Two-wavelength Lidar Measurement of Cloud-aerosol Optical Properties

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参数化的多次散射激光雷达方程和它的反演理论 Ⅰ:方程

本文提出了一个参数化的多次散射激光雷达方程,该方程基于本文引出的四个因子,即几何消光因子、消光分布因子、前向散射因子和后向散射因子.前两个因子表征多次散射成分对大气消光系数分布、激光的发散角和接收视场角以及接收孔径的依赖关系,后两个因子表征多次散射成分对散射相函数的依赖关系.这个参数化多次散射雷达方程在241个数值试验中得以检验,这些试验包含很宽的大气条件和雷达几何参数,包括14个大气散射相函数,均匀和不均匀的大气消光系数分布,0.5至1之间变化的一次散射反照率,地基和空间站激光雷达两种情形.数值试验表明,在小于4的光学厚度内参数化的解和Monte-Carlo解之间的标准偏差小于27％,而本模式的计算时间比Monte-Carlo方法偏小4个数量级左右.本模式不仅适合于研究多次散射对激光回波信号和激光大气遥感的效应,而且对于考虑多次散射的激光大气探测而言,是一个合适的应用模式.     

Mie 散射激光雷达探测大气气溶胶的进展

简要论述了激光雷达探测大气的优点,以及求解M ie散射激光雷达方程的理论方法,并阐述了国内外近20 a来M ie散射激光雷达探测大气气溶胶的主要成果,及其存在的问题。     

Constraint Inversion Algorithm of lidar equation for deriving aerosol optical property

A key question of the backward integration algorithm to lidar equation is how to determine the far-end boundary value. This paper develops a Constraint Inversion Algorithm (CIA) for deriving the value and then the aerosol extinction profile from lidar signals, which uses the ground-level horizontal lidar signals as the constraint information. The smaller the wavelength is, the more sensitive to the variation of aerosol ex-tinction to backscatter ratio solved by CIA. According to the property an algorithm is further proposed to simultaneously retrieve the aerosol extinction profile, the size distribution and the imaginary part of its re-flective index from the multi-wavelength lidar observations. CIA is tested in the inversion simulations with satisfactory result.     

Numerical simulations of optical properties of Saharan dust aerosols with emphasis on lidar applications

In the framework of the Saharan Mineral Dust Experiment (SAMUM) for the first time the spectral dependence of particle linear depolarization ratios was measured by combining four lidar systems. In this paper these measurements are compared with results from scattering theory based on the T-matrix method. For this purpose, in situ measurements—size distribution, shape distribution and refractive index—were used as input parameters; particle shape was approximated by spheroids. A sensitivity study showed that lidar-related parameters—lidar ratio   S _p   and linear depolarization ratio  δ _p   —are very sensitive to changes of all parameters. The simulated values of the  δ _p   are in the range of 20% and 31% and thus in the range of the measurements. The spectral dependence is weak, so that it could not be resolved by the measurements. Calculated lidar ratios based on the measured microphysics and considering equivalent radii up to 7.5 μm show a range of possible values between 29 and 50 sr at  λ= 532 nm  . Larger   S _p   might be possible if the real part of the refractive index is small and the imaginary part is large. A strict validation was however not possible as too many microphysical parameters influence   S _p   and  δ _p   that could not be measured with the required accuracy.     

THE INVERSE PROBLEM OF KLEIN-GORDON EQUATION BOUNDARY VALUE PROBLEM AND ITS APPLICATION IN DATA ASSIMILATION

Since the solution of elliptic partial differential equations continuously depends on the boundary condition, the Euler equation derived from variational method cannot be solved without boundary condition. It is often difficult to provide the exact boundary condition in the practical use of variational method. However, in some application problems such as the remote sensing data assimilation, the values can be easily obtained in the inner region of the domain. In this paper, the boundary condition is tried to be retrieved by using part solutions in the inner area. Firstly, the variational problem of remote sensing data assimilation within a circular area is established. The Klein-Gordon elliptic equation is derived from the Euler method of variational problems with assumed boundary condition. Secondly, a computer-friendly Green function is constructed for the Dirichlet problem of two-dimensional Klein-Gordon equation, with the formal solution according to Green formula. Thirdly, boundary values are retrieved by solving the optimal problem which is constructed according to the best approximation between formal solutions and high-accuracy measurements in the interior of the domain. Finally, the assimilation problem is solved on substituting the retrieved boundary values into the Klein-Gordon equation. It is a type of inverse problem in mathematics. The advantage of this method lies in that it overcomes the inherent instability of the inverse problem of Fredholm integral equation and alleviates the error introduced by artificial boundary condition in data fusion using variational method in the past.     

Determination of the Atmospheric Boundary Layer Height from Radiosonde and Lidar Backscatter

The height of the atmospheric boundary layer is derived with the help of two different measuring systems and methods. From radiosoundings the boundary layer height is determined by the parcel method and by temperature and humidity gradients. From lidar backscatter measurements a combination of the averaging variance method and the high-resolution gradient method is used to determine boundary layer heights. In this paper lidar-derived boundary layer heights on a 10 min basis are presented. Datasets from four experiments – two over land and two over the sea – are used to compare boundary layer heights from both methods. Only the daytime boundary layer is investigated because the height of the nighttime stable boundary layer is below the range of the lidar. In many situations the boundary layer heights from both systems coincide within ±200 m. This corresponds to the standard deviation of lidar-derived 10-min values within a 1-h interval and is due to the time and space variability of the boundary layer height. Deviations appear for certain situations and depend on which radiosonde method is applied. The parcel method fails over land surfaces in the afternoon when the boundary layer stabilizes and over the ocean when the boundary layer is slightly stable. An automatic radiosonde gradient method sometimes fails when multiple layers are present, e.g. a residual layer above the growing convective boundary layer. The lidar method has the advantage of continuous tracing and thus avoids confusion with elevated layers. On the other hand, it mostly fails in situations with boundary layer clouds     

参数化的多次散射雷达方程和它的反演理论 Ⅱ:反演理论

本文根据参数化的多次散射雷达方程,分析了激光多次散射对激光回波信号和一次散射雷达方程反演结果的效应,提出了迭代前向积分法和迭代后向积分法以求解参数化的多次散射雷达方程,并根据多次散射信号对云和气溶胶的前向散射相函数的高度敏感性提出了一个从双接收视场的多次散射激光回波信号,同时确定云和气溶胶消光系数分布和前向散射相函数的方法.此外,本文还根据数值试验分析了这些反演方法在地基激光雷达和空间站激光雷达两种情形下的适用性.     

降雨强度对激光雷达测风精度的影响研究

多普勒激光雷达在大气、环境以及风能等领域得到越来越广泛的应用,但对于复杂天气下多普勒激光雷达的适用性仍然有待深入研究。为此本研究采用2020年8—10月期间位于福建三沙的地基多普勒激光雷达与边界层高塔所搭载的超声风温仪观测的风场数据进行对比,发现多普勒激光雷达在水平风速、风向方面具有稳定的高精度探测性能,与超声风温仪之间相关系数达到了0.948和0.984。相比之下,激光雷达垂直风速的探测误差较大,与超声风温仪之间相关系数仅有0.353。研究发现,降雨强度与激光雷达垂直风速误差呈正相关关系,强降雨下垂直风速偏差最大可达到9 m/s。     

Lidar and Sun photometer observations of atmospheric boundary-layer characteristics over an urban area in a mountain valley

We present measurements of the vertical aerosol structure and the aerosol optical depth in the lower troposphere performed above the city of Sofia (an urban area situated in a mountain valley), western Bulgaria by means of a ground-based aerosol lidar operating continuously for a number of years. The lidar measurements were accompanied by measurements of the aerosol optical depth (AOD) in the visible and near infrared regions of the spectrum performed in October 2004 using Microtops II radiometers. The maximum values of the AOD were found to occur 1–2 h before the complete development of the atmospheric boundary layer, i.e. during the residual layer destruction, which confirms our hypothesis concerning the slope circulation effect on the processes taking place in the atmospheric boundary layer. The AOD values obtained by the lidar are lower than those taken by the sun photometer. Further, the AOD exhibits two different types of behaviour. In the case of a ‘clear atmosphere’ (i.e. in the absence of volcanic eruptions and/or dust transport from the Sahara) most of the aerosol accumulated within the atmospheric boundary layer over the urban area considered. The combined use of the two instruments allows the comparison between the optical characteristics of the atmospheric aerosol (e.g. aerosol extinction coefficient, etc.) obtained by the lidar and through an independent method (sun photometer).     

Aerosol climatology for the planetary boundary layer derived from regular lidar measurements

Regular aerosol extinction and backscatter measurements using a UV Raman Lidar have been performed for almost 3 years in Hamburg in the frame of the German Lidar Network. A set of 92 aerosol extinction and 164 aerosol backscatter profiles has been used for statistical investigations. Mean values and variances of the aerosol extinction and backscatter in the boundary layer have been calculated. Large fluctuations during the whole year have been found. The measured aerosol extinction over Hamburg shows a seasonal cycle with highest values in early fall and a second less prominent peak in spring.An analysis of the data using back trajectories showed a dependence of the aerosol extinction on the origin of the air mass. The residence time of the air mass over industrialized areas was found to be an important parameter for the measured aerosol extinction at Hamburg. However, only a small part of the total variability could be explained by the air mass origin.For 75 cases of aerosol extinction measurements under cloud-free conditions, the aerosol backscatter profile and therefore, the lidar ratio as a function of altitude could be determined. Winter measurements of the lidar ratio are often close to model results for maritime aerosol, the summer measurements are close to the model results for urban or continental aerosols.The high quality of the data has been proven by intercomparisons with other lidar systems and with star photometer measurements of the aerosol optical depth during the Lindenberg Aerosol Characterization Experiment (LACE'98) field campaign.     

A lidar study of the atmospheric entrainment zone and mixed layer over Hong Kong

In this paper we present the lidar study of the atmospheric boundary layer using the City University of Hong Kong lidar system. Three cases of determination of the entrainment zone thickness and the mixed layer depth in the atmospheric boundary layer over Hong Kong were selected for detailed study. The data collected have been analysed using the visual inspection method and the Steyn et al. [J. Atmos. Ocean. Technol. 16 (1999) 953] detection method. During the cold front passage, the mixed layer depth stayed at the level almost constant over the transition period, and the entrainment zone was thickening at a steady entrainment rate.     

Water vapour flux profiles in the convective boundary layer

Summary Water vapour flux profiles in the atmospheric boundary layer have been derived from measurements of water vapour density fluctuations by a ground-based Differential Absorption Lidar (DIAL) and of vertical wind fluctuations by a ground-based Doppler lidar. The data were collected during the field experiment LITFASS-2003 in May/June 2003 in the area of Lindenberg, Germany. The eddy-correlation method was applied, and error estimates of ±50 W/m² for latent heat flux were found. Since the sampling error dominates the overall measurement accuracy, time intervals between 60 and 120 min were required for a reliable flux calculation, depending on wind speed. Rather large errors may occur with low wind speed because the diurnal cycle restricts the useful interval length. In the lower height range, these measurements are compared with DIAL/radar-RASS fluxes. The agreement is good when comparing covariance and error values. The lidar flux profiles are well complemented by tower measurements at 50 and 90 m above ground and by area-averaged near surface fluxes from a network of micrometeorological stations. Water vapour flux profiles in the convective boundary layer exhibit different structures mainly depending on the magnitude of the entrainment flux. In situations with dry air above the boundary layer a positive entrainment flux is observed which can even exceed the surface flux. Flux profiles which linearly increase from the surface to the top of the boundary layer are observed as well as profiles which decrease in the lower part and increase in the upper part of the boundary layer. In situations with humid air above the boundary layer the entrainment flux is about zero in the upper part of the boundary layer and the profiles in most cases show a linear decrease.     

Constraint inversion Algorithm of Lidar Equationfor Deriving Aerosol Optical Property

1.IntroductionLidarisincreasinglyusedinmeasuringtheopticalpropertiesofaerosolsandcloudssincethe1960's.Ithasbeenshownthatthedeterminationoftheextinctioncoefficientasafunctionofheightisfeasible(Klett,1980;Fernald,1984;LuDarenetal.,1977;Spinhirneetal.,...     

A New Method for Aerosol Retrieval Based on Lidar Observations in Beijing

Lidar has been used extensively in the area of atmospheric aerosol measurement. Two unknowns at the reference altitude, the lidar ratio and the backscatter coefficient, need to be resolved from the lidar equation. In the actual application, these two values are difficult to obtain, particularly the backscatter coefficient. To better characterize the optical properties of aerosols, optical thickness, and attenuated backscatter obtained by other instruments are usually used as the input for joint inversion. However, this method is limited by location and time. In this study, the authors propose a new method for aerosol retrieval by using Mie scatter- ing lidar data to solve this problem. The authors take the horizontal aerosol extinction coefficient as the con- straint to begin the iteration until a self-consistent aerosol vertical profile was obtained. By comparing their results with Aerosol Robotic Network （AERONET） data, the authours determine that the aerosol extinction coefficient obtained by combining horizontal and vertical lidar observations is more pre- cise than that obtained by using the traditional Fernald method. This new method has been adopted for re- trieving the extinction coefficient of aerosols during the observation days.     

边界微分方程及其应用

本文讨论二维Helmholtz方程外边值问题的求解,以较为严格的方式建立了更精准的新的边界微分方程.在贴体坐标系下,Helmholtz方程可转化为非齐次Bessel方程.将Bessel方程的一般解代入Sommerfeld辐射条件可以得到等价于原Helmholtz方程的积分-微分方程,再利用分部积分消去其中积分,即可建立高频问题的边界微分方程.文中通过若干算例对新得到的边界微分方程进行了数值验证.     

拉曼雷达重叠函数的模拟与校准

重叠函数的校准对地基激光雷达低空大气探测的准确性至关重要。目前被广泛用于校准拉曼激光雷达重叠函数的双通道实验标定法,需要满足弹性散射通道与氮气拉曼散射通道的重叠函数近似相等的前置条件。但实际仪器光路往往会偏离理想状态,使得该前置条件无法得到满足,导致校准失败。本文使用光线追踪法模拟重叠函数,计算了各种光路失调情况下弹性散射通道与氮气拉曼散射通道的比值,并引入了一种镜头遮蔽实验来评估双通道实验标定法的前置条件是否得到满足。数值模拟结果表明,当雷达接收面的不同象限被遮蔽时,如果弹性散射通道与氮气通道的信号强度比值基本保持不变,则满足前置条件;如果弹性散射通道与氮气通道的信号强度比值有显著差异,则可判定仪器光学系统失调,需要调整直至满足上述前置条件时才能使用双通道实验标定法标定。利用该方法对南京市气象局安装的拉曼激光雷达进行了光路测评和调整,并与CCD(charge-coupled device)侧向成像激光雷达观测信号做对比,结果显示调整后的定标效果更好。     

基于机载观测资料订正雷达比及其垂直分布特征

雷达比是激光雷达反演气溶胶光学特性的重要参数和影响因素。利用北京地区2016年一次清洁过程（12月10日）和两次污染过程（11月15～18日和12月16～19日）的微脉冲激光雷达、机载浊度计和黑碳仪以及多种地基观测设备,综合研究基于飞机观测订正雷达比的方法及其分布特征。清洁过程地面PM_2.5浓度低于40 μg m?3;污染严重时期的PM_2.5均高于150 μg m?3且能见度低于5 km,污染过程1存在高空传输的特征。研究结果表明相较于采用单一的柱平均雷达比,利用本文方法获得的雷达比垂直廓线反演得到的气溶胶消光系数和光学厚度更接近原位跟踪观测,精度均有提升。基于此方法获得的雷达比在污染发展不同时期垂直分布差异较大,主要分布在19～76 sr之间,清洁时期雷达比较小且垂直分布差异不大。污染过程1雷达比随高度波动增加至边界层顶（19～45 sr）;污染过程2严重期边界层内雷达比随高度由70 sr降低到20 sr;边界层以上均呈现小幅波动变化。边界层内雷达比垂直分布与气溶胶来源特别是高空气溶胶传输有密切联系,混有沙尘的区域传输显著提升了所在高度的雷达比值。边界层以上雷达比受少量大粒子或者强吸收性的气溶胶粒子的影响波动变化。边界层内消光系数增大时雷达比呈增加趋势;当相对湿度高于40%,边界层内雷达比随相对湿度增加而增大。     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part II: Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration) are designed to deal with the singularity of the Green’s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction) component to zero,the other component of the solution can be computed in two ways:(1) Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2) Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.     

拉萨上空大气气溶胶光学特性的 激光雷达探测

叙述了大气气溶胶激光雷达探测方程的求解方法,以及1998年夏季在拉萨使用激光雷达观测的一些结果,并与日本名古屋市上空的探测资料进行了对比分析,得到了拉萨上空气溶胶光学性质的一般特征,并对其成因进行了讨论。