变分伴随正则化方法从雷达回波反演海洋波导 Ⅰ.理论推导部分

针对传统统计反演算法在雷达回波反演海洋波导(RFC)方面计算量过大的问题,提出一种变分伴随正则化物理反演算法.在变分伴随方法中分别导出切线性模式、伴随方程及伴随边界条件、伴随方程求解表达式、以及泛函梯度的数学表达形式;讨论了伴随方法求泛函梯度对复方程如何协调的问题.考虑到雷达电磁波传播的特征,选择了适当的正则化项来解决反演中的不适定问题.最后给出反演算法实施中的迭代格式.     

遗传算法结合正则化方法反演海洋大气波导

针对正则化方法在解决实际反演问题时既能克服问题的不适定性又可以很大程度上抑制噪声和误差的传播, 本文提出了利用遗传算法结合正则化方法的新算法, 在遗传算法适应度函数中引入正则化项来反演波导参数; 然后对算法进行仿真试验, 结果表明新算法与传统遗传算法相比具有较高的反演精度, 并指出当噪声误差小于10%时, 算法具有较强的“去噪”性能; 最后利用机载雷达在Wallops岛探测的海表面处局部回波资料进行反演试验, 将反演结果与实测大气折射率廓线进行比较, 说明该算法的有效性. 新方法为海洋大气波导反演研究提供了一种新思路.     

大气廓线参数反演中基于大气可反演指数的正 则化参数选择方法

以大气可反演指数为指标, 采用Nelder-Mead单纯形法求解方法, 提出了一种卫星遥感资料反演大气廓线算法中动态的正则化参数选择方案. 同时针对四条典型区域廓线, 进行了选择试验. 从选择结果看, 不同廓线所对应的最优正则化参数变化幅度非常小, 因此在实际反演过程中, 为提高计算效率, 可近似取正则化参数为固定值. 这为利用卫星遥感资料进行大气廓线反演问题中正则化参数的选择提供了一种可借鉴的方法.     

雷达回波资料反演海洋波导的算法和抗噪能力研究

利用海洋环境中大气波导的参数化模型及电磁波传播的地型抛物方程,建立电磁波传播正问题,获得电磁波传播功率损耗.结合正演模式,通过遗传算法反演出大气波导参数,并对遗传算法参数的设置进行了讨论,对反演系统进行了抗噪能力的分析.发现当误差小于10%时,遗传算法仍能保持较高的反演精度;当误差大于10%时,该算法的精度开始受到显著的影响.研究结果可能会对雷达仪器设计和应用提供参考. 关键词： 波导 电磁波传播方程 遗传算法 反演     

应用一维变分法反演GPS掩星大气温湿廓线

GPS掩星观测的折射率是大气温度、湿度状态的函数, 应用一维变分方法 (1DVAR) 可以从折射率资料中同时反演出大气温、湿度廓线, 利用COSMIC 2011年中国区域掩星观测数据对这一方法进行了测试, 背景场采用ECMWF大气廓线, 反演结果与相匹配的探空观测有较好一致性. 重点研究了一维变分反演方法中非理想气体效应 (non-ideal effect) 对温度、湿度反演误差的影响, 不同月份的比较结果表明, 非理想气体效应对掩星反演大气廓线是一种系统性影响, 考虑这一效应可对温度反演改进0.1 K的偏差 (bias), 对比湿可改进约0.5%偏差. 掩星资料作为数值天气预报资料同化中少数无需偏差改正的卫星遥感资料, 非理想气体效应改正是无疑是非常重要的, 此外, 考虑这一效应对掩星资料的气候应用也有重要价值. 关键词： 一维变分 掩星 非理想气体效应     

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.     

梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用

大气Ekman层湍流系数的准确计算对数值天气预报和污染物扩散计算有着重要的意义. 将集合计算和变分法结合起来, 提出了目标泛函梯度计算的集合变分方案, 并根据正演模式的线性化情况提出了两种计算流程. 利用这种集合变分梯度算法及两种流程对Ekman层湍流系数进行了反演试验, 结果表明这种算法实施简单、方便, 根据观测资料能够比较准确地反演湍流系数值. 关键词： 梯度计算 集合变分 湍流系数 反演     

L曲线方法在地基红外高光谱反演温度廓线中的应用

利用地基红外高光谱辐射数据可以反演得到高时间分辨率的边界层大气温度廓线。目前的AERIoe最优化反演算法相比于传统的“剥洋葱”算法有较大的改进,且对初值的依赖程度较低。但AERIoe算法中正则化算子的选择对反演结果的稳定性和反演时间有重要影响。目前主要采用经验的方法选择正则化算子,迭代步数较多,耗费大量的计算时间。提出了利用L曲线方法代替经验法选取正则化算子的改进方案,以提高AERIoe方法的反演速度。改进后的算法通过绘制解范数和残余范数的二维曲线图,取其拐点作为最优的正则化参数,相比于传统的经验法有着更好的理论基础。采用2011年美国大气辐射测量计划中SGP站点的晴空大气红外辐射数据进行反演实验。结果表明,利用该方法得到的反演结果具有很好的稳定性、收敛性和精度。相比于经验的方法,利用L曲线方法获得的正则化算子反演温度廓线时的收敛速度更快,迭代步数较少,可以节约大量的计算时间;在反演精度方面,L曲线方法在边界层中上层的反演精度更高,1～3 km高度上温度廓线的RMSE值提高了大约0.2 K。     

基于二阶离散变分方法的非线性映射参数估计

提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点. 关键词： 非线性映射 参数估计 二阶离散变分方法 伴随方程     

激光雷达精确修正对流层目标定位误差

提出了一种利用纯转动拉曼激光雷达修正对流层目标定位误差的方法,其基本思想是通过接收氮气和氧气的纯转动拉曼回波信号反演大气折射率垂直廓线,根据目标定位误差理论修正不同高度处目标物的总折射角和高度定位修正值.结果表明：通过纯转动拉曼激光雷达反演大气折射率廓线,可较好修正目标定位误差.计算定位误差时得出相同高度处目标物的总折射角和高度定位修正值随视仰角的增加而减小.当视仰角为10°时,位于8 km高度处的目标物总偏折角可达3.15′,高度定位修正值为14.55 m.当视仰角为30°时,相同高度处目标物总偏折角仅 关键词： 激光雷达 定位误差 大气折射指数 大气温度     

Propagation modeling of ocean-scattered low-elevation GPS signals for maritime tropospheric duct inversion

The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface,and it can significantly affect the performance of many shore-based/shipboard radar and communication systems.We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system(GPS) signals.Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile.On the basis of a parabolic equation method and bistatic radar equation,we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct.A new GPS scattering initial field is defined for this model to start the propagation modeling.A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea.Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.     

Inversion for atmosphere duct parameters using real radar sea clutter

This paper addresses the problem of estimating the lower atmospheric refractivity (M profile) under nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled using five parameters and the horizontal structure is modeled using five parameters. The refractivity model is implemented with and without a priori constraint on the duct strength as might be derived from soundings or numerical weather-prediction models. An electromagnetic propagation model maps the refractivity structure into a replica field. Replica fields are compared with the observed clutter using a squared-error objective function. A global search for the 10 environmental parameters is performed using genetic algorithms. The inversion algorithm is implemented on the basis of S-band radar sea-clutter data from Wallops Island, Virginia (SPANDAR). Reference data are from range-dependent refractivity profiles obtained with a helicopter. The inversion is assessed (ⅰ) by comparing the propagation predicted from the radar-inferred refractivity profiles with that from the helicopter profiles, (ⅱ) by comparing the refractivity parameters from the helicopter soundings with those estimated. This technique could provide near-real-time estimation of ducting effects.     

Adjoint modeling for acoustic inversion

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.     

Monitoring of the ducting by a ground-based GPS receiver

In this paper, we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays. The vertical structure of the refractive environment is modeled using three parameters, i.e., duct height, duct thickness, and duct slope. The refractivity model is implemented with a priori constraints on the duct height, thickness, and strength, which might be derived from soundings or numerical weather-prediction models. A ray propagation model maps the refractivity structure into a replica field. Replica fields are compared with the simulation observed data using a squared-error objective function. A global search for the three environmental parameters is performed using genetic algorithm. The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated. This technique could provide near-real-time estimation of ducting effect. The results suggest that ground-based GPS provides significant atmospheric refractivity information, despite certain fundamental limitations of ground-based measurements. Radiosondes typically are launched just a few times daily. Consequently, estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates using radiosonde data alone.     

Refractivity estimation from radar sea clutter

This paper addresses the problem of estimating lower atmospheric refractivity under the nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled by using a five-parameter model, and the horizontal structure is modeled as range-independent. The electromagnetic propagation in the troposphere is simulated by using a split-step fast Fourier transform based on parabolic approximation to the wave equation. A global search marked as a modified genetic algorithm (MGA) for the 5 environmental parameters is performed by using a genetic algorithm (GA) integrated with a simulated annealing technique. The retrieved results from simulated runs demonstrate the ability of this method to make atmospheric refractivity estimations. A comparison with the classical GA and the Bayesian Markov Chain Monte Carlo (Bayesian-MCMC) technique shows that the MGA can not only shorten the inverse time but also improve the inverse precision. For real data cases, the inversion values do not match the reference data very well. The inverted profile, however, can be used to synoptically describe the real refractive structure.     

Monitoring of ducting by using a ground-based GPS receiver

In this paper,we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays.The vertical structure of the refractive environment is modeled using three parameters,i.e.,duct height,duct thickness,and duct slope.The refractivity model is implemented with a priori constraints on the duct height,thickness,and strength,which might be derived from soundings or numerical weather-prediction models.A ray propagation model maps the refractivity structure into a replica field.Replica fields are compared with the simulation observed data using a squarederror objective function.A global search for the three environmental parameters is performed using a genetic algorithm.The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated.This technique could provide near-real-time estimation of the ducting effect.The results suggest that ground-based GPS provides significant atmospheric refractivity information,despite certain fundamental limitations of ground-based measurements.Radiosondes are typically launched just a few times daily.Consequently,estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates caused by using radiosonde data alone.     

基于雷达海杂波的区域性非均匀蒸发波导反演方法

由于不同海域上空气象条件的不同, 海上蒸发波导在大尺度海面上空发生时通常是区域性非均匀的, 这一特性使得该环境中的电波传播特性相对于水平均匀的蒸发波导环境情况而明显不同, 因此, 进行区域性非均匀的蒸发波导探测反演对正确预测电波传播特性及提高雷达系统的工作性能具有重要的意义. 考虑到实际应用中蒸发波导信息获取手段的多样性, 将中尺度数值气象模式MM5预报的区域性蒸发波导修正折射率剖面作为先验信息, 提出了一种含该先验信息的区域性非均匀蒸发波导的雷达海杂波后验概率估计模型. 该模型使用主分量分析法对蒸发波导的水平非均匀性进行参数化建模, 然后通过贝叶斯理论将修正折射率剖面参数的先验概率分布、后验概率分布和似然函数联系起来, 利用雷达海杂波实现蒸发波导剖面参数的最大后验概率估计反演. 通过我国东海海域的实际区域性非均匀蒸发波导反演测试, 表明该模型能够以更高的精度实现区域性非均匀蒸发波导的反演.     

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian-MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter(RFC) is a complicated nonlinear optimization problem.This paper deals with the RFC problem in a Bayesian framework.It uses the unbiased Markov Chain Monte Carlo(MCMC) sampling technique,which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework.In contrast to the global optimization algorithm,the Bayesian-MCMC can obtain not only the approximate solutions,but also the probability distributions of the solutions,that is,uncertainty analyses of solutions.The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar seaclutter data.Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter.The inversion algorithm is assessed(i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data;(ii) the one-dimensional(1D) and two-dimensional(2D) posterior probability distribution of solutions.