FOURTH STOKES PARAMETER IN POLARIMETRIC PASSIVE REMOTE SENSING FROM TWO-LAYER ROUGH SURFACES

Recently there has been growing interest in the application of polarimetry to active microwave remote sensing of geophysical terrain. However, for passive microwave remote sensing, the third and fourth Stokes parameters were usually neglected in the past. In this paper, we make theoretical calculations of brightness temperatures of the third and fourth Stokes parameters for geophysical terrain. The calculations are based on vector radiative transfer theory with emission vector for random discrete scatterers. We also derive the reciprocal relations between emission of third and fourth Stokes parameters and the bistatic scattering coefficients for rough surface problems. Numerical results are illustrated. It is shown that brightness temperatures for third and fourth Stokes parameters can be as large as ±60°K for certain statistical asymmetrical configurations of scatterers.

Measurements are reported of the fourth Stokes parameter as observed from space by the SMAP polarimetric radiometer. The SMAP radiometer has a digital back-end that provides fully polarimetric processing, including the direct measurement of the third and fourth Stokes parameters. The data provide a first look at the fourth Stokes parameter from space at L-band. Features are reported that can be associated with RFI and the characteristics of the antenna pattern. With processing to remove such effects, features associated with the surface, such as snow/ice over Greenland and land vegetation canopy have also been observed

A new tapered wave integral equation method was derived to simulate the conical diffraction of electromagnetic waves from rough surfaces. Both the full matrix inversion and the banded matrix iterative approaches are developed. By using the principle of reciprocity and energy conservation, all four Stokes parameters are calculated for polarimetric passive remote sensing of rough surfaces. We show in this paper that for a moderately rough surface, the third Stokes parameter can be as high as ±20°K. The tapered wave integral equation approach can deal with a rough surface with a large slope. The new method presented in this paper is compared with the previously published plane wave integral equation method and the extended boundary condition method. Very good agreement is obtained. Unlike the plane wave integral equation method and the extended boundary condition method, the tapered wave integral equation method does not have the kinks imposed by Floquet models and it requires a shorter surface length in most applications.

In the present paper, different methods are proposed for the detection and mitigation of the undesirable effects of radio frequency interference (RFI) in microwave radiometry. The first of these makes use of kurtosis to detect the presence of non-Gaussian signals, whereas the second imposes a threshold on the standard deviation of brightness temperatures, in order to distinguish natural emission variations from RFI. Finally, the third approach is based on the use of a threshold applied to the third and fourth Stokes parameters. All of these methods have been applied and tested, with a CAROLS radiometer operating in the L-band, on data acquired during airborne campaigns made in spring 2009 over the South West of France. The performance of each, or of two combined approaches is analyzed with our database. We thus show that the kurtosis method is well adapted to pulsed RFI, whereas the method based on the second moment is well adapted to continuous-wave RFI.

Measurements of both the Soil Moisture and Ocean Salinity (SMOS) and Aquarius L-band microwave radiometers show a significant presence of radio frequency interference (RFI), although they operate in a protected frequency band where transmission is prohibited. RFI detection and mitigation remain a challenging problem for both missions, especially for low or moderate (i.e., on the order of 10 K or less) amplitude contributions. An algorithm for low-level source detection and mitigation is already included in Aquarius data sets, and both Aquarius and SMOS have distinct attributes that can potentially enable further improvements in detection and mitigation of these sources to some degree. The combination of SMOS and Aquarius data sets may enable further future improvements as well. Initial efforts toward this goal are reported in this paper. Similarities and differences in RFI effects on SMOS and Aquarius are examined, with a particular focus on instrument properties that cause differences in received RFI power in SMOS and Aquarius observations of a specific source. A study is also performed of SMOS observations for regions reported by Aquarius to contain “low-level” RFI. It is shown that the detection of these sources in the SMOS data set is challenging and that the dependence of the SMOS third and fourth Stokes parameters on incidence angle makes the polarimetric features of SMOS difficult to utilize for low-level source detection. However, an angular fitting procedure suggested previously in the literature can, in some cases, detect such sources in horizontal and vertical polarizations.

A novel microwave calibration source for a fully polarimetric radiometer (FPoR) is proposed for internal calibration by the electrical operation instead of a mechanical structure at S‐band. The proposed correlated noise calibration source (CNCS) using microwave components can generate vertical and horizontal polarized signals; additionally, linearly and circularly polarized signals (third and fourth Stokes parameters) are also estimated by injecting correlated noise. In contrast to existing mechanical calibration sources, this calibration source can be designed by miniaturization. Based on measured quantities under realistic conditions, the uncertainty was evaluated according to the states of the SPDT switches and phase shifters of the CNCS.

We report a laboratory study on the scattering, energy dissipation and mean flow induced by internal gravity waves incident upon slopes with varying surface roughness. The experiment was performed in a rectangular box filled with thermally stratified water. The roughness of the slope surface, $\lambda$ , defined as the height of a roughness element over its base width, and the off-criticality $\gamma =(\alpha -\beta )/\beta$ , with $\alpha$ and $\beta$ being the angles of the incident wave and the slope, are used as two control parameters. The distribution of energy dissipation in the direction normal to the slope is found to be more uniform in the rough surface cases. Counter-intuitively, both the maximum value in the dissipation profile and the total energy dissipation near the slope are reduced by surface roughness under most circumstances. The measured peak width (the full width at half-maximum of the peaks) of the dissipation profile is found to be broadened significantly in the rough surface cases. We also observed that there exists a non-zero optimal off-criticality ( $\gamma =0.17$ for the present measurement resolution) for the normalized average dissipation and total dissipation, which may be due to the strongest wave energy near the slope at this $\gamma$ . Unlike surface roughness, the off-criticality has a small effect on the distribution of energy dissipation. Moreover, surface roughness is also found to change the structure of the scattering-induced mean flow and enhance its strength. The present study provides new perspectives on how the surface roughness on topographic features influences energy dissipation.

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.

Starting with Zenneck and Sommerfeld wave propagation over a flat finitely conducting surface has been extensively studied by Wait (see IEEE Antennas Propagat. Mag., vol.40, p.7-24, 1998) and many other authors. We examine propagation over a finitely conducting rough surface, also studied by many people including Feinberg (1944), Bass and Fuks (1979), and Barrick (see Radio Sci., vol.6, p.517-26, and vol.6., p.527-33). This paper extends the multiple scattering theories based on Dyson and Bethe-Salpeter equations and their smoothing approximations. The theory developed here applies to rough surfaces with small root-mean-square (RMS) heights (/spl sigma/<0.1/spl lambda/). We limit ourselves to the one-dimensional (1-D) rough surface with finite conductivity excited by a magnetic line source, which is equivalent to the Sommerfeld dipole problem in two dimensions (x-z plane). With the presence of finite roughness, the total field decomposes into the coherent field and the incoherent field. The coherent (average) field is obtained by using Dyson's equation, a fundamental integral equation based on the modified perturbation method. Once the coherent field has been obtained, we determine the Sommerfeld pole, the effective surface impedance, and the Zenneck wave for rough surfaces of small RMS heights. The coherent field is written in terms of the Fourier transform, which is equivalent to the Sommerfeld integral. Numerical examples of the attenuation function are compared to Monte Carlo simulations and are shown to contrast the flat and rough surface cases. Next, we obtain the general expression for the incoherent mutual coherence functions and scattering cross section for rough conducting surfaces.

The paper explores the dual-continuum unsaturated filtration model in heterogeneous porous media with rough surface topography. The rough surface topography plays a crucial role in determining the flow process and incorporates multiscale features. The mathematical model is based on the Richard’s equation with a Robin boundary condition for the rough surface boundary. The Online Generalized Multiscale Finite Element Method (Online GMsFEM) is used for coarse-grid discretization. Multiscale basis functions that encompass small-scale heterogeneities are created. Additional basis functions are generated to accommodate the impact of boundary conditions on rough surfaces. We present a consrtuction of online mulsticale basis functions that based on local residuals. All multiscale basis functions are coupled and take into account transfer term between continuums. Numerical results for a two-dimensional problem are provided, and relative errors between multiscale and reference solutions are calculated for varying numbers of multiscale basis functions to verify the results. The influence of online bases on the algorithm’s accuracy is also discussed.

For detection of a two-layered rough surface structure through ground-penetrating radar, the estimation of the profile of each layered rough surface is an important problem to be solved. In modeling and calculating the scattering of two-layered rough surfaces, we found that the profile of the upper rough surface can be observed directly through the figure of the echo from the upper surface. However, the echo of the lower rough surface has a quite different shape from its surface profile, because of the influence of the scattering of the upper rough surface. This is disadvantageous to the estimation and imaging of the profile of the lower rough surface. To solve this problem, a time-delay calibration method is proposed in this paper to be applied to the profile estimation of the lower rough surface in the case of two-layered rough interface detection. By introducing a smooth surface, the expression of time delay is derived to eliminate the influence of the scattering of the upper surface. Applying the derived expression of time delay to the echo data from the lower rough surface, the echo outline of the lower rough surface can be corrected to reflect the surface's profile shape. The calibrated B-scan echo shape shows good agreement with the profile of the lower rough surface. With this method, we can get the profile shape of the lower rough surface quickly and simply by calibrating the echo data directly. This method can be used for fast microwave imaging of two-layered rough surface and for eliminating the interference of scattering from rough surface on the echoes of nearby targets. The purpose of this paper is to solve the problem we have found in our previous work. The work of this paper is an extension of the previous work.

Measurements of down-welling microwave radiation from raining clouds performed with the Advanced Microwave Radiometer for Rain Identification (ADMIRARI) radiometer at 10.7-21-36.5 GHz during the Global Precipitation Measurement Ground Validation "Cloud processes of the main precipitation systems in Brazil: A contribution to cloud resolving modeling and to the Global Precipitation Measurement" (CHUVA) campaign held in Brazil in March 2010 represent a unique test bed for understanding three-dimensional (3D) effects in microwave radiative transfer processes. While the necessity of accounting for geometric effects is trivial given the slant observation geometry (ADMIRARI was pointing at a fixed 30 elevation angle), the polarization signal (i.e., the difference between the vertical and horizontal brightness temperatures) shows ubiquitousness of positive values both at 21.0 and 36.5 GHz in coincidence with high brightness temperatures. This signature is a genuine and unique microwave signature of radiation side leakage which cannot be explained in a 1D radiative transfer frame but necessitates the inclusion of three-dimensional scattering effects. We demonstrate these effects and interdependencies by analyzing two campaign case studies and by exploiting a sophisticated 3D radiative transfer suited for dichroic media like precipitating clouds.

Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium

Compared with the traditional microwave radiometer, one dimensional synthetic aperture microwave radiometer can effectively improve the spatial resolution of sea surface temperature retrieval. However, the spaceborne one dimensional synthetic aperture microwave radiometer is multiple incidence angle observation for the sea target and the incidence angle changes from 0° to 55°. In order to develop sea surface temperature inversion algorithms suited to one dimensional synthetic aperture microwave radiometer, it is necessary to evaluate the sensitivities of brightness temperature to oceanic and atmospheric environmental elements. Using the sea surface emissivity model and the atmospheric radiative transfer model, we construct a oceanic and atmospheric radiative transfer mode suited to the one dimensional synthetic aperture microwave radiometer. In this paper, the sensitivity changes of C-band vertical and horizontal polarization brightness temperature to oceanic and atmospheric environmental elements at different incidence angles are studied, and the corresponding sensitivity coefficients are calculated. The results indicate that the sensitivities of vertical and horizontal polarization brightness temperature to oceanic and atmospheric environmental elements show different characteristics. With the increase of the incidence angle, the sensitivity of the vertical polarization brightness temperature to the sea surface temperature is enhanced, and the sensitivity to the sea surface wind field is relatively weakened; but the horizontal polarization brightness temperature is opposite. The vertical and horizontal polarization brightness temperature errors caused by the errors of atmospheric water vapor content and cloud liquid water content increase with the increasing of the incidence angle, however, even at a large incidence angle of 55°, the errors of vertical and horizontal polarization brightness temperature are still less than 0.12 K. If the accuracy of sea surface temperature inversion is higher than 1 K, the calibration precision of one dimensional synthetic aperture microwave radiometer should be better than 0.6 K. Overall, the results of this paper are of great significance to the research of sea surface temperature retrieval with multiple incidence angle for one dimensional synthetic aperture microwave radiometer.

Wave propagation in random media, and scattering from rough surfaces have been studied extensively during the past few decades. However, the combined problem of propagation in random media with rough boundaries has not been well investigated. Yet there are many situations where there is a need for models involving random media and rough boundaries. To address this people have used hybrid approaches that directly add procedures from random media and rough surface scattering theories. Another popularly used approach for this problem is the radiative transfer theory. In contrast to these we present in this paper a unified approach which treats volumetric scattering and surface scattering on an equal footing. For illustration, we choose the following model. The permittivity of the random medium layer has a deterministic part and a randomly fluctuating part. The rough boundaries are parallel planes on the average. All random fluctuations of the problem are zero-mean stationary processes independent of each other. A point source excites waves in the random medium layer and we are interested in the propagation characteristics of waves in the layer.