GPS/LEO掩星技术中Abel积分变换的奇点问题

在GPS／LEO无线电掩星反演地球大气技术中，Abel积分是反演地球大气折射指数的最常用的方法，Abel积分存在积分奇点的问题，根据这一问题讨论了解决奇异积分的几种不同的积分方法，并提出了一种直接求Abel积分变换的解析解．通过数值积分模拟计算，对比了各种不同积分方法引入了的计算误差。     

GPS掩星振幅反演中的天顶补偿项

推导了GPS无线电掩星振幅观测反演地球大气技术中Abel积分变换中的天顶补偿项，定性地说明了天顶补偿项对计算过程和反演剖面的影响。     

GPS掩星振幅反演中的天顶补偿项

推导了GPS无线电掩星振幅观测反演地球大气技术中Abel积分变换中的天顶补偿项 ,定性地说明了天顶补偿项对计算过程和反演剖面的影响。     

读诗谈天象之五 大气造成的天文现象(下)

大气折射对天文观测的影响大气折射还造成另一个影响天文观测的效应,称为大气色散。原来,空气的折射率还与光的波长(即颜色)有关,不同颜色的光在相同的介质中传播,因折射率不同而分散,雨后彩虹展现由红到紫的七色景象,正是由于同样原因(光被悬浮在空气中的小水滴折射并产生色散)。由于大气色散,使得我们观测到的天体像,无论是目视的眼睛所见还是照相的底片留影,星像都呈现为一条垂直的细小光谱,紫端靠近天顶。天顶距越大,色散也越大。     

提高中性大气折射延迟改正精度的可能途径

针对空间大地测量技术对中性大气折射延迟改正精度的要求,阐述了折射延迟改正值应随测站和随方位而异的必要性．指出,在尚不能直接测定天文大气折射值的情况下,现有的各种改正模型对大气分布模型的依赖性,不能达到预期的精度和降低观测的截止角．根据云南天文台低纬子午环的特殊结构,和测定大气折射的实践,提出了提高折射延迟改正精度的新方法,即：利用各观测站不同方位从天顶附近直到低地平高度角的天文大气折射实测数据,求解得到折射率差和映射函数的参数,从而建立随测站和随方位而异的大气折射延迟改正模型．这一新方法的实施,将能在不需采用大气分布模型的情况下,把天顶延迟的改正精度提高到1 mm以内,低地平高度角的折射延迟改正精度提高到厘米级,并且把截止高度角压缩到5°以内．     

关于大气分布模型

简述了大气垂直分布情况和高空探测方法,分析了目前只能采用球对称大气分布模型的原因;论证了随观测站、随方位而异的天文大气折射实测模型和折射延迟改正模型,已经包含了观测站上空大气实际分布的非球对称特性,不必再去寻找或建立随地势而异和随季节而变的大气分布模型,避免了大气分布模型选择不当的影响,从一个方面为提高天文大气折射改正精度和电磁波大气折射延迟改正精度提供了保证。     

大气对地球自转变化的影响-方法和数据的深入分析

大气相对固体地球的运动产生大气相对角动量，它的变化可以激发地球自转多时间尺度的变化．计算大气相对角动量现在采用两种不同的垂直积分高度，一种为从地形表面积分到顶层大气，称之为SP方法；另一种为从1000hPa积分到顶层大气，称之为BP方法，对采用这两种方法所得到的大气相对角动量进行了详细的比较．应用欧洲中距气象预报中心（ECMWF）和美国国家环境预报中心（NCEP）大气再分析数据，重新研究了大气相对角动量变化的时空特征．通过对大气相对角动量季节平均，季节振幅和时空特征的分析，得出ECMWF和NCEP的大气相对角动量变化对地球自转周年极移的影响，在亚洲季风区域和南极洲区域差别最为明显．     

映射函数对天文大气折射的改进

本文利用大气折射积分母函数方法,分别给出在射电波段和光学波段上天文大气折射改正的映射函数,并完整地考虑了天文学和空间技术所需要的物理和地球物理因素引入的改正．本文还利用探空气球的资料分析了新天文大气折射改正公式的实际精度;计算结果证明：它在2°高度角时达到5”左右,而在5°高度角时约为1”．我们认为：限制计算精度的主要因素是真实地球大气分布与理论大气模型的区别．     

二维射线跟踪技术中的掩星面坐标系

在大气球对称假设下,可以从弯曲角观测资料通过Abel积分变换反演得到折射率廓线。在低层大气中,折射率水平不均匀性可能导致Abel反演在近地面的误差达到10%。避免该误差的一种有效方法是不通过Abel反演而采用非对称模式下二维射线跟踪算子直接将弯曲角同化到数值天气预报模式中。文章介绍了非对称模式下二维射线跟踪技术的背景、原理和数学模型,讨论了掩星面坐标系与地心惯性坐标系之间的转换关系。     

大气折射母函数方法、大气折射解析解和映射函数

回顾了作为实用天学和大地测量学中基本研究课题之一的大气折射映射函数研究的进展。介绍了近几年上海天台发展的大气折射母函数方法，以及由此导出的大气折射解析解。对如今广泛地应用在空间测量技术中的几种映射函数做出评述；分析了NMF模型的优点和不足之处。介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天大气折射的映射函数方法。利用VLBI实验中高度截止角与基线长度重复率的关系、探空气球(radiosonde)观测资料、PRARE资料比较了各种映射函数的结果。特别指出了映射函数方法对天大气折射和光学波段测距精度的改进。讨论了大气折射计算中的主要误差源。     

Correcting the superrefraction effect in the GPS/LEO occultation technique

The Abel integral transformation in GPS/LEO occultation technique requires the atmospheric index of refraction n to be a single-valued function of the refractional radius a. This condition is broken when the vertical refractivity gradient is less than a critical value dN/dr∼-0.16 N-units m⁻¹, and it is called superrefraction. The Abel integral transformation is no longer valid under this condition, and, if the classical Abel transformation is still formally applied, then a negative refractivity bias occurs in results. The physical characteristics and mathematical expression of the superrefraction phenomenon in the lower troposphere are described. In the frame of a general Abel integral transformation, the inversion algorithm of the atmospheric profiles in and below the superrefraction layer is discussed. Under a simple assumption of the constant vertical gradient of refractivity in the sampling interval, the simulation calculation is carried out on UK High Resolution Radiosonde Data. The computational results have verified the relationship between the negative refractivity bias and the superrefraction phenomenon, as well as the validity of the general Abel transformation proposed.     

TEC Compensated Inversion Method of Ionospheric Occultation

For the inversion of ionospheric occultation data, the Abel inversion method of calibrated TEC is usually adopted, but the spherical asymmetry of the real ionosphere will bring errors to the inversion result of electron densities. This paper studies a TEC compensated inversion method. By combining with a background field, this method may eliminate the effect of the horizontal variability of electron density on the TEC, and improve the applicability of the assumption of spherical symmetry as well as the inversion accuracy. Applying this method to the inversion of simulative occultation events, the result demonstrates that compared with the traditional Abel transform inversion, the TEC compensated inversion method can reduce the inversion error. Comparing the various background fields obtained in different ways, it is shown that the higher the coincidence level between the background field and the real field, the better the inversion result.     

Meteorological assessment of the surface temperatures on Titan: constraints on the surface type

The latitudinal profile of near-surface air temperature on Titan retrieved by Voyager 1 has been difficult to understand and raised several speculations about possible exotic processes that might be occurring near Titan's surface, while the thermal properties of the surface itself are unknown. This study systematically investigates the seasonal and spatial variation of the surface temperature and air temperature in the lower troposphere by a 3-dimensional general circulation model for different putative surface types (porous icy regolith, rock-ice mixture, hydrocarbon lakes). For any viable surface type the surface temperature is unlikely to be constant through the year and should more or less vary seasonally and even diurnally, most likely by a few K. Recent observations of tropospheric clouds may be evidence of seasonal variation of the surface temperature and the model predicts in the case of solid surface the development of a convective layer with superadiabatic lapse rates near the surface exactly at those latitudes and seasons where clouds have been identified. The latitudinal profile of the surface temperature retrieved from Voyager 1 infrared spectra can be explained without invoking exotic effects, provided the thermal inertia of the surface is relatively small and/or the surface albedo is low. A dominance of water ice (high thermal inertia and high albedo) at the surface is unfavorable to reproduce the observation. The latitudinal gradient of the surface temperature is particularly large at the hydrocarbon lake surface due to low albedo and small surface drag. Local anomalies of the surface albedo or surface thermal inertia are likely to cause substantial inhomogeneities of the surface temperature. Quasi-permanent accumulation of stratospheric haze at both poles would create a perennial equator-to-pole contrast of the surface temperature, but also a substantially lower global-mean surface temperature due to an enhanced anti-greenhouse effect in summer. The air temperature in the lower troposphere exhibits a tiny latitudinal gradient and a pole-to-pole gradient due to the presence of a pole-to-pole Hadley circulation, indicating that the temperature within the planetary boundary layer may exhibit a vertical profile characteristic of season, location and scenario. There may be a shallow near-surface inversion layer in cold seasons and a shallow convective layer in warm seasons.     

On the reduction of occultation light curves

In the first two sections of this paper, the two basic methods of reducing occultation light curves—curve fitting and inversion—are reviewed and compared. It is shown that the curve fitting methods have severe problems of nonuniqueness. In addition, in the case of occultation curves dominated by spikes, it is not clear that such solutions are meaningful. The inversion method does not suffer from these drawbacks. Methods of deriving temperature profiles from refractivity profiles are dealt with in the third section. It is shown that, although the temperature profiles are sensitive to small errors in the refractivity profile, accurate temperatures can be obtained, particularly at the deeper levels of the atmosphere. The final section contains a brief discussion of the ambiguities that arise when the occultation curve straddles the turbopause.     

Observed nonpotential magnetic fields and the inferred flow of electric currents at a location of repeated flaring

We have analyzed the vector magnetic field of an active region at a location of repeated flaring to determine the nature of the currents flowing in the areas where the flares initiated. The component of electric current density crossing the photosphere along the line-of-sight was derived from the observed transverse component of the magnetic field. The maximum concentrations of these currents occurred exactly at the sites of flare initiation and where the photospheric field was sheared the most. The calculated distribution of current density at the flare sites suggested that currents were flowing out of an area of positive magnetic polarity and across the magnetic inversion line into two areas of negative polarity. This interpretation was reinforced by a calculation of the source field, the magnetic field produced in the photosphere by the electric currents above the photosphere. In the vicinity of the flare sites, the calculated source field exhibited three particular characteristics: (1) maximum magnitudes at the sites of flare initiation, (2) a rotational direction where the vertical current density was concentrated, and (3) a fairly constant angular orientation with the magnetic inversion line. The source field was thus very similar to the field produced by two arcades of currents crossing the inversion line at the locations of greatest magnetic shear with orientations of about 60° to the inversion line. With this orientation, the inferred arcades would be aligned with the observed chromospheric fibrils seen in the H data so that the currents were field-aligned above the photosphere. The field thus exhibited a vertical gradient of magnetic shear with the shear decreasing upward from the photosphere. We estimated the currents in the two arcades by matching the source field derived from observations with that produced by a model of parallel loops of currents. We found that the loops of the model would each have a radius of 4500 km, a separation of 1830 km, and carry a current of 0.15 × 10¹² A. Values of vertical current densities and source fields appearing in the umbrae of the two large sunspots away from the flare sites were shown to lie at or below the level of uncertainty in the data. The main source of this uncertainty lay in the method by which the 180° ambiguity in the azimuth of the transverse field is resolved in umbral areas. We thus concluded that these quantities in large umbrae should be treated with a healthy skepticism. Finally, we found that the source field at the flare sites was produced almost entirely by the angular difference between the observed and potential field and not by the difference in field intensity.     

Maximum Entropy Regularization Method of Ionospheric Occultation

With the increasing of applications of Global Positioning System (GPS), the research on the factors affecting the radio signals is becoming more and more important. One of the most significant effects on ionosphere monitoring is the ionospheric radio occultation (IRO), and the IRO data is now serving as one of the most important monitoring sources for the ionospheric measurements. Meanwhile the inversion of the occultation data is a popular topic. The traditional Abel inversion process through compensated total electron content (TEC) is a linear inversion method, thus it would transfer the measurement errors directly to the inversion results. In order to improve the occultation results, we introduce in this paper two nonlinear methods, namely the regularization method and the maximum entropy regularization method. Through designed simulative experiments, we verify and compare these three methods, and conclude that the maximum entropy regularization method can reduce significantly the influence of measurement errors.     

电离层掩星反演的正则最大熵法

电离层掩星数据现已成为电离层观测数据的重要来源,对掩星数据的反演研究一直是掩星研究的热点.传统采用的改正TEC(1btal Electron Content)的Abel变换反演法为线性反演法,它会把测量误差带入反演结果中.为改善反演效果受测量误差的影响,引入两种非线性的反演方法一正则化和正则最大熵反演法.随后设计模拟试验,对3种方法进行验证、比较,得到正则最大熵反演法可以很好地减小测量误差的影响.     

Thermal conduction between an accretion disc and a corona in active galactic nuclei: vertical structure of the transition layer

We study the vertical structure of the transition layer between an accretion disc and a corona in the context of the existence of a two-phase medium in thermally unstable regions. The disc is illuminated by hard X-ray radiation, and satisfies the condition of hydrostatic equilibrium. We take into account the energy exchange between the hot, Compton-heated corona (∼10⁸ K) and cool disc (∼10⁴ K) arising from both radiative processes and thermal conduction. In the case including thermal conduction, we perform a local stability analysis, and conclude that thermal conduction does not suppress thermal instability. In spite of the continuous temperature profile T ( τ ) there are regions of strong temperature gradient, in which spontaneous perturbations can lead to cloud condensation in the transition layer. We determine the minimum size λ _TC of such a perturbation.     

GPS掩星折射率剖面一维变分同化

近年来,GPS／LEO(全球定位系统／低地球轨道)卫星无线电掩星技术给出了地球大气探测的新途径．从LEO卫星观测到的掩星数据可以反演的地球大气的气压、水汽、温度等剖面;它们对气象和大气科学研究,是具有潜在价值的数据资源．掩星数据资料的同化技术可以有效地改进这些气象参数的剖面,从而改进目前的数值天气预报模式．在当前采用的一维变分同化反演技术中,可以用掩星观测资料的大气折射率或弯曲角剖面进行同化,来反演大气水汽和温度剖面以及海平面压强．作为独立自主开发的GPD／LEO掩星技术系统的一部分,以欧洲中尺度天气预报分析(ECMWF)资料为背景场,CHAMP 掩星观测得到的折射率剖面为观测值,采用Levenberg—Marquardt方法实行GPS掩星资料一维变分同化．在讨论中,用掩星观测点附近相应的探空气球资料来检验CHAMP掩星资料变分同化的结果．