Wenmo Chang

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

Microwave Scattering and Medium Characterization for Terrestrial Snow With QCA–Mie and Bicontinuous Models: Comparison Studies

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Wave Propagation in Parallel Plate Metallic Waveguide With Finite Conductivity and Three Dimensional Roughness

. 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.

A PARTIAL COHERENT PHYSICAL MODEL OF THIRD AND FOURTH STOKES PARAMETERS OF SASTRUGI SNOW SURFACES OVER LAYERED MEDIA WITH ROUGH SURFACE BOUNDARY CONDITIONS OF CONICAL SCATTERING COMBINED WITH VECTOR RADIATIVE TRANSFER THEORY

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.

Bicontinuous DMRT model extracted from multi-size QCA with application to terrestrial snowpack

We study the effects of random roughness on wave propagation in a parallel plate metallic waveguide with finite conductivity. The rough surface is three dimensional (3D) with roughness heights varying in both horizontal directions. Integral equations are obtained from the extinction theorem formulated with layered medium Greens function. The second order small perturbation method is then applied to solve the integral equations. A closed form expression for the coherent wave is derived, which is expressed in terms of a three-fold Sommerfeld type integral due to the waveguide structure. Approximate methods are applied to calculate the Sommerfeld integral. The results based on the approximations are shown to agree with that of direct integration. The coherent wave enhancement factors of absorption are computed. Results of the present 3D roughness case are compared with the previous results of two dimensional (2D) roughness. The results for waveguides are also compared with the results obtained for a plane wave incident on a metal surface with 3D roughness. Results are illustrated for 3D roughness with a variety of power spectra. It is shown that enhancement factors of 3D roughness are larger than for 2D roughness. We also show that enhancement factors for a waveguide are larger than that of the plane wave case. Comparisons are also made between the theoretical results and measurements.

Conical electromagnetic waves diffraction from sastrugi type surfaces of layered snow dunes on Greenland ice sheets in passive microwave remote sensing

In this paper, a partial coherent approach is used to study the third and fourth Stokes parameters in passive microwave remote sensing of Sastrugi snow surface over layered snow structures. The incoherent part of the model consists of using radiative transfer theory for the snow layers. The coherent part of the model is using numerical solutions of Maxwell equations to derive the bistatic scattering and transmission coefficients of conical scattering by sastrugi surfaces which have large heights and large slopes. We then use the rough surface boundary conditions of conical scattering from the coherent part, in the incoherent radiative transfer equations. The radiative transfer equations are then solved iteratively that includes multiple interactions between the layered structures and the rough surfaces. Simulation results indicate that large third and fourth Stokes parameters are obtained because of the coupling of large angle transmissions of the rough surfaces with the internal reflections of layered structures. The partial coherent approach also eliminates the coherent interference patterns in angular variations from multiple reflections of layer boundaries that were present in the fully coherent approach.

Simulation and measurement correlation of random rough surface effects in interconnects

In terrestrial snow, the ice particles are irregular and densely packed together. At microwave frequencies (X-band to Ka-band), there are thousands of ice grains packed within one-wavelength cube. The interaction of the propagation wave and ice particles is coherent. The bicontinuous model is using computer-generated samples to construct the snow microstructures and numerically solve the Maxwell equations to include coherent wave and incoherent wave. There are two input parameters in the model, the scale parameter ζ and the size distribution parameter b. We related those two inputs with the ground measurement by comparing scattering coefficient of the bicontinuous model and multiple size spheres model. In the multi-size sphere model, the modified gamma distribution is used to describe size distribution of the different spheres. The scattering properties of the multi-size models are calculated by quasi-crystalline approximation (QCA). The incoherent wave is calculated with the distorted Born approximation in terms of the T-matrix and Fourier transform of the Percus-Yevick (PY) cross-pair distribution function. The scale parameter is related to the mean size of the ice particles. Therefore we can extract the size distribution parameter b of the bicontinuous model from the multi-size QCA by comparing the scattering coefficients.

Dense random media model applied to active and passive microwave remote sensing of terrestrial snow

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.

Bicontinuous/DMRT model applied to active and passive microwave remote sensing of terrestrial snow

We study the effects of three dimensional (3D) random roughness on wave propagation in a parallel plate metallic waveguide with finite conductivity. The surface roughness is characterized as a random process characterized by root mean square (rms) height, correlation length and power spectral density (PSD) function. The second order small perturbation method (SPM2) is applied to compute the coherent wave enhancement factors of absorption. A microstrip line structure is designed for validation of these enhancement factor results. Rough surface height profiles are measured on the substrate and the PSD is extracted. With the PSD we obtain the enhancement factor for the specific surface roughness. The attenuation constant of the microstrip line with rough surface can be estimated using a field solution for a smooth surface and the enhancement factor. The results for waveguides are also compared with the results obtained for a plane wave incident on a metal surface with 3D roughness. Comparison between the estimated and measured attenuation constant shows that the enhancement factor derived by SPM2 gives a better estimation than the standard Hammerstad and Bekkadal equation. The waveguide model gives more accurate enhancement factors than the plane wave model at frequencies above 20 GHz, especially for rough surfaces with rms heights larger than 2 μm.