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.     

Analytical determination of the regularization parameter in the retrieval of atmospheric vertical profiles

In the retrieval of vertical profiles of atmospheric constituents, regularization methods are frequently used to improve the conditioning of the solution. The regularization reduces the retrieval errors and causes the vertical resolution to deteriorate. One obtains a trade-off by tuning the strength of the regularization by way of a regularization parameter. A new analytical method for determining the regularization parameter is presented. This method is suitable for operational retrievals, for which an unattended procedure is required. The performance of the new method is compared with that of the L-curve method, and the results show that a better trade-off between retrieval errors and vertical resolution is obtained.     

Bayesian Approach to Retrieving a Vertical Ozone Profile from Radiometric Measurement Data

We propose a technique for retrieving a vertical profile of the atmospheric ozone number density from ground-based radiometry data. The technique is based on the Bayesian approach to solving inverse problems and permits one, by allowing for measurement noise and using certain a priori information on the retrieved profile, to construct the probability distribution of the ozone number density in the entire altitude range being monitored. Using the proposed technique, we compare the retrieval results obtained for various (both well-known and suggested for the first time in this paper) methods of approximation and regularization of retrieved profiles. Model examples demonstrate that the proposed technique is capable of retrieving ozone-profile disturbances which accompany the formation of ozone holes.     

Information operator approach and iterative regularization methods for atmospheric remote sensing

In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO₂ retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen.     

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.     

垂直天线阵观测信息反演大气折射率廓线

利用垂直天线阵观测得到的电磁场信息建立目标泛函,从电磁波抛物方程传播模式出发,利用偏微分方程最优控制中的伴随方法研究大气折射率廓线反演问题. 针对反演的不适定性,采用正则化思想对目标泛函进行改造,并根据变分同化思想构建反演迭代格式. 数值模拟试验验证了理论算法的可行性. 由于采用分步Fourier算法求解电磁波抛物方程传播模式和伴随模式过程中产生的固有误差随着传播距离的增加累积增大,反演廓线在传播距离较远时不能收敛于观测廓线. 在这种情况下,引入较好的初猜廓线和背景场可以有效地改进反演结果. 关键词： 大气折射率 电磁波抛物方程 变分伴随 正则化     

合成孔径雷达资料反演海面风场的正则化方法研究

针对基于散射计地球物理模型函数的合成孔径雷达资料反演海面风场中背景风向存在很大误差的问题,提出了利用正则化方法反演海面风场,并通过L曲线准则对正则化参数进行最优选择,然后对该方法进行仿真试验.试验结果显示,正则化方法反演海面风场的风速和风向的反演精度均优于变分同化方法,分析不同真实风向情况下的反演精度表明,真实风向在45°和135°附近时,风速反演的精度高,真实风向在0°和90°时,风向反演的精度高,这种现象与地球物理模型函数中后向散射截面相对于风向的导数相关. 关键词： 合成孔径雷达 正则化 L曲线准则 变分同化     

An efficient inversion algorithm for atmospheric remote sensing with application to UV limb observations

In this paper we present a retrieval algorithm for atmospheric remote sensing. The algorithm combines Tikhonov regularization and the iteratively regularized Gauss-Newton method and is devoted to the solution of multi-parameter inverse problems with simple bounds on the variables. The basic features of the algorithm: the solution of the bound-constrained minimization problem, the selection of the optimal regularization parameter, the derivation of the global regularization matrix and the characterization of the solution (error analysis) are discussed in detailed. The inversion algorithm is applied to ozone retrieval from SCIAMACHY limb scatter measurements in the ultraviolet spectral range.     

Regularization methods in radio interferometry

The problem of image retrieval in radio interferometry is a classical example of an ill-posed problem. In this paper, we consider a new approach to the radio-interferometric imaging based on regularization, which is computationally more flexible. A new type of a weighting function suitable for managing the interferometer antenna pattern is obtained. The regularization procedure was implemented in the VLBI-image processing software developed at the Astrospace Center of the Lebedev Physical Institute (ASC LPI). It is shown that the joint use of the developed regularization methods with traditional deconvolution algorithms such as CLEAN and self-calibration improve the quality of images of cosmic radio-emission sources. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 453–460, June 2007.     

基于GOSAT卫星数据的大气甲烷反演误差分析及校正

大气甲烷(CH₄)高精度反演受到多种因素的影响,其中地表特征和大气状态的不确定性是重要的影响因素,如地表反射率、温度、湿度和压力廓线。地表反射率受到诸多因素的影响,难以获得精确的数据,会给反演结果带来较大误差。温度、湿度和压力廓线的不确定性亦是反演误差的重要来源,由此产生的系统误差难以避免,单独利用CH₄吸收带进行反演难以消除此种误差。针对各种参数不确定性的影响,本文提出比值光谱法和CO₂吸收带校正法进行校正。比值光谱法通过将绝对辐亮度谱转化为比值光谱,抑制地表反射率在反演过程中的作用。CO₂吸收带校正法利用CO₂ 1.61 μm吸收带,将CH₄柱含量转化为CH₄体积混合比,校正温度、湿度和压力廓线不确定性引起的系统误差。通过将两种校正方法结合,可同时抑制地表反射率和温度、湿度、压力廓线不确定性产生的影响,减小反演误差。利用温室气体观测卫星(GOSAT)的观测数据进行大气CH₄反演,采用比值光谱法和CO₂吸收带校正上述误差,结果显示校正后的CH₄体积混合比与GOSAT-Level2产品相当接近,反演精度可达-0.24%,反演结果较为稳健可靠。研究表明,比值光谱法和CO₂吸收带校正法可有效校正地表特征和大气状态参数不确定性引起的误差,提高大气CH₄反演精度。     

A comparison of regularization techniques for atmospheric trace gases retrievals

A comparison of regularization techniques aimed at maximizing the information content for atmospheric trace gas retrievals at an acceptable total error is presented. The total error of a retrieval is associated with the condition number of the regularized inverted matrix, which amplifies the measurement noise when moving from the measurement space to the state space as a noise error, and also together with the characteristics of the stabilizer, injects regularization error into the retrieval. Four different stabilizers: (i) the identity matrix, (ii) the first derivative operator, (iii) the second derivative operator, and (iv) the a-priori covariance matrix are used in this study to characterize the retrieval process under various regularization matrices using the regularized trust region method. For the cases simulated, it is found that the a-priori covariance matrix, which is used in traditional optimal estimation, and the identity matrix, which is used as a regularization in the Levenberg-Marquardt method, produce the highest total error, whereas the discrete one-dimensional Laplace first and second derivative operators produce the least total error at reasonably high information content.     

Determination of atmosphere parameters using navigation satellite signals

The height profile of the refractive index is determined from the solution of the inverse problem by phase measurement of navigation satellite signals. An integral equation of the first kind with a nonlinear kernel is solved on the basis of an iterative algorithm, by which a linear Fredholm equation of the first kind is solved by statistical or Tikhonov’s regularization methods in each step. The density profile and total content of water vapor in the vertical atmosphere column are found from the water vapor contribution to the retrieved profile of the refractive index. Statistical estimates of the accuracy of determination of atmosphere parameters as a function of the measurement accuracy are obtained by numerical simulation for ensembles of meteorological data under different climate conditions. The first results of retrieval of the refractive index profile using the “Transit” satellite navigation system are presented. Institute of Physics of the Atmosphere of the Russian Academy of Sciences, Moscow; Radiophysical Research Institute, Nizhny Novgorod; Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1093–1116, September, 1998.     

含噪动态光散射测量数据反演中正则化算法与Chahine算法的比较

采用两种常用的粒度反演方法——正则化和Chahine算法,对90nm与250nm单峰分布、50nm与200nm双峰分布、100nm与300nm双峰分布的模拟动态光散射数据,以及105nm、300nm标准颗粒的实测动态光散射数据进行了反演分析.结果表明:噪声水平的高低是影响粒度分布反演准确性的关键因素之一,反演结果的准确性随噪声水平的增加而降低,噪声水平超过某一阈值后,将无法得到有意义的反演结果;不同反演方法具有不同的抗噪能力,在低噪声水平下反演结果无显著差别,随着噪声水平的增加,反演结果表现出很大差异;正则化方法通过正则参数的选择可以有效抑制噪声影响,表现出强于Chahine算法的抗噪能力;与Chahine算法相比,正则化方法不需要假定初始分布,因此,在噪声较大的实验或生产过程中进行颗粒分布测量时,宜采用正则化方法.     

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。     

Application of Tikhonov regularization method to wind retrieval from scatterometer data Ⅱ: cyclone wind retrieval with consideration of rain

According to the conclusion of the simulation experiments in paper I, the Tikhonov regularization method is applied to cyclone wind retrieval with a rain-effect-considering geophysical model function (called GMF+Rain). The GMF+Rain model which is based on the NASA scatterometer-2 (NSCAT2) GMF is presented to compensate for the effects of rain on cyclone wind retrieval. With the multiple solution scheme (MSS), the noise of wind retrieval is effectively suppressed, but the influence of the background increases. It will cause a large wind direction error in ambiguity removal when the background error is large. However, this can be mitigated by the new ambiguity removal method of Tikhonov regularization as proved in the simulation experiments. A case study on an extratropical cyclone of hurricane observed with SeaWinds at 25-km resolution shows that the retrieved wind speed for areas with rain is in better agreement with that derived from the best track analysis for the GMF+Rain model, but the wind direction obtained with the two-dimensional variational (2DVAR) ambiguity removal is incorrect. The new method of Tikhonov regularization effectively improves the performance of wind direction ambiguity removal through choosing appropriate regularization parameters and the retrieved wind speed is almost the same as that obtained from the 2DVAR.     

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.     

高阶光学强度相干成像的相位恢复方法改进

为了提高强度相干方法对空间目标的成像质量,避免复杂的相位估计过程及其引入的额外误差,对高阶强度相干的相位恢复方法进行了改进.在对高阶强度相干相位测量信噪比定量讨论的基础上,选择三阶强度相干方法对远场目标测量过程进行仿真,针对相位解算过程中频谱模值传递噪声放大等问题,根据相位估计与相位测量结合的思路,提出了相位闭合正则项改进算法.通过室内强度相干成像实验,比较改进算法与最速下降法、先验信息迭代方法对相同测量结果的图像恢复效果.实验结果表明,改进算法得到的图像误差值低于原有方法,较为有效地提高了成像质量.     

Regularization methods for the extraction of depth profiles from simulated ARXPS data derived from overlayer/substrate models

Starting from posited input depth profiles of silicon oxide on silicon, 100 sets of noisy simulated ARXPS data were created for each oxide layer thickness of 3, 6, 9, 12, 15, 18, 21, 24 and 27 Å. Oxygen depth profiles were then recovered from the noisy simulated data using regularized inversion methods, including maximum entropy and Tikhonov regularization. Three regularization parameters were used: one determined by the S-curve method, one determined by the L-curve method and a third corresponding to the closest correspondence between the input and extracted profiles. The various regularization schemes evaluated were ranked with respect to their ability to reproduce the input profile.     

Bayesian approach to recovery of the vertical profile of the stratosphere temperature from the ground-based measurements of solar radiation in millimeter absorption lines of molecular oxygen

We propose a method for recovery of the altitude profile of the stratosphere temperature using ground-based radiometric measurements. The method is based on the Bayesian approach to solving inverse problems and involves determining the probability distribution for the temperature in the entire range of the sounded altitudes. In this case, we use some assumptions on noise in the experimental data and available a priori information about the recovered profile. Using the proposed approach, we compare the recovery results for two methods of approximation and regularization of the recovered profile. It is shown that using the ground-based observations of solar radiation in the oxygen absorption line 27_, it is possible to recover the temperature profile in the altitude range 20–55 km.     

Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry

This work introduces the concept of edge-field regularization into photothermal inverse depth profilometry problems. An edge field allows prior information concerning the depth location of material interfaces in a sample to be introduced into a Tikhonov regularization problem by a simple binary encoding. The edge-field regularization allows Nth-order Tikhonov stabilization constraints to be applied independently to multiple zones or segments of a depth profile between defined interface positions. This allows the reconstruction of continuous depth-profile information within known layers, without the globally imposed smoothing and edge oscillations of the classical regularization methods. This method successfully reconstructs both the amplitude of the interface discontinuities and the photothermal depth-contrast variations within the bounding edges, to a resolution limited by the resolving kernel for the underlying Nth-order Tikhonov constraint. The edge-field regularization dramatically reduces the errors associated with profiling photothermal contrast in bounded zones that are depth-displaced in the sample. Received: 19 September 2002 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-514/398-3797, E-mail: joan.power@mcgill.ca