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Article(id=1322506504125661946, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506406058635943, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.11.538, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1732550400000, receivedDateStr=2024-11-26, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239721566, onlineDateStr=2026-10-29, pubDate=1763136000000, pubDateStr=2025-11-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239721566, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239721566, creator=13701087609, updateTime=1793239721566, updator=13701087609, issue=Issue{id=1322506406058635943, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='11', pageStart='1101', pageEnd='1210', issueExtLink='null', onlineDate='null', pubDate='1763136000000', pubDateStr='2025-11-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239698184, creator='13701087609', updateTime=1793239698184, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1115, endPage=1120, ext={EN=ArticleExt(id=1322506504343765756, articleId=1322506504125661946, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Ocean Tide Loading Displacement Inversion Based on Multi-GNSS Considering Mass Loading, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

We use data from 9 CORS stations in Hong Kong from 2016 to 2021 to invert OTLD parameters, and evaluate the OTLD parameter inversion results based on the mean OTLD parameter values of EOT20, FES2014b, HAMTIDE11a, and TPXO9.2a ocean tide models. The results show that compared with GPS inversion results, the error of K1, K2, and S2 tide components in multi-GNSS inversion can reduce by 15%-50%. In addition, comparing the changes of OTLD parameters in multi-GNSS inversion before and after mass loading correction, it can be seen that the improvement effect of OTLD parameters in vertical and east-west directions can reach 6.88% and 9.85%, respectively. However, due to the influence of internal interactions of mass loading, there is no significant improvement effect in north-south direction. Meanwhile, the improvement percentage of OTLD parameters in multi-GNSS inversion after mass loading correction is concentrated about 20%, which is positively correlated with OTLD.

, authors=Fengxian XIAO1, Huayi ZHANG2, Qijie WANG1, 3, *, Mengrui WANG1, authorsList=Fengxian XIAO, Huayi ZHANG, Qijie WANG, Mengrui WANG, authorCompany=null, correspAuthors=Qijie WANG, authorNote=

XIAO Fengxian, postgraduate, majors in surface deformation based on GNSS and InSAR, E-mail:

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利用香港地区9个CORS站2016-2021年数据进行海潮负荷位移(OTLD)参数反演, 以EOT20、FES2014b、HAMTIDE11a、TPXO9.2a海潮模型的OTLD参数均值为参考, 对OTLD参数反演结果进行评价。结果表明, 相比GPS反演结果, 多模GNSS反演的K1、K2、S2分潮误差降低15%~50%。此外, 对比质量负荷修正前后多模GNSS反演的OTLD参数变化情况可知, 垂直向和东西向OTLD参数的改善效果可达到6.88%和9.85%, 但受质量负荷内部分量相互作用的影响, 南北向改善效果不明显。同时, 质量负荷修正对多模GNSS反演的OTLD参数的改善百分比集中在20%左右, 且与OTLD呈正相关。

, authors=肖凤仙1, 张化疑2, 王琪洁1, 3, *, 王梦芮1, authorsList=肖凤仙, 张化疑, 王琪洁, 王梦芮, authorCompany=null, correspAuthors=王琪洁, authorNote=

肖凤仙, 硕士生, 主要从事GNSS与InSAR地表形变研究, E-mail:

, correspAuthorsNote=

王琪洁, 博士, 教授, 博士生导师, 主要从事变形观测与数据处理、遥感图像处理与应用、海洋潮汐负荷研究, E-mail:

WANG Qijie, PhD, professor, PhD supervisor, majors in deformation observation and data processing, remote sensing image processing and its application, and ocean tide loading, E-mail:

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XIAO Fengxian, postgraduate, majors in surface deformation based on GNSS and InSAR, E-mail:

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caption=The correlation between OTLD improved percentage and OTLD, figureFileSmall=5vDghsdHdtTveo0HoBdlFQ==, figureFileBig=FZUshBJxR/oDl/8ObiMJpQ==, tableContent=null), ArticleFig(id=1322506512887563069, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=CN, label=图6, caption=OTLD改善百分比与海潮负荷位移的相关性, figureFileSmall=5vDghsdHdtTveo0HoBdlFQ==, figureFileBig=FZUshBJxR/oDl/8ObiMJpQ==, tableContent=null), ArticleFig(id=1322506512979837758, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=EN, label=Tab. 1, caption=

Information of selected ocean tide models

, figureFileSmall=null, figureFileBig=null, tableContent=
海潮模型 发布机构 分辨率/(°)
EOT20 德国(DGFI) 0.125 0
FES2014b 法国(FTG) 0.062 5
HAMTIDE11a 德国(UH) 0.125 0
TPXO9.2a 美国(OSU) 0.033 3
), ArticleFig(id=1322506513042752320, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=CN, label=表1, caption=

所选用的海潮模型信息

, figureFileSmall=null, figureFileBig=null, tableContent=
海潮模型 发布机构 分辨率/(°)
EOT20 德国(DGFI) 0.125 0
FES2014b 法国(FTG) 0.062 5
HAMTIDE11a 德国(UH) 0.125 0
TPXO9.2a 美国(OSU) 0.033 3
), ArticleFig(id=1322506513189552961, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=EN, label=Tab. 2, caption=

RMSE of OTLD parameters between GNSS inversion and ocean tide models

, figureFileSmall=null, figureFileBig=null, tableContent=
数据来源 模型 潮波 总和 去除K1和K2
M2 S2 N2 K2 K1 O1 P1 Q1
GPS FES2014b 1.25 1.87 0.32 2.70 4.12 1.20 0.61 0.32 12.39 5.56
EOT20 1.36 1.86 0.33 2.69 3.97 1.28 0.61 0.33 12.44 5.78
HAMTIDE11a 1.08 1.86 0.39 2.72 4.30 1.08 0.62 0.37 12.40 5.38
TPXO9.2a 1.26 1.94 0.30 2.65 4.09 1.20 0.62 0.33 12.39 5.65
多模
GNSS		 FES2014b 0.76 1.49 0.29 0.93 1.33 1.00 0.65 0.30 6.75 4.49
EOT20 0.88 1.49 0.30 0.92 1.20 1.08 0.63 0.30 6.80 4.68
HAMTIDE11a 0.51 1.60 0.26 0.86 1.61 0.87 0.62 0.31 6.63 4.16
TPXO9.2a 0.83 1.53 0.27 0.93 1.36 1.00 0.61 0.30 6.83 4.54
), ArticleFig(id=1322506513277633346, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=CN, label=表2, caption=

GNSS反演的OTLD参数与海潮模型的RMSE

, figureFileSmall=null, figureFileBig=null, tableContent=
数据来源 模型 潮波 总和 去除K1和K2
M2 S2 N2 K2 K1 O1 P1 Q1
GPS FES2014b 1.25 1.87 0.32 2.70 4.12 1.20 0.61 0.32 12.39 5.56
EOT20 1.36 1.86 0.33 2.69 3.97 1.28 0.61 0.33 12.44 5.78
HAMTIDE11a 1.08 1.86 0.39 2.72 4.30 1.08 0.62 0.37 12.40 5.38
TPXO9.2a 1.26 1.94 0.30 2.65 4.09 1.20 0.62 0.33 12.39 5.65
多模
GNSS		 FES2014b 0.76 1.49 0.29 0.93 1.33 1.00 0.65 0.30 6.75 4.49
EOT20 0.88 1.49 0.30 0.92 1.20 1.08 0.63 0.30 6.80 4.68
HAMTIDE11a 0.51 1.60 0.26 0.86 1.61 0.87 0.62 0.31 6.63 4.16
TPXO9.2a 0.83 1.53 0.27 0.93 1.36 1.00 0.61 0.30 6.83 4.54
), ArticleFig(id=1322506513348936515, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=EN, label=Tab. 3, caption=

RMSE of OTLD parameters between ocean tide models and gauge stations

, figureFileSmall=null, figureFileBig=null, tableContent=
模型 潮波 总和 去除K1和K2
M2 S2 N2 K2 K1 O1 P1 Q1
FES2014b 7.74 15.06 1.06 4.59 29.84 22.12 9.47 4.04 93.92 59.50
EOT20 7.86 14.94 1.03 4.50 29.80 22.20 9.37 4.16 93.85 59.55
HAMTIDE11a 12.96 13.79 1.88 4.16 13.50 17.05 4.37 3.70 71.41 53.75
TPXO9.2a 19.02 13.87 1.11 4.51 7.74 29.80 3.53 6.97 86.55 74.30
), ArticleFig(id=1322506515005686596, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506504125661946, language=CN, label=表3, caption=

海潮模型OTLD参数与验潮站的RMSE

, figureFileSmall=null, figureFileBig=null, tableContent=
模型 潮波 总和 去除K1和K2
M2 S2 N2 K2 K1 O1 P1 Q1
FES2014b 7.74 15.06 1.06 4.59 29.84 22.12 9.47 4.04 93.92 59.50
EOT20 7.86 14.94 1.03 4.50 29.80 22.20 9.37 4.16 93.85 59.55
HAMTIDE11a 12.96 13.79 1.88 4.16 13.50 17.05 4.37 3.70 71.41 53.75
TPXO9.2a 19.02 13.87 1.11 4.51 7.74 29.80 3.53 6.97 86.55 74.30
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顾及质量负荷的多模GNSS海潮负荷位移反演
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肖凤仙 1 , 张化疑 2 , 王琪洁 1, 3, * , 王梦芮 1
大地测量与地球动力学 | 地球物理解释 2025,45(11): 1115-1120
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大地测量与地球动力学 |地球物理解释 2025 , 45 (11) : 1115 -1120
顾及质量负荷的多模GNSS海潮负荷位移反演
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肖凤仙1 , 张化疑2, 王琪洁1, 3, * , 王梦芮1
作者信息
  • 1 中南大学地球科学与信息物理学院, 长沙市麓山南路932号, 410083
  • 2 自然资源部第一海洋研究所, 青岛市仙霞岭路6号, 266061
  • 3 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 长沙市麓山南路932号, 410083
通讯作者:

王琪洁, 博士, 教授, 博士生导师, 主要从事变形观测与数据处理、遥感图像处理与应用、海洋潮汐负荷研究, E-mail:

WANG Qijie, PhD, professor, PhD supervisor, majors in deformation observation and data processing, remote sensing image processing and its application, and ocean tide loading, E-mail:

作者简介:

肖凤仙, 硕士生, 主要从事GNSS与InSAR地表形变研究, E-mail:

Ocean Tide Loading Displacement Inversion Based on Multi-GNSS Considering Mass Loading
Fengxian XIAO1 , Huayi ZHANG2, Qijie WANG1, 3, * , Mengrui WANG1
Affiliations
  • 1 School of Geosciences and Info-Physics, Central South University, 932 South-Lushan Road, Changsha 410083, China
  • 2 First Institute of Oceanography, MNR, 6 Xianxialing Road, Qingdao 266061, China
  • 3 Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, 932 South-Lushan Road, Changsha 410083, China

    • XIAO Fengxian, postgraduate, majors in surface deformation based on GNSS and InSAR, E-mail:

出版时间: 2025-11-15 doi: 10.14075/j.jgg.2024.11.538
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摘要
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利用香港地区9个CORS站2016-2021年数据进行海潮负荷位移(OTLD)参数反演, 以EOT20、FES2014b、HAMTIDE11a、TPXO9.2a海潮模型的OTLD参数均值为参考, 对OTLD参数反演结果进行评价。结果表明, 相比GPS反演结果, 多模GNSS反演的K1、K2、S2分潮误差降低15%~50%。此外, 对比质量负荷修正前后多模GNSS反演的OTLD参数变化情况可知, 垂直向和东西向OTLD参数的改善效果可达到6.88%和9.85%, 但受质量负荷内部分量相互作用的影响, 南北向改善效果不明显。同时, 质量负荷修正对多模GNSS反演的OTLD参数的改善百分比集中在20%左右, 且与OTLD呈正相关。

多模GNSS  /  海潮负荷位移  /  质量负荷  /  海潮模型

We use data from 9 CORS stations in Hong Kong from 2016 to 2021 to invert OTLD parameters, and evaluate the OTLD parameter inversion results based on the mean OTLD parameter values of EOT20, FES2014b, HAMTIDE11a, and TPXO9.2a ocean tide models. The results show that compared with GPS inversion results, the error of K1, K2, and S2 tide components in multi-GNSS inversion can reduce by 15%-50%. In addition, comparing the changes of OTLD parameters in multi-GNSS inversion before and after mass loading correction, it can be seen that the improvement effect of OTLD parameters in vertical and east-west directions can reach 6.88% and 9.85%, respectively. However, due to the influence of internal interactions of mass loading, there is no significant improvement effect in north-south direction. Meanwhile, the improvement percentage of OTLD parameters in multi-GNSS inversion after mass loading correction is concentrated about 20%, which is positively correlated with OTLD.

multi-GNSS  /  ocean tide loading displacement  /  mass loading  /  ocean tide model
肖凤仙, 张化疑, 王琪洁, 王梦芮. 顾及质量负荷的多模GNSS海潮负荷位移反演. 大地测量与地球动力学, 2025 , 45 (11) : 1115 -1120 . DOI: 10.14075/j.jgg.2024.11.538
Fengxian XIAO, Huayi ZHANG, Qijie WANG, Mengrui WANG. Ocean Tide Loading Displacement Inversion Based on Multi-GNSS Considering Mass Loading[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (11) : 1115 -1120 . DOI: 10.14075/j.jgg.2024.11.538
正文
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日月引力作用导致的海底负载变化和固体地球周期性响应称为海潮负荷效应[1-2]，这种响应引起的地表形变称为海潮负荷位移(ocean tide loading displacement, OTLD)。离海岸线越近，海潮负荷效应的影响越显著，近海区OTLD可达到cm量级[3-4]。因此，为实现高精度形变监测，海潮负荷效应研究至关重要。
当前研究已证明基于GPS技术反演OTLD参数的可靠性，但也发现其中存在的共同问题：GPS反演的OTLD参数在K1、K2、S2分潮误差较大[5-8]。研究表明，多模GNSS可以有效减小单一GPS星座产生的误差。Zhao等[9]研究发现，基于GPS+GLONASS反演的OTLD参数在收敛速度和反演精度方面均优于单一GPS反演结果。Wei等[10]对GPS和多模GNSS(涉及GPS/GLONASS/Galileo/Beidou四个系统的2种组合方式)反演的OTLD参数进行分析，结果表明，多模GNSS反演的太阳分潮(K2、S2、K1、P1)精度显著提升。Wang等[11]进一步对不同组合多模GNSS反演的OTLD参数结果进行比较发现，多模GNSS可以有效提高太阳分潮(K2、S2、K1、P1)反演精度。
除不同GNSS星座组合可以影响OTLD参数反演结果外，质量负荷(mass loading, ML)在参数反演过程中也会引入误差。Zhou等[12]基于香港地区测站资料分析质量负荷对GPS反演OTLD参数的影响，结果表明，质量负荷修正后S2分潮反演误差降低10%。这说明质量负荷修正可以提高GPS反演S2分潮参数的精度，但当前研究未涉及质量负荷对多模GNSS反演OTLD参数精度的影响。
为对比GPS和多模GNSS反演OTLD参数的差异，并进一步分析质量负荷对多模GNSS反演OTLD参数的影响，本文以EOT20、FES2014b、HAMTIDE11a、TPXO9.2a海潮模型为参考，首先基于香港地区9个CORS站，对比GPS与多模GNSS(GPS+ GLONASS+Galileo+Beidou组合)反演OTLD参数的差异；然后基于质量负荷修正前后多模GNSS反演的OTLD参数，分析质量负荷对多模GNSS反演OTLD参数的影响；最后分析质量负荷修正对多模GNSS反演的OTLD参数的改善百分比与OTLD时间序列的相关性。
1 模型与原理
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1.1 海潮模型
现有的海潮模型主要分为2类，一类是基于经验模型得到，另一类是基于同化模型构建。本文采用的海潮模型中除EOT20为经验模型外，FES2014b、HAMTIDE11a、TPXO9.2a均为同化模型，海潮模型基本信息见表 1。海潮模型数据来自Bos-Scherneck网站。
1.2 OTLD参数反演基本原理
本文采用调和分析法对CORS站数据进行OTLD参数反演，其本质为最小二乘拟合[13], 表达式为：
$\begin{gather*}y(t)=b_{0}+b_{1} t+ \\\sum\limits_{l=1}^{L}\left[A_{l} \cos \left(\delta_{l} t\right)+B_{l} \sin \left(\delta_{l} t\right)\right] \end{gather*}$
式中，y(t)为测站坐标时间序列；l为海潮负荷对应的分潮；b0、b1、Al、Bl为待求参数；δl为对应分潮的角速度。
1.3 OTLD参数差异评价
CORS站反演的OTLD参数与海潮模型OTLD参数具有一致性，两者的差异被定义为“观测均方根误差”[14]，本文简称为均方根误差(RMSE)。以4个全球海潮模型的OTLD参数均值作为参考，对于k(k=U、E、N)方向的第j个分潮，N个测站的RMSE可表示为：
$\begin{gather*}\operatorname{RMSE}_{j, k}= \\\left(\frac { 1 } { N } \sum _ { n = 1 } ^ { N } \frac { 1 } { 2 } \left[\left(A_{n} \cos P_{n}-\bar{A}_{\text {model }} \cos \bar{P}_{\text {model }}\right)_{j, k}^{2}+\right.\right. \\\left.\left.-\left(A_{n} \sin P_{n}-\bar{A}_{\text {model }} \sin \bar{P}_{\text {model }}\right)_{j, k}^{2}\right]\right)^{1 / 2} \end{gather*}$
式中，An、Pn分别为CORS站坐标时间序列反演的分潮振幅、相位；$\bar{A}_{\text {model }}、\bar{P}_{\text {model }}$ 分别为全球海潮模型在对应测站的振幅、相位均值。
1.4 质量负荷对OTLD时间序列的影响
为分析质量负荷对CORS站反演的OTLD参数的影响，基于质量负荷修正前后CORS站反演的OTLD参数，对OTLD时间序列进行计算。以选定的4个全球海潮模型计算的平均OTLD时间序列为参考，计算各时刻的OTLD改善百分比OTLDimproved，具体计算公式如下：
$\begin{equation*}\mathrm{OTLD}_{\text {improved }}=\frac{\sqrt{d_{0, t}^{2}}-\sqrt{d_{1, t}^{2}}}{\sqrt{d_{0, t}^{2}}} \times 100 \% \end{equation*}$
式中，$d_{0, t}=\mathrm{OTLD}_{0, t}-\overline{\mathrm{OTLD}}_{\text {model }, t}, d_{1, t}=$$\mathrm{OTLD}_{1, t}-\overline{\mathrm{OTLD}}_{\text {model }, t}$，其中$\mathrm{OTLD}_{0, t}$ 和$\mathrm{OTLD}_{1, t}$分别表示t时刻质量负荷修正前后CORS站反演的海潮负荷位移，$\mathrm{OTLD}_{\text {model }, t}$表示利用海潮模型获得的t时刻海潮负荷位移均值。利用式(3)可以评价t时刻质量负荷修正对OTLD参数反演的影响，OTLDimproved值越大，表明质量负荷修正对多模GNSS反演的OTLD参数的改善效果越显著。
2 结果分析
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2.1 GPS与多模GNSS反演OTLD参数结果对比
选取香港地区9个CORS站(图 1)2016-01-01—2021-04-15观测数据进行OTLD参数反演。
使用Net_Diff软件[15]，采用动态PPP技术分别解算单GPS和多模GNSS观测数据，利用最小二乘法对获得的坐标时间序列进行调和分析，反演8个主要分潮的OTLD参数。基于4个海潮模型的分潮参数，求解各分潮参数的均值并以此为参考值，计算CORS站反演的OTLD参数与参考值的RMSE。
图 2为HKST测站频谱分析结果，可以看出，在3个方向上，K1分潮对应的峰值最大，其次为M2、O1分潮，K2分潮在东西向和南北向峰值较大，Q1分潮在垂直向和东西向峰值较大，但在南北向较小，其余分潮对应的峰值都较小。此外，从GPS和多模GNSS频谱差异的角度分析，K1、K2分潮的差异在3个方向都较显著；S2分潮在垂直向和南北向的差异明显，在东西向无明显差异；P1分潮在垂直向无明显差异；其余潮波对应的峰值差异均相对较小。多模GNSS频谱图振幅在水平向明显降低。
上述现象说明GPS坐标时间序列中存在与海潮负荷周期相近的信号，会与海潮负荷信号产生混叠，如大气信号中的S1、S2分潮会与海潮负荷信号中的S2分潮产生混叠。而多模GNSS解算的坐标时间序列可以在一定程度上对这种混叠信号进行修正[10-11]，从而提升OTLD参数反演精度。
为进一步评价GPS和多模GNSS反演OTLD参数的精度，给出9个CORS站坐标时间序列反演的OTLD参数与海潮模型值的RMSE(图 3)。相比于GPS的调和分析结果，多模GNSS的调和分析精度在垂直向得到显著提升。其中，K1、K2分潮的RMSE减小2~3 mm，降幅达到50%以上，K2分潮的RMSE从mm级降为亚mm级；S2分潮的RMSE减小15%，但仍为mm级。结合图 2可知，GPS与多模GNSS振幅在K1、K2分潮对应周期处的差异最显著，其次为S2分潮，说明GPS坐标时间序列中包含与其频率相对应的噪声，且这种噪声在多模GNSS中能够得到一定程度的修正。在东西向，K2、P1分潮的RMSE减小0.7~0.8 mm，精度提升50%以上；K1、M2、O1分潮的RMSE均有所降低；S2、N2、Q1分潮的RMSE无明显变化。在南北向，S2、K2、K1分潮的RMSE降低较明显，其余分潮均无明显变化。
上述分析说明，相比于GPS反演结果，多模GNSS反演的OTLD参数精度更高，其中多模GNSS反演的K1、K2分潮OTLD参数在3个方向的精度都显著高于GPS反演结果。GPS反演的K1、K2分潮OTLD参数精度较差主要是由GPS卫星系统所致，容易受到多路径效应和轨道误差的干扰。而多模GNSS涉及多个卫星系统的平差求解，可以有效克服单一卫星系统引入的误差。
2.2 GNSS反演结果与验潮站数据对比
为验证GPS、多模GNSS反演OTLD参数的可靠性，选取香港地区Hong Kong和North Point两个验潮站数据作为外部验证[8]。首先利用式(2)分别计算选定的全球海潮模型OTLD参数与CORS站反演的OTLD参数的RMSE，结果见表 2(单位mm)。然后基于双线性内插法获取海潮模型在验潮站对应位置的潮波参数，并计算其与验潮站资料获取的潮波参数的RMSE，结果见表 3(单位cm)。
由表 2可知，当考虑所有分潮的综合影响时，GPS、多模GNSS反演的OTLD参数的RMSE分别为12.39~12.44 mm和6.63~6.83 mm，多模GNSS反演结果误差较小，且不同模型的RMSE差距不大。当不考虑K1、K2分潮时，反演结果与HAMTIDE11a模型最接近，RMSE分别为5.38 mm和4.16 mm，与EOT20和TPXO9.2a模型差距最大。对比表 3可知，当不考虑K1、K2分潮的影响时，HAMTIDE11a与香港地区验潮站数据拟合最好，TPXO9.2a与验潮站数据拟合最差。表 2、3所得结论一致，说明CORS站反演的OTLD参数是可靠的。
2.3 质量负荷对多模GNSS反演OTLD参数的影响
为进一步研究质量负荷对多模GNSS反演OTLD参数的影响，采用国际质量负荷服务(international mass loading service, IMLS)提供的网格文件获取图 1中CORS站对应位置的质量负荷时间序列，并将其与多模GNSS解算的坐标时间序列进行差分，得到质量负荷修正后的坐标时间序列。其中，质量负荷数据的空间分辨率为2′×2′，时间分辨率为3 h。图 4为HKST测站坐标时间序列在质量负荷修正前后的频谱分析结果，图中多模GNSS和多模GNSS-ML分别表示质量负荷修正前后的结果。
由图 4可知，经过质量负荷修正后，频谱图差异主要出现在全日潮对应的周期处。在垂直向，K1、O1分潮对应的周期处振幅明显减小，东西向差异主要体现在O1、Q1分潮上，而南北向影响很小，这是因为质量负荷中的大气负荷和非潮汐海洋负荷在南北向呈现较强的负相关[12]，会相互抵消。上述结果说明，质量负荷信号会与多模GNSS坐标时间序列中的海潮负荷信号发生混叠，从而影响OTLD参数反演结果。为定量分析质量负荷对多模GNSS反演OTLD参数精度的影响，分别计算8个分潮的RMSE，结果如图 5所示。
由图 5可知，在垂直向，K1分潮的RMSE降低最明显，可达到6.88%，O1、S2分潮次之，N2分潮的RMSE变化最小，这与频谱分析结果对应，说明质量负荷修正可以有效提高部分全日朝、半日潮的反演精度。但经过质量负荷修正后，P1、Q1分潮的RMSE反而增大，这可能是由于质量负荷误差导致坐标时间序列被过度修正，使得部分分潮的反演效果不佳。在东西向，Q1、S2、P1分潮的改善比分别达到9.85%、6.40%、4.31%；在南北向，全日潮总体改善效果不显著，但半日潮M2可达到2.71%。结合图 4频谱分析结果可知，质量负荷修正可以提高多模GNSS反演OTLD参数的精度，尤其是全日潮，但受质量负荷内部分量相互作用的影响，南北向改善效果不明显。
2.4 质量负荷对多模GNSS反演OTLD的影响
为进一步研究质量负荷对多模GNSS反演OTLD的影响，基于多模GNSS反演的OTLD参数，对HKST测站2022—2026年、时间间隔为1 d的OTLD时间序列进行预测。同时，以选定的4个全球海潮模型计算的平均OTLD时间序列为参考，利用式(3)计算各时刻的质量负荷修正对HKST测站OTLD参数的改善百分比，结果如图 6所示。
从图 6(a)可以看出，OTLD改善百分比具有明显的周年变化特征，OTLD越大，质量负荷修正对OTLD参数的改善效果越明显，且当OTLD为0~20 mm时，改善百分比主要集中在0~20%。部分OTLD参数的改善百分比大于20%，主要原因为质量负荷修正前后CORS站反演的OTLD差值较小。另外，部分OTLD参数的改善百分比为负值，说明质量负荷修正可能使OTLD反演精度降低。原因主要有以下2种可能：一是海潮模型在近海地区存在误差[2]，使得作为评价指标的OTLD存在一定偏差，导致出现负值；二是基于海潮模型对OTLD进行预报会受交点因子和订正角等的影响，导致预测的OTLD与真值存在差异。从图 6(b)可以看出，改善百分比为正值占比64.99%，负值占比35.01%，正值占比为负值的1.86倍。因此，OTLD改善百分比整体较好，且与OTLD大小呈正相关。
3 结语
收起
本文基于动态PPP技术，通过调和分析法对香港地区9个CORS站2016-01-01—2021-04-15的数据进行OTLD参数反演。通过对比GPS与多模GNSS反演结果以及质量负荷修正前后的多模GNSS反演结果，得到以下结论：
1) 相比于GPS反演结果，多模GNSS反演的OTLD参数精度在K1、K2、S2分潮得到显著提升。
2) 质量负荷修正可以提高多模GNSS反演全日潮OTLD参数的精度，但由于南北向大气负荷和非潮汐负荷的相互作用，RMSE在垂直向和东西向改善效果更显著。
3) 质量负荷修正对多模GNSS反演的OTLD参数的改善百分比具有显著的周年特征，与OTLD大小呈正相关，且大部分集中在0~20%之间。
基金
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  • 国家自然科学基金(42474058)
  • 长沙市自然科学基金(kq2208262)
文献
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2025年第45卷第11期
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doi: 10.14075/j.jgg.2024.11.538
  • 接收时间：2024-11-26
  • 首发时间：2026-10-29
  • 出版时间：2025-11-15
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  • 收稿日期：2024-11-26
基金
National Natural Science Foundation of China(42474058)
国家自然科学基金(42474058)
Natural Science Foundation of Changsha(kq2208262)
长沙市自然科学基金(kq2208262)
作者信息
    1 中南大学地球科学与信息物理学院, 长沙市麓山南路932号, 410083
    2 自然资源部第一海洋研究所, 青岛市仙霞岭路6号, 266061
    3 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 长沙市麓山南路932号, 410083

通讯作者:

王琪洁, 博士, 教授, 博士生导师, 主要从事变形观测与数据处理、遥感图像处理与应用、海洋潮汐负荷研究, E-mail:

WANG Qijie, PhD, professor, PhD supervisor, majors in deformation observation and data processing, remote sensing image processing and its application, and ocean tide loading, E-mail:

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