Space-Wise,Time-Wise,Torus and Rosborough Representations in Gravity Field Modelling

The decade of the geopotentials started July 2000 with the launch of the German high-low SST mission CHAMP. Together with the joint NASA-DLR low-low SST mission GRACE and the ESA gradiometry mission GOCE an unprecedented wealth of geopotential data becomes available over the next few years. Due to the sheer number of unknown gravity field parameters (up to 100 000) and of observations (millions), especially the latter two missions are highly demanding in terms of computational requirements. In this paper several modelling strategies are presented that are based on a semi-analytical approach. In this approach the set of normal equations becomes block-diagonal with maximum block-sizes smaller than the spherical harmonic degree of resolution. The block-diagonality leads to a rapid and powerful gravity field analysis tool. Beyond the more-or-less conventional space-wise and time-wise formulations, the torus approach and Rosborough's representation are discussed. A trade-off between pros and cons of each of the modelling strategies will be given. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamic orbit propagation in a gravitational field of an inhomogeneous attractive body using the Lagrange coefficients

The analytical methods have nearly been replaced by the numerical methods due to their higher accuracy and accessibility of computation facilities. The semi-analytical Lagrange method of orbit propagation using f and g series is a competitive alternative to the numerical integration technique if the Lagrange coefficients are derived in a full gravitational field. In this paper, a generalization of the Lagrange method of orbit propagation is introduced. In other words, we introduce a complete form of the Lagrange coefficients in all force fields developed in the spherical harmonics for example full gravitational field of the Earth. The method is numerically compared with the numerical integration technique. In order to show the numerical performance of the method, it has been implemented for orbit propagation of a GPS-like MEO and CHAMP-like LEO satellites. Discrepancy at centimeter level for CHAMP-like and sub-millimeter accuracy for GPS-like satellites shows relatively high performance of the developed algorithm. Compared to integration method, the proposed Lagrange method is nearly faster by a factor two for small Nmax and four for large Nmax.     

Comparison of the observed and modeled low- to mid-latitude thermosphere response to magnetic activity: Effects of solar cycle and disturbance time delay

The performance of JB2008 and NRLMSISE-00 models, in describing the response of the thermosphere to magnetic activity are evaluated against total mass density retrieved from accelerometer measurements made onboard CHAMP satellite during 5 years. We show that the global low- to mid-latitude disturbance amplitude is correctly described by the JB2008 model for low solar activity conditions and by both the JB2008 and the NRLMSISE-00 models for high solar activity conditions. For low solar activity conditions, statistics based on almost 3 years of data confirm the large underestimation by the NRLMSISE-00 model quantified by Lathuillère et al. (2008) for the year 2004. We also found that the time delay between low- to mid-latitude global thermosphere disturbance and magnetic activity is statistically well estimated by the NRLMSISE-00 and JB2008 models for disturbed conditions. For moderately disturbed conditions however, the time delay estimated by the JB2008 model is too large by about 3 h. For very disturbed conditions, we found different time delays during day-time and night-time, using new geomagnetic proxies with a 30-min time resolution.     

AIUB-CHAMP02S: The influence of GNSS model changes on gravity field recovery using spaceborne GPS

The gravity field model AIUB-CHAMP02S, which is based on six years of CHAMP GPS data, is presented here. The gravity field parameters were derived using a two step procedure: In a first step a kinematic trajectory of a low Earth orbiting (LEO) satellite is computed using the GPS data from the on-board receiver. In this step the orbits and clock corrections of the GPS satellites as well as the Earth rotation parameters (ERPs) are introduced as known. In the second step this kinematic orbit is represented by a gravitational force model and orbit parameters.     

深空卫星重力测量计划研究综述

地球卫星重力测量计划CHAMP(CHAllenging Minisatellite Payload)、GRACE(Gravity Recovery and Climate Experiment)、GOCE(Gravity field and steady-state Ocean Circulation Explorer)和月球卫星重力测量计划(Gravity Recovery and Interior Laboratory,GRAIL)的成功实施,以及下一代地球重力卫星(GRACE Follow-On)的即将发射昭示着我们将迎来一个前所未有的高精度和高空间分辨的深空卫星重力探测时代。围绕深空卫星重力测量的研究背景、必要性、可行性、卫星重力反演软件平台构建、轨道摄动和未来研究方向开展了研究论证。研究表明:深空卫星重力测量作为新世纪重力探测技术,在精化量体重力场、提高惯性导航精度、天体动力学、天体物理学和军事技术的研究,以及促进国民经济发展和提高社会效益等方面具有广泛的应用前景。     

An empirical relation to correct storm-time thermospheric mass density modeled by NRLMSISE-00 with CHAMP satellite air drag data

With the help of STAR (Spatial Triaxial Accelerometer for Research) accelerometer measurements on board CHAMP (Challenging Minisatellite Payload), the global distributions of total mass density changes at about 400 km height during major magnetic storms are studied, aiming to improve the capability of current thermospheric model for predicting the storm-time mass density distribution. The density calculated by the NRLMSISE-00 model without using the geomagnetic active index as input is taken as a reference on top of which the storm-time changes are added. In total 19 storm events during 2001–2004 are used to perform a comprehensive statistical analysis. A relative calibration of drag coefficient along with accelerometer calibration parameters is made by fitting the CHAMP observed initial mass densities in with the NRLMSISE-00 model on quiet days before each storm. The dependences of the storm-time changes in mass density on both the total global Joule heating power, ∑_Qj$\sum Q_{\text{j}}$ and the high-resolution ring current index, Sym-H, are investigated. The lag times of mass density changes with respect to the Joule heating and Sym-H variation are obtained as a function of latitude and sunlight. By using a multiple linear regression analysis with proper time shift, an empirical relation connecting storm-time changes in mass density for 400 km height with the two parameters, ∑_Qj$\sum Q_{\text{j}}$ and Sym-H, has been worked out for different latitude and sunlight conditions (day-side or night-side). Adding a correction calculated from the empirical relation to the NRLMSISE-00 model reference leads to a better prediction of storm-time thermospheric mass density distribution.     

Properties of traveling atmospheric disturbances (TADs) inferred from CHAMP accelerometer observations

Densities derived from accelerometer measurements on the CHAMP satellite near 400 km are used to statistically establish characteristics of large-scale (>1000 km) traveling atmospheric disturbances (TADs). Only TADs that at least propagate from the auroral zone to the equator are analyzed here, and a total of 21 identifiable events are found over the years 2001–2007. The average speed of all TADs, regardless of local time, is 646 ± 122 ms⁻¹. The average speeds on the dayside and nightside are 595 ± 127 ms⁻¹ and 685 ± 106 ms⁻¹, respectively, i.e., the speed appears to be 10% higher on average on the nightside. On six occasions TADs were only detected on the night side; however, TADs on the dayside often appear more distinctly in the data. Moreover, contrary to some theoretical expectations, dayside TADs do not dissipate more readily than night side TADs, although much less are detected between 8–20 solar local time. No clear dependence of TAD amplitude or phase speed with respect to Kp, or rate of increase of Kp, is found.     

高功率微波导弹发展现状分析研究

简要介绍了高功率微波武器的概念、毁伤机理、基本特点,对高功率微波武器的发展脉络进行了梳理.重点介绍了美国CHAMP高功率微波导弹的发展情况,对其可能的应用情况进行了探讨.     

基于CHAMP卫星观测数据对热层大气密度的经验正交分析

对2003年(太阳活动较高年)至2007年(太阳活动低年)CHAMP卫星的热层大气密度观测数据进行了经验正交函数(EOF)分析,得到了400 km高度上白天平均大气密度ρ的太阳活动周变化与年度变化等不同变化分量.研究结果表明,ρ受太阳活动影响较大,其太阳周变化分量与F_(10.7)指数变化之间的相关系数可高达94.5%;ρ的太阳周变化分量随纬度增加而减小,且在中高纬地区,南半球的值明显大于北半球的值,在低纬地区则出现基本对称的双峰分布,即赤道质量密度异常(EMA)结构.在ρ的年变化中,呈现出明显的季节变化,即夏季低冬季高;同时ρ的年变化幅度随太阳活动增加而增强,随纬度增加而增强.将本文结果与经验模式NRLMSISEOO在观测条件下的输出数据进行对比,发现两者的太阳周变化与年变化分量基本一致,但本文观测数据的太阳周成分随纬度变化略小,年变化幅度略大,且NRLMSISEOO模式不能再现EMA结构.研究结果对揭示热层气候学变化特征具有重要意义.     

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.