{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:09:11Z","timestamp":1760144951020,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42161067","202202AD080010"],"award-info":[{"award-number":["42161067","202202AD080010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Yunnan Major Science and Technology Special Plan of China","award":["42161067","202202AD080010"],"award-info":[{"award-number":["42161067","202202AD080010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Improving the accuracy of zenith tropospheric delay (ZTD) models is an important task. However, the existing ZTD models still have limitations, such as a lack of appropriate vertical adjustment function and being unsuitable for China, which has a complex climate and great undulating terrain. A new approach that considers the time-varying vertical adjustment and delicate diurnal variations of ZTD was introduced to develop a new grid ZTD model (NGZTD). The NGZTD model employed the Gaussian function and considered the seasonal variations of Gaussian coefficients to express the vertical variations of ZTD. The effectiveness of vertical interpolation for the vertical adjustment model (NGZTD-H) was validated. The root mean squared errors (RMSE) of the NGZTD-H model improved by 58% and 22% compared to the global pressure and temperature 3 (GPT3) model using ERA5 and radiosonde data, respectively. The NGZTD model\u2019s effectiveness for directly estimating the ZTD was validated. The NGZTD model improved by 22% and 31% compared to the GPT3 model using GNSS-derived ZTD and layered ZTD at radiosonde stations, respectively. Seasonal variations in Gaussian coefficients need to be considered. Using constant Gaussian coefficients will generate large errors. The NGZTD model exhibited outstanding advantages in capturing diurnal variations and adapting to undulating terrain. We analyzed and discussed the main error sources of the NGZTD model using validation of spatial interpolation accuracy. This new ZTD model has potential applications in enhancing the reliability of navigation, positioning, and interferometric synthetic aperture radar (InSAR) measurements and is recommended to promote the development of space geodesy techniques.<\/jats:p>","DOI":"10.3390\/rs16112023","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T11:48:50Z","timestamp":1717501730000},"page":"2023","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Grid Zenith Tropospheric Delay Model Considering Time-Varying Vertical Adjustment and Diurnal Variation over China"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9810-3538","authenticated-orcid":false,"given":"Jihong","family":"Zhang","sequence":"first","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqing","family":"Zuo","sequence":"additional","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shipeng","family":"Guo","sequence":"additional","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8199-3678","authenticated-orcid":false,"given":"Shaofeng","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Yang","sequence":"additional","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4840-3645","authenticated-orcid":false,"given":"Yongning","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuefu","family":"Yue","sequence":"additional","affiliation":[{"name":"Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"ref_1","first-page":"2218","article-title":"A New Global Zenith Tropospheric Delay Model GZTD","volume":"56","author":"Yao","year":"2013","journal-title":"Chin. J. Geophys."},{"key":"ref_2","first-page":"285","article-title":"Analysis on Performance of Water Vapor Detection Based on BeiDou Satellite","volume":"41","author":"Shi","year":"2016","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/S1464-1895(01)00091-6","article-title":"Calculation of Zenith Delays from Meteorological Data Comparison of NWP Model, Radiosonde and GPS Delays","volume":"26","author":"Vedel","year":"2001","journal-title":"Phys. Chem. Earth"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5392","DOI":"10.1109\/JSTARS.2021.3079699","article-title":"An Improved Model for Detecting Heavy Precipitation Using GNSS-Derived Zenith Total Delay Measurements","volume":"14","author":"Li","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.5194\/isprs-archives-XLII-3-W10-1197-2020","article-title":"Research on Zenith Tropospheric Delay Modeling of Regional Cors Network","volume":"42","author":"Yang","year":"2020","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4487","DOI":"10.1029\/JC074i018p04487","article-title":"Two-quartic Tropospheric Refractivity Profile for Correcting Satellite Data","volume":"74","author":"Hopfield","year":"1969","journal-title":"J. Geophys. Res."},{"key":"ref_7","first-page":"247","article-title":"Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging Satellites","volume":"15","author":"Saastamoinen","year":"1972","journal-title":"Use Artif. Satell. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1029\/JB083iB04p01825","article-title":"An Easily Implemented Algorithm for the Tropospheric Range Correction","volume":"83","author":"Black","year":"1978","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"127","DOI":"10.5194\/npg-23-127-2016","article-title":"An Improved Global Zenith Tropospheric Delay Model GZTD2 Considering Diurnal Variations","volume":"23","author":"Yao","year":"2016","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1017\/S0373463300001107","article-title":"Assessment of EGNOS Tropospheric Correction Model","volume":"54","author":"Penna","year":"2001","journal-title":"J. Navig."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10291-007-0077-5","article-title":"UNB3m_pack: A Neutral Atmosphere Delay Package for Radiometric Space Techniques","volume":"12","author":"Leandro","year":"2008","journal-title":"GPS Solut."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10291-013-0316-x","article-title":"The TropGrid2 Standard Tropospheric Correction Model","volume":"18","year":"2014","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s00190-007-0135-3","article-title":"Short Note: A Global Model of Pressure and Temperature for Geodetic Applications","volume":"81","author":"Heinkelmann","year":"2007","journal-title":"J. Geod."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1002\/grl.50288","article-title":"GPT2: Empirical Slant Delay Model for Radio Space Geodetic Techniques","volume":"40","author":"Lagler","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10291-014-0403-7","article-title":"Development of an Improved Empirical Model for Slant Delays in the Troposphere (GPT2w)","volume":"19","author":"Schindelegger","year":"2015","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00190-017-1066-2","article-title":"VMF3\/GPT3: Refined Discrete and Empirical Troposphere Mapping Functions","volume":"92","author":"Landskron","year":"2018","journal-title":"J. Geod."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1029\/2019EA000701","article-title":"An ERA5-based Model for Estimating Tropospheric Delay and Weighted Mean Temperature over China with Improved Spatiotemporal Resolutions","volume":"6","author":"Sun","year":"2019","journal-title":"Earth Space Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ding, J.S., and Chen, J.P. (2020). Assessment of Empirical Troposphere Model GPT3 Based on NGL\u2019s Global Troposphere Products. Sensors, 20.","DOI":"10.3390\/s20133631"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2132","DOI":"10.1007\/s11434-012-5010-9","article-title":"A New Global Zenith Tropospheric Delay Model IGGtrop for GNSS Applications","volume":"57","author":"Li","year":"2012","journal-title":"Chin. Sci. Bull."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s10291-022-01354-9","article-title":"An Improved Global Grid Model for Calibrating Zenith Tropospheric Delay for GNSS Applications","volume":"27","author":"Huang","year":"2023","journal-title":"GPS Solut."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/s10291-019-0925-0","article-title":"Assessment of the Positioning Performance and Tropospheric Delay Retrieval with Precise Point Positioning Using Products from Different Analysis Centers","volume":"24","author":"Zhou","year":"2020","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Xiong, C.B., Yu, L.N., and Zhao, L.W. (2019). Analysis on the Impacts of Slant Tropospheric Delays on Precise Point Positioning. Appl. Sci., 9.","DOI":"10.3390\/app9224884"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jastp.2018.05.002","article-title":"GGOS Tropospheric Delay Forecast Product Performance Evaluation and Its Application in Real-Time PPP","volume":"175","author":"Yao","year":"2018","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Guo, L.J., Huang, L.K., Li, J.Y., Liu, L.L., Huang, L., Fu, B.L., Xie, S.F., He, H.C., and Ren, C. (2021). A Comprehensive Evaluation of Key Tropospheric Parameters from ERA5 and MERRA-2 Reanalysis Products Using Radiosonde Data and GNSS Measurements. Remote Sens., 13.","DOI":"10.3390\/rs13153008"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sun, Z.Y., Zhang, B., and Yao, Y.B. (2019). A Global Model for Estimating Tropospheric Delay and Weighted Mean Temperature Developed with Atmospheric Reanalysis Data from 1979 to 2017. Remote Sens., 11.","DOI":"10.3390\/rs11161893"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1007\/s11433-011-4530-7","article-title":"Establishment of a New Tropospheric Delay Correction Model over China Area","volume":"54","author":"Song","year":"2011","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/s10291-023-01503-8","article-title":"A Global Zenith Tropospheric Delay Model with ERA5 and GNSS-Based ZTD Difference Correction","volume":"27","author":"Li","year":"2023","journal-title":"GPS Solut."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3724\/SP.J.1246.2012.00053.1","article-title":"A Zenith Tropospheric Delay Correction Model Based on the Regional CORS Network","volume":"3","author":"Huang","year":"2012","journal-title":"Geod. Geodyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s10291-021-01138-7","article-title":"A Global Grid Model for the Correction of the Vertical Zenith Total Delay Based on a Sliding Window Algorithm","volume":"25","author":"Huang","year":"2021","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7223","DOI":"10.5194\/gmd-16-7223-2023","article-title":"A Global Grid Model for the Estimation of Zenith Tropospheric Delay Considering the Variations at Different Altitudes","volume":"16","author":"Huang","year":"2023","journal-title":"Geosci. Model Dev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1186\/s43020-022-00088-w","article-title":"Refining the ERA5-Based Global Model for Vertical Adjustment of Zenith Tropospheric Delay","volume":"3","author":"Zhu","year":"2022","journal-title":"Satell. Navig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1007\/s10291-017-0644-3","article-title":"A Simplified GNSS Tropospheric Delay Model Based on the Nonlinear Hypothesis","volume":"21","author":"Sun","year":"2017","journal-title":"GPS Solut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1016\/j.asr.2018.10.035","article-title":"A New Method for Vertical Stratification of Zenith Tropospheric Delay","volume":"63","author":"Hu","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/JSTARS.2022.3228917","article-title":"High-Precision ZTD Model of Altitude-Related Correction","volume":"16","author":"Zhao","year":"2023","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s00704-014-1286-9","article-title":"Temperature Trend\u2013Altitude Relationship in China during 1963\u20132012","volume":"122","author":"Dong","year":"2015","journal-title":"Theor. Appl. Climatol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106247","DOI":"10.1016\/j.atmosres.2022.106247","article-title":"High-Precision GNSS PWV Retrieval Using Dense GNSS Sites and in-Situ Meteorological Observations for the Evaluation of MERRA-2 and ERA5 Reanalysis Products over China","volume":"276","author":"Huang","year":"2022","journal-title":"Atmos. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4015","DOI":"10.1073\/pnas.1700304115","article-title":"Climate Change, Human Impacts, and Carbon Sequestration in China","volume":"115","author":"Fang","year":"2018","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/qj.828","article-title":"The ERA-Interim Reanalysis: Configuration and Performance of the Data Assimilation System","volume":"137","author":"Dee","year":"2011","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Jiang, C.H., Xu, T.H., Wang, S.M., Nie, W.F., and Sun, Z.Z. (2020). Evaluation of Zenith Tropospheric Delay Derived from ERA5 Data over China Using GNSS Observations. Remote Sens., 12.","DOI":"10.3390\/rs12040663"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"e2021EA001796","DOI":"10.1029\/2021EA001796","article-title":"A Global Assessment of Precipitable Water Vapor Derived from GNSS Zenith Tropospheric Delays with ERA5, NCEP FNL, and NCEP GFS Products","volume":"8","author":"Chen","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"106664","DOI":"10.1016\/j.atmosres.2023.106664","article-title":"Evaluation of the Weighted Mean Temperature over China Using Multiple Reanalysis Data and Radiosonde","volume":"285","author":"Sun","year":"2023","journal-title":"Atmos. Res."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhou, C.C., Peng, B.B., Li, W., Zhong, S.M., Ou, J.K., Chen, R.J., and Zhao, X.L. (2017). Establishment of a Site-Specific Tropospheric Model Based on Ground Meteorological Parameters over the China Region. Sensors, 17.","DOI":"10.3390\/s17081722"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10291-012-0291-7","article-title":"Estimation and Evaluation of Hourly Updated Global GPS Zenith Total Delays over Ten Months","volume":"17","author":"Dousa","year":"2013","journal-title":"GPS Solut."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhao, Q.Z., Yang, P.F., Yao, W.Q., and Yao, Y.B. (2019). Hourly PWV Dataset Derived from GNSS Observations in China. Sensors, 20.","DOI":"10.3390\/s20010231"},{"key":"ref_45","first-page":"283","article-title":"EGM 2008 and Its Application Analysis in Chinese Mainland","volume":"38","author":"Zhang","year":"2009","journal-title":"Acta Geod. Cartogr. Sin."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/11\/2023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:53:45Z","timestamp":1760108025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/11\/2023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,4]]},"references-count":45,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["rs16112023"],"URL":"https:\/\/doi.org\/10.3390\/rs16112023","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,6,4]]}}}