Recent progress on the retrieval and modeling of thermosphere mass density
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摘要: 热层是位于地球表面大约90 km到近1000 km的大气圈层，它与电离层和低层大气都存在着复杂的耦合关系；同时热层作为人类航天器空间活动的主要区域，其大气直接影响着各类低轨航天器的运行轨迹. 近年来，热层大气观测资料的逐步增加推动了热层大气变化特性的研究和大气模式的发展. 本文首先综述了基于多源卫星观测数据的热层大气密度反演算法. 着重介绍了基于精密轨道数据以及加速度计数据反演密度的主要算法，以及各种反演策略的优缺点. 总结了当前工程常用的MSIS、Jacchia以及DTM热层大气模式在数据源、算法实现过程及其适用范围等方面的异同. 接着介绍了基于当前最新大气密度观测数据结合已有大气模式，应用多项式、稀疏矩阵拟合以及数据同化等技术的大气模式优化研究进展. 最后概述了基于观测数据研究热层大气响应磁暴、耀斑以及日食等空间事件方面的科学进展.Abstract: The thermosphere is the atmospheric layer extending from about 90 km to nearly 1000 kilometers, which is an important interreaction area between the Sun and the Earth. Under the effects of solar radiation flux changes, geomagnetic activities, and low atmospheric forcings, the thermosphere could undergo significant changes. On the other hand, the thermospheric molecule flow collides with space objects, leading to the drag effect, which impacts significantly on the trajectories of space objects. In this paper, we first survey multiple density retrieval methods. The space object tracking data has the advantage of a large amount of data and has long been used for density retrieval since the 1960s. However, the density from this method suffers from low accuracy and time resolution. With the development of the Global Navigation Satellite System (GNSS), satellite Precise Orbit Determination (POD) data was utilized to derive thermospheric density with higher accuracy and time resolution. The accelerometers of some geodesic satellites offer the highest accuracy of measurements. Subsequently, three widely-used empirical thermospheric models (Mass Spectrometer Incoherent Scatter MSIS, Jacchia, and Drag Temperature Model DTM) were summarized. The methodologies and data sources were further compared. Based on the derived neutral densities and thermospheric models, several new approaches in improving the previous atmospheric models were overviewed. Since the exospheric temperature is the crucial parameter for empirical models, one of the effective ways to improve models is to modify the exospheric temperature using accelerometer-based densities. The polynomial fitting as well as the Principal Component Analysis (PCA) techniques, were utilized to reconstruct the global density. Other methods such as assimilation and particle filter were also applied to improve atmospheric models. Finally, based on the derived neutral densities, the thermospheric responses to solar and astronomical events such as geomagnetic storms, solar flares, and solar eclipses were further reviewed.
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Key words:
- thermosphere /
- neutral density retrieval /
- thermospheric model
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图 1 利用MSISE00热层大气经验模型获得的北京地区所在经纬度（116°E，40°N）大气分别在太阳活动高年与低年的温度（a）和密度（b）随高度分布情况
Figure 1. Altitude profiles of atmospheric temperature (a) and density (b) during solar maximum and minimum, based on the MSISE00 model, over Beijing (116°E, 40°N)
图 2 2009年第32天CHAMP卫星大气阻尼系数与有效面积乘积的变化
Figure 2. The products of CHAMP drag coefficients and cross-section areas during day 32, 2009
图 3 Starshine-1/2/3卫星轨道高度（a）和基于TLE数据的反演密度（b）. Starshine-1/2/3分别发射于1999年5月27日、2001年12月5日和2001年9月29日
Figure 3. The altitudes of Starshine-1/2/3 satellites (a) and the TLE-based orbital densities (b). Starshine-1/2/3 satellites were launched on 27 May 1999, 5 December 2001 and 29 September, 2001, respectively
图 4 基于GRACE卫星精密轨道数据以及加速度计数据反演的2011—2016年热层大气密度（修改自Calabia and Jin, 2017）
Figure 4. POD-based thermospheric mass densities from 2011 to 2016. The densities derived from accelerometer data are plotted as references (modified from Calabia and Jin, 2017)
图 5 基于CHAMP精密轨道数据（蓝线）与加速度计数据（红线）之比对（修改自Sang et al., 2012）
Figure 5. The comparison of CHAMP orbital density derived from POD data and that from accelerometer data (modified from Sang et al., 2012)
图 6 2006年1月1日基于GRACE卫星精密轨道数据反演得到的非保守力加速度（蓝线）与加速度计测量结果（红线）之比对（修改自Li and Lei, 2021b）
Figure 6. The comparison of GRACE along-track non-conservative forces derived from POD data on 1 January, 2006, and those from the accelerometer (modified from Li and Lei, 2021b)
图 7 基于GRACE卫星精密轨道数据反演得到的2017年9月磁暴期间的热层大气密度（a, b）与加速度计反演密度（e, f）. 密度单位为10−12 kg/m3. 磁暴期间行星际磁场By、Bz以及AE指数在子图（c, d）和（g, h）中给出（修改自Li and Lei, 2021b）
Figure 7. Thermospheric mass densities retrieved from GRACE POD data and those from the accelerometer data during the 2017 September storm (in units of 10−12 kg/m3). The interplanetary magnetic field By, Bz components, and the AE index are shown in the bottom for reference (modified from Li and Lei, 2021b)
图 8 利用MSISE00经验模式和热层大气密度探测值提取等效逃逸层温度流程图
Figure 8. The exospheric temperature derived from MSISE00 and thermospheric density
图 9 CHAMP卫星热层大气密度（a）和提取的逃逸层温度（b），以及对应的MSISE00模式日均值结果
Figure 9. Thermospheric density (a) and exospheric temperature (b) derived from CHAMP observation and MSISE00 empirical model
图 10 MSISE00以及ETM模式模拟的逃逸层温度（a）和GRACE卫星所在高度热层大气密度（b）与探测值的相对误差统计结果
Figure 10. The statistics of relative errors of (a) exospheric temperature and (b) density with GRACE measurements for the ETM (blue line) and MSISE00 (red line)
图 11 （a-e）第一至第五阶主成分系数（PC1-PC5）随纬度与地方时变化的分布图，（f）及其在理论模型数据库中占所有变化的比重（修改自Ruan et al., 2018）
Figure 11. Variations of the basis functions (a-e) PC1–PC5 as a function of local time and latitude and (f) their relative contributions to the total variance (modified from Ruan et al., 2018)
图 12 探测数据驱动技术示意图（修改自Ruan et al., 2018）
Figure 12. Schematic diagram for the data-driven process (modified from Ruan et al., 2018)
图 13 2004年第80—280天平均的GUVI临边观测（a）温度与（c）密度高度剖面（灰色：观测；蓝色：TIEGCM；红色：PIDA）. （b）温度与（d）密度的模拟与观测比值的统计平均（蓝色：TIEGCM；红色：PIDA）. 统计标准差由图（b）和图（d）中相应的彩色阴影表示（修改自Ren and Lei, 2020）
Figure 13. The altitude profiles of the temporal and spatial averaged (a) temperature and (c) density from Limb observations (gray dotted lines) and the corresponding simulation results from TIEGCM (blue dotted lines) and PIDA (red dotted lines). The mean ratio of the simulation results (blue line for TIEGCM; red line for PIDA) to observations for (b) temperature and (d) density. The standard deviations were marked by the corresponding colored shading in (b) and (d) (modified from Ren and Lei, 2020)
图 14 预报模式GOFT示意图. 彩色圆点表示GOFT中的粒子，其大小与粒子权重成正比. 红色曲线表示概率密度函数（修改自Ren and Lei, 2022）
Figure 14. Schematic view of the forecast model GOFT. The solid dot symbols indicate the particles in the GOFT with the symbol sizes proportional to the weighting of the particles. The red curve represents the probability density function (modified from Ren and Lei, 2022)
图 15 GOFT（红色点线）和TIEGCM（蓝色点线）对（a）CHAMP和（b）GRACE轨道平均密度的30天平均预报误差随预报时长的变化. 阴影表示统计标准差. （c）TIEGCM和（d）GOFT对150～600 km轨道平均临边密度的30天预报误差随预报时长和高度的变化（修改自Ren and Lei, 2022）
Figure 15. Statistical results for the 30-day forecast from the GOFT and TIEGCM. The GOFT (red line) and TIEGCM (blue line) averaged relative forecasting errors with the standard deviations (corresponding colored shading) for the orbital mean mass density from (a) CHAMP and (b) GRACE satellites during the 30-day forecast interval. The statistical average of the relative forecasting errors for limb orbital mean mass density by TIMED-GUVI from the (c) TIEGCM and (d) GOFT (modified from Ren and Lei, 2022)
图 16 1958年7月磁暴期间的Ap指数变化（a），以及空间目标1958
$ \mathrm{\delta } $ 1（SPUTNIK 3 rocket）运行周期变化率（b）. 航天器轨道周期变化率可以表征大气密度的变化（修改自Prölss, 2011）Figure 16. Ap index (a) and the orbit period change rate of space object 1958
$ \mathrm{\delta } $ 1 (b) during geomagnetic storm in July, 1958. The change rate of the space object represents the orbital density (modified from Prölss, 2011)
图 17 CHAMP（a, b）和GRACE（c, d）卫星观测到的热层大气对2003年11月20日磁暴的响应（修改自Bruinsma et al., 2006）
Figure 17. The thermospheric response to 20 November, 2003 geomagnetic storm observed by CHAMP (a, b) and GRACE (c, d) satellites (modified from Bruinsma et al., 2006)
图 18 2003年10月28—31日磁暴期间（a）行星际磁场Bz分量、地磁（b）Kp、（c）Dst指数，（d）归一化至390 km高度的CHAMP卫星白天（红色）和夜晚（绿色）轨道平均密度，（e）基于TIMED/SABER观测的100～200 km高度上NO冷却率的轨道平均，以及（f）125 km高度上白天（红色）、夜晚（蓝色）的NO平均冷却率. 其中密度单位为10−12 kg/m3. 图（d）中虚线表示最平静时期的大气密度；NO冷却率单位为107 erg/cm3/s（修改自Lei et al., 2012）
Figure 18. Variations of (a) interplanetary magnetic field Bz, geomagnetic (b) Kp and (c) Dst indices, (d) dayside (red) and nightside (green) orbital averaged densities from CHAMP (normalized to 390 km), orbital averaged NO cooling rate from TIMED/SABER (e) between 100 and 200 km, and (f) dayside (red) and nightside (blue) averaged NO cooling rates at 125 km during 28-31 October 2003. Note that the mass densities in (d) are in units of 10−12 kg/m3, and the dashed lines stand for mass densities during the quietest period on October 28; NO cooling rates in (e-f) are in units of 107 erg/cm3/s (modified from Lei et al., 2012)
图 19 2010年1月15日日食结束后GOCE卫星轨道密度相对背景密度的绝对变化. 背景密度定义为日食前8个轨道的平均密度. 密度单位为10-12 kg/m3. 图（a-c）表示观测密度；（d-f）表示模拟结果. 红色三角形代表卫星位置，右上角时间为当前时间（修改自Li et al., 2021）
Figure 19. The absolute changes of neutral densities after the 15 January 15, 2010 solar eclipse with respect to the background density from (a-c) GOCE observation and that (d-f) from TIE-GCM simulation. Note that the densities are in units of 10-12 kg/m3 and the background density is defined as the mean density of eight orbits before the eclipse. The red triangles stand for satellite positions at the specific times shown in the top right-hand corner of each column (modified from Li et al., 2021)
表 1 ONERA静电加速度计主要技术指标
Table 1. The technical indicators of some on-board electrostatic accelerometers made by ONERA
名称 STAR SuperSTAR GRADIO SuperSTAR-FO 搭载卫星 CHAMP GRACE GOCE GRACE-FO 分辨率/$ (\mathrm{m}/{\mathrm{s}}^{2}/{\mathrm{H}\mathrm{z}}^{1/2} $) $ 3\times {10}^{-9} $ $ {10}^{-10} $ $ 2\times {10}^{-12} $ $ {10}^{-10} $ 测量带宽/$ \mathrm{H}\mathrm{z} $ $ {10}^{-4}\text{～}0.1 $ $ {10}^{-4}\text{～}0.1 $ $ {5\times 10}^{-3}\text{～}0.1 $ $ {5\times 10}^{-5}\text{～}2.5 $ 量程/($ \mathrm{m}/{\mathrm{s}}^{2} $) $ {\pm 10}^{-4} $ $ {\pm 5\times 10}^{-5} $ $ {\pm 6.5\times 10}^{-6} $ $ {\pm 5\times 10}^{-4} $ 
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表 2 Jacchia系列模式基本情况
Table 2. Brief introductions of Jacchia models
版本 太阳活动输入参数 成分 参考文献 J64 F10.7, Ap N2, O2, He, O, H Jacchia（1964） J70 F10.7, Ap（Kp） N2, O2, He, Ar, O, H Jacchia（1970） J71 F10.7, Ap（Kp） N2, O2, He, Ar, O, H Jacchia（1971） J77 F10.7, Ap（Kp） N2, Ar, He, O, H Jacchia（1977） JB2006 F10.7, S10.7, M10.7, Ap N2, O2, O, Ar, He, H Bowman等（2008a） JB2008 F10.7, S10.7, M10.7, Y10, Dst N2, O2, O, Ar, He, H Bowman等（2008b）
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表 3 MSIS系列模式基本情况
Table 3. Brief introductions of MSIS models
版本 太阳活动输入参数 成分 参考文献 MSIS F10.7, Ap N2, O2, Ar, He, O, H Hedin等（1977a, 1977b） MSIS83 F10.7, Ap N2, O2, Ar, He, O, H Hedin（1983） MSIS86 F10.7, Ap N2, O2, Ar, He, O, H, N Hedin（1987） MSIS90 F10.7, Ap N2, O2, Ar, He, O, H, N Hedin（1991） MSISE00 F10.7, Ap N2, O2, Ar, He, O, H, N, 异常“O” Picone等（2002） MSIS 2.0 F10.7, Ap N2, O2, Ar, He, O, H, N, 异常“O” Emmert等（2021）
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表 5 热层大气密度经验模型最新版本信息
Table 5. Summary of the selected empirical thermosphere models
模式 MSIS 2.0 JB2008 DTM2013 参考文献 Emmert等 (2021) Bowman等 (2008b) Bruinsma (2015) 所用数据 质谱仪、非相干散射雷达、轨道及加速度探测数据、卫星遥感、探空火箭等数据 175～1000 km轨道资料提取的大气密度数据 质谱仪、非相干散射雷达、轨道和加速度数据 所用数据时段 1961—2013 1997—2007 1961—2012 拟合方法 最小二乘方法 在J70基础上进行最小二乘方法 最小二乘方法 底边界高度 0 km 90 km 120 km 中间层温度和
密度变化情况变化 120 km处变化 不变 温度廓线形式 120 km以上采用Bates指数形式，120 km以下采用三次样条 125 km以上使用反三角函数，125 km以下采用多项式 采用Bates指数形式 太阳活动作用 温度和密度与F10.7呈二次方形式 逃逸层温度采用4个太阳活动指数表示 温度和密度与F30呈二次方形式 地磁作用 温度和密度随3小时或日平均地磁Ap指数，并随纬度和地方时变化 逃逸层温度随地磁Dst指数非线性变化，也可以表示为Ap的变化 密度随地磁二次方变化，温度随地磁线性变化，并考虑纬度分布影响 地方时 日、半日、1/3日变化，并受到太阳F10.7影响 逃逸层温度使用三角函数 日、半日、1/3日变化，并受到太阳F30影响 纬度 6阶球谐函数，并考虑太阳F10.7影响 逃逸层温度采用纬度的三角函数 6阶球谐函数，并考虑太阳F30影响 经度 球谐函数2波结构，并考虑地磁作用 无 无 世界时 球谐函数，并考虑地磁作用 无 无 季节 温度和密度存在年、半年对称和不对称变化，并受到太阳F10.7影响 密度考虑了年、半年变化，并考虑幅度随高度和太阳活动影响 温度和密度存在年、半年对称和不对称变化，并受到地方时、纬度和太阳F30影响 重力场作用 随高度和纬度变化 随高度变化 随高度变化 注：F30表示30 cm太阳辐射通量.
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