Matrix Doubling Method Research Articles

Estimation of rain parameters for microwave backscattering model using PSO

The intention of the geophysical modelling of rain is to provide a better explanation for the effect of rainfall to the microwave backscattering and thus to interpret radar measurements. However, in the model, physical characteristic of raindrops should be estimated primarily and accurately by considering observation system, measurements and suitable rain rate retrieval algorithms to calculate backscattering coefficients from rainfall. In this study, a geophysical microwave backscattering model of rain type precipitation over sea surface is constructed by using Particle Swarm Optimization (PSO) algorithm in the multilayered Vector Radiative Transfer (VRT) model to estimate vertical profile of rain by using GPM DPR data. Rain column is partition into sublayers and for each sublayer, physical properties of raindrops such as drop radius, water volume fraction or layer thickness are estimated by using PSO to provide the best fit with measurements by searching within certain limits defined by rain rate. Backscattering coefficients from entire rain is provided by the solution of VRT equations via Matrix Doubling Method to consider multilayer effect. Results show that, vertical profile of rain parameters can be estimated accurately for moderate /high rain rates (up to 11–12 mm/h) by using presented model.

Microwave Scattering (1–10 GHz) From a Vertically Heterogeneous Grass Canopy

This study concerns the effects of considering vertically heterogeneous canopy structure when modeling microwave scattering from grassland with the Tor Vergata (TVG) model, which uses the matrix doubling method (MDM). The TVG model was extended with the M-volume approach to accommodate height-dependent variation in structure for every scatterer type. Used approach was to reproduce 1 – 10 GHz backscatter for all linear polarization combinations from an alpine meadow measured by a ground-based scatterometer with both the default (1-volume) and the M-volume approach with 3 volumes. Measured in-situ vegetation parameters were used to constrain the model. We found that both models were able to reproduce the angle-dependent backscattering for C- and X-band, measured on two afternoons, and the 31-day average measured radar return power for L-, S-, C-, and X-band within, or close to, the measurement uncertainty. Our analysis proved inconclusive on whether the 1- or 3-volume approach worked better for the considered grassland, but did show that the 3-volume approach allows for more flexibility in reproducing the actual angle-dependent backscattering for multiple frequencies, a flexibility that may prove necessary when more scattering angles are considered. Furthermore, predictions of the bistatic scattering coefficient at higher frequencies (C- and X-band) were significantly different between both models. For X-band with hh polarization differences up to 3 dB were found for the specular direction. We conclude that considering vertical heterogeneity of vegetation canopy structure with MDM leads to significantly different results than with the vertically homogeneous canopy approximations typically used.

Signatures of Microwave Emission From Foam-Covered Ocean Surface

Good understanding the emission in the presence of foam layer is essential for effective retrieval of oceanic parameter from microwave measurements. In general, microwave emissivity is enhanced by the foam layer, depending not only on the macroscopic dielectric properties and the foam layer thickness, but also on the absorption and scattering of the bubbles. In this paper, a numerical emission model is developed based on a matrix doubling method by which the volume scattering effects in foam layer are accounted for. We explore the effects of the water fraction and foam layer thickness on total emission from foam-covered ocean surface, by analyzing the contributions from both the up-welling and the down-welling emissions from foam layer, and the emission from the seawater. In particular, the dependence of emission, consisting of the three effective emission sources, on the foam layer thickness and water fraction at L-band to Ka-band are investigated. Results are compared with predictions by the incoherent method. Physical reasons given rise to the depolarized emissivity at high frequency bands, and the dry sub-layers at the top of foam layer are discussed.

Foam-Scattering Effects on Microwave Emission From Foam-Covered Ocean Surface

In this letter, we investigate volume-scattering effects on microwave emission from a foam-covered ocean surface by a comparative study of emissivities and polarization indexes of a numerical radiative transfer model and an incoherent emission model. The matrix doubling method is applied in the numerical model, which fully accounts for the multiple scattering in the foam layer and at the interfaces. The incoherent emission model considers incoherent interactions between air–foam and foam–seawater interfaces but ignores the volume scattering in the foam layer. Model analyses show that foam volume scattering affects both the magnitude and polarization index of emission from the foam-covered ocean surface. Foam volume scattering reduces the rate of increase in emissivity with increasing foam water fraction. Results also show that polarization index is more sensitive to volume scattering at a large observation angle and at a low foam water fraction. Comparison between model predictions and experimental measurements accentuate the need to account for foam-scattering effects in interpreting emission measurements from the foam-covered ocean surface.

MULTILAYER MODEL FORMULATION AND ANALYSIS OF RADAR BACKSCATTERING FROM SEA ICE

The Antarctic continent is an extremely suitable environ- ment for the application of remote sensing technology as it is one of the harshest places on earth. Satellite images of the terrain can be properly interpreted with thorough understanding of the microwave scattering process. The proper model development for backscatter- ing can be used to test the assumptions on the dominating scattering mechanisms. In this paper, the formulation and analysis of a multi- layer model used for sea ice terrain is presented. The multilayer model is extended from the previous single layer model developed based on the Radiative Transfer theory. The Radiative Transfer theory is chosen because of its simplicity and ability to incorporate multiple scattering efiects into the calculations. The propagation of energy in the medium is characterized by the extinction and phase matrices. The model also incorporates the Dense Medium Phase and Amplitude Correction Theory (DM-PACT) where it takes into account the close spacing ef- fect among scatterers. The air-snow interface, snow-sea ice interface and sea ice-ocean interface are modelled using the Integral Equation Method (IEM). The simulated backscattering coe-cients for co- and cross-polarization using the developed model for 1GHz and 10GHz are presented. In addition, the simulated backscattering coe-cients from the multilayer model were compared with the measurement results ob- tained from Coordinated Eastern Artic Experiment (CEAREX) (Gren- fell, 1992) and with the results obtained from the model developed by Saibun Tjuatja (based on the Matrix Doubling method) in 1992.

Improvement of a 3D radar backscattering model using matrix-doubling method

Radiative transfer models have been widely used to simulate the radar backscattering from forested areas. A three-dimensional radar backscatter model of forest canopy developed in previous studies takes full account of spatial position of trees in a forest stand, and the interactions among crown, trunk and ground surface. The model predicted well for the co-polarized backscatter measurements, but underestimated the backscattering for cross-polarization, primarily because only the first-order scattering within tree crowns was considered in the model. The backscattering at cross-polarization depends strongly on multiple scattering within tree crowns. To produce good estimations for cross-polarized component, the matrix-doubling method is employed here to compute multiple-scattering within the crown. The modified model is compared with the original model, and the field forest measurements and AIRSAR data are used for validation of the modified model. The cross-polarization backscattering is improved in different degrees for different crown structures and at different bands.

Comparison between a multi-scattering and multi-layer snow scattering model and its parameterized snow backscattering model

Snow Water Equivalent (SWE) is a crucial parameter in the study of climatology and hydrology. Active microwave remote sensing is one of the most promising techniques for estimating the distribution of SWE at high spatial resolutions in large areas. Development of reliable and accurate inversion techniques to recover SWE is one of the most important tasks in current microwave researches. However, a number of snow pack properties, including snow density, particle size, crystal shape, stratification, ground surface roughness and soil moisture, affect the microwave scattering signals and need to be properly modeled and exploited. In this paper, we developed a multi-layer, multi-scattering model for dry snow based on recent theoretical advances in snow and surface modeling. In the proposed multi-layer model, Matrix Doubling method is used to account for scattering from each snow layer; and Advanced Integral Equation Model (AIEM) is incorporated into the model to describe surface scattering. Comparisons were made between the model predictions and field observations from NASA Cold Land Processes Field Experiment (CLPX) during Third Intensive Observation Period (IOP3) and SARALPS-2007 field experiment supported by ESA. The results indicated that model predictions were in good agreement with field observations. With the confirmed confidence, the analyses on multiple scattering, scatterer shape, and snow stratification effects were further made based on the model simulations. Furthermore, a parameterized snow backscattering model with a simple form and high computational efficiency was developed using a database generated by the multiple-scattering model. For a wide range of snow and soil properties, this parameterized model agrees well with the multiple-scattering model, with the root mean square error 0.20 dB, 0.24 dB and 0.43 dB for VV, HH and VH polarizations, respectively. This simplified model can be useful for the development of SWE retrieval algorithm and for fast simulations of radar signals over snow cover in land data assimilation systems.

An analysis of scattering and emission from sea ice

Abstract Scattering and emission models for multilayered inhomogeneous media are developed based on the matrix doubling method. They are made applicable to media closely packed with scatterers by using the complete scattered field expression in the derivation of the scattering phase function. These models are applied to sets of multifrequency, multiangle, multipolarization, active and passive measurements from simulated sea ice prepared under laboratory conditions and from field experiments on sea ice where ground truths were gathered. It is found that identical surface and ice parameters in agreement with ground truth information may be used to predict both emission and scattering. Such a combined approach can give an indication as to the consistency between active and passive data levels and angular trends. Furthermore, it is found that for thin lossy ice above a water surface, scattering and emission from water could be significant.

A matrix doubling formulation of internal emission from a layer with irregular boundaries

A formulation for internal emission from a thermal scattering layered medium with irregular boundaries is developed. The matrix doubling method is utilized to obtain the upward and downward thermal intensities inside the scattering layer. The scattering layer is assumed to be a slab embedded with randomly positioned thermal scattering particles, and the upper and lower boundaries are assumed to be random rough surfaces. The developed emission model may be useful for the understanding of the internal emission problem where a radiometer is located inside an emitting medium with irregular rough boundaries. >

Radar Backscatter from a Vegetation Layer with Rough Ground Boundary

The problem of radar backscattering from a vegetation layer with a smooth or a rough ground boundary is formulated by a Monte Carlo method. The vegetation layer is assumed to contain a mixture of randomly distributed dielectric discs and thin prolate ellipsoids whose phase matrices are known and whose distributions of angular orientations can be prescribed independently. The ground boundary is modelled by a Fresnel reflection coefficient for a plane lossy surface or a Kirchhoff lossy surface as the case may be. Results from the Monte Carlo simulations are compared with calculations of a matrix-doubling method by [9], and also with measurements from fields of wheat, soyabean, milo and corn [7,20]. The results indicate that the Monte Cario method presented in this paper can give a good fit with experimental data, using parameters which are believed to be reasonable.

An empirical model for polarized and cross-polarized scattering from a vegetation layer

An empirical model for scattering from a vegetation layer above an irregular ground surface is developed in terms of the first-order solution for like-polarized scattering and the second-order solution for cross-polarized scattering. The effects of multiple scattering within the layer and at the surface-volume boundary are compensated by using a correction factor based on the matrix doubling method. The major feature of this model is that all parameters in the model are physical parameters of the vegetation medium. There are no regression parameters. Comparisons of this empirical model with theoretical matrix-doubling method and radar measurements indicate good agreements in polarization, angular trends, and k a up to 4, where k is the wave number and a is the disc radius. The computational time is shortened by a factor of 8, relative to the theoretical model calculation.

Scattering from a Layered Medium Connected with Rough Interfaces: Matrx Doubling Method

A theoretical scattering model is developed that computes the scattered and transmitted intensities from an inhomogeneous layered medium above the half-space. A matrix doubling method technique is extended to handle multilayer scattering problems of which each scattering layer of spherical particles has rough boundary interfaces. Incoherent scattering is assumed in the formulation so that the Stokes vector representations are used to calculate the polarimetric multiple scattering effects. The scattering coefficients are computed for a two-layered Rayleigh scattering medium with a rough boundary. The developed scattering model of a radiative transfer approach is useful for scattering computations dealing with a random medium often encountered in active and passive microwave remote-sensing problems.

A scatter model for vegetation up to Ku-band

A scatter model is developed based on the matrix doubling method for volume scattering and the Kirchhoff method in rough surface scattering. Scattering from vegetation is assumed to be dominated by leaves and a single leaf is modeled by a thin dielectric disc. In developing the phase matrix for the disc, field within the disc is taken to be constant over the disc thickness, but phase changes across the surface of the disc are accounted for. Comparisons of this scatter model with radar measurements indicate good agreements in polarization, angular trends, and frequency up to Ku-band. This represents a considerable improvement over low-frequency scatter models which are valid up to S-band.

A review of volume scatter theories for modeling applications

Volume scatter theories commonly applied to develop scatter models for vegetation, snow, and sea ice are reviewed. These include (1) the first‐order theories based on the Born approximation, the distorted Born approximation, and the renormalization method and (2) the multiple scatter theories based on the radiative transfer method and the matrix doubling method. Applications of the scatter models developed from a first‐order theory and a multiple scatter theory are illustrated. Additional applications available in the literature are cited.

Emission from a Rayleigh layer with irregular boundaries

A theory of microwave emission from an irregular layer of Rayleigh scatterers is developed by combining an existing matrix doubling method for volume scattering with the Kirchhoff method in surface scattering. Effects of the layer boundaries are illustrated by comparing layers with plane boundaries vs layers with rough top or bottom boundaries and irregular layers. It is found that the major effect of an irregular top layer boundary is to slow down the variation of the layer emission as a function of the nadir angle and the major effect of an irregular bottom boundary is to increase the level of the layer emission. Comparisons of the developed layer model with snow emission indicate the potential use of such models in data interpretation.

Polarization dependence in EM scattering from Rayleigh scatterers embedded in a dielectric slab. I. Theory

The matrix doubling method developed by Twomey, Jacobowitz, and Howell for calculating radiation transfer from a medium has been extended to permit calculations of the polarization components of the light intensity scattered from a slab medium illuminated with polarized light. Calculations have been performed for scattering in the incident plane from a Rayleigh scattering medium for various albedos and optical thicknesses. Expressions were also developed that permit calculations in terms of the same variables if the scattering centers are embedded in a dielectric slab medium. The results calculated from these expressions differ significantly from those obtained from simple refraction of the medium’s multiple scattering angular distribution. Calculated results indicate that the dielectric interface amplifies the scattering from the medium over that obtained without the interface. This amplification is most significant for the scattered depolarized components, which result exclusively from multiple scattering.