合成孔径雷达图像反演海面风向新方法的研究

提出了利用基于Tikhonov正则化的二维数值微分方法来反演合成孔径雷达图像海面风向的新方法. 首先将高分辨率合成孔径雷达图像去噪、降采样并分割成数个子图像,利用基于Tikhonov正则化的二维数值微分方法求解所关注子图像每一个点的梯度方向,在此基础上通过带有距离权重的目标函数确定子图像整体强度的梯度方向,该梯度的垂线方向就是所要求解的风向,然后进行模拟试验,在添加误差为10%的随机扰动情况下,分别基于Tikhonov正则化的二维数值微分方法与基于有限差分的Sobel算子方法来反演风向,结果表明,前者误差为0.7293°,后者误差为13.5069°,最后进行了实例试验,结果显示,Sobel算子方法的部分风向反演结果偏离整体风向明显,而基于Tikhonov正则化的二维数值微分方法的风向反演结果一致性较好. 将三个船舶报风向与相应位置合成孔径雷达图像的海面风向反演结果进行对比,Sobel算子方法的风向反演结果平均误差在9.0331°,而基于Tikhonov正则化的二维数值微分方法的风向反演结果平均误差仅为1.1148°. 关键词： 合成孔径雷达 海面风向 数值微分 Sobel算子     

基于变分方法的有限区域风场分解与重构I: 理论框架和仿真实验

众所周知, 风场分解与重构最有效的方法就是引入速度势和流函数, 其一般通过求解两个Poisson 方程得到. 由于速度势和流函数在边界上的耦合性质,有限区域风场分解是不唯一的, 这对风场分解带来了很大困难. 本文采用变分伴随结合正则化方法来克服风场分解的不唯一性, 其核心是把速度势和流函数的边值作为控制变量来反演. 目标泛函由两部分组成, 一是衡量重构风场误差大小的观测项; 二是保证风场分解问题适定的正则化项, 其目的在于寻求具有气象意义的稳定正则化解. 数值试验结果表明, 在正确选取正则化参数后, 利用变分伴随结合正则化方法进行有限区域风场分解与重构是有效可行的.     

一阶复的超定偏微分方程组的拟Riemann-Hilbert问题

本文考虑一阶非线性超定组的拟Riemann-Hilbert问题,首先考虑全纯函数的拟R-H问题,得到解的表达式,然后考虑线性问题的拟R-H问题,把问题化为标准化形式,指出一部分指标对讨论拟R-H问题已失去作用,最后讨论非线性问题,利用Schwartz公式及不动点定理,证明了在一定条件下问题是可解的。     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅱ)——ON THE POSSIBILITY OF TAYLOR EXPANSION, M CRITERION AND NONLINEAR WAVE SPEED FORMULAS

In this part, the nonlinear wave speed formulas are discussed. Because the nonlinear wave speed formulas are relative to wave form, we introduce a non-dimensional quantity M, which describes the nonlinear wave pattern and qualitatively determines the nonlinear degree. It is called M criterion. The wave speed formulas of the nonlinear Rossby wave and the nonlinear inertial gravity wave are also discussed. The wave speed of the former decreases with the growth of the amplitude but that of the latter is on the opposite. Furthermore we have also discussed the problems which must be taken note of in applying the Taylor expansion as we solve the approximate solution of nonlinear waves.     

Application of the Tikhonov regularization method to wind retrieval from scatterometer data I. Sensitivity analysis and simulation experiments

Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction error, so it is important to find where the error mainly comes. Does it mainly result from the background field, the normalized radar cross-section (NRCS) or the method of wind retrieval? It is valuable to research. First, depending on SDP2.0, the simulated `true' NRCS is calculated from the simulated 'true' wind through the geophysical model function NSCAT2. The simulated background field is configured by adding a noise to the simulated 'true' wind with the non-divergence constraint. Also, the simulated 'measured' NRCS is formed by adding a noise to the simulated 'true' NRCS. Then, the sensitivity experiments are taken, and the new method of regularization is used to improve the ambiguity removal with simulation experiments. The results show that the accuracy of wind retrieval is more sensitive to the noise in the background than in the measured NRCS; compared with the two-dimensional variational (2DVAR) ambiguity removal method, the accuracy of wind retrieval can be improved with the new method of Tikhonov regularization through choosing an appropriate regularization parameter, especially for the case of large error in the background. The work will provide important information and a new method for the wind retrieval with real data.     

Remote sensing of atmospheric duct parameters using simulated annealing

Simulated annealing is one of the robust optimization schemes. Simulated annealing mimics the annealing process of the slow cooling of a heated metal to reach a stable minimum energy state. In this paper, we adopt simulated annealing to study the problem of the remote sensing of atmospheric duct parameters for two different geometries of propagation measurement. One is from a single emitter to an array of radio receivers (vertical measurements), and the other is from the radar clutter returns (horizontal measurements). Basic principles of simulated annealing and its applications to refractivity estimation are introduced. The performance of this method is validated using numerical experiments and field measurements collected at the East China Sea. The retrieved results demonstrate the feasibility of simulated annealing for near real-time atmospheric refractivity estimation. For comparison, the retrievals of the genetic algorithm are also presented. The comparisons indicate that the convergence speed of simulated annealing is faster than that of the genetic algorithm, while the anti-noise ability of the genetic algorithm is better than that of simulated annealing.     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅰ)——ON THE PSEUDO-ENERGY, THE PSEUDO-ENERGY INFLUENCE FUNCTION AND THEIR USE

In this paper various non-dispersion solutions of nonlinear waves in the atmosphere are discussed. We turn the nonlinear partial differential equations into the nonlinear ordinary differential equations after the phase angle function has been introduced. The nature around the equilibrium points and singular points of these ordinary differential equations is discussed and various analytic expressions of the nondispersion solutions are obtained. In part (Ⅰ), two problems are dealt with mainly. (ⅰ) The relation between pseudo-energy and the pseudo-energy influence function and nonlinear waves is discussed. Through the discussion of the pseudo-energy influence function, we can determine the existential condition of the periodic solution, the solitary wave solution, the discontinuous periodic solution and the discontinuous solitary wave solution. We also indicate that if there exists an external source, which occasions infinitely small changes in the pseudo-energy influence function, the nonlinear solitary     

全球风场构建涡度、散度的新方法

目前在数值预报中通常利用风场借助于差分方法来构建涡度和散度场,这个问题涉及到观测资料求微分的问题,从数学上来说,此问题是不适定的.在有限区域上构建时可以采用一维数值微分来实现,但此方法在端点部分的资料必须是精确的,本文提出了新的方法,该方法借助于周期函数的一维数值微分,并用该方法应用到全球风场构建涡度、散度中去,同时与通常的差分方法进行了比较,利用涡度、散度计算了流函数和势函数,然后用流函数和势函数重构初始风场.结果表明,本文提出的方法算法稳定、可行且计算精度比差分方法高,为应用到全球气象资料的诊断分析及预报中提出了新的思路.