Atmospheric trace gases profile retrievals using the nonlinear regularized total least squares method

We discuss the regularized total least squares (RTLS) method for the nonlinear overdetermined ill-posed problem of atmospheric trace gas retrieval. The RTLS method is used for the automatic determination of the regularization strength of the ill-conditioned matrix in an iterative process, and a mixed quadratic and cubic line search method is used for the nonlinear retrievals. Additional retrieval metrics, such as the model resolution matrix and the degrees of freedom in the retrieval, which characterize the vertical resolution of the retrievals, are also derived. Simulated retrievals as well as the retrieval from the data of a balloon-based spectroscopic measurement will be discussed. Retrieval results obtained using O₃ and CH₄ as test cases will be presented.     

大气CO2卫星遥感中植物叶绿素荧光影响的校正

大气CO₂卫星遥感监测的关键在于高精度,而植物叶绿素荧光存在与大气散射相似的光谱特征,干扰大气散射相关参数的反演结果,从而影响CO₂的反演精度。因植物叶绿素荧光强度微弱且影响特征与大气散射高度相关而难以准确校正。鉴于现有大气CO₂卫星遥感精度不足,以及植物叶绿素荧光对大气CO₂反演存在不可忽视的影响程度和复杂性,设计了O₂-A、1.6和2.06 μm CO₂三个光谱带协同的参数化校正方法。首先通过对大气散射采取基于光子路径长度概率密度函数（PPDF）的参数化建模,降低叶绿素荧光与大气散射参数的光谱相关性;其次,针对叶绿素荧光强度弱,难以准确反演的问题,基于轨道碳观测器（OCO-2）的叶绿素荧光产品构建了5km分辨率的全球叶绿素荧光先验信息库,增强CO₂与叶绿素荧光同步反演中对叶绿素荧光的先验约束,提高叶绿素荧光的反演精度。通过O₂-A、1.6和2.06 μm CO₂三个光谱带的协同同时反演大气散射、叶绿素荧光和大气CO₂,并结合叶绿素荧光丰富的先验信息,能够较准确剥离大气散射和叶绿素荧光而提高大气CO₂的反演精度。选择叶绿素荧光强度明显较高的柱总碳观测网络（TCCON）中的Park Falls（45.945°N,90.273°W）站点开展验证,对该站点近4年每年8月份的温室气体观测卫星（GOSAT）数据进行反演,发现植被叶绿素荧光导致GOSAT XCO₂反演结果系统偏低2×10-6(ppm)左右,通过本文的方法进行校正,反演结果的低估程度有明显改善,最大低估由2.58 ppm降低到1.49 ppm,且离散程度也有一定程度的改善,明显控制了CO₂反演中叶绿素荧光的影响,对于实现1%（~4 ppm）的CO₂反演精度来说,提供了有力支撑。     

AIRS与COSMIC反演大气温湿廓线比较

将福卫三号星系计划(COSMIC)气象、电离层及气候卫星探测系统、大气红外探测器(AIRS)反演的大气温度和湿度廓线与时间、空间匹配的欧洲中心中期天气预报(ECMWF)、美国环境预报中心(NCEP)分析值和无线电探空观测值进行比较, 结果表明, COSMIC具有垂直分辨率高、全天候的观测特点, 反演的大气温度和湿度廓线相对于AIRS而言与无线电探空观测值更接近, 能提供大气廓线的更精细结构, 但受掩星事件发生时所能探测最低高度的限制, 不能得到该高度以下的大气信息。AIRS在晴空时大气温湿廓线反演精度较高, 但受云天的限制, 在云层以下, 反演精度就大大降低。     

A new method for information retrieval in two-dimensional grating-based X-ray phase contrast imaging

Grating-based X-ray phase contrast imaging has been demonstrated to be an extremely powerful phase-sensitive imaging technique.By using two-dimensional(2D) gratings,the observable contrast is extended to two refraction directions.Recently,we have developed a novel reverse-projection(RP) method,which is capable of retrieving the object information efficiently with one-dimensional(1D) grating-based phase contrast imaging.In this contribution,we present its extension to the 2D grating-based X-ray phase contrast imaging,named the two-dimensional reverseprojection(2D-RP) method,for information retrieval.The method takes into account the nonlinear contributions of two refraction directions and allows the retrieval of the absorption,the horizontal and the vertical refraction images.The obtained information can be used for the reconstruction of the three-dimensional phase gradient field,and for an improved phase map retrieval and reconstruction.Numerical experiments are carried out,and the results confirm the validity of the 2D-RP method.     

Preparation of cluster states with trapped electrons on a liquid helium surface

We present a scheme for the preparation of one-dimensional (1D) and two-dimensional (2D) cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions (the x direction) serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.     

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.     

大气SO2柱总量遥感反演算法比较分析及验证

卫星遥感技术已成为城市污染气体SO₂监测和全球火山活动监测及预警的重要手段. 目前新的PCA (principal component analysis)算法有效减小了反演数据噪声, 并替代之前业务算法BRD (band residual difference)用于边界层SO₂柱总量产品的反演. 然而, 目前对PCA算法反演产品精度的评价和验证研究较少, 缺少与BRD算法产品进行长时间序列的比较以评估算法适用性, 尤其在中国大气污染重点城市区域. 本文利用地基多轴差分吸收光谱仪(MAX-DOAS)观测及多尺度空气质量模式系统(RAMS-CMAQ)大气化学模式模拟等数据, 评估PCA和BRD 反演算法的精度及误差. 另外, 选取洁净海洋地区、中国大气污染重点城市区域和高浓度火山喷发三种情况, 比较分析PCA 与BRD SO₂ 总量的时空格局变化差异及对不同SO₂总量下的适用性, 并对两种算法反演不确定性进行分析讨论. 结果表明, 在中国京津冀、珠江三角洲和长江三角洲区域, PCA SO₂总量反演值低于BRD, BRD反演结果更接近于地基的MAX-DOAS观测值, 冬季BRD和PCA SO₂总量值低于RAMS-CMAQ 模拟结果, 夏季7月和8月BRD SO₂总量值高于RAMS-CMAQ 模拟结果. 在SO₂总量接近于0 值的洁净海洋地区, PCA 算法产品噪声水平低于BRD算法, 但PCA 反演结果整体偏差大于BRD算法. 在高浓度火山喷发情况下, 当SO₂总量大于25 DU时BRD SO₂总量反演值低于PCA, 且随着SO₂ 总量增大, 两种算法反演值差异亦增大. 该研究对于OMI (Ozone Monitering Instrument) SO₂产品的应用具有重要的参考价值, 通过分析不同反演算法的差异及对其不确定性追因, 对于算法改进研究也具有重要的科学意义.     

Angular and radial mode analyzer for optical beams

We describe an approach to determining both the angular and the radial modal content of a scalar optical beam in terms of optical angular momentum modes. A modified Mach-Zehnder interferometer that incorporates a spatial rotator to determine the angular modes and an optical realization of the fractional Hankel transform (fHT) to determine the radial modes is analyzed. Varying the rotation angle and the order of the fHT produces a two-dimensional (2D) interferogram from which we extract the modal coefficients by simple 2D Fourier analysis.     

Spectral line finding program for atmospheric remote sensing using full radiation transfer

We have developed a line-by-line code to simulate atmospheric spectra in the infrared spectral region assuming a remote light source of selectable temperature. Selecting the source temperature allows simulation of, for example, solar absorption spectra, lunar absorption spectra or emission spectra. The code is applicable for different geometries, from the ground, balloon or from satellite, and allows a simple search for the most suitable lines for the retrieval of atmospheric trace gas concentrations for the different geometries. In addition, a first estimate of the optimized microwindow size and the most important interfering gases that need to be considered is calculated automatically. This approach is of importance in cases where it is necessary to analyze numerous lines simultaneously to get sufficient precision in the trace gas concentration retrievals. Examples for H₂O and CO are given.     

利用红外高光谱资料CrIS反演大气温湿廓线的模拟研究

大气温湿廓线是数值预报中最基本的气象参数,高光谱红外卫星可以观测到较高垂直分辨率的大气信息,为了准确获取廓线信息,利用搭载于美国对地观测卫星Suomi NPP(national polar-orbiting partnership)平台上的CrIS(cross-track infrared sounder)红外高光谱观测资料,讨论了通道选取方法,采用特征向量统计法反演法得到初始大气廓线,利用非线性牛顿迭代法进一步提高反演精度。将反演结果和全球数据同化系统GDAS(global data assimilation system)模式分析数据以及配对的无线探空值进行比较,发现反演结果与真值趋势一致,较之初始廓线有显著提高,在100～700 hPa之间,温度廓线反演精度最高,均方差小于1 K,在300～900 hPa之间,湿度廓线反演精度最高,均方差小于20%,与所选取通道的雅各比峰值区间一致。     

Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.     

Optimal interpolation method for intercomparison of atmospheric measurements

Intercomparison of atmospheric measurements is often a difficult task because of the different spatial response functions of the experiments considered. We propose a new method for comparison of two atmospheric profiles characterized by averaging kernels with different vertical resolutions. The method minimizes the smoothing error induced by the differences in the averaging kernels by exploiting an optimal interpolation rule to map one profile into the retrieval grid of the other. Compared with the techniques published so far, this method permits one to retain the vertical resolution of the less-resolved profile involved in the intercomparison.     

Non-Voigt line-shape effects on retrievals of atmospheric ozone: Collisionally isolated lines

This paper addresses the question of errors in retrievals of vertical profiles of ozone from atmospheric spectra caused by assuming that the absorption lines have pure Voigt line shapes. The case of collisionally isolated transitions (no line mixing) is treated by considering only the effects of the speed dependence (SD) of the pressure broadening. The case of O₃ retrievals from a sequence of limb transmission spectra is first treated theoretically. The results show that the influence of SD is very small, leading to changes in the residuals and in the retrieved O₃ mixing ratios smaller than 1%. These findings are then confirmed by treating a series of spectra recorded by the ACE-FTS instrument. Similar exercises are also made for other observation techniques by treating simulated or measured limb and nadir emission spectra as well as ground-based solar and in-situ laser transmission data. All lead to the general conclusion that SD (and Dicke narrowing) can be neglected in retrievals of ozone amounts from recorded atmospheric spectra. Indeed, the biases caused in the ozone profiles by the use of pure Voigt line shapes still remain significantly smaller than the total error/uncertainty from other sources such as improper line intensities and widths, uncertainty in the instrument function, errors in the pressure and temperature profiles and so forth.     

太阳光谱对高分辨吸收光谱反演大气CO2浓度影响的研究

以太阳光为辐射源的近红外波段高分辨率吸收光谱广泛应用于大气参数遥测.以CO2浓度反演为例,研究了太阳光谱分辨率的影响.利用美国AER公司编制的太阳光谱计算程序得到大气上界的理论计算太阳光谱作为辐射源,结合自行编制的高分辨率大气透过率模拟软件HRATS对大气中CO2平均浓度进行模拟反演.数值模拟计算结果表明,太阳光谱的准确度对浓度反演非常重要,特别是在超分辨光谱反演中异常重要,虽然反演浓度的偏差与观测分辨率没有明显的线性变化规律,但有趋势:观测分辨率的降低对太阳光谱分辨率的要求也降低,为了精确反演大气中CO2浓度,因此需要充分利用大气层顶的高分辨太阳辐射光谱数据.     

Integrable generalizations of oscillator and Coulomb systems via action-angle variables

Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N−1)-dimensional system. We present the action-angle formulation of such models in terms of the radial degree of freedom and the action-angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion.     

DOAS tomography for the retrieval of trace gas profiles from satellite-based UV-Vis limb spectra

A new method is employed for retrieving the profiles of trace gas number densities from satellite-based ultraviolet-visible (UV-Vis) spectra of scattered sunlight, which are recorded from the limb atmosphere over a range of tangent heights. The slant column abundances of trace gas along the lines of sight (LOSs) are obtained by differential optical absorption spectroscopy (DOAS), and the tomographic technique is applied to such column abundances to retrieve two-dimensional (2D) concentration profiles. For validation of the tomographic technique, the slant column abundances are simulated by a tested 2D NO2 profile set with latitudes from 90°S to 90°N between altitudes of 0 and 100 km, and the retrieval of number density profiles on 1-km grids is performed. The results suggest that between ±80°, the retrieved structure is almost the same as the test data. According to the comparison of the selected cross sections of the vertical profiles between retrieved and true concentrations, the NO2 number densities have been retrieved with an accuracy of 15% or better and 5% for altitudes between 25 and 40 km. The validation of the retrieved data shows good agreement between the retrieved and true profiles.     

Retrieval of the vertical column of an atmospheric constituent from data fusion of remote sensing measurements

Techniques of data fusion are presently being considered with increasing interest for application to atmospheric observations from space because of their capability to optimally exploit the complementary information provided by different instruments operating aboard on-going and future satellite missions. The task of combining measurements of the same target, when carried out at the level of the retrieved state vectors, faces with two major problems: the need to interpolate the products represented on different retrieval grids which determines a loss of information and the presence of a priori information in the products that can determine a bias in the product of the data fusion. The measurement space solution method avoids these problems. Based on this method we present a novel approach to retrieve the vertical column of an atmospheric constituent from data fusion of remote sensing measurements. We apply the method to retrieve the ozone column from the fusion of simulated measurements of the IASI nadir-viewing spectrometer onboard the METOP-A platform and of the MIPAS limb sounder onboard the ENVISAT satellite. The performance of the method is evaluated in terms of retrieval errors and averaging kernels of the products. The results show the evidence of improved retrieval quality when comparing the outcome of data fusion with that of the inversion process applied to spectra from either of the two instruments.     

Two-dimensional, self-consistent, three-moment simulation of RFglow discharge

A two-dimensional self-consistent nonequilibrium fluid model is used to simulate radio frequency (RF) glow discharges to evaluate the quantitative effects of the radial and axial flow dynamics inside a cylindrically symmetric parallel-plate geometry. This model is based on the three moments of the Boltzmann equation and on Poisson's equation. Radial/axial flow dynamics of plasma in low-pressure parallel plate RF glow discharges are investigated. Instead of uniform profiles along the radial direction, which are assumed in one-dimensional models, nonplate profiles are obtained from the two-dimensional simulations. Ionization rate and three moment distributions of plasma density, average velocity, and mean energy are presented in a two-dimensional configuration. The maximum ionization rate occurs in the radial sheath region and agrees with experimental results. Variations in ion density distributions at different positions, various gas pressures frequencies, and applied fields are discussed     

固体火箭发动机羽烟紫外辐射特性分析

为了研究推进剂类型和铝粉含量对固体火箭发动机羽烟紫外辐射特性的影响,采用二维流场和三维辐射传输相结合的方式建立羽烟紫外辐射模型,模型中可考虑热发射、CO+O化学发光、OH自由基化学发光、以及不同状态和直径Al2O3颗粒辐射特性等紫外辐射机理。利用模型计算了双基、改性双基和复合推进剂羽烟的紫外辐射分布,并以复合推进剂为例,研究了铝粉含量对羽烟紫外辐射特性的影响。研究结果为紫外预警系统判断导弹的类型,以及导弹紫外隐身性能的提高提供了参考。     

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.