{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T03:07:38Z","timestamp":1783307258024,"version":"3.54.6"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,2]],"date-time":"2020-01-02T00:00:00Z","timestamp":1577923200000},"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":["11673050"],"award-info":[{"award-number":["11673050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Program of Special Development funds of Zhangjiang National Innovation Demonstration Zone","award":["ZJ2018-ZD-009"],"award-info":[{"award-number":["ZJ2018-ZD-009"]}]},{"name":"National Key R&amp;D Program of China","award":["2018YFB0504300"],"award-info":[{"award-number":["2018YFB0504300"]}]},{"name":"Key R&amp;D Program of Guangdong Province","award":["2018B030325001"],"award-info":[{"award-number":["2018B030325001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model\u2014Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5\u00b0 \u00d7 2.0\u00b0 in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD\u2019s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling.<\/jats:p>","DOI":"10.3390\/rs12010165","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T04:43:03Z","timestamp":1578026583000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["SHAtropE\u2014A Regional Gridded ZTD Model for China and the Surrounding Areas"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2899-7677","authenticated-orcid":false,"given":"Junping","family":"Chen","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"},{"name":"Shanghai Key Laboratory of Space Navigation and Positioning Techniques, Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7060-5342","authenticated-orcid":false,"given":"Jungang","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4440-1263","authenticated-orcid":false,"given":"Ahao","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"College of Surveying and Geo-Informatics, Tong Ji University, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9693-4999","authenticated-orcid":false,"given":"Junsheng","family":"Ding","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9117-8087","authenticated-orcid":false,"given":"Yize","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"College of Marine Technology, Tokyo University of Marine Science and Technology, Tokyo 1358533, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"B\u00f6hm, J., and Schuh, H. (2013). Atmospheric Effects in Space Geodesy, Springer.","DOI":"10.1007\/978-3-642-36932-2"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1029\/93JB02162","article-title":"Evaluation of very long baseline interferometry atmospheric modeling improvements","volume":"99","author":"MacMillan","year":"1994","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.rse.2015.07.023","article-title":"Improved wet path delays for all ESA and reference altimetric missions","volume":"169","author":"Fernandes","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wu, Z., Wang, J., Liu, Y., He, X., Liu, Y., and Xu, W. (2019). Validation of 7 Years in-Flight HY-2A Calibration Microwave Radiometer Products Using Numerical Weather Model and Radiosondes. Remote Sens., 11.","DOI":"10.3390\/rs11131616"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15787","DOI":"10.1029\/92JD01517","article-title":"GPS Meteorology\u2014Remote Sensing of Atmospheric Water Vapor Using the Global Positioning System","volume":"97","author":"Bevis","year":"1992","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1","DOI":"10.1186\/BF03352809","article-title":"Ray-traced troposphere slant delays for precise point positioning","volume":"60","author":"Hobiger","year":"2008","journal-title":"Earth Planets Space"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1017\/S0373463314000265","article-title":"A New Method to Accelerate PPP Convergence Time by using a Global Zenith Troposphere Delay Estimate Model","volume":"67","author":"Yao","year":"2014","journal-title":"J. Navig."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1007\/s00190-017-1005-2","article-title":"Improving BeiDou real-time precise point positioning with numerical weather models","volume":"91","author":"Lu","year":"2017","journal-title":"J. Geod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1093\/gji\/ggw451","article-title":"Enhancing real-time precise point positioning with zenith troposphere delay products and the determination of corresponding tropospheric stochastic models","volume":"208","author":"Yao","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_10","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":"2017","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, J., and Liu, Z. (2019). Improving GNSS PPP accuracy through WVR PWV augmentation. J. Geod.","DOI":"10.1007\/s00190-019-01278-2"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10291-008-0104-1","article-title":"Assessment of time-series of troposphere zenith delays derived from the Global Data Assimilation System numerical weather model","volume":"13","author":"Andrei","year":"2008","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10291-010-0200-x","article-title":"Assessment of ZTD derived from ECMWF\/NCEP data with GPS ZTD over China","volume":"15","author":"Chen","year":"2011","journal-title":"GPS Solut."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","unstructured":"Henriksen, S.W., Mancini, A., and Chovitz, B.H. (1972). Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging Satellites. The Use of Artificial Satellites for Geodesy, American Geophysical Union.","DOI":"10.1029\/GM015"},{"key":"ref_16","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_17","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":"2007","journal-title":"GPS Solut."},{"key":"ref_18","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_19","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_20","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00190-008-0229-6","article-title":"Testing of global pressure\/temperature (GPT) model and global mapping function (GMF) in GPS analyses","volume":"83","author":"Kouba","year":"2009","journal-title":"J. Geod."},{"key":"ref_21","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_22","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_23","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_24","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_25","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_26","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s00190-014-0761-5","article-title":"New versions of the BDS\/GNSS zenith tropospheric delay model IGGtrop","volume":"89","author":"Li","year":"2014","journal-title":"J. Geod."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1007\/s11430-015-5173-8","article-title":"A global empirical model for estimating zenith tropospheric delay","volume":"59","author":"Yao","year":"2015","journal-title":"Sci. China Earth Sci."},{"key":"ref_29","first-page":"213","article-title":"SHA: The GNSS Analysis Center at SHAO","volume":"160","author":"Chen","year":"2012","journal-title":"China Satell. Navig. Conf. (CSNC) 2012 Proc."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Blewitt, G., Hammond, W., and Kreemer, C. (2018). Harnessing the GPS Data Explosion for Interdisciplinary Science. Eos, 99.","DOI":"10.1029\/2018EO104623"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rzepecka, Z. (2015). Time series analysis of radio signal WET tropospheric delays for short-term forecast. Acta Geodyn. Geomater., 345\u2013354.","DOI":"10.13168\/AGG.2015.0031"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1007\/s11433-013-5181-7","article-title":"GNSS clock corrections densification at SHAO: From 5 min to 30 s","volume":"57","author":"Chen","year":"2013","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","unstructured":"Jin, S., Park, J.-U., Cho, J.-H., and Park, P.-H. (2007). Seasonal variability of GPS-derived zenith tropospheric delay (1994\u20132006) and climate implications. J. Geophys. Res., 112.","DOI":"10.1029\/2006JD007772"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Lou, Y., Huang, J., Zhang, W., Liang, H., Zheng, F., and Liu, J. (2017). A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China. Sensors, 18.","DOI":"10.3390\/s18010065"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5000","DOI":"10.1029\/2019GL082136","article-title":"Retrieving Precipitable Water Vapor From Shipborne Multi-GNSS Observations","volume":"46","author":"Wang","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/s10291-004-0099-1","article-title":"Tropospheric corrections to SAR interferometry from GPS observations","volume":"8","author":"Janssen","year":"2004","journal-title":"GPS Solut."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Boehm, J., Niell, A., Tregoning, P., and Schuh, H. (2006). Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophys. Res. Lett., 33.","DOI":"10.1029\/2005GL025546"},{"key":"ref_39","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions (2010) (IERS Technical Note No. 36), IERS."},{"key":"ref_40","first-page":"91","article-title":"Effects of Antenna Orientation on GPS Carrier Phase","volume":"18","author":"Wu","year":"1993","journal-title":"Manuscr. Geod."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10291-016-0523-3","article-title":"Assessment of precise orbit and clock products for Galileo, BeiDou, and QZSS from IGS Multi-GNSS Experiment (MGEX)","volume":"21","author":"Guo","year":"2016","journal-title":"GPS Solut."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/1\/165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:28:37Z","timestamp":1760362117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/1\/165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,2]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["rs12010165"],"URL":"https:\/\/doi.org\/10.3390\/rs12010165","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,2]]}}}