral of bistatic scattering coefficients. The inclusion of cyclical terms in first-order radiative transfer (RT) accounts for the enhancement of the double bounce contribution and makes the results the same as that of distorted Born approximation in volume-surface interactions. In this paper, we develop the methodology of cyclical corrections within the framework of DMRT beyond first order to all orders of multiple scattering. The active DMRT equation is solved using a numerical iterative approach followed by cyclical corrections. Both quasi-crystalline approximation (QCA)-Mie theory with sticky spheres and bicontinuous media scattering model are used to illustrate the results. The cyclical correlation introduces around 1 dB increase in backscatter with a moderate snowpack optical thickness of

Physical Models of Layered Polar Firn Brightness Temperatures From 0.5 to 2 GHz

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Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scatterers using broadband Green's function with low wavenumber extraction (BBGFL).

. The bicontinuous/DMRT model is next applied to compare with data acquired in the Nordic Snow Radar Experiment (NoSREx) campaign in the snow season of 2010-2011. The model results are validated against coincidental active and passive measurements using the same set of physical parameters of snow in all frequency and polarization channels. Results show good agreement in multiple active and passive channels.

Multiple Scattering Effects With Cyclical Correction in Active Remote Sensing of Vegetated Surface Using Vector Radiative Transfer Theory

We investigate physical effects influencing 0.5-2 GHz brightness temperatures of layered polar firn to support the Ultra Wide Band Software Defined Radiometer (UWBRAD) experiment to be conducted in Greenland and in Antarctica. We find that because ice particle grain sizes are very small compared to the 0.5-2 GHz wavelengths, volume scattering effects are small. Variations in firn density over cm- to m-length scales, however, cause significant effects. Both incoherent and coherent models are used to examine these effects. Incoherent models include a “cloud model” that neglects any reflections internal to the ice sheet, and the DMRT-ML and MEMLS radiative transfer codes that are publicly available. The coherent model is based on the layered medium implementation of the fluctuation dissipation theorem for thermal microwave radiation from a medium having a nonuniform temperature. Density profiles are modeled using a stochastic approach, and model predictions are averaged over a large number of realizations to take into account an averaging over the radiometer footprint. Density profiles are described by combining a smooth average density profile with a spatially correlated random process to model density fluctuations. It is shown that coherent model results after ensemble averaging depend on the correlation lengths of the vertical density fluctuations. If the correlation length is moderate or long compared with the wavelength (~0.6x longer or greater for Gaussian correlation function without regard for layer thinning due to compaction), coherent and incoherent model results are similar (within ~1 K). However, when the correlation length is short compared to the wavelength, coherent model results are significantly different from the incoherent model by several tens of kelvins. For a 10-cm correlation length, the differences are significant between 0.5 and 1.1 GHz, and less for 1.1-2 GHz. Model results are shown to be able to match the v-pol SMOS data closely and predict the h-pol data for small observation angles.

Full wave simulation of snowpack applied to microwave remote sensing of sea ice

The broadband Greens function with low wavenumber extraction (BBGFL) is applied to the calculations of band diagrams of two-dimensional (2D) periodic structures with dielectric scatterers. Periodic Greens functions of both the background and the scatterers are used to formulate the dual surface integral equations by approaching the surface of the scatterer from outside and inside the scatterer. The BBGFL are applied to both periodic Greens functions. By subtracting a low wavenumber component of the periodic Greens functions, the broadband part of the Greens functions converge with a small number of Bloch waves. The method of Moment (MoM) is applied to convert the surface integral equations to a matrix eigenvalue problem. Using the BBGFL, a linear eigenvalue problem is obtained with all the eigenmodes computed simultaneously giving the multiband results at a point in the Brillouin zone Numerical results are illustrated for the honeycomb structure. The results of the band diagrams are in good agreement with the planewave method and the Korringa Kohn Rostoker (KKR) method. By using the lowest band around the Γ point, the low frequency dispersion relations are calculated which also give the effective propagation constants and the effective permittivity in the low frequency limit.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical thickness and scattering albedo of the vegetation layer are large. When both the albedo and the optical thickness exceed 0.4, higher orders contribute significantly (e.g., vertical polarization at L-band). The approach is applied to vegetated surfaces using typical crop structure for backscattering from L-band to Ku-band. For corn fields at L-band, multiple scattering effects are more important for vertical scattered wave with vertical incidence (VV). For example, when vegetation water content (VWC) is 3kg/m2, the deviation between first order and multiple scattering for corn field for VV could be 3.5 dB while 0.7 dB for horizontal scattered wave with horizontal incidence (HH). The iterative approach also allows the separation of the contribution to backscattering from each scattering order and scattering mechanism. Each scattering mechanism is associated with a unique scattering path. By examining the duality of the paths, we are able to identify the cyclical terms with existence of a reflective boundary. The cyclical correction to the backscattering accounts for backscattering enhancement effects on the copolarization by a factor of two. The approach is validated against the SMAPVEX12 L-band corn dataset over the entire crop growth and large soil moisture variations. The model prediction matches the observation with 1.93 and 1.46 dB root-mean-square error (RMSE) for VV and HH, respectively, while correlations are 0.67 and 0.88, respectively. Time-series retrieval is also applied successfully for both soil moisture and VWC with 0.06 cm3/cm3 and 0.44 kg/m2 RMSE, respectively, while correlations are 0.7 and 0.92, respectively. For large VWC, this approach corrects the underestimated backscatters in the single scattering caused by large attenuation.

Microwave Signatures of Snow Cover Using Numerical Maxwell Equations Based on Discrete Dipole Approximation in Bicontinuous Media and Half-Space Dyadic Green's Function

A fully coherent snowpack scattering and emission model is developed by numerically solving Maxwells 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 Greens 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.

Uniaxial Effective Permittivity of Anisotropic Bicontinuous Random Media Using NMM3D

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxters sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Validation of physical model and radar retrieval algorithm of snow water equivalent using SnowSAR data

A three-dimensional snowpack scattering and emission model is developed by numerically solving Maxwells equations (NMM3D) over the entire snowpack on an underlying half-space. The solutions are crucial to microwave remote sensing that requires the preservation of coherent phase information. The heterogeneous snowpack is represented as a bicontinuous medium. Effects of the underlying half-space are included through a half-space Greens function in a volume integral equation formulation. The volume integral equation is then solved using the discrete dipole approximation. The fast Fourier transform is effectuated for all three dimensions with half-space Greens function rather than the conventional free space Greens function. To overcome the snow volume truncation in the finite numerical calculations, periodic boundary conditions are applied in the lateral extent. Thus, in NMM3D, the physical microwave scattering and emission problem is solved without using any radiative transfer equations. In this formulation, the scattering matrix of the snowpack accounts for both the magnitude and phase. The NMM3D simulations are demonstrated at Ku-band frequency for a snow cover up to 25-cm thick. The results are applicable to remote sensing of snow over sea ice, and thin layers of terrestrial snow. Quantitative values of backscattering and bistatic scattering coefficients are derived for active microwave remote sensing, and brightness temperatures for passive microwave remote sensing. The full wave simulation results are compared with those of the partially coherent approach of the dense media radiative transfer (DMRT). The NMM3D results capture effects of backscattering enhancement and coherent layering that are missed in DMRT. The full wave solution to Maxwell equations is important to advance radar polarimetry, interferometry, and tomography that require the preservation of the full phase information and all interface interactions for applications to radar remote sensing of snow cover on land and on sea ice.