Dense Media Radiative Transfer Theory Research Articles

Comparison of local scale measured and modelled brightness temperatures and snow parameters from the CLPX 2003 by means of a dense medium radiative transfer theory model

AbstractSome 27 years of passive microwave satellite observations have demonstrated the value of remote sensing for cryospheric applications, albeit at regional to hemispheric scales due to the relatively large sensor footprints (e.g. ∼25 km × 25 km for the advanced microwave scanning radiometer). At the other extreme there is the primarily local‐scale in situ experience of the snow community. Until higher‐resolution sensors become available, understanding the effects of sub‐pixel heterogeneity and the downscaling of observations remains an important topic.In order to provide a baseline for performing scaling studies and for future radiance‐based hydrological assimilation schemes, an evaluation of snowpack forward radiance modelling at the plot scale (least heterogeneous scale) is carried out. Snow microwave radiance models based on dense medium radiative transfer (DMRT) theory incorporate a high degree of physical fidelity, yet dense medium models are particularly sensitive to snowpack structural parameters such as grain size, density, and depth (parameters that may vary substantially within a snowpack). The DMRT performance is evaluated through the use of a fitting technique with respect to snow grain size, a hydrologically important parameter related to the total amount of melt water stored in a snowpack, snowpack metamorphism, vertical energy transport and melt dynamics, as well as various quantities useful in surface energy balance studies. All remaining snow input parameters to the model are derived from snow pit measurements. Model‐predicted radiances are evaluated using microwave brightness measurements collected during the NASA Cold Land Process Experiment (CLPX) by the University of Tokyo's Ground‐Based Microwave Radiometer‐7 (GBMR‐7) system at 18·7, 36·5, and 89 GHz, with incidence angles ranging from 30 to 70 °. The detailed CLPX microwave and snow data provide an excellent opportunity to gain insight into the strengths and weaknesses of this approach. Copyright © 2006 John Wiley & Sons, Ltd.

Modeling the passive microwave remote sensing of snow using dense media radiative transfer theory with NMM3D rough-surface boundary conditions

The effects of volume scattering and rough-surface scattering in passive microwave remote sensing are treated. The volume-scattering model is based on dense medium radiative transfer (DMRT) theory with quasicrystalline approximation (QCA) for densely distributed sticky particles. The rough-surface bistatic scattering and emission are modeled using the numerical Maxwell model of 3D simulations (NMM3D). 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 are illustrated for a layer of dry snow over rough ground at 18.7 and 36.5 GHz. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 557–562 2006; Published online in Wiley InterScience (www.interscience.wiley.com) DOI 10.1002/mop.21407

INTEGRATED SNOW OBSERVATION DURING THE COLD LAND PROCESSES FIELD EXPERIMENT AND ITS APPLICATION FOR THE DEVELOPMENT OF RADIATIVE TRANSFER MODEL FOR SNOW

This paper introduces microwave radiometric data, snow pack properties and meteorological forcing data observation collected during the winter season '02/'03 in Fraser, Colorado, USA. The observation was part of the NASA Cold Land Processes Field Experiment (CLPX) at the Local Scale Observation Site (LSOS). Apart from continuous observation of meteorological data, which can be used to constrain physically based snow models, intensive ground-based passive microwave observations have been implemented during the winter season. Furthermore regular observations of snow pit properties have been conducted, including the snow density and snow grain size profiles. The data set provides the possibility to evaluate and improve radiative transfer models for snow and satisfactory modeling results have been achieved using the dense media radiative transfer theory (DMRT). All data will be released to the public on October 1, 2004 and are available from the website of the National Snow and Ice Data Center.

Applications of dense media radiative transfer theory for passive microwave remote sensing of foam covered ocean

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.

Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow

Dense media radiative transfer (DMRT) equations based on quasicrystalline approximation (QCA) for densely distributed moderate size particles are developed. We first compute the effective propagation constant and coherent transmission into a dense medium on the basis of the generalized Lorentz‐Lorenz law and the generalized Ewald‐Oseen extinction theorem. The absorption coefficient of the dense media is then calculated. The distorted Born approximation is next applied to a thin layer to determine the bistatic scattering coefficients and the scattering coefficient. The phase matrix in DMRT is then obtained as bistatic scattering coefficient per unit volume. The model is applied to multiple sizes and for sticky particles. Numerical results are illustrated for extinction and brightness temperatures in passive remote sensing using typical parameters in snow terrain. The QCA‐based DMRT is also used to compare with satellite Special Sensor Microwave Imager (SSM/I) brightness temperatures for four channels at 19 and 37 GHz with vertical and horizontal polarizations and for two snow seasons. It shows reasonable agreement to snow depth of 1 m.

Application of the dense medium radiative transfer theory for calculating microwave emissivities of different sea ice types

The dense medium radiative transfer theory (DMRT) was used to calculate microwave emissivities of different undeformed sea ice types in the Arctic and Antarctic. The computed results were compared with measurements. More often taken for describing snow, we show that the DMRT can be applied to both sea ice and snow cover. While doing so the choice of appropriate parameters needed in the DMRT is discussed. As a result a multi-layered, uniform model for a variety of sea ice types including snow cover is obtained.

Modeling of Millimeter Wave Backscatter of Time-Varying Snowcover — Summary

The temporal variation of millimeter wave backscatter signature of snowcover is studied based on a dense medium radiative transfer (DMRT) theory and a one-dimensional mass and energy balance model of snow named SNTHERM. The multilayer DMRT scattering model of snowcover developed in this work takes into account the reflection and refraction at the snow-snow interfaces. Appropriate boundary conditions, quadrature points and weights are selected for using the discrete-ordinate eigenanalysis method to solve the multilayer DMRT equations. It shows that the inclusion of reflection and refraction at the snow-snow interfaces may affect the model prediction. Cohesive spherical particles are applied to account for the clustering feature of snow grains. To model the time-varying behavior of snowcover, SNTHERM is employed to simulate the aging process of snow. SNTHERM provides pertinent snow parameters, such as grain size, density, liquid water content, and stratification with a high resolution in time and depth. These snow properties are then used in modeling the temporal radar signatures of snowcover. The comparisons of temporal model responses with time series polarimetric backscatter data at 35 and 95 GHz are presented. Good agreement is demonstrated between model and measurements in both timing and magnitude. The results indicated that the coupled DMRT and SNTHERM model can be useful in studying the electromagnetic interactions with time-varying snow microstructure.

Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow

Monte Carlo simulations are used to derive the phase matrix, effective permittivity, and scattering coefficient for a random medium consisting of densely packed spheres up to 5000 in number. The results include correlated scattering and coherent wave interaction among the scatterers. The Monte Carlo simulations are based on a multiple‐scattering formulation of the Foldy‐Lax equations. It is shown that the derived phase matrix is in good agreement with dense media radiative transfer theory for copolarized scattering. The depolarization, however, can be substantially larger than conventional theory. Two methods are used to analyze the behavior of the coherent wave to obtain the real part of the effective permittivity. For the small particle case both methods yield values of permittivity that agree with the results of mixing formulas such as the Clausius‐Mossoti mixing formula. The phase matrix and scattering coefficient obtained by simulation are used in a second‐order radiative transfer model to predict the amount of backscatter from a layer of snow. It is also shown that sticky spheres, which can be used to model metamorphosed snow, produce high levels of copolarized and depolarized backscatter that can exceed the independent scattering model.

Dense medium radiative transfer theory for two scattering layers with a Rayleigh distribution of particle sizes

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. >

Dense Media Radiative Transfer Theory for Dense Discrete Random Media with Particles of Multiple Sizes and Permitivities

Dense Media Radiative Transfer Theory for Dense Discrete Random Media with Particles of Multiple Sizes and Permitivities

Dense medium radiative transfer theory: comparison with experiment and application to microwave remote sensing and polarimetry

The dense medium radiative transfer theory is used to study the multiple scattering of electromagnetic waves in a slab containing densely distributed spherical particles overlying a homogeneous half-space. This theory is used to explain phenomena observed in a controlled laboratory experiment. The experimental data indicate that, in a dense medium with small particles, both the coherent attenuation rate and bistatic intensities first increase with the volume fraction of the particles until a maximum is reached, and then decrease when the volume fraction further increases. Thus, attenuation rates and bistatic scattering exhibit a peak as a function of the concentration of particles. The magnitudes of both are also less than those predicted by the independent scattering assumption and the conventional radiative transfer theory. These phenomena cannot be explained by the conventional radiative transfer theory. It is shown that the dense medium radiative transfer theory is in agreement with these experimental features. >