Electromagnetic backscattering from one-dimensional drifting fractal sea surface Ⅱ:Electromagnetic backscattering model

Sea surface current has a significant influence on electromagnetic(EM) backscattering signals and may constitute a dominant synthetic aperture radar(SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section(NRCS) discrepancies between the model for a coupled wavecurrent fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle,as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface.     

Microwave backscattering from the sea surface with breaking waves

Based on the effective medium approximation theory of composites, the whitecap-covered sea surface is treated as a medium layer of dense seawater droplets and air. Two electromagnetic scattering models of randomly rough surface are applied to the investigation of microwave backscattering of breaking waves driven by strong wind. The shapes of seawater droplets are considered by calculating the effective dielectric constant of the whitecap layer. The responses of seawater droplets shapes, such as sphere and ellipsoid, to the backscattering coefficient are discussed. Numerical results of the models are in good agreement with the experimental measurements of horizontally and vertically polarized backscattering at microwave frequency 13.9GHz and different incidence angles.     

Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 520–544, June, 2000.     

Electromagnetic backscattering from one-dimensional drifting fractal sea surface I: Wave-current coupled model

To study the electromagnetic backscattering from a one-dimensional drifting fractal sea surface, a fractal sea surface wave-current model is derived, based on the mechanism of wave-current interactions. The numerical results show the effect of the ocean current on the wave. Wave amplitude decreases, wavelength and kurtosis of wave height increase, spectrum intensity decreases and shifts towards lower frequencies when the current occurs parallel to the direction of the ocean wave. By comparison, wave amplitude increases, wavelength and kurtosis of wave height decrease, spectrum intensity increases and shifts towards higher frequencies if the current is in the opposite direction to the direction of ocean wave. The wave-current interaction effect of the ocean current is much stronger than that of the nonlinear wave-wave interaction. The kurtosis of the nonlinear fractal ocean surface is larger than that of linear fractal ocean surface. The effect of the current on skewness of the probability distribution function is negligible. Therefore, the ocean wave spectrum is notably changed by the surface current and the change should be detectable in the electromagnetic backscattering signal.     

Optical backscattering measurements from fractal surfaces and their possible relevance to radar scattering from the sea surface

In spite of recent progress, existing theories of electromagnetic wave scattering by rough surfaces cannot yet explain several important features of microwave sea echo, particularly in grazing incidence geometries. To explain them it is necessary to develop scattering models that can reproduce the features in a robust way. The aim of this paper is to report laboratory optical frequency experiments designed to aid achievement of this objective. In particular, polarization sensitive measurements of the backscattered intensity are reported for a range of characterized fractal surfaces using visible laser radiation. The appearance of enhanced backscattering peaks are observed even quite close to grazing incidence for some types of surfaces and indicate the importance of multiple scattering. It is also shown that the dependence of the backscattering cross-section on incidence angle bears some gross similarities to that obtained from microwave scattering from the sea surface for high index fractal surfaces that exhibit intermittency.     

Measurement of sea ice backscattering characteristics

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 495–399, April, 1989.     

Monostatic Radar Cross Section of an object above a sea surface from a rigorous method

The rigorous computation of the monostatic RCS (Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to solve a problem involving a high number of unknowns. Thus, a recently developed fast numerical method, called E-PILE (Extended Propagation-Inside-Layer Expansion), was combined with FB-SA (Forward–Backward with Spectral Acceleration). Two objects are considered in this article: the cross and the cylinder. Results obtained from E-PILE + FB-SA allow us to understand the physical mechanisms involved in the coupling between the object and the sea surface.     

Leaky helical flexural wave backscattering contributions from tilted water-filled cylindrical shells

Helical flexural waves on a bluntly truncated tilted water-filled cylindrical steel shell in water are found to give large contributions to the backscattering above the coincidence frequency. The presence of the water inside the shell increases the damping of the leaky wave when short tone bursts are used. The magnitude of the scattering is found by modifying a ray analysis developed for empty shells. When longer bursts are used, some of the internally radiated energy (corresponding to the case of one internal chord) is superposed on the ordinary helical ray backscattering. This occurs as a consequence of the internal excitation of helical rays.     

A time domain rough surface scattering model based on wedge diffraction: application to low-frequency backscattering from two-dimensional sea surfaces

A time domain method for calculating the acoustic impulse response of impenetrable, rough, two-dimensional (2D) surfaces is presented. The method is based on an extension of the wedge assemblage (WA) method to 2D surfaces and objects. Like the WA method for one-dimensional (1D) surfaces, the approach for 2D surfaces uses Biot's and Tolstoy's exact solution for the impulse response of an infinite impenetrable wedge [J. Acoust. Soc. Am. 29, 381-391 (1957)] as its fundamental building block. The validity of the WA method for backscattering from 2D sea surfaces is assessed through comparisons with calculations based on Milder's operator expansion (OE) method [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Average intensities for backscattering from 2D fully developed seas (20 m/s wind speed) were computed by the WA and OE methods using 50 surface realizations and compared at 11 frequencies between 100 and 200 Hz. A single, moderately low grazing angle of incidence (20 degrees) and several scattered grazing angles (90 degrees, 45 degrees, 20 degrees , and 10 ) were considered. Excellent overall agreement between the two models was obtained. The utility of the WA method as a tool to describe the physics of the scattering process is also discussed.     

波破碎下海洋表面微波辐射率的一种模式

利用有效介质近似理论方法，本文提出了计算强风驱动下海浪破碎的海洋表面微波辐射率的一种修正模式。该模式修正Pandey等人的经验模式，通过把海浪破碎的白冠层等效为海水和空气的复合介质，并利用复合介质有效介电常数的计算方法，在该模式中充分考虑了海洋表面水滴形态、白冠层厚度和覆盖率对海洋表面微波辐射率的影响。实验表明，该模式在不同风速、不同水滴形态以及微波频率下（6.6GHz,10.7GHz,37GHz）计算的海洋表面微波辐射率与实测结果一致。     

Observation of sunlight enhanced backscattering from the sea bottom near the beach

The paper describes a natural manifestation of the enhanced backscattering effect in conditions when sunlight is scattered by the sea bottom covered by shallow rippled water. In this system the water surface plays the role of a phase screen that focuses the light on the bottom, while the sandy bottom acts as a set of random single scatterers.     

HF ground wave propagation over a curved rough sea surface

For a vertically polarized line source, in the context of HF (3–30?MHz) ground wave propagation over a curved rough sea surface, this paper presents different asymptotic and rigorous methods to compute the attenuation function. When the Earth's curvature is taken into account, the attenuation function is expressed as a series, in which the roots of a differential equation, depending on the Airy function, must be calculated. In addition, from Taylor series expansions, different closed-form expressions can be obtained. For a smooth sea surface, the purpose of this paper is to compare these different formulations with fast rigorous numerical methods, such as the BMIA-CAG (Banded-Matrix-Iterative Approach CAnonical-Grid) and FB-SA (Forward-Backward Spectral-Acceleration) methods, based on the method of moments and originally developed for rough surfaces. These methods are especially efficient to solve a problem with huge unknowns, which is required to predict the ground wave propagation over a long surface. In addition, from a partial fraction expansion of the attenuation function in the Laplace domain, the Bremmer asymptotic expansion is extended to any order by including the surface roughness.     

Theory of radio wave scattering at a rough sea surface

The problem of the reflection of a plane single-frequency electromagnetic wave from a statistically rough dielectric boundary with arbitrary is solved in the perturbation approximation. The statistical characteristics (scattering cross section, change of polarization, and frequency spectrum) of a radar signal reflected from a rough sea surface are investigated. The model used for the surface—a small ripple superimposed on large waves—enables the perturbation theory approach to be extended to the decimeter and centimeter wave band.Izvestiya VUZ. Radiofizika, Vol. 9, No. 5, pp. 876–887, 1966     

A versatile composite surface model for electromagnetic backscattering from seas

A versatile composite surface model (VCSM) is presented for estimation of the electromagnetic backscattering coefficient of the sea. Taking into account the statistical characteristics of the sea surface and the validity conditions of component models for the small-scale and large-scale surfaces in the composite surface model (CSM), a method for the two-scale decomposition of sea surfaces is introduced. On this basis, the cutoff wavenumber with wind speed dependence and incident wave frequency dependence is applied to separate the sea spectrum into large- and small-scale components at different sea states with increased accuracy. Then, numerical results of the backscattering coefficient are evaluated and discussed in the case of different wind speeds, polarizations as well as incident frequencies. Finally, the VCSM is verified through the comparisons with the available experimental data, and the comparisons of the VCSM results and the classical CSM results also show that the VCSM behaves better.     

A stochastic model for backscattering on the sea

Backscattering of radar waves on the sea takes place even when there is no target. It appears as a noise which it is necessary to study in decision problems. Today, the model of a mixing of Gaussian for spectra seems widely agreed. In this paper, we show that it is equivalent to a mixing of monochromatic waves whose trajectories are time perturbed by Gaussian processes. In addition, this model explains linear variations of Doppler shifts and spectral widths with the emitted frequencies.     

Study on electromagnetic backscattering and Doppler spectrum of a moving spherical target above time-varying sea surface

The surface electric current of the sea surface and the first-order scattering field from the spherical target were obtained by employing Physical Optics method and Mie theory, respectively. The backscattering field of the time-evolving sea surface was calculated by using Kirchhoff Approximation. Meanwhile, by taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary coupling scattering fields from the spherical target above the sea surface was reduced. The dependence of the secondary coupling backscattering field on the size and the position of the spherical target was discussed, and the characteristic of the Doppler spectrum of the composite backscattering field with different incident angles was analyzed in detail. Supported by the National Natural Science Foundation of China (Grant No. 60571058) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070701010)     

Electromagnetic wave backscattering from a cloud of alpha-emitting radioactive elements in air

A track model is proposed for the electromagnetic wave scattering from a cloud of radioactive elements in air. Relationships are derived for estimating the radar cross section of the cloud of alpha-emitting radioactive elements as a function of the cloud activity and the wavelength of the electromagnetic wave. The activity of a cloud detected by a standard radar is estimated.     

Study of backscattering from a complex scatterer at 3mm wave band

The backscattering characteristics of complex scatterer has been studied theoretically at 3 mm wavelength for the first time. RCS of the practial complex scatterer was calculated with GTD and the physical optics. The constrict model was also measured. The experimental results are in agreement with the theoretical calculations.