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Article(id=1322506502464712965, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506501562937604, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.12.578, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1734883200000, receivedDateStr=2024-12-23, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239721169, onlineDateStr=2026-10-29, pubDate=1765728000000, pubDateStr=2025-12-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239721169, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239721169, creator=13701087609, updateTime=1793239721169, updator=13701087609, issue=Issue{id=1322506501562937604, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='12', pageStart='1211', pageEnd='1316', issueExtLink='null', onlineDate='null', pubDate='1765728000000', pubDateStr='2025-12-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239720954, creator='13701087609', updateTime=1793239720954, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1211, endPage=1214, ext={EN=ArticleExt(id=1322506502800257286, articleId=1322506502464712965, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=A Fine-Scale Stratification ZTD Model Considering the Spatiotemporal Factors of Lapse Rate in China, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to improve the accuracy of ZTD model, a fine-scale stratification ZTD (ZTDFS) model in China is proposed. The new model is finely stratified below 10 km and takes into account the seasonal and daily variation characteristics of each layer. At the same time, the model also fully considers the spatiotemporal variation of the vertical lapse rate of third-order exponential function. The radiosonde data shows that the mean RMSE of ZTDFS model is 31.43 mm, which is 36.6% smaller than that of GPT3 model. The GNSS ZTD data shows that above 500 m, the mean RMSE of ZTDFS model is 28.64 mm, which is improved by 9% compared to GPT3. With the increase in altitude, the performance advantage of ZTDFS model gradually emerges.

, authors=Huizhong ZHU1, Guangsheng LIU1, Xiang GAO2, Shaoni CHEN1, Tianyu YANG1, Shuaimin WANG3, Song LI4, Chunhua JIANG1, authorsList=Huizhong ZHU, Guangsheng LIU, Xiang GAO, Shaoni CHEN, Tianyu YANG, Shuaimin WANG, Song LI, Chunhua JIANG, authorCompany=null, correspAuthors=null, authorNote=

ZHU Huizhong, PhD, professor, majors in high-precision GNSS positioning, 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=1322506506327666957, articleId=1322506502464712965, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=一种顾及递减因子时空因素的中国区域精细分层ZTD模型, 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=

为提高ZTD垂直外推精度，提出一种中国区域精细分层的ZTD(zenith tropospheric delay fine-scale stratification, ZTDFS)垂直改正模型，该模型在10 km以下精细分层并顾及每层季节和日内变化特征，同时充分考虑了三阶指数函数的递减因子的时空变化特征。探空数据结果显示，ZTDFS模型的RMSE均值为31.43 mm，较GPT3模型精度提升36.6%。GNSS ZTD数据评估结果表明，在500 m以上，ZTDFS模型的RMSE均值为28.64 mm，较GPT3性能提升9%。随着高度的上升，ZTDFS模型的性能优势逐渐显现。

, authors=祝会忠1, 刘广盛1, 高祥2, 陈少妮1, 杨添宇1, 王帅民3, 李耸4, 蒋春华1, authorsList=祝会忠, 刘广盛, 高祥, 陈少妮, 杨添宇, 王帅民, 李耸, 蒋春华, authorCompany=null, correspAuthors=null, authorNote=

祝会忠，博士，教授，主要研究方向为高精度GNSS定位，E-mail:

, correspAuthorsNote=null, copyrightStatement=版权所有，未经授权，不得转载。, copyrightOwner=大地测量与地球动力学编辑部, extLink=null, articleAbsUrl=null, sourceXml=0T+50S3iFDiVXk5hKoHy2w==, magXml=PRfIr4BeSrPmgJZmcGGF5A==, pdfUrl=null, pdf=y6fmuwtaO3TjRVUQnZxKVg==, pdfFileSize=2466594, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=RKGWuWYJDi+PKG+09fn85A==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=IMrwzGFMQSsPnib3ifrLzg==, mapNumber=null, fund=null)}, authors=[Author(id=1322506507569180955, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=zhuhuizhong@lntu.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322506507678232861, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, authorId=1322506507569180955, language=EN, stringName=Huizhong ZHU, firstName=Huizhong, middleName=null, lastName=ZHU, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=1, address=1 School of Geomatics, Liaoning Technical University, 88 Yulong Road, Fuxin 123000, China, bio={"content":"

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ZHU Huizhong, PhD, professor, majors in high-precision GNSS positioning, E-mail:

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GPT3 ZTD with GNSS ZTD, figureFileSmall=X/Mg4VNmWyxZGJk0S53aOQ==, figureFileBig=97dWhe+oLYir7kxz1BiSKg==, tableContent=null), ArticleFig(id=1322506513126633812, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, language=CN, label=图3, caption=ZTDFS和GPT3 ZTD与GNSS ZTD的RMSE和bias分布, figureFileSmall=X/Mg4VNmWyxZGJk0S53aOQ==, figureFileBig=97dWhe+oLYir7kxz1BiSKg==, tableContent=null), ArticleFig(id=1322506513189548373, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, language=EN, label=Tab. 1, caption=

Statistics of bias and RMSE of ZTDFS and GPT3 ZTD with radiosonde ZTD

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模型bias/mmRMSE/mm
最小值最大值均值最小值最大值均值
ZTDFS-70.259.58-3.0013.0596.6331.43
GPT3-44.2046.5124.0019.2184.5649.54
), ArticleFig(id=1322506513260851542, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, language=CN, label=表1, caption=

ZTDFS和GPT3 ZTD与探空ZTD的bias和RMSE统计

, figureFileSmall=null, figureFileBig=null, tableContent=
模型bias/mmRMSE/mm
最小值最大值均值最小值最大值均值
ZTDFS-70.259.58-3.0013.0596.6331.43
GPT3-44.2046.5124.0019.2184.5649.54
), ArticleFig(id=1322506513340543319, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, language=EN, label=Tab. 2, caption=

Statistics of bias and RMSE of ZTDFS and GPT3 ZTD with GNSS ZTD in different height interval

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模型高度bias/mmRMSE/mm
最小值最大值均值最小值最大值均值
ZTDFS500 m以下-21.6618.89-0.3520.3766.4248.56
GPT3500m以下-25.0837.93-1.3021.0866.8448.70
ZTDFS500m以上-18.289.18-1.8914.3450.0228.64
GPT3500m以上-7.5838.1611.3711.3650.2531.49
), ArticleFig(id=1322506513411846488, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506502464712965, language=CN, label=表2, caption=

ZTDFS和GPT3模型不同高度区间内ZTD与GNSS ZTD的bias和RMSE统计

, figureFileSmall=null, figureFileBig=null, tableContent=
模型高度bias/mmRMSE/mm
最小值最大值均值最小值最大值均值
ZTDFS500 m以下-21.6618.89-0.3520.3766.4248.56
GPT3500m以下-25.0837.93-1.3021.0866.8448.70
ZTDFS500m以上-18.289.18-1.8914.3450.0228.64
GPT3500m以上-7.5838.1611.3711.3650.2531.49
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一种顾及递减因子时空因素的中国区域精细分层ZTD模型
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祝会忠 1 , 刘广盛 1 , 高祥 2 , 陈少妮 1 , 杨添宇 1 , 王帅民 3 , 李耸 4 , 蒋春华 1
大地测量与地球动力学 | 现代大地测量 2025,45(12): 1211-1214
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大地测量与地球动力学 |现代大地测量 2025 , 45 (12) : 1211 -1214
一种顾及递减因子时空因素的中国区域精细分层ZTD模型
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祝会忠1 , 刘广盛1, 高祥2, 陈少妮1, 杨添宇1, 王帅民3, 李耸4, 蒋春华1
作者信息
  • 1 辽宁工程技术大学测绘与地理科学学院, 辽宁省阜新市玉龙路88号, 123000
  • 2 长安大学地质工程与测绘学院, 西安市雁塔路126号, 710054
  • 3 河北工程大学矿业与测绘工程学院, 河北省邯郸市太极路19号, 056038
  • 4 山东大学空间科学研究院, 山东省威海市文化西路180号, 264209
作者简介:

祝会忠，博士，教授，主要研究方向为高精度GNSS定位，E-mail:

A Fine-Scale Stratification ZTD Model Considering the Spatiotemporal Factors of Lapse Rate in China
Huizhong ZHU1 , Guangsheng LIU1, Xiang GAO2, Shaoni CHEN1, Tianyu YANG1, Shuaimin WANG3, Song LI4, Chunhua JIANG1
Affiliations
  • 1 School of Geomatics, Liaoning Technical University, 88 Yulong Road, Fuxin 123000, China
  • 2 Schoo of Geological Engineering and Geomatics, Chang'an University, 126 Yanta Road, Xi'an 710054, China
  • 3 School of Mining and Geomatics Engineering, Hebei University of Engineering, 19 Taiji Road, Handan 056038, China
  • 4 Institute of Space Science, Shandong University, 180 West-Wenhua Road, Weihai 264209, China

    • ZHU Huizhong, PhD, professor, majors in high-precision GNSS positioning, E-mail:

出版时间: 2025-12-15 doi: 10.14075/j.jgg.2024.12.578
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为提高ZTD垂直外推精度，提出一种中国区域精细分层的ZTD(zenith tropospheric delay fine-scale stratification, ZTDFS)垂直改正模型，该模型在10 km以下精细分层并顾及每层季节和日内变化特征，同时充分考虑了三阶指数函数的递减因子的时空变化特征。探空数据结果显示，ZTDFS模型的RMSE均值为31.43 mm，较GPT3模型精度提升36.6%。GNSS ZTD数据评估结果表明，在500 m以上，ZTDFS模型的RMSE均值为28.64 mm，较GPT3性能提升9%。随着高度的上升，ZTDFS模型的性能优势逐渐显现。

精细分层  /  ZTD  /  递减因子  /  ERA5  /  探空站  /  GNSS

In order to improve the accuracy of ZTD model, a fine-scale stratification ZTD (ZTDFS) model in China is proposed. The new model is finely stratified below 10 km and takes into account the seasonal and daily variation characteristics of each layer. At the same time, the model also fully considers the spatiotemporal variation of the vertical lapse rate of third-order exponential function. The radiosonde data shows that the mean RMSE of ZTDFS model is 31.43 mm, which is 36.6% smaller than that of GPT3 model. The GNSS ZTD data shows that above 500 m, the mean RMSE of ZTDFS model is 28.64 mm, which is improved by 9% compared to GPT3. With the increase in altitude, the performance advantage of ZTDFS model gradually emerges.

fine-scale stratification  /  ZTD  /  lapse rate  /  ERA5  /  radiosonde  /  GNSS
祝会忠, 刘广盛, 高祥, 陈少妮, 杨添宇, 王帅民, 李耸, 蒋春华. 一种顾及递减因子时空因素的中国区域精细分层ZTD模型. 大地测量与地球动力学, 2025 , 45 (12) : 1211 -1214 . DOI: 10.14075/j.jgg.2024.12.578
Huizhong ZHU, Guangsheng LIU, Xiang GAO, Shaoni CHEN, Tianyu YANG, Shuaimin WANG, Song LI, Chunhua JIANG. A Fine-Scale Stratification ZTD Model Considering the Spatiotemporal Factors of Lapse Rate in China[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (12) : 1211 -1214 . DOI: 10.14075/j.jgg.2024.12.578
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天顶对流层延迟(ZTD)是卫星信号在中性大气层中的总延迟，直接影响GNSS精密定轨定位的精度[1]。精确的ZTD对于提高精密单点定位(PPP)的性能至关重要，特别是在垂直方向和收敛时间估计方面。对流层延迟模型作为估算ZTD的主要方法，广泛应用于定位、气象、灾害等领域。因此，精确的ZTD模型在空间大地测量和大气科学研究方面具有重要意义[2]。
早期的对流层延迟模型，如Saastamoinen、Black等模型依赖于温度、气压等观测变量，这会限制其适用性[3-4]。针对该问题，部分学者提出无气象观测变量的ZTD模型，如UNB、GPT等，这些模型通过内插或外推方法获取所需的气象变量，结合物理模型计算对流层延迟[5-6]。随着多源气象数据同化能力的提高，越来越多的高精度数值天气数据被用于构建优化的ZTD模型。
李薇等[7]利用美国国家环境预报中心的数据，建立考虑了对流层延迟随经纬度变化的IGGtrop模型，精度约为4.0 cm。Yao等[8]结合球面谐波函数和指数函数，同时考虑对流层延迟的日变化建立GZTD2模型，其RMSE为3.9 cm，较GZTD模型提高3 mm。谐波函数等模型可以捕捉对流层的周期性变化特征，但在准确反映对流层的垂直变化方面存在局限性。为此，Zhu等[9]基于ERA5数据构建全球尺度的ZTD分段模型GZTD-P，与GPT3模型相比，精度提高0.96 cm。Huang等[10]考虑ZTD垂直递减率建立GGZTD-H模型，精度约为4.11 cm。
上述模型虽能在一定程度上提升ZTD垂直拟合精度，但在大高度外推和复杂时空变化下仍存在误差积累的问题。为进一步提升ZTD垂直改正精度，本文提出一种中国区域精细分层的对流层延迟模型ZTDFS。该模型在垂直方向上精细分层，并引入三阶指数函数表征垂向变化特征，同时还考虑了ZTD及递减因子的时空变化特征，以精准刻画ZTD垂直结构。新模型基于ERA5格网数据构建，并利用探空和GNSS数据进行精度验证。
1 数据和方法
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1.1 数据介绍
利用2016—2019年ERA5气压层的温度、气压、比湿和位势高参数构建ZTDFS模型，并使用全球综合无线电探空档案库(IGRA)提供的2020年中国及周边区域92个无线电探空站数据(https://www.ncei.noaa.gov)和2015年202个中国大陆构造环境监测网络GNSS观测数据验证新模型的精度。
1.2 ZTD计算方法
ZTD可通过积分方法确定，表达式为：
$N=K_{1} \frac{(P-e)}{T}+K_{2} \frac{e}{T}+K_{3} \frac{e}{T^{2}}$
$e=\frac{\mathrm{Sh} \cdot P}{0.622} $
$\mathrm{ZTD}=10^{-6} \int_{H_{0}}^{H^{\text {top }}} N \mathrm{~d} h $
式中，N为总大气折射率；T为温度；e为水汽压；P为气压；Sh为比湿；H0、Htop分别为剖面底和剖面顶的高度；h为高度；K1、K2、K3为常数系数，分别为77.604 K/hPa、64.79 K/hPa、375 463 K2/hPa。
2 ZTDFS模型构建
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本研究将0~10 km的ZTD垂直空间细化为10层，间隔1 km，利用式(4)表征每个垂直层内各1°×1°格网点的年变化、半年变化和日变化；利用式(5)所示三阶指数函数拟合垂直ZTD剖面[11]；利用式(6)对ZTD递减因子的年度和半年周期项建立分辨率为1°×1°的格网模型。综合式(4)~(6)，即可得到中国区域ZTD垂直改正模型ZTDFS：
$\begin{gather*}\mathrm{ZTD}_{h}^{k}= \\a_{0}^{k}+a_{1}^{k} \cos \left(\frac{2 \pi \mathrm{DOY}}{365.25}\right)+a_{2}^{k} \sin \left(\frac{2 \pi \mathrm{DOY}}{365.25}\right)+ \\a_{3}^{k} \cos \left(\frac{4 \pi \mathrm{DOY}}{365.25}\right)+a_{4}^{k} \sin \left(\frac{4 \pi \mathrm{DOY}}{365.25}\right)+ \\a_{5}^{k} \cos \left(\frac{2 \pi \mathrm{HOD}}{24}\right)+a_{6}^{k} \sin \left(\frac{2 \pi \mathrm{HOD}}{24}\right), \\k=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \end{gather*}$
$\begin{gather*}\mathrm{ZTD}_{t}=\mathrm{ZTD}_{r} \cdot \exp \left[\beta_{1}\left(h_{t}-h_{r}\right)+\right. \\\left.\beta_{2}\left(h_{t}^{2}-h_{r}^{2}\right)+\beta_{3}\left(h_{t}^{3}-h_{r}^{3}\right)\right] \end{gather*}$
$\begin{gather*}\beta_{i}=A_{0}^{i}+\sum\limits_{n=1}^{2}\left[A_{n}^{i} \sin \left(\frac{2 \pi n \mathrm{DOY}}{365.25}\right)+\right. \\\left.B_{n}^{i} \cos \left(\frac{2 \pi n \mathrm{DOY}}{365.25}\right)\right], i=1, 2, 3 \end{gather*}$
式中，$a_{0}^{k}$ 为第$k$ 层ZTD的年均值；$a_{1}^{k}、a_{2}^{k}、a_{3}^{k}、a_{4}^{k}、a_{5}^{k}$ 和$a_{6}^{k}$ 分别为季节和日间周期项系数；$\mathrm{ZTD}_{t}$ 和$\mathrm{ZTD}_{r}$ 分别为目标高度$h_{t}$ 和参考高度$h_{r}$ 处的ZTD值；$\beta_{1}、\beta_{2}、\beta_{3}$ 分别为ZTD的$1 \sim 3$ 阶递减因子；$A_{0}^{i}、A_{n}^{i}、B_{n}^{i}$ 分别为ZTD递减率的年均值、年和半年振幅项; HOD和DOY分别为1 d中的小时和年积日。
在使用模型时，输入经纬度、海拔、DOY和HOD，然后确定目标高度处4个最近模型网格点的ZTD值，最后采用双线性插值法计算目标位置的ZTD。
3 精度验证与分析
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使用bias和RMSE评价新模型的准确率。
3.1 基于探空数据的验证
以2020年中国及周边区域探空站剖面数据为参考值，分别利用ZTDFS和GPT3模型计算探空站剖面上所有点的ZTD并作差，统计结果见表 1。
表 1中ZTDFS模型的bias和RMSE的均值分别为-3.00 mm和31.43 mm，GPT3模型的bias和RMSE的均值分别为24.00 mm和49.54 mm。ZTDFS模型的RMSE均值比GPT3模型小18.11 mm，表明其整体精度较GPT3提高36.6%。ZTDFS模型进行了精细分层并将垂直外推高度控制在1 km以内，能有效降低误差积累，同时采用三阶指数函数提高ZTD的垂直拟合精度，引入周期性递减因子增强季节适应性，从而提升了ZTD整体估计精度。
从图 1(a)和1(b)可以看出，GPT3模型的bias表现为明显的正偏差，而ZTDFS模型的bias更小，且大部分接近于0，说明ZTDFS模型能更好地捕捉ZTD的时空变化特征。由图 1(c)和1(d)可知，ZTDFS模型在中国及周边区域具有较小的RMSE值，尤其在中国西北青藏高原和黄土高原等高海拔区域，复杂的地形和显著的时空变化特征更加突显了垂直分层和递减因子优化对提高ZTD计算精度的重要作用。
从图 2(a)可以看出，GPT3模型在2 km以下呈现正偏差，在2 km以上呈现负偏差，且负偏差随高度不断增大。而ZTDFS模型在各高度区间均呈现较小的正偏差，这可能与ZTDFS模型垂向上各层的外推距离均在1 km以内有关，保证了垂直外推的稳定性。由图 2(b)可知，ZTDFS模型的RMSE值随着海拔升高保持在较小的范围内且有减小的趋势，这进一步验证了ZTDFS模型在高海拔地形复杂地区的精度和稳定性优势。
3.2 基于GNSS ZTD的验证
本文进一步利用2015年中国区域202个GNSS观测站的ZTD数据，评估ZTDFS和GPT3模型的ZTD精度，并从高度和分布特征2个方面进行详细分析。从表 2可以看出，500 m以下ZTDFS与GPT3模型的bias均值呈现较小负值，RMSE均值相当，ZTDFS模型精度提升优势不明显。500 m以上区间共有139个站点，数量占比69%，该高度区间内ZTDFS与GPT3模型的RMSE均值分别为28.64 mm和31.49 mm，RMSE均值减小2.85 mm，性能提升9%，并且随着高度的上升，ZTDFS模型的优势愈加明显。
从图 3(a)和3(b)可以看出，ZTDFS模型的bias更小，说明ZTDFS模型的系统性偏差更小。相比于GPT3，在天山山脉和喜马拉雅山脉区域，ZTDFS模型的bias减小程度更加明显。进一步对比图 3(c)和3(d)可知，在中国西北高海拔区域，ZTDFS模型的RMSE明显小于GPT3，进一步证实了ZTDFS模型在高海拔地区具有优越的垂直外推性能。这主要是因为ZTDFS模型在垂直方向上进行了精细分层，并考虑了三阶指数递减率的周期变化特征，能够准确捕捉ZTD的垂直变化特征，提高模型在高海拔地区的预测精度。
4 结语
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本文提出一种中国区域精细分层的ZTD垂直改正模型ZTDFS。探空站数据评估结果表明，ZTDFS模型的bias和RMSE均值分别为-3.00 mm和31.43 mm，较GPT3模型精度提升36.6%。此外，ZTDFS模型的RMSE值随着海拔升高呈现减小趋势，进一步验证了其在西北高海拔地区的精度和稳定性优势。GNSS ZTD评估结果表明，在500 m以上高度区间(占站点数量的69%)，ZTDFS模型的RMSE值较GPT3模型减少2.85 mm，性能提升9%，且随着高度的上升，ZTDFS模型的性能优势逐渐显现，尤其在中国西北的高海拔区域。ZTDFS模型垂直方向的精细分层及对三阶指数递减率年变化和半年变化特征的充分考虑，增强了模型对ZTD垂直变化特征的捕捉能力，显著提升了其在高海拔地区的预测精度。
基金
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  • 国家自然科学基金(42074012)
  • 国家自然科学基金(42030109)
  • 国家自然科学基金(41904037)
  • 辽宁省振兴人才计划(XLYC2203162)
  • 河北省自然科学基金(D2023402024)
  • 辽宁省自然科学基金(20240347)
  • 辽宁省自然科学基金(20240336)
  • 辽宁省自然科学基金(20240350)
文献
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参考文献 引证文献
排序方式：
1
Xu G C , Xu Y . GPS: Theory, Algorithms and Applications[M]. Berlin Heidelberg: Springer, 2016
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Zhang Z Y , Lou Y D , Zhang W X , et al. Dynamic Stochastic Model for Estimating GNSS Tropospheric Delays from Air-Borne Platforms[J]. GPS Solutions, 2023, 27
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Saastamoinen J. Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging Satellites[M]//Henriksen S W, Mancini A, Chovitz B H. The Use of Artificial Satellites for Geodesy. Washington: American Geophysical Union, 1972
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Black H D . An Easily Implemented Algorithm for the Tropospheric Range Correction[J]. Journal of Geophysical Research: Solid Earth, 1978, 83 (B4): 1825- 1828
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Leandro R, Santos M, Langley R. UNB Neutral Atmosphere Models: Development and Performance[C]. Proceedings of ION NTM, Monterey, 2006
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Landskron D , Böhm J . VMF3/GPT3:Refined Discrete and Empirical Troposphere Mapping Functions[J]. Journal of Geodesy, 2018, 92, 349- 360
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李薇, 袁运斌, 欧吉坤, 等. 全球对流层天顶延迟模型IGGtrop的建立与分析[J]. 科学通报, 2012, 57 (15): 1317- 1325
Li Wei , Yuan Yunbin , Ou Jikun , et al. A New Global Zenith Tropospheric Delay Model IGGtrop for GNSS Applications[J]. Chinese Science Bulletin, 2012, 57 (15): 1317- 1325
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Yao Y B , Hu Y F , Yu C , et al. An Improved Global Zenith Tropospheric Delay Model GZTD2 Considering Diurnal Variations[J]. Nonlinear Processes in Geophysics, 2016, 23 (3): 127- 136
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Zhu G , Huang L K , Yang Y Z , et al. Refining the ERA5-Based Global Model for Vertical Adjustment of Zenith Tropospheric Delay[J]. Satellite Navigation, 2022, 3 (1)
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Huang L K , Zhu G , Peng H , et al. An Improved Global Grid Model for Calibrating Zenith Tropospheric Delay for GNSS Applications[J]. GPS Solutions, 2023, 27 (1)
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Jiang C H , Gao X , Zhu H Z , et al. An Improved Global Pressure and Zenith Wet Delay Model with Optimized Vertical Correction Considering the Spatiotemporal Variability in Multiple Height-Scale Factors[J]. Geoscientific Model Development, 2024, 17 (15): 5939- 5959
2025年第45卷第12期
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文章信息
doi: 10.14075/j.jgg.2024.12.578
  • 接收时间：2024-12-23
  • 首发时间：2026-10-29
  • 出版时间：2025-12-15
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出版历史
  • 收稿日期：2024-12-23
基金
National Natural Science Foundation of China(42074012)
国家自然科学基金(42074012)
National Natural Science Foundation of China(42030109)
国家自然科学基金(42030109)
National Natural Science Foundation of China(41904037)
国家自然科学基金(41904037)
Liaoning Revitalization Talents Program(XLYC2203162)
辽宁省振兴人才计划(XLYC2203162)
Natural Science Foundation of Hebei Province(D2023402024)
河北省自然科学基金(D2023402024)
Natural Science Foundation of Liaoning Province(20240347)
辽宁省自然科学基金(20240347)
Natural Science Foundation of Liaoning Province(20240336)
辽宁省自然科学基金(20240336)
Natural Science Foundation of Liaoning Province(20240350)
辽宁省自然科学基金(20240350)
作者信息
    1 辽宁工程技术大学测绘与地理科学学院, 辽宁省阜新市玉龙路88号, 123000
    2 长安大学地质工程与测绘学院, 西安市雁塔路126号, 710054
    3 河北工程大学矿业与测绘工程学院, 河北省邯郸市太极路19号, 056038
    4 山东大学空间科学研究院, 山东省威海市文化西路180号, 264209
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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.12.578
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