{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T06:22:17Z","timestamp":1771482137739,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,2]],"date-time":"2018-08-02T00:00:00Z","timestamp":1533168000000},"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":["41474004"],"award-info":[{"award-number":["41474004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Water vapor is an important driving factor in the related weather processes in the troposphere, and its temporal-spatial distribution and change are crucial to the formation of cloud and rainfall. Global Navigation Satellite System (GNSS) water vapor tomography, which can reconstruct the water vapor distribution using GNSS observation data, plays an increasingly important role in GNSS meteorology. In this paper, a method to improve the distribution of observations in GNSS water vapor tomography is proposed to overcome the problem of the relatively concentrated distribution of observations, enable satellite signal rays to penetrate more tomographic voxels, and improve the issue of overabundance of zero elements in a tomographic matrix. Numerical results indicate that the accuracy of the water vapor tomography is improved by the proposed method when the slant water vapor calculated by GAMIT is used as a reference. Comparative results of precipitable water vapor (PWV) and water vapor density (WVD) profiles from radiosonde station data indicate that the proposed method is superior to the conventional method in terms of the mean absolute error (MAE), standard deviations (STD), and root-mean-square error (RMS). Further discussion shows that the ill-condition of tomographic equation and the richness of data in the tomographic model need to be discussed separately.<\/jats:p>","DOI":"10.3390\/s18082526","type":"journal-article","created":{"date-parts":[[2018,8,3]],"date-time":"2018-08-03T03:03:15Z","timestamp":1533265395000},"page":"2526","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Method to Improve the Distribution of Observations in GNSS Water Vapor Tomography"],"prefix":"10.3390","volume":"18","author":[{"given":"Fei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation, Wuhan University, Wuhan 430079, China"},{"name":"Research Center for High Accuracy Location Awareness, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5427-6481","authenticated-orcid":false,"given":"Jiming","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation, Wuhan University, Wuhan 430079, China"},{"name":"Research Center for High Accuracy Location Awareness, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junbo","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lv","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"College of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"National Geomatics Center of China, Beijing 100830, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15787","DOI":"10.1029\/92JD01517","article-title":"GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System","volume":"97","author":"Bevis","year":"1992","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1097\/00003072-197806000-00014","article-title":"Reconstruction tomography in diagnostic radiology and nuclear medicine","volume":"3","author":"Bramlet","year":"1978","journal-title":"Clin. Nucl. Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1029\/92GL00261","article-title":"Crust and upper mantle tomography in Tibet using surface waves","volume":"19","author":"Bourjot","year":"1992","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19635","DOI":"10.1029\/93JB03138","article-title":"Initial reference models in local earthquake tomography","volume":"99","author":"Kissling","year":"1994","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1002\/aic.690470904","article-title":"Experimental study of gas-induced liquid-flow structures in bubble columns","volume":"47","author":"Degaleesan","year":"2001","journal-title":"Aiche J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1029\/97RS02615","article-title":"Tomography of the ionosphere four-dimensional simulation","volume":"33","author":"Howe","year":"2016","journal-title":"Radio Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00585-000-0223-7","article-title":"4D tropospheric tomography using GPS slant wet delays","volume":"18","author":"Flores","year":"2000","journal-title":"Ann. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1186\/BF03352308","article-title":"Local GPS tropospheric tomography","volume":"52","author":"Hirahara","year":"2000","journal-title":"Earth Planets Space"},{"key":"ref_9","unstructured":"Nilsson, T., Gradinarsky, L., and Elgered, G. (2004, January 20\u201324). GPS tomography using phase observations. Proceedings of the 2004 IEEE International Geoscience and Remote Sensing Symposium, Anchorage, AK, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s11434-006-0607-5","article-title":"3D water vapor tomography with Shanghai GPS network to improve forecasted moisture field","volume":"51","author":"Song","year":"2006","journal-title":"Chin. Sci. Bull."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.atmosres.2009.03.013","article-title":"Local tomography troposphere model over mountains area","volume":"93","author":"Rohm","year":"2009","journal-title":"Atmos. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1016\/j.asr.2010.05.034","article-title":"Development of a GNSS water vapor tomography system using algebraic reconstruction techniques","volume":"47","author":"Bender","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1016\/j.asr.2015.01.025","article-title":"4D-tomographic reconstruction of water vapor using the hybrid regularization technique with application to the North West of Iran","volume":"55","author":"Adavi","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1990","DOI":"10.1002\/2017JD027748","article-title":"Adaptive Node Parameterization for Dynamic Determination of Boundaries and Nodes of GNSS Tomographic Models","volume":"123","author":"Ding","year":"2018","journal-title":"J. Geophys. Res. Atoms."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2211","DOI":"10.1016\/j.asr.2005.07.002","article-title":"Tomography determination of the spatial distribution of water vapor using GPS observations","volume":"37","author":"Troller","year":"2006","journal-title":"Adv. Space Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s00376-006-0551-y","article-title":"Preliminary results of 4-D water vapor tomography in the troposphere using GPS","volume":"23","author":"Bi","year":"2006","journal-title":"Adv. Atmos. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.atmosres.2011.12.008","article-title":"The precision of humidity in GNSS tomography","volume":"107","author":"Rohm","year":"2012","journal-title":"Atmos. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.5194\/angeo-31-1805-2013","article-title":"GNSS troposphere tomography based on two-step reconstruction using GPS observation and COSMIC profiles","volume":"31","author":"Xia","year":"2013","journal-title":"Ann. Geophys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Benevides, P., Nico, G., and Catalao, J. (2015, January 26\u201331). Merging SAR interferometry and GPS tomography for high-resolution mapping of 3D tropospheric water vapor. Proceedings of the Geoscience and Remote Sensing Symposium, Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326602"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"911","DOI":"10.5194\/angeo-32-911-2014","article-title":"Near real-time water vapor tomography using ground-based GPS and meteorological data: Long-term experiment in Hong Kong","volume":"32","author":"Jiang","year":"2014","journal-title":"Ann. Geophys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5249","DOI":"10.5194\/amt-9-5249-2016","article-title":"Assessing the performance of troposphere tomographic modeling using multi-source water vapor data during Hong Kong\u2019s rainy season from May to October 2013","volume":"9","author":"Chen","year":"2016","journal-title":"Atoms. Meas. Tech."},{"key":"ref_22","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. Geodesy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1175\/1520-0450(1994)033<0379:GMMZWD>2.0.CO;2","article-title":"GPS meteorology: Mapping zenith wet delays onto precipitable water","volume":"33","author":"Bevis","year":"1943","journal-title":"J. Appl. Meteorol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF02826630","article-title":"Determination of weighted mean tropospheric temperature using ground meteorological measurement","volume":"4","author":"Liu","year":"2001","journal-title":"Geo-Spat. Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Astudillo, J., Lau, L., Tang, Y., and Moore, T. (2018). Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Package. Sensors, 18.","DOI":"10.3390\/s18020580"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Dong, Z., and Jin, S. (2018). 3-D Water Vapor Tomography in Wuhan from GPS, BDS and GLONASS Observations. Remote Sens., 10.","DOI":"10.3390\/rs10010062"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1029\/2000GL011525","article-title":"Obtaining single path phase delays from GPS double differences","volume":"27","author":"Alber","year":"2000","journal-title":"Geophys. Res. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2291","DOI":"10.1029\/97GL52283","article-title":"Improving the vertical resolution of ionospheric tomography with GPS occultations","volume":"24","author":"Rius","year":"1999","journal-title":"Geophys. Res. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5880","DOI":"10.1109\/JSTARS.2016.2546316","article-title":"An optimal weighting method of Global Positioning System (GPS) troposphere tomography","volume":"9","author":"Guo","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0079-1946(97)00254-1","article-title":"An experiment for estimation of the spatial and temporal variations of water vapor using GPS data","volume":"23","author":"Rius","year":"1998","journal-title":"Phys. Chem. Earth"},{"key":"ref_31","first-page":"491","article-title":"Influence analysis of constraint conditions on GPS water vapor tomography","volume":"39","author":"Yu","year":"2010","journal-title":"Acta Geodesy Cartogr. Sin."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1175\/1520-0450(1996)035<0830:GMDEOT>2.0.CO;2","article-title":"GPS meteorology: Direct estimation of the absolute value of precipitable water","volume":"35","author":"Duan","year":"1996","journal-title":"J. Appl. Meteorol."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhou, C., Peng, B., Li, W., Zhong, S., Ou, J., Chen, R., and Zhao, X. (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_34","doi-asserted-by":"crossref","unstructured":"Wang, Z., Xin, P., Li, R., and Wang, S. (2017). A Method to Reduce Non-Nominal Troposphere Error. Sensors, 17.","DOI":"10.3390\/s17081751"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5019","DOI":"10.1029\/97JB03534","article-title":"Estimating horizontal gradients of tropospheric path delay with a single GPS receiver","volume":"103","author":"Kroger","year":"1998","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1137\/0609045","article-title":"Eigenvalues and condition numbers of random matrices","volume":"9","author":"Edelman","year":"1989","journal-title":"Siam J. Matrix Anal. Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2526\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:16:09Z","timestamp":1760195769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/8\/2526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,2]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["s18082526"],"URL":"https:\/\/doi.org\/10.3390\/s18082526","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,2]]}}}