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Article(id=1322941100842951215, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322940829001724376, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.05.223, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1715356800000, receivedDateStr=2024-05-11, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343337497, onlineDateStr=2026-10-30, pubDate=1747238400000, pubDateStr=2025-05-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343337497, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343337497, creator=13701087609, updateTime=1793343337497, updator=13701087609, issue=Issue{id=1322940829001724376, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='5', pageStart='441', pageEnd='550', issueExtLink='null', onlineDate='null', pubDate='1747238400000', pubDateStr='2025-05-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343272686, creator='13701087609', updateTime=1793343272686, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=512, endPage=517, ext={EN=ArticleExt(id=1322941101253993008, articleId=1322941100842951215, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Precision Assessment and Correction of Global Ionospheric Maps Based on Jason-1/2/3 VTEC, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

This paper employs VTEC data from the Jason-1/2/3 satellite series to analyze the accuracy of global ionospheric maps (GIMs) from temporal and spatial perspectives, and establishes corresponding correction equations using solar activity components, diurnal variation components, and seasonal variation components. The results indicate: 1) The residuals(G-J) between CODE GIMs and Jason series satellite data exhibit a quadratic function relationship with F10.7, showing a 24-hour periodic characteristic in diurnal variation and a semi-annual variation pattern in seasonal changes. The correction equations can effectively amend the GIMs data. 2) The mean value of G-J reaches its maximum in the low-latitude regions of the Pacific and its minimum in southern Australia; the plasma transport within the equatorial anomaly leads to a bimodal feature in the median error of G-J; the relative error of G-J attains its maximum in the southern Atlantic Ocean, particularly in the marine areas off southern Africa.

, authors=Di MENG1, Kaixin WANG1, Jiandi FENG1, 2, *, Zhihao ZHANG1, authorsList=Di MENG, Kaixin WANG, Jiandi FENG, Zhihao ZHANG, authorCompany=null, correspAuthors=Jiandi FENG, authorNote=

MENG Di, postgraduate, majors in characteristics of ionospheric variations, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322941105179861575, articleId=1322941100842951215, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于Jason-1/2/3 VTEC的全球电离层地图精度评估及修正, columnId=1322506169105633839, journalTitle=大地测量与地球动力学, columnName=现代大地测量, runingTitle=null, highlight=null, articleAbstract=

本文使用Jason-1/2/3系列卫星的VTEC数据, 从时间、空间等角度分析全球电离层地图的精度情况, 并利用太阳活动分量、日变化分量和季节变化分量建立相应的修正方程。结果表明: 1) CODE GIMs与Jason系列卫星的残差(G-J)与F10.7呈二次函数关系, 在日变化上呈24 h的周期特征, 在季节变化上呈半年变化周期特征, 修正方程能够有效修正GIMs数据。2) G-J的平均值在太平洋的低纬度地区取得最大值, 在澳大利亚南部取得最小值; 赤道异常中的等离子输送导致G-J的中误差呈现双峰特征; G-J的相对误差在大西洋南部, 尤其是非洲南部的海洋地区取得极大值。

, authors=孟迪1, 王开心1, 冯建迪1, 2, *, 张志豪1, authorsList=孟迪, 王开心, 冯建迪, 张志豪, authorCompany=null, correspAuthors=冯建迪, authorNote=

孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

, correspAuthorsNote=

冯建迪, 博士, 教授, 主要从事GNSS数据处理及电离层研究, E-mail:

FENG Jiandi,PhD,professor, majors in GNSS data processing and ionosphere, E-mail:

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MENG Di, postgraduate, majors in characteristics of ionospheric variations, E-mail:

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孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

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孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

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Time points of Jason series satellites

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卫星名 发射时间 变轨日期 退役日期
Jason-1 2001-12 2009-02 2013-07
Jason-2 2008-06 2016-10 2019-10
Jason-3 2016-01 2022-04 -
), ArticleFig(id=1322941110703760002, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941100842951215, language=CN, label=表1, caption=

Jason系列卫星时间点

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卫星名 发射时间 变轨日期 退役日期
Jason-1 2001-12 2009-02 2013-07
Jason-2 2008-06 2016-10 2019-10
Jason-3 2016-01 2022-04 -
), ArticleFig(id=1322941110812811907, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941100842951215, language=EN, label=Tab. 2, caption=

Statistics of mean, standard deviation and relative error of G-J

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G-J 平均值/TECu 标准差/TECu 相对误差
G-J1(2001—2009年) -1.45 5.23 0.22
G-J2(2008—2016年) -0.09 5.04 0.24
G-J3(2016—2022年) 3.09 2.77 0.56
), ArticleFig(id=1322941110896697988, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322941100842951215, language=CN, label=表2, caption=

G-J的平均值、标准偏差和相对误差

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G-J 平均值/TECu 标准差/TECu 相对误差
G-J1(2001—2009年) -1.45 5.23 0.22
G-J2(2008—2016年) -0.09 5.04 0.24
G-J3(2016—2022年) 3.09 2.77 0.56
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基于Jason-1/2/3 VTEC的全球电离层地图精度评估及修正
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孟迪 1 , 王开心 1 , 冯建迪 1, 2, * , 张志豪 1
大地测量与地球动力学 | 现代大地测量 2025,45(5): 512-517
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大地测量与地球动力学 |现代大地测量 2025 , 45 (5) : 512 -517
基于Jason-1/2/3 VTEC的全球电离层地图精度评估及修正
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MENG Di, postgraduate, majors in characteristics of ionospheric variations, E-mail:

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MENG Di, postgraduate, majors in characteristics of ionospheric variations, E-mail:

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孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

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孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

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孟迪1 , 王开心1, 冯建迪1, 2, * , 张志豪1
作者信息
  • 1 山东理工大学建筑工程与空间信息学院, 山东省淄博市新村西路266号, 255000
  • 2 武汉大学测绘学院, 武汉市珞喻路129号, 430079
通讯作者:

冯建迪, 博士, 教授, 主要从事GNSS数据处理及电离层研究, E-mail:

FENG Jiandi,PhD,professor, majors in GNSS data processing and ionosphere, E-mail:

作者简介:

孟迪, 硕士生, 主要从事电离层变化特性研究, E-mail:

Precision Assessment and Correction of Global Ionospheric Maps Based on Jason-1/2/3 VTEC
Di MENG1 , Kaixin WANG1, Jiandi FENG1, 2, * , Zhihao ZHANG1
Affiliations
  • 1 School of Civil Engineering and Geomatics, Shandong University of Technology, 266 West-Xincun Road, Zibo 255000, China
  • 2 School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China

    • MENG Di, postgraduate, majors in characteristics of ionospheric variations, E-mail:

出版时间: 2025-05-15 doi: 10.14075/j.jgg.2024.05.223
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摘要
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本文使用Jason-1/2/3系列卫星的VTEC数据, 从时间、空间等角度分析全球电离层地图的精度情况, 并利用太阳活动分量、日变化分量和季节变化分量建立相应的修正方程。结果表明: 1) CODE GIMs与Jason系列卫星的残差(G-J)与F10.7呈二次函数关系, 在日变化上呈24 h的周期特征, 在季节变化上呈半年变化周期特征, 修正方程能够有效修正GIMs数据。2) G-J的平均值在太平洋的低纬度地区取得最大值, 在澳大利亚南部取得最小值; 赤道异常中的等离子输送导致G-J的中误差呈现双峰特征; G-J的相对误差在大西洋南部, 尤其是非洲南部的海洋地区取得极大值。

总电子含量  /  全球电离层地图  /  测高卫星  /  Jason系列卫星

This paper employs VTEC data from the Jason-1/2/3 satellite series to analyze the accuracy of global ionospheric maps (GIMs) from temporal and spatial perspectives, and establishes corresponding correction equations using solar activity components, diurnal variation components, and seasonal variation components. The results indicate: 1) The residuals(G-J) between CODE GIMs and Jason series satellite data exhibit a quadratic function relationship with F10.7, showing a 24-hour periodic characteristic in diurnal variation and a semi-annual variation pattern in seasonal changes. The correction equations can effectively amend the GIMs data. 2) The mean value of G-J reaches its maximum in the low-latitude regions of the Pacific and its minimum in southern Australia; the plasma transport within the equatorial anomaly leads to a bimodal feature in the median error of G-J; the relative error of G-J attains its maximum in the southern Atlantic Ocean, particularly in the marine areas off southern Africa.

total electron content  /  global ionosphere maps  /  altimeter satellite  /  Jason satellite series
孟迪, 王开心, 冯建迪, 张志豪. 基于Jason-1/2/3 VTEC的全球电离层地图精度评估及修正. 大地测量与地球动力学, 2025 , 45 (5) : 512 -517 . DOI: 10.14075/j.jgg.2024.05.223
Di MENG, Kaixin WANG, Jiandi FENG, Zhihao ZHANG. Precision Assessment and Correction of Global Ionospheric Maps Based on Jason-1/2/3 VTEC[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (5) : 512 -517 . DOI: 10.14075/j.jgg.2024.05.223
正文
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电离层是地球大气层的重要组成部分，位于地面以上60~2 000 km的高度。在太阳射线和宇宙射线的作用下，电离层中的中性原子和分子被电离，释放出自由电子和离子，这些带电粒子使电磁波路径弯曲，产生电离层延迟。电离层延迟可以通过总电子含量(total electron content，TEC)和信号频率来计算，而TEC对于研究电离层的时空分布和变化规律至关重要[1]。
国际全球导航卫星系统服务(IGS)通过多个电离层分析中心，采用不同建模方法构建全球电离层地图(global ionosphere maps，GIMs)，精度大约在2~8 TECu之间[2]。欧洲轨道确定中心(CODE)利用球谐函数生产的GIMs能有效描述全球TEC的时空变化，适用于电离层延迟校正[3]。然而，IGS地面站主要分布在陆地，在海洋地区分布相对稀疏，球谐函数虽然能够合理外推，但这仍会导致GIMs在海洋地区精度不足[4]。此外，赤道地区TEC的梯度变化大，利用垂直方向TEC(vertical TEC，VTEC)计算也会引入较大误差[5]。
1992年，美国国家航空航天局和法国航天局发射Topex/Poseidon卫星，自此卫星高度计成为海洋测高研究的重要工具。测高卫星不受地表形态限制，能进行全球观测，其双频信号反射后可用来反演海洋上空至测高卫星高度范围的VTEC，有效补充了GIMs产品。全球研究者基于测高卫星进行了大量研究，评估GIMs精度[6-12]，探讨电离层特性[5, 13]。尽管测高卫星轨道低于电离层顶部，无法直接测量轨道上空的TEC，但通过统计和数据融合提高了电离层产品的准确性[14-18]。
自1998年起，IGS持续发布GIMs数据产品，积累了超过20 a的历史数据，覆盖超过2个太阳活动周期。CODE GIMs产品应用广泛，了解其精度至关重要。尽管已有研究评估了GIMs精度，但缺乏系统性。本文利用Jason-1/2/3 VTEC数据，从时间、空间等角度对CODE GIMs产品进行全面评估，并提出修正方程对GIMs进行修正，使其精度提升至双频校正值水平。
1 数据及建模方法
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Jason系列卫星有254条轨道，上升轨道66.15°S~66.15°N(记为奇数)，下降轨道66.15°N ~66.15°S(记为偶数)，轨道高度为1 336 km，轨道倾角为66°，卫星重访周期约9.9 d。Jason系列卫星携带双频雷达高度计，以Ku波段为主频段(13.575 GHz)，以C波段为辅助频段(5.3 GHz)，沿轨道发射双频信号采集数据，采样频率为1 Hz，约18 s前进1°[19-20]。表1描述Jason系列卫星的发射时间、变轨时间及退役时间，目前Jason-1和Jason-2已退役，Jason-3仍在轨。本文仅使用变轨之前的数据进行研究。以Jason-3测高卫星为例，给出该卫星在1 d和1个周期内VTEC的地理分布(图1)。从图可见，该数据主要集中在66°S~66°N之间，覆盖中低纬度的海洋地区，在陆地上空则没有数据，这是因为当测高卫星运行到陆地上空时，其信号会被陆地吸收。
本文使用雷达高度计数据库系统(http://rads.tudelft.nl/rads/data/authentication.cgi)提供的测高数据进行研究。申请的数据包括时间、经度、纬度、平滑后的双频电离层校正值。其中，时间是从1985-01-01 00：00：00起算的累积秒数，经度范围为-180°~180°，纬度范围为-66.15°~66.15°。由于采样频率较高，对Jason-3 VTEC进行疏化处理，即每隔18个数据保留1个数据。基于平滑后的双频电离层校正值，本文利用式(1)计算相应的Jason-1/2/3 VTEC，用于评估CODE GIMs产品的精度：
$\mathrm{VTEC}=-\frac{\mathrm{d} R \cdot f^2}{40.3}$
式中，dR是Ku波段对应的平滑后的双频电离层校正值；f是Ku波段的频率；VTEC是Jason系列卫星对应的垂直总电子含量。
本文使用的CODE GIMs数据来源于CODE分析中心，该数据是最终产品，延迟约11 d。CODE GIMs的纬度范围为87.5°N~87.5°S，间隔为2.5°；经度范围为180°W~180°E，间隔为5°。在2014-10-19以前，CODE GIMs的时间分辨率为2 h。通过线性插值，将该数据的时间分辨率调整为1 h，以匹配更多的测高数据。
太阳极紫外辐射是反映太阳活动变化的最佳参数。然而，空间观测手段费用昂贵，且获取的极紫外数据缺乏连续性。因此，一般采用太阳活动代理指数代替。太阳10.7 cm辐射通量(F10.7)表征太阳极紫外辐射的优势明显，是常用的太阳活动指数之一[21]。本文使用F10.7来描述太阳活动水平。行星性3 h磁情指数(Kp)是用来描述太阳风相互耦合产生的全球地磁扰动程度的参数，本文所进行的精度评估仅针对地磁平静期，所以剔除了Kp>5时对应的TEC数据。
本研究将CODE GIMs与不同测高卫星VTEC的差值定义为残差，采用符号G-J来统一表示，其中，G-J1、G-J2、G-J3分别是利用Jason-1、Jason-2以及Jason-3卫星计算的残差。本文利用残差平均值(MEAN)、残差标准差(STD)及相对误差(REL)来评估GIMs精度，评估指标的计算如下：
$\operatorname{MEAN}=\frac{1}{N} \sum\limits_{i=1}^N(\operatorname{GTEC}-\mathrm{JTEC})$
$\mathrm{STD}=\sqrt{\frac{1}{N-1} \sum\limits_{i=1}^N(\mathrm{GTEC}-\mathrm{JTEC}-\mathrm{MEAN})}$
$\text { REL }=\frac{1}{N} \sum\limits_{i=1}^N \frac{\mid \text { GTEC }- \text { JTEC }- \text { MEAN } \mid}{\text { JTEC }}$
式中，GTEC代表CODE GIMs；JTEC代表Jason-1/2/3 VTEC；N是采样点数量。
在每个网格点处建立CODE GIMs修正方程：
$\operatorname{Gcorr}\left(F_{10.7}, \text { LT }, \text { doy }\right)=F_1 \cdot F_2 \cdot F_3$
$F_1=a \cdot F_{10.7}^2+b \cdot F_{10.7}+c$
$F_2=1+d \cdot \cos \frac{2 \pi(\mathrm{LT}-e)}{24}$
$F_3=1+f \cdot \cos \frac{4 \pi(\mathrm{doy}-g)}{365.25}$
式中，Gcorr代表CODE GIMs的修正量；F1代表太阳活动分量；F2代表日变化分量；F3代表季节变化分量；输入变量为太阳活动指数F10.7、地方时(LT)和年积日(doy)；每个网格点处共7个参数(a~g)，采用非线性最小二乘进行求解。
2 残差分析
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2.1 时间角度
图2描述Jason系列卫星VTEC的年际变化。可以看出，Jason系列卫星的运行时间覆盖约2个太阳活动周期。其中，Jason-1主要位于第22太阳活动周下降相，Jason-2主要位于第23太阳活动周，Jason-3主要位于第24太阳活动周上升相。Jason-1/2/3 VTEC之间存在系统误差，这可能与卫星硬件及电离层校正方法有关[9]。
本文定量统计G-J的平均值、标准差及相对误差，见表2。可以看出，G-J1和G-J2的平均值为负数，分别为-1.45 TECu和-0.09 TECu，G-J3的平均值为3.09 TECu。可以观察到G-J呈逐步增大的趋势，这可能由以下2个原因引起：一是Jason系列卫星的电离层校正方法得到优化；二是随着地面监测站的数量增加，CODE GIMs的精度也随之提高。Jason-1与Jason-2的标准差分别为5.23 TECu和5.04 TECu，而Jason-3的标准差为2.77 TECu。其中，Jason-1和Jason-2覆盖了更多的太阳活动水平，而Jason-3主要反映的是低太阳活动水平下的精度。相对误差随着太阳活动水平增强而减小，Jee等[18]指出，这可能表明等离子体层对夜间电离层维持的贡献并不随着太阳活动水平的增强而增加。
图3给出G-J随太阳活动水平的变化。可以看出，随太阳活动水平增强，G-J呈增加趋势，其中，G-J1、G-J2与F10.7主要呈线性函数关系(二次函数关系不明显)，G-J3与F10.7呈二次函数关系。整体上，这一规律可以用一个二次函数拟合，如式(6)所示。图4给出G-J随地方时的变化。可以看出，G-J与TEC的日变化规律一致，即G-J在正午附近取得最大值，在夜间取得极小值，这一规律可以用一个周期为24 h的余弦函数描述，如式(7)所示。图5给出了G-J随年积日的变化，4条黑色实线依次代表春分日、夏至日、秋分日和冬至日。可以看出，G-J与VTEC的季节变化规律一致，即G-J在春分、秋分附近取得极大值，在夏至、冬至取得极小值，这一规律可以用一个周期为半年的余弦函数描述，如式(8)所示。
2.2 空间角度
图6~8依次描述G-J的平均值、标准差及相对误差的地理分布。由图6可见，G-J的平均值随纬度升高而减小，在太平洋的低纬度地区取得最大值，在澳大利亚南部取得最小值(负值)。由图7可见，G-J的标准差体现出双峰特征，这与赤道异常引起的等离子体输运有关，它在大西洋或太平洋的低纬度地区取得最大值。由图8可见，G-J的相对误差在南大西洋，尤其是在非洲南部的海洋地区取得极大值。受中性风等因素影响，威德尔海至澳大利亚地区的电离层变化复杂，且地面监测站少，因而GIMs不能很好地描述该地区的VTEC变化。
图9定量描述G-J随纬度的变化。可以看出，G-J1介于-5~1 TECu，G-J2介于-4~2 TECu，G-J3介于1~5 TECu。整体上，随纬度增加，G-J增大。在赤道两侧，G-J存在极值，反映了赤道异常。在40°S附近，G-J存在极小值，对应于从威德尔海至澳大利亚的海洋地区。
3 模型验证
收起
基于公式(5)~(8)，本文利用不同测高卫星系统对GIMs进行修正。为了验证修正效果，图10为利用Jason数据，结合平均值、标准差和相对误差指标进行内符合精度评估的结果。本文将修正残差定义为GIMs修正值与对应测高卫星VTEC的差值。
由图10可见，修正残差的平均值近似为0 TECu，标准差及相对误差则变化不大。图11给出修正残差随纬度的变化，可以看出，Gcorr-J1主要介于-0.3~0.2 TECu之间，Gcorr-J2主要介于-0.2~0.2 TECu之间，Gcorr-J3主要介于-0.1~0.1 TECu之间。在南纬60°附近，Gcorr-J2与Gcorr-J3变化显著，且绝对值较大，此区域的修正效果较差。在赤道附近，Gcorr-J呈现双峰特征。整体而言，修正方程具有良好的适用性。
4 结语
收起
本文基于Jason-1/2/3 VTEC数据，在时间及空间角度对CODE GIMs的精度进行评估，并给出一种GIMs修正方法，得到以下结论：
1) G-J1(2001—2009年)、G-J2(2008—2016年)及G-J3(2016—2022年)的平均值分别为-1.45 TECu、-0.09 TECu、3.09 TECu；标准差分别为5.23 TECu、5.04 TECu、2.77 TECu；相对误差分别为0.22、0.24、0.56。
2) G-J与F10.7呈二次函数关系，在日变化中呈24 h的周期特征，在季节变化上呈半年变化特征。本文通过太阳活动分量、日变化分量和季节变化分量建立修正方程，该方程可有效修正CODE GIMs数据。
3) G-J的平均值在太平洋的低纬度地区取得最大值，在澳大利亚南部取得最小值；G-J的标准差呈现双峰特征；G-J的相对误差在大西洋南部，尤其是在非洲南部的海洋地区取得极大值。
基金
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  • 地理信息工程国家重点实验室开放基金(202318)
文献
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参考文献 引证文献
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2025年第45卷第5期
32
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引用本文
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文章信息
doi: 10.14075/j.jgg.2024.05.223
  • 接收时间：2024-05-11
  • 首发时间：2026-10-30
  • 出版时间：2025-05-15
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  • 收稿日期：2024-05-11
基金
Open Fund of State Key Laboratory of Geo-Information Engineering(202318)
地理信息工程国家重点实验室开放基金(202318)
作者信息
    1 山东理工大学建筑工程与空间信息学院, 山东省淄博市新村西路266号, 255000
    2 武汉大学测绘学院, 武汉市珞喻路129号, 430079

通讯作者:

冯建迪, 博士, 教授, 主要从事GNSS数据处理及电离层研究, E-mail:

FENG Jiandi,PhD,professor, majors in GNSS data processing and ionosphere, E-mail:

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