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In passive microwave remote sensing of the Earth's surface, it is essential to relate the emission to geophysical parameters. The emissivity ranges between 0 and 1. Hence, a slight emissivity variation leads to a significant change in brightness temperature. Many sources of error contribute to such tiny variations in emission. This paper quantifies microwave emission variability from a rough surface through model simulation due to the non-Gaussianity in height probability density (HPD) and power spectrum density (PSD). We considered Gaussian and exponential distributions for surface height and correlation functions, representing two extremes of asperity and skewness. Additionally, the surface under consideration contains multiscale roughness. The impact of the HPD and multiscale roughness on the polarization index of the emissivity is evaluated as a function of frequency and roughness. In general, assuming that Gaussian-distributed height leads to an underestimation of the emissivity, with V polarization being less sensitive to the non-Gaussian HPD and PSD effects than H polarization, the emissions are enhanced at high roughness with small look angles but are reduced for smooth surfaces at large look angles under non-Gaussian PSD. In a specific scenario, the dynamic range of the difference between exponential and Gaussian HPD is 0~10%, and the difference in emissivity caused by non-Gaussian PSD ranges from −2% to 16%. These results should be helpful in interpreting the radiometric measurements that exhibit fluctuations and differences with model predictions. [ABSTRACT FROM AUTHOR]

Natural rough surfaces have inherent multiscale roughness. This article presents the modeling and analysis of microwave emission from a multiscale soil surface. Unlike the linear superposition of different correlation functions with various correlation lengths, we applied the frequency modulation concept to characterize the multiscale roughness, in which the modulation does not destroy the surface's curvature but only modifies it. The multiscale effect on emission under different observation geometries and surface parameters was examined using an AIEM model. The paper provides new insights into the dependence of polarized emissivity on multiscale roughness: V-polarized emissivity is much less sensitive to multiscale roughness across the moisture content from dry to wet (5–30%). The H-polarized is sensitive to multiscale roughness, especially at higher moisture content. The predicted emissivity will have considerable uncertainty, even for the same baseline correlation length, without accounting for the multiscale roughness effect. V-polarized emissivity is less sensitive to the multiscale effect than H-polarized and the higher modulation ratio indicates larger emissivity. The higher modulation ratio indicates larger emissivity. Multiscale roughness weakens the polarization difference, particularly in higher moisture conditions. In addition, ignoring the multiscale effect leads to underestimated emissivity to a certain extent, particularly at the larger RMS height region. Finally, when accounting for multiscale roughness, model predictions of emission from a soil surface are in good agreement with two independently measured data sets. [ABSTRACT FROM AUTHOR]

In modeling a rough surface, it is common to assume a Gaussian height distribution. This hypothesis cannot describe an eventual asymmetry between crests and troughs of natural surfaces. We analyzed the bistatic scattering from a rough surface with non-Gaussian height distributions using the Kirchhoff scattering theory. Two extreme cases of Gamma-distributed surfaces were compared in particular: exponential and Gaussian distributions. The bistatic angular dependence was examined under various root mean square (RMS) heights and power spectrum densities. Contribution sources to the coherent and incoherent scattering components were singled out relating to the surface height distribution. For an exponential height surface, the coherent scattering strengthens even as the surface becomes rough. The non-Gaussian effect on the incoherent scattering is connected with surface power spectrum density. The height distribution impacts differ in the different regions of the bistatic scattering plane and thus complicate the differentiation of the scattering patterns due to height distribution. [ABSTRACT FROM AUTHOR]

In this study, the bistatic radar scattering coefficients related to an oil-covered sea surface are predicted by modeling both the oil damping effect on surface roughness–through the advanced integral equation method–and the oil modification on the dielectric properties of the scattering surface. The bistatic scattering is analyzed in the whole upper scattering space under different radar frequencies, incidence angles, wind speeds, and oil thicknesses. Numerical predictions show that the scattering energy of an oil-covered sea surface is generally higher in the forward scattering zone than that in the backward one. In addition, the oil damping effect is the main mechanism ruling the scattering behavior in the backward region. The information related to the bistatic scattering geometry is also explored to retrieve oil thickness, representing one of the key parameters for radar-based marine oil pollution observation. A new index is proposed to quantify the sensitivity of bistatic scattering coefficients to oil thickness in different cases: single-polarization features, dual co-polarization features, namely, the polarization ratio (PR) and the normalized polarization difference index (NPDI), and dual-angular scattering features. Numerical results show that the bistatic scattering coefficients result in an enhanced sensitivity to oil thickness with respect to the monostatic case. The single HH-polarized scattering coefficients show better oil thickness sensitivity in the backward region, while the VV-polarized ones are more sensitive to oil thickness in the forward region. The combination of dual-polarized scattering coefficients significantly improves the oil thickness sensitivity compared to single-polarization radar observations, especially in the forward region. PR outperforms NPDI, even though the latter can suppress the effect of wind speed. The combination of dual-angular observations can significantly increase its sensitivity of oil thickness in the backward region but at the expense of reduced sensitivity in the forward region. [ABSTRACT FROM AUTHOR]

This article presents a numerical study of the wave scattering from a modulated rough surface characterized by a modulated correlation function that shows zero crossings along the lag distance. The zero crossings imply the presence of multiscale roughness. In such a way, we treat the rough surface to include a baseband correlation length and a modulation length. The modulation ratio, the ratio of baseband correlation length, and the modulated length determine the degree of multiscale roughness. We then examine the dependence of bistatic scattering, both in level and angular trends, on the modulation length. The results indicate that as the modulation ratio increases, the scattering coefficients reduce in the incident plane. Comparing the model predictions with two independent sets of measurement data demonstrates a good agreement of the scattering coefficients between the experimental data and the model predictions with modulation effects. The proposed modulated rough surface concept offers higher flexibility to model the radar scattering of multiscale rough surface. [ABSTRACT FROM AUTHOR]

Numerical simulation of random rough surface finds wide applications in scientific disciplines, e.g., radar remote sensing of terrain and sea. In scattering simulation of rough surface, not only energy conservation must be ensured, but also, perhaps equally important, the surface inherent properties must be preserved. However, the proper choice of surface and grid sizes that are statistically representative poses a problematic issue. This study applied the entropy measure to determine such parameter settings by examining the relative error of sample entropy associated with roughness parameters and by noticing the fact that a rough surface with certain roughness parameters, including power spectrum density function, must have unique sample entropy. It is found that if the two criteria are met, proper choice of surface length and grid size is attainable to warrant minimum uncertainties of rough surfaces and maximum information content for different roughness spectra density functions under different correlation lengths. The feasibility and superiority of the proposed entropy-based method are validated in terms of minimum error of roughness parameters and also the energy conservation in bistatic scattering coefficients of rough surfaces generated using obtained simulation parameters. [ABSTRACT FROM AUTHOR]

This article presents a new index, polarization-conversion ratio (PCR) to characterize depolarized bistatic scattering from rough surfaces with dielectric inhomogeneity and spatial anisotropy. We then investigate the dependence of PCR on both surface and radar parameters. Numerical results show that the distribution of PCR on the scattering plane varies with the polarization state of the incident wave and incident angle. The PCR clusters more in the cross-plane for horizontally polarized incidence. However, for vertically polarized incidence, the PCR disperses as “triangular shape” on the whole scattering plane with a sharp valley occurring in the incident plane. The following points can be drawn: 1) the inhomogeneity effectively enhances the PCR in the cross-plane; 2) the effect of anisotropy on the PCR is relatively weak, because the scattering is less affected by correlation length; 3) the impacts of surface rms height on the PCR are negative on the whole scattering plane; and 4) as the background permittivity increases, at the horizontally polarized incidence, the PCR is enhanced in the backward and forward regions, while at vertically polarized incidence, it is enhanced in the incident plane and the forward region. As is demonstrated, the PCR is an effective measure of the sensitivity of depolarization, making it potentially useful as a new reliable index for surface parameter inversion. [ABSTRACT FROM AUTHOR]

This article attempts to examine the Brewster effect of incoherent scattering from a lossy inhomogeneous rough surface with a vertical dielectric profile. Five typical dielectric profiles are selected for the purpose of illustration. In calculating the reflection coefficients, a transition model is used to convert the angle of incidence to local incidence, which accounts for the surface roughness. Numerical results show that the Brewster angle gradually moves to the large incident angle with an increase in the background dielectric constant and in the surface root-mean-squared (rms) height. The angular dependence of reflection coefficients, both the level and the trend, is slightly affected by the correlation length. The scattering strength is much more sensitive to the rms height than to the correlation length. The results could be useful in the retrieval of vertical soil moisture content when proper radar observation is available. [ABSTRACT FROM AUTHOR]

This paper examines the properties of bistatic scattering from an inhomogeneous rough surface, which, in this paper, is modeled by the transitional layer as a function of depth. The lower medium of the rough surface is horizontally uniform but vertically inhomogeneous. Both linear and circular polarizations are investigated in light of the dependences of transition rate, background dielectric constant, and surface roughness. The presence of dielectric inhomogeneity generally leads to several features that do not appear in the homogeneous surface, such as the scattering coefficient on the whole scattering plane is enhanced; the dynamic range of HH and VV over the azimuth plane is reduced; HV can be greater than VH; and the difference of LR and RR is decreased. With the increasing transition rate, the scattering coefficients for both the linear and circular polarizations are enhanced. As the background dielectric constant increases, the scattering responses of the linear and circular polarizations are quite different. For the linear polarization, HH exhibits a stronger angular dependence; VV reduces in the forward region and enhances notably in the backward region; and HV decreases but VH increases. For circular polarizations, the cross-polarized LR increases in the backward region but decreases in the forward region, and the copolarized RR enhances on the whole scattering plane. With the increasing surface roughness, the scattering coefficient becomes more evenly distributed over the entire scattering plane. [ABSTRACT FROM AUTHOR]

This paper examines the polarized backscattering of spatially anisotropic rough surfaces. To better explore the physical mechanisms that control the azimuthal dependence of the backscattering from anisotropic surfaces, the effects of surface roughness [correlation length and root-mean-square (rms) height], dielectric constant, and radar parameters from anisotropic surfaces are studied. The advanced integral equation model (AIEM) is used to simulate both co- and cross-polarized backscattering coefficients, including the single and multiple scattering. Numerical results suggest that the multiple scattering exhibits a stronger azimuthal dependence for HH than VV polarization, especially more so at a larger incident angle. For weakly anisotropic surface, the azimuthal variation of backscattering tends to be a sinusoidal-like pattern. However, with the enhancement of anisotropy, such a scattering pattern is distorted, and the sharp dip appears at up/down direction. As the rms height and dielectric constant increase, the scattering is enhanced on the whole. The HH/VV ratio at lower dielectric constant is greater than that at higher one. In comparison, scattering shows stronger dependence on anisotropy at lower dielectric constant, especially at a larger incident angle. As an application example, we compare the model predictions with reported measurements from two different sites. Preliminary results are quite encouraging, and thus, the analysis presented in this paper is potentially useful to predict and interpret backscattering from crop field surface, where strong anisotropic surfaces commonly present due to plowing or raking practice. [ABSTRACT FROM AUTHOR]

We apply Shannon entropy, an information content measure, in sensitivity analysis (SA), stemming from the fact that the essence of SA is to preserve the maximum information content of the parameters of interest that are inverted from the radar response. Then, the sensitivity to the observation configuration and surface parameters is subsequently analyzed. Attempts are also made to explore advantages, by maximizing the information content, of dual-polarization and multi-angle in improving the parameter retrieval from radar sensing of rough surface. Simulation results show that the entropy is a good indicator of the sensitivity of the radar response to the surface parameter, as it contains information on not only the probability distribution of the scattering coefficient but also on its deviation. By information entropy, richer details, to large extent, on the scattering behavior are offered through quantitatively predicting the scattering signal saturation, evaluating the effect of using multi-polarization and multi-angle observation configuration, and identifying non-significant variables. It is found that Shannon entropy, compared to Renyi entropy, appears to better represent the sensitivity with respect to monotonic variation and narrower parameter ranges. The proposed entropy-based SA method helps to deepen our understanding of the microwave scattering behavior in response to surface parameters. [ABSTRACT FROM AUTHOR]

In this paper, an attempt is made to investigate the angular signatures of bistatic scattering, in the azimuthal direction, from rough surfaces, with the aim of deepening our understanding of the bistatic scattering behaviors and exploring its potential applications. Three distinct angular features, dip angle, scattering strength, and angular width, as a function of the surface roughness and dielectric constant, are identified. Brewster’s scattering, and its role in angular behavior, is examined at limited extent. Results reveal that the angular features strongly correlate with the surface parameters and scattering geometry. For small scattering angle, dip angle and width are independent of surface roughness. Comparatively, for larger incident and scattering angles, beyond 50°, the dip angle and scattering strength are sensitive, simultaneously, to rms height and dielectric constant, while the dip width only responses to rms height. Dips, induced by Brewster’s scattering effect, not only shift in the polar direction, but also in the azimuthal direction, and are strongly dependent on surface parameters and bistatic geometry. Increasing the surface roughness or, equivalently, the incident angle tends to promote the disappearance of dips. The main contributions of this paper can be summarized as follows: 1) quantitative description of dip features, including angle, scattering strength, and angular width; 2) comprehensive characterization of the dip features and their dependence on surface parameters and bistatic geometries; and 3) limited investigation of the behavior of Brewster’s scattering-induced dip. [ABSTRACT FROM PUBLISHER]

Theoretical modeling plays a significant role as forward and inverse problem in active and passive microwave remote sensing. Understanding the validity and limitations of the models is essential for model refinements and, perhaps more importantly, model applications. Motivated by these, this paper presents a comprehensive analysis of the scattering, both backscattering and bistatic scattering, and emission of rough soil surface predicted by the advanced integral equation model (AIEM), a well-established theoretical model. Numerically simulated data, covering a wide range of surface parameters, and in situ measurement data set of well-characterized bare soil surfaces were used to evaluate the performance of AIEM in predicting the scattering coefficient and microwave emissivity over a wide range of geometric parameters and ground surface conditions. The results show that the AIEM predictions are generally in good consistency with both numerical simulations and experiment measurements in terms of angular, frequency, and polarization dependences, except for some deviations in a few cases (e.g., at large incident angles and dry soil conditions). Extensive comparison confirms the effectiveness and practicability of AIEM for both scattering and emission of rough soil surface. Possible explanations for the discrepancy between the model prediction and data are given, together with suggestions for model usage and refinements. [ABSTRACT FROM AUTHOR]

In this paper, a physically based numerical electromagnetic approach, by solving Maxwell's equations, is developed to investigate the scattering and the emission from double-layered media, where both the top and bottom interfaces are random sastrugi surfaces with a random horizontal shift between the two corresponding negative-slope facets of both interfaces. Numerical simulations are illustrated for bistatic scattering and four Stokes parameters at L-, C-, X-, and K-bands. Results indicate that the bistatic scattering and Stokes parameters are asymmetric for the double-sastrugi media, whereas for the other two structures, sastrugi surface alone and sastrugi surface with a planar bottom boundary, their scattering and the first two Stokes parameters are even symmetric relative to the azimuthal angle of 90°, and the third and fourth Stokes parameters are odd symmetric. In particular, the Stokes results no longer have the strong coherent fluctuations in angular variations shown in periodic double-layered structures because the random double-layered structure eliminates the coherent interference. It is interesting to observe that the internal total reflection may cancel if the coupled interactions between the two sastrugi interfaces are very strong, which results in decreasing scattering at the L-band, and its Stokes parameters are similar to those of the sastrugi alone. Numerical results also reveal that the maxima of cross-polarized specular scattering from double-sastrugi structures can be observed at cross incidence; however, they are at a deep dip for the latter two statistical symmetric structures. The sastrugi-sastrugi structure, being geometrically anisotropic, is capable of generating strong cross-polarized scattering and, subsequently, significant amounts of the third and fourth Stokes. The azimuthal patterns, at a viewing angle of 55°, of four Stokes parameters, although more complex, are feature rich where two striking extrema of third and fourth Stokes are presented. Compared with the L-band, the C-band presents strong azimuthal dependence of four Stokes. The simulation results offer deeper insights into the scattering and emission process in sastrugi surface and may lead to better retrieval of surface parameters from radar or radiometric measurements. [ABSTRACT FROM PUBLISHER]

This paper investigates the radar image statistics of rough surfaces by simulating the scattered signal's dependence on the surface roughness. Statistically, the roughness characteristics include the height probability density (HPD) and, to the second-order, the power spectral density (PSD). We simulated the radar backscattered signal by computing the far-field scattered field from the rough surface within the antenna beam volume in the context of synthetic aperture radar (SAR) imaging. To account for the non-Gaussian height distribution, we consider microscopic details of the roughness on comparable radar wavelength scales to include specularly, singly, and multiply scatterers. We introduce surface roughness index (RSI) to distinguish the statistical characteristics of rough surfaces with different height distributions. Results suggest that increasing the RMS height does not impact the Gaussian HPD surface but significantly affects the Weibull surface. The results confirm that as the radar frequency increases, or reaches a relatively larger roughness, the surface's HPD causes significant changes in incoherent scattering due to more frequent multiple scattering contributions. As a result, the speckle move further away from the Rayleigh model. By examining individual RSI, we see that the Gaussian HPD surface is much less sensitive to RMS height than the Weibull HPD surface. We demonstrate that to retrieve the surface parameters (both dielectric and roughness) from the estimated RCS, less accuracy is expected for the non-Gaussian surface than the Gaussian surface under the same conditions. Therefore, results drawn from this study are helpful for system performance evaluations, parameters estimation, and target detection for SAR imaging of a rough surface. [ABSTRACT FROM AUTHOR]

Fully bistatic radar scattering from rough surfaces is of vital importance in terrain remote sensing, but results in bulky data volume. The scattering is dependent on physical parameters of the media and is controlled by the radar observation geometry. Together, the two sets of parameters determine the scattering patterns in a bistatic plane confined by incident and polar angles in both incident and scattering directions. For radar remote sensing, it is desirable to infer surface parameters of interest, with satisfactory accuracy, from large volumes of measured data sets. This is essentially a task of data mining. In this paper, we present model-generated bistatic radar scattering data, followed by a sensitivity analysis, to identify a suitable configuration in terms of parameter inversion from fully bistatic measurements by a Kalman filter-trained dynamic learning neural network (DLNN). Results indicate that with bistatic observation, superior retrieval performance (as compared to backscattering observation) can be readily achieved. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate, by means of experimental measurements and full-wave simulations, the dominant factors for the very high-resolution (VHR) radar image speckles from exponentially correlated rough surfaces. A Ka-band radar system was used to collect the return signal from such a surface sample fabricated by 3D printing and that signal was further processed into images at different resolution scales, where the image samples were obtained by horizontally turning around the surface sample. To cross-validate the results and to further discuss the VHR speckle properties, full wave simulations by full 3D Finite Difference Time Domain (FDTD) method were conducted with 1600 realizations for the speckle analysis. At the considered very high resolution, speckle statistics show divergence from the fully developed Rayleigh distribution. The factors that impact on the high-resolution speckle properties from exponentially correlated rough surface, are analyzed in views of the equivalent number of scatterers theory and scattering scales, respectively. From the data results and extended discussions, it is evident that both of the above factors matter for VHR speckle of backscattering, from the exponentially correlated rough surface as a good representative for the ground surface. [ABSTRACT FROM AUTHOR]

We investigate the magnitude of Sun-glint through modeling the Soil Moisture Active Passive (SMAP) brightness temperature (BT). Model results show that the specular reflection of Sun-glint in the L-band can spread over a wide range of view angles due to the roughness and undulation of the land surface and therefore affect SMAP radiometer observations. Due to SMAP’s low incidence angle (40°), Sun-glint in the specular direction is never observed, and only the noncoherent component of Sun-glint has influence on SMAP observations. Sun-glint is particularly an issue over wet soil surfaces at low solar zenith angles (SZAs), and caution has to be taken for the terrain effect even for high SZAs, because the local solar incident angle can be significantly changed by the terrain slope and then the specular reflection of Sun-glint can be viewed by SMAP. Model results also show that BT in V-pol is less contaminated by Sun-glint than that in H-pol. During an intense solar radio burst, it was found that the land surface BT in H-pol increased by 50 K in the forward scattering direction from the SMAP observation. This is roughly equivalent to 1 K increment by every 100 solar flux units on a dry soil and/or dense vegetation. When the solar activity is quiet in 2015, the Sun-glint from both wet land and ocean surfaces can reach up to 10 K in the SMAP L1B BT product. This paper suggests that BT observations around the solar specular direction should be masked for soil moisture retrieval at the L-band. [ABSTRACT FROM PUBLISHER]

Electromagnetic scattering and emission from 1-D rough surfaces with multiple elevations are studied using full-wave simulations. Both the root-mean-square (rms) heights and the surface length are large compared to the wavelength. A novel multilevel steepest decent-sparse matrix canonical grid (MLSD-SMCG) method is proposed to address limitations in the original SMCG. The uniform Nystrom method and neighborhood impedance boundary condition (NIBC) are also incorporated in solving the dual surface integral equations (SIEs) of the method of moments (MoM). Simulation results are illustrated at L-band for soil and ocean surfaces. The surface rms heights and lengths are up to 1.43 and 243.8 m corresponding to 6 and 1024 wavelengths at 1.26 GHz, respectively. For ocean surfaces, the wind speeds up to 20 m/s are considered, and the entire spectrum is included to capture all relevant surface length scales. Numerical results indicate the proposed approach is computationally efficient and accurate. Energy conservation checks in simulations are at 10−4 for ocean scattering and emission. Also, the effects of wind-driven roughness on ocean emissivity are further investigated using the proposed approach in terms of wind speed and observation angle for both polarizations. [ABSTRACT FROM AUTHOR]