Theoretical model for scattering of radar signals in K u - and C-bands from a rough sea surface with breaking waves

Abstract

A small-slope approximation (SSA) is used for numerical calculations of a radar backscattering cross section of the ocean surface for both K _u - and C-bands for various wind speeds and incident angles. Both the lowest order of the SSA and the one that includes the next-order correction to it are considered. The calculations were made by assuming the surface-height spectrum of Elfouhaily et al for fully developed seas. Empirical scattering models CMOD2-I3 and SASS-II are used for comparison. Theoretical calculations are in good overall agreement with the experimental data represented by the empirical models, with the exception of HH-polarization in the upwind direction. It was assumed that steep breaking waves are responsible for this effect, and the probability density function of large slopes was calculated based on this assumption. The logarithm of this function in the upwind direction can be approximated by a linear combination of wind speed and the appropriate slope. The resulting backscattering cross section for upwind, downwind and cross-wind directions, for winds ranging between 5 and 15 m s^?1, and for both polarizations in both wave bands corresponds to experimental results within 1–2 dB accuracy.     

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.     

Microwave Breakdown Field in a Resonant Spherical Cavity

In the present work, the microwave breakdown threshold in a gas‐filled spherical resonator, is determined for the case when the cavity is excited in its lowest order mode, which implies that the microwave field strength depends on both radius and azimuthal angle. A semi‐analytical approximation of the breakdown threshold is found using a direct variational approach. The variational predictions are compared with the results of full numerical calculations and demonstrate very good agreement     

Simulation of coherent backscattering of light in nematic liquid crystals

Multiple scattering of light by the fluctuations of the director in a nematic liquid crystal (NLC) aligned by a magnetic field is considered. A peak of coherent backscattering is calculated by numerical simulation. Since the indicatrix of single scattering for a liquid crystal (LC) is known exactly, the calculations are carried out without any simplifying assumptions on the parameters of the liquid crystal. Multiple scattering is simulated as a random walk of photons in the medium. A peak of coherent backscattering in such a medium is very narrow; therefore, the so-called semianalytical method is applied. The parameters of the backscattering peak obtained by numerical simulation are compared with the available experimental data and with the results of analytical approximations. It turns out that the experimental data are in good agreement with the results of simulation. The results of numerical simulation adequately describe the anisotropy and the width of the backscattering peak.     

Correction of temperature influence on the wind retrieval from a mobile Rayleigh Doppler lidar

A mobile Rayleigh Doppler lidar based on double-edge technique is implemented for simultaneously observing wind and temperature at heights of 15 km-60 km away from ground.Before the inversion of the Doppler shift due to wind,the Rayleigh response function should be calculated,which is a convolution of the laser spectrum,Rayleigh backscattering function,and the transmission function of the Fabry-Perot interferometer used as the frequency discriminator in the lidar.An analysis of the influence of the temperature on the accuracy of the Une-of-sight winds shows that real-time temperature profiles are needed because the bandwidth of the Rayleigh backscattering function is temperature-dependent.An integration method is employed in the inversion of the temperature,where the convergence of this method and the high signal-to-noise ratio below 60 km ensure the accuracy and precision of the temperature profiles inverted.Then,real-time and on-site temperature profiles are applied to correct the wind instead of using temperature profiles from a numerical prediction system or atmosphere model.The corrected wind profiles show satisfactory agreement with the wind profiles acquired from radiosondes,proving the reliability of the method.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

Numerical study of laser-induced collision process in Eu-Sr in strong field

Theoretically based on the four-level model, one LICET process in Eu-Sr system in both weak and strong fields was calculated by immediate numerical integrations. Numerical results in weak field are in fair to good agreement with analytical ones. Numerical results in strong field show that: (a) the peak of the LICET profiles moves to the violet side and the tuning range of the profiles obviously becomes narrower when the laser field intensity increases; and (b) numerical results in strong field differ a lot from analytical ones, which indicates that in strong field, the analytical expressions are not applicable any longer.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

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.     

数值模拟输运问题的一种破开算子方法

本文通过破开算子方法,把二维输运问题的控制方程破开为对流问题和扩散问题。在任意四边形网格的离散下,用特征线法解对流问题,并采用伽辽金加权余量法,从而有效地减少插值所引起的数值阻尼,提高计算精度。用有限单元法和迭代计算格式解扩散问题。由于采用了辛普生积分公式,在每个时间步长都不需要求逆矩律,节省了计算时间。算例表明,本文数值模拟结果与精确的理论解吻合较好。     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

大气风场和温度对无线电声波探测系统探测高度影响的数值研究

从声波扰动介质中的电波波动方程出发, 使用时域有限差分(FDTD)方法, 结合声波传播的FDTD 模型, 构建了描述声波和电波相互作用的数值模型, 并运用该模型分析风场和温度对无线电声波探测系统的探测高度的影响. 数值模拟结果表明: 温度与风场剖面的存在改变声波和电波散射回波的传播轨迹; 温度梯度剖面主要影响声波的传播速度, 风场剖面导致作为电波散射体的声波波阵面的偏移, 降低电波散射回波的强度并改变回波路径, 使得接收数据减少, 限制无线电声波探测系统的探测高度; 在强风背景下, 若降低声波散射体高度, 电波散射回波“聚束点”的偏移会有较大的改善, 但同时意味着探测高度的降低. 为了改善风场背景下无线电声波探测系统的探测高度, 可以使用双基地雷达或者增大接收天线面积等方法来实现.     

Simplification of an analytical solution of the fourth-moment equation

The equation for the fourth moment of a wave propagating in a multiply scattering random medium has been solved by various methods. When the analytical solutions are compared with numerical solutions of the equation it is found that the fundamental solution together with a first-order correction term agree very closely with the numerical results over a wide range of distances and scattering strengths. Unfortunately, the correction term involves multiple integrals and so is difficult to evaluate. This paper shows how some of these integrations can be carried out and the results combined in such a way that an analytical form similar to the fundamental solution is obtained involving only a single integral. This simplified combined solution also agrees very closely with the numerical results.     

Scattering of a TM plane wave from periodic random surfaces

This paper deals with the scattering of a TM plane wave from conductive periodic random surfaces. By means of the stochastic functional approach, the scattered field is expressed in terms of a harmonic series representation, in which the coefficients are homogeneous random functions and are given by Wiener-Hermite expansions. An approximate solution for the Wiener kernels is obtained up to the second order. Several anomalies appear in the angular distribution of the incoherent scattering because of combinations of scattering due to surface randomness and diffraction due to surface periodicity. These are incoherent Wood's anomalies associated with guided surface waves propagating along the surface, enhanced backscattering and diffracted backscattering enhancement. The physical reasons for these anomalies and numerical results are discussed.     

光子晶体传输特性的时域精细积分法分析

将精细积分法应用于时域有限差分法中,提出了一种求解光子晶体传输特性的时域精细积分法,并对其计算精度及稳定性进行了分析.从一阶麦克斯韦方程出发,在空间上采用Yee元胞进行差分离散,结合吸收边界条件及激励源表达式将方程整理为标准的一阶常微分方程组形式.通过时间步长的精细划分和指数矩阵的加法定理,在时间上利用精细积分法对齐次微分方程进行积分求解,并结合激励向量的特解得到空间离散的场分量,最终通过傅里叶变换求得方程的解.利用时域精细积分法对光子晶体进行了实例计算,并将其结果分别与时域有限差分法和四阶龙格库塔法在精度、稳定性等方面进行了比较,结果表明时域精细积分法具有更高的计算精度,并且克服了时域有限差分法以及四阶龙格库塔法在计算稳定性上对时间步长的限制.提出的方法具有精确、稳定的特点,为光子晶体传输特性的研究提供了一种新的有效的分析方法.     

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional veryrough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximationat microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation andintegral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancementon the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

Harmonic Generation of High-Power Microwave in Plasma Filled Waveguide

The harmonic generation of high power microwave in plasma filled waveguide is studied and the analytical theory is presented, and the numerical calculation and analysis of second harmonic are done in this paper. The theoretical and numerical analysis show that high power microwave can generate harmonic in the plasma filled waveguide.     

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation mad with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional very rough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximation at microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation and integral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancement on the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

Parametrically excited non-linear multidegree-of-freedom systems with repeated natural frequencies

A method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented. Attention is given to the ordering of the various terms (linear and non-linear) in the governing equations. The analysis is based on the method of multiple scales. As a numerical example involving a parametric resonance, panel flutter is discussed in detail in order to illustrate the type of results one can expect to obtain with this analysis. Some of the analytical results are verified by a numerical integration of the governing equations.