{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T06:25:28Z","timestamp":1771482328319,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T00:00:00Z","timestamp":1533600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key projects of National Natural Science Foundation","award":["4P179511"],"award-info":[{"award-number":["4P179511"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global Navigation Satellite System (GNSS) troposphere tomography has become one of the most cost-effective means to obtain three-dimensional (3-d) image of the tropospheric water vapour field. Traditional methods divide the tomography area into a number of 3-d voxels and assume that the water vapour density at any voxel is a constant during the given period. However, such behaviour breaks the spatial continuity of water vapour density in a horizontal direction and the number of unknown parameters needing to be estimated is very large. This is the focus of the paper, which tries to reconstruct the water vapor field using the tomographic technique without imposing empirical horizontal and vertical constraints. The proposed approach introduces the layered functional model in each layer vertically and only an a priori constraint is imposed for the water vapor information at the location of the radiosonde station. The elevation angle mask of 30\u00b0 is determined according to the distribution of intersections between the satellite rays and different layers, which avoids the impact of ray bending and the error in slant water vapor (SWV) at low elevation angles on the tomographic result. Additionally, an optimal weighting strategy is applied to the established tomographic model to obtain a reasonable result. The tomographic experiment is performed using Global Positioning System (GPS) data of 12 receivers derived from the Satellite Positioning Reference Station Network (SatRef) in Hong Kong. The quality of the established tomographic model is validated under different weather conditions and compared with the conventional tomography method using 31-day data, respectively. The numerical result shows that the proposed method is applicable and superior to the traditional one. Comparisons of integrated water vapour (IWV) of the proposed method with that derived from radiosonde and European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim data show that the root mean square (RMS)\/Bias of their differences are 3.2\/\u22120.8 mm and 3.3\/\u22121.7 mm, respectively, while the values of traditional method are 5.1\/\u22123.9 mm and 6.3\/\u22125.9 mm, respectively. Furthermore, the water vapour density profiles are also compared with radiosonde and ECMWF data, and the values of RMS\/Bias error for the proposed method are 0.88\/0.06 g\/m3 and 0.92\/\u22120.08 g\/m3, respectively, while the values of the traditional method are 1.33\/0.38 g\/m3 and 1.59\/0.40 g\/m3, respectively.<\/jats:p>","DOI":"10.3390\/rs10081241","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T11:20:23Z","timestamp":1533640823000},"page":"1241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Troposphere Water Vapour Tomography: A Horizontal Parameterised Approach"],"prefix":"10.3390","volume":"10","author":[{"given":"Qingzhi","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Geomatics, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7723-4601","authenticated-orcid":false,"given":"Yibin","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Wanqiang","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Geomatics, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,7]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Development of a water vapor tomography system using low cost L1 GPS receivers","volume":"2226","author":"Braun","year":"1999","journal-title":"Proc. Ninth Anrruai ARM Sci. Team Meet."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1186\/BF03352307","article-title":"3-d distribution of water vapor estimated from tropospheric delay of GPS data in a mesoscale precipitation system of the Baiu front","volume":"52","author":"Seko","year":"2000","journal-title":"Earth Planets Space"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"9156","DOI":"10.1002\/2014JB011552","article-title":"Tropospheric delay ray tracing applied in VLBI analysis","volume":"119","author":"Eriksson","year":"2014","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1007\/s00190-017-1000-7","article-title":"Application of ray-traced tropospheric slant delays to geodetic VLBI analysis","volume":"91","author":"Hofmeister","year":"2017","journal-title":"J. Geodesy"},{"key":"ref_6","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_7","first-page":"1","article-title":"3-D refractivity field from GPS double difference tomography","volume":"29","author":"Troller","year":"2000","journal-title":"Geophys. Res. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"230","DOI":"10.5081\/jgps.4.1.230","article-title":"Troposphere modeling in a regional GPS network","volume":"4","author":"Skone","year":"2005","journal-title":"J. Glob. Position. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2927","DOI":"10.1109\/TGRS.2006.877755","article-title":"Water vapor tomography using GPS phase observations: Simulation results","volume":"44","author":"Nilsson","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.5194\/angeo-25-1727-2007","article-title":"Preconditions to ground based GPS water vapour tomography","volume":"25","author":"Bender","year":"2007","journal-title":"Ann. Geophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/s00190-011-0454-2","article-title":"4D GPS water vapor tomography: New parameterised approaches","volume":"85","author":"Perler","year":"2011","journal-title":"J. Geodesy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"553","DOI":"10.5194\/amt-7-553-2014","article-title":"A GPS network for tropospheric tomography in the framework of the Mediterranean hydrometeorological observatory C\u00e9vennes-Vivarais (southeastern France)","volume":"7","author":"Brenot","year":"2014","journal-title":"Atmos. Meas. Tech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00703-016-0450-4","article-title":"A novel, optimized approach of voxel division for water vapor tomography","volume":"129","author":"Yao","year":"2016","journal-title":"Meteorol. Atmos. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.5194\/angeo-31-1805-2013","article-title":"GNSS troposphere tomography based on two-step reconstructions using GPS observations and COSMIC profiles","volume":"31","author":"Xia","year":"2013","journal-title":"Ann. Geophys."},{"key":"ref_15","unstructured":"Alshawaf, F. (2013). Constructing Water Vapor Maps by Fusing InSAR, GNSS and WRF Data. [Ph.D. Dissertation, Karlsruhe Institute of Technology]."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Heublein, M., Zhu, X.X., Alshawaf, F., Mayer, M., Bamler, R., and Hinz, S. (2015). Compressive sensing for neutrospheric water vapor tomography using GNSS and InSAR observations. Geosci. Remote Sens. Symp. (IGARSS), 5268\u20135271.","DOI":"10.1109\/IGARSS.2015.7327023"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Benevides, P., Nico, G., Catalao, J., and Miranda, P. (2015). Merging SAR interferometry and GPS tomography for high-resolution mapping of 3D tropospheric water vapour. Geosci. Remote Sens. Symp. (IGARSS), 3607\u20133610.","DOI":"10.1109\/IGARSS.2015.7326602"},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"143","DOI":"10.5194\/angeo-34-143-2016","article-title":"A method to improve the utilization of GNSS observation for water vapor tomography","volume":"34","author":"Yao","year":"2016","journal-title":"Ann. Geophys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1016\/j.asr.2010.05.034","article-title":"Development of a GNSS water vapour tomography system using algebraic reconstruction techniques","volume":"47","author":"Bender","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_21","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_22","first-page":"9","article-title":"GPS real-time estimation of precipitable water vapor-Hong Kong experiences","volume":"36","author":"Chen","year":"2007","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_23","unstructured":"Herring, T.A., King, R.W., and McClusky, S.C. (2010). Documentation of the GAMIT GPS Analysis Software Release 10.4, Department of Earth and Planetary Sciences, Massachusetts Institute of Technology."},{"key":"ref_24","first-page":"1","article-title":"Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data","volume":"33","author":"Niell","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_25","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_26","first-page":"161","article-title":"An introduction to the variance-covariance component estimation of Helmert type","volume":"105","author":"Grafarend","year":"1980","journal-title":"Z. Vermess."},{"key":"ref_27","unstructured":"Mikhail, E., and Ackerman, F. (1976). Observation and Least Square, University Press of America."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bartlett, M.S. (1937). Properties of sufficiency and statistical tests. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 268\u2013282.","DOI":"10.1098\/rspa.1937.0109"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1175\/1520-0426(1995)012<0468:GSOAWV>2.0.CO;2","article-title":"GPS\/STORM-GPS sensing of atmospheric water vapor for meteorology","volume":"12","author":"Rocken","year":"1995","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1175\/1520-0426(2001)018<0830:COMOAW>2.0.CO;2","article-title":"Comparison of measurements of atmospheric wet delay by radiosonde, water vapor radiometer, GPS, and VLBI","volume":"18","author":"Niell","year":"2001","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1175\/JAMC-D-11-0119.1","article-title":"Analysis of water vapor over nigeria using radiosonde and satellite data","volume":"51","author":"Adeyemi","year":"2012","journal-title":"J. Appl. Meteorol. Clim."},{"key":"ref_32","unstructured":"M\u00f6ller, G. (2017). Reconstruction of 3D Wet Refractivity Fields in the Lower Atmosphere along Bended GNSS Signal Paths. [Ph.D. Thesis, TU Wien, Department for Geodesy and Geoinformation]. Available online: http:\/\/amalthea.hg.tuwien.ac.at\/~members\/Moeller\/Thesis_Gregor_Moeller_final_version.pdf."},{"key":"ref_33","first-page":"2849","article-title":"Water vapor weighted mean temperature and its impact on the determination of precipitable water vapor and its linear trend","volume":"121","author":"Wang","year":"2016","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_34","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_35","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1002\/2013RS005280","article-title":"The rapid and precise computation of GPS slant total delays and mapping factors utilizing a numerical weather model","volume":"49","author":"Zus","year":"2014","journal-title":"Radio Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2011JB008916","article-title":"The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)","volume":"117","author":"Pavlis","year":"2012","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1029\/2002JD003235","article-title":"On the determination of atmospheric water vapor from GPS measurements","volume":"108","author":"Hagemann","year":"2003","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2927","DOI":"10.1029\/2005JD006215","article-title":"Global estimates of water vapor weighted mean temperature of the atmosphere for gps applications","volume":"110","author":"Wang","year":"2005","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/0098-3004(96)00021-0","article-title":"Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW)","volume":"22","author":"Bartier","year":"1996","journal-title":"Comput. Geosci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s00190-014-0715-y","article-title":"Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model","volume":"88","author":"Chen","year":"2014","journal-title":"J. Geodesy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"7185","DOI":"10.1109\/TGRS.2016.2597241","article-title":"Maximally using gps observation for water vapor tomography","volume":"54","author":"Yao","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/8\/1241\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:17:04Z","timestamp":1760195824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/8\/1241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,7]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["rs10081241"],"URL":"https:\/\/doi.org\/10.3390\/rs10081241","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,7]]}}}