{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T09:43:32Z","timestamp":1784627012509,"version":"3.55.0"},"reference-count":19,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2020,6,28]],"date-time":"2020-06-28T00:00:00Z","timestamp":1593302400000},"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":["No.11673050"],"award-info":[{"award-number":["No.11673050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Key Program of Special Development funds of Zhangjiang National Innovation Demonstration Zone","award":["No. ZJ2018-ZD-009"],"award-info":[{"award-number":["No. ZJ2018-ZD-009"]}]},{"name":"National Key R&amp;D Program of China","award":["No. 2018YFB0504300"],"award-info":[{"award-number":["No. 2018YFB0504300"]}]},{"name":"the Key R&amp;D Program of Guangdong province","award":["No. 2018B030325001"],"award-info":[{"award-number":["No. 2018B030325001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Tropospheric delay is one of the major error sources in GNSS (Global Navigation Satellite Systems) positioning. Over the years, many approaches have been devised which aim at accurately modeling tropospheric delays, so-called troposphere models. Using the troposphere data of over 16,000 global stations in the last 10 years, as calculated by the Nevada Geodetic Laboratory (NGL), this paper evaluates the performance of the empirical troposphere model GPT3, which is the latest version of the GPT (Global Pressure and Temperature) series model. Owing to the large station number, long time-span and diverse station distribution, the spatiotemporal properties of the empirical model were analyzed using the average deviation (BIAS) and root mean square (RMS) error as indicators. The experimental results demonstrate that: (1) the troposphere products of NGL have the same accuracy as the IGS (International GNSS Service) products and can be used as a reference for evaluating general troposphere models. (2) The global average BIAS of the ZTD (zenith total delay) estimated by GPT3 is \u22120.99 cm and the global average RMS is 4.41 cm. The accuracy of the model is strongly correlated with latitude and ellipsoidal height, showing obviously seasonal variations. (3) The global average RMS of the north gradient and east gradient estimated by GPT3 is 0.77 mm and 0.73 mm, respectively, which are strongly correlated with each other, with values increasing from the equator to lower latitudes and decreasing from lower to higher latitudes.<\/jats:p>","DOI":"10.3390\/s20133631","type":"journal-article","created":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T11:17:17Z","timestamp":1593429437000},"page":"3631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":57,"title":["Assessment of Empirical Troposphere Model GPT3 Based on NGL\u2019s Global Troposphere Products"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9693-4999","authenticated-orcid":false,"given":"Junsheng","family":"Ding","sequence":"first","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2899-7677","authenticated-orcid":false,"given":"Junping","family":"Chen","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Shanghai Key Laboratory of Space Navigation and Positioning Techniques, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,28]]},"reference":[{"key":"ref_1","first-page":"116","article-title":"Error sources in GPS positioning","volume":"Volume 4","author":"Wang","year":"2016","journal-title":"GPS Surveying and Data Processing"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yang, F., Guo, J.M., Shi, J.B., Zhou, L., Xu, Y., and Chen, M. (2018). A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography. Sensors, 18.","DOI":"10.3390\/s18082526"},{"key":"ref_3","first-page":"286","article-title":"A two-step estimation method of troposphere delay with consideration of mapping function errors","volume":"48","author":"Fan","year":"2019","journal-title":"Acta Geod. Cart. Sin."},{"key":"ref_4","first-page":"862","article-title":"A high-accuracy method for tropospheric zenith delay error correction by fusing atmospheric numerical model","volume":"48","author":"Mao","year":"2019","journal-title":"Acta Geod. Cart. Sin."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, Z.P., Xin, P.M., Liu, R., and Wang, S.J. (2017). A Method to Reduce Non-Nominal Troposphere Error. Sensors, 17.","DOI":"10.3390\/s17081751"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4487","DOI":"10.1029\/JC074i018p04487","article-title":"Two-quartic troposphere refractivity profile for correcting satellite data","volume":"74","author":"Hopfield","year":"1969","journal-title":"J. Geophys. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02521844","article-title":"Contribution to the theory of atmospheric refraction","volume":"105","author":"Saastamoinen","year":"1972","journal-title":"Bull. Geod."},{"key":"ref_8","first-page":"684","article-title":"A New Global Zenith Tropospheric Delay Model","volume":"38","author":"Mao","year":"2013","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Chen, J.P., Wang, J.G., Wang, A.H., Ding, J.S., and Zhang, Y.Z. (2020). SHAtropE\u2014A Regional Gridded ZTD Model for China and the Surrounding Areas. Remote Sens., 12.","DOI":"10.3390\/rs12010165"},{"key":"ref_10","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_11","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":"Boehm","year":"2007","journal-title":"J. Geod."},{"key":"ref_12","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_13","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_14","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":"2017","journal-title":"J. Geod."},{"key":"ref_15","first-page":"1408","article-title":"Research Progress and Prospect of GNSS Space Environment Science","volume":"46","author":"Yao","year":"2017","journal-title":"Acta Geod. Cart. Sin."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, H.X., Yuan, Y.B., Li, W., Li, Y., and Chai, Y.J. (2016). Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region. Sensors, 16.","DOI":"10.3390\/s16010122"},{"key":"ref_17","first-page":"1656","article-title":"Assessment of Tropospheric Delay Correction Models over China","volume":"41","author":"Wang","year":"2016","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Blewitt, G., Hammond, W.C., and Kreemer, C. (2018). Harnessing the GPS Data Explosion for Interdisciplinary Science. EOS, 99.","DOI":"10.1029\/2018EO104623"},{"key":"ref_19","unstructured":"Armin, H. (2016). Determination of Path Delays in the Atmosphere for Geodetic VLBI by Means of Ray-Tracing. [Ph.D. Thesis, Technische Universit\u00e4t Wien]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/13\/3631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:44:08Z","timestamp":1760175848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/13\/3631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,28]]},"references-count":19,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["s20133631"],"URL":"https:\/\/doi.org\/10.3390\/s20133631","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,28]]}}}