{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:18:48Z","timestamp":1780384728892,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,11,26]],"date-time":"2020-11-26T00:00:00Z","timestamp":1606348800000},"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":["41674008"],"award-info":[{"award-number":["41674008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41974026"],"award-info":[{"award-number":["41974026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["4P184081"],"award-info":[{"award-number":["4P184081"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>As one of the atmosphere propagation delays, the tropospheric delay is a significant error source that should be properly handled in high-precision global navigation satellite system (GNSS) applications. We propose an improved zenith tropospheric delay (ZTD) modeling method whereby the piecewise model of the atmospheric refractivity is introduced. Compared with using the exponential model to fit ZTD in vertical direction, the ZTD piecewise model has a better performance. Based on ERA5 2.5\u00b0 \u00d7 2.5\u00b0 reanalysis data produced by the European Centre for Medium-Range Weather Forecasting (ECMWF) from 2013 to 2017, we establish the regional gridded ZTD model (RGZTD) using a trigonometric function for China and the surrounding areas, which ranges from 70\u00b0 E to 135\u00b0 E in longitude and from 15\u00b0 N to 55\u00b0 N in latitude. To verify the performance of RGZTD model, the ERA5 ZTD data in 2017\u20132018, the radiosonde ZTD data from 86 radiosonde stations over China in 2017\u20132018, and the tropospheric delay products on 251 GNSS stations from Crustal Movement Observation Network of China (CMONOC) in 2016\u20132017 are used as external compliance check data. The results show that the overall accuracy of RGZTD model is better than that of exponential model, UNB3m model, and GPT3 model. Moreover, the accuracy can be improved by about 13.4%, 7.1%, and 6.2% when ERA5 reanalysis data, radiosonde data, and CMONOC data are used as reference values, respectively. High-accuracy ZTD data can be provided because the RGZTD model takes into account the vertical variation of ZTD through the new piecewise model.<\/jats:p>","DOI":"10.3390\/rs12233876","type":"journal-article","created":{"date-parts":[[2020,11,26]],"date-time":"2020-11-26T09:04:15Z","timestamp":1606381455000},"page":"3876","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Improved Zenith Tropospheric Delay Modeling Using the Piecewise Model of Atmospheric Refractivity"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3552-3579","authenticated-orcid":false,"given":"Liu","family":"Yang","sequence":"first","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingxiang","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5870-6327","authenticated-orcid":false,"given":"Dantong","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nanshan","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zengke","family":"Li","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,26]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s00190-017-1080-4","article-title":"Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning","volume":"92","author":"Zheng","year":"2018","journal-title":"J. Geod."},{"key":"ref_3","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_4","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. (1896\u20131977)"},{"key":"ref_5","unstructured":"Saastamoinen, J. (1972, January 15\u201317). Atmospheric correction for troposphere and stratosphere in radio ranging of satellites. Proceedings of the 3rd Int Symp on the Use of Artificial Satellites for Geodesy, Washington, DC, USA."},{"key":"ref_6","unstructured":"Collins, J.P., and Langley, R.B. (1997). A Tropospheric Delay Model for the User of the Wide Area Augmentation System, Department of Geodesy and Geomatics Engineering, University of New Brunswick."},{"key":"ref_7","unstructured":"Collins, P., Langley, R., and LaMance, J. (1996, January 19\u201321). Limiting factors in tropospheric propagation delay error modelling for GPS airborne navigation. Proceedings of the 52nd ION Annual Meeting, Cambridge, MA, USA."},{"key":"ref_8","unstructured":"Ueno, M., Hoshinoo, K., Matsunaga, K., Kawai, M., Nakao, H., Langley, R.B., and Bisnath, S.B. (2001, January 11\u201314). Assessment of atmospheric delay correction models for the Japanese MSAS. Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), Salt Lake City, UT, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5276","DOI":"10.1109\/TGRS.2018.2812850","article-title":"IGGtrop_SH and IGGtrop_rH: Two Improved Empirical Tropospheric Delay Models Based on Vertical Reduction Functions","volume":"56","author":"Li","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","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_11","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_12","first-page":"2218","article-title":"A new global zenith tropospheric delay model GZTD","volume":"56","author":"Yao","year":"2013","journal-title":"Chin. J. Geophys. Chin. Ed."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10291-013-0316-x","article-title":"The TropGrid2 standard tropospheric correction model","volume":"18","author":"Schueler","year":"2014","journal-title":"Gps Solut."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1002\/2014GL060271","article-title":"An improved model for calculating tropospheric wet delay","volume":"41","author":"Dousa","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Chen, P., Ma, Y., Liu, H., and Zheng, N. (2020). A New Global Tropospheric Delay Model Considering the Spatiotemporal Variation Characteristics of ZTD With Altitude Coefficient. Earth Space Sci., 7.","DOI":"10.1029\/2019EA000888"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, L., Xu, Y., Yan, L., Wang, S., Liu, G., and Liu, F. (2020). A Regional NWP Tropospheric Delay Inversion Method Based on a General Regression Neural Network Model. Sensors, 20.","DOI":"10.3390\/s20113167"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Charoenphon, C., and Satirapod, C. (2020). Improving the accuracy of real-time precipitable water vapour using country-wide meteorological model with precise point positioning in Thailand. J. Spat. Sci.","DOI":"10.1080\/14498596.2020.1758969"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chen, J., Wang, J., Wang, A., Ding, J., and Zhang, Y. (2020). SHAtropE-A Regional Gridded ZTD Model for China and the Surrounding Areas. Remote Sens., 12.","DOI":"10.3390\/rs12010165"},{"key":"ref_20","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":"Boehm","year":"2015","journal-title":"GPS Solut."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.5194\/hess-22-3515-2018","article-title":"ERA-5 and ERA-Interim driven ISBA land surface model simulations: Which one performs better?","volume":"22","author":"Albergel","year":"2018","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_23","unstructured":"Hersbach, H., and Dee, D. (2020, October 17). ERA5 Reanalysis Is in Production. Available online: https:\/\/www.ecmwf.int\/en\/newsletter\/147\/news\/era5-reanalysis-production."},{"key":"ref_24","unstructured":"Ge, S. (2006). GPS Radio Occultation and the Role of Atmospheric Pressure on Spaceborne Gravity Estimation over Antarctica. [Ph.D. Thesis, The Ohio State University]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1049\/el.2015.0195","article-title":"Modelling radio refractive index in the atmospheric surface layer","volume":"Volume 51","author":"Salamon","year":"2015","journal-title":"Electronics Letters"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1109\/JRPROC.1959.287242","article-title":"Models of the Atmospheric Radio Refractive Index","volume":"47","author":"Bean","year":"1959","journal-title":"Proc. IRE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1029\/RS022i003p00379","article-title":"Estimation of tropospheric delay for microwaves from surface weather data","volume":"22","author":"Askne","year":"1987","journal-title":"Radio Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Huang, L., Jiang, W.-P., Liu, L., Chen, H., and Ye, S. (2018). A new global grid model for the determination of atmospheric weighted mean temperature in GPS precipitable water vapor. J. Geod.","DOI":"10.1007\/s00190-018-1148-9"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/23\/3876\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:37:45Z","timestamp":1760179065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/23\/3876"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,26]]},"references-count":28,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["rs12233876"],"URL":"https:\/\/doi.org\/10.3390\/rs12233876","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,26]]}}}