{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T16:02:12Z","timestamp":1769270532713,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T00:00:00Z","timestamp":1557446400000},"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"}]},{"DOI":"10.13039\/100012547","name":"Natural Science Foundation of Guangxi Zhuang Autonomous Region","doi-asserted-by":"publisher","award":["2018GXNSFBA050006"],"award-info":[{"award-number":["2018GXNSFBA050006"]}],"id":[{"id":"10.13039\/100012547","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>With the development of Global Navigation Satellite System (GNSS) reference station networks that provide rich data sources containing atmospheric information, the precipitable water vapor (PWV) retrieved from GNSS remote sensing has become one of the most important bodies of data in many meteorological departments. GNSS stations are distributed in the form of scatters, generally, these separations range from a few kilometers to tens of kilometers. Therefore, the spatial resolution of GNSS-PWV can restrict some applications such as interferometric synthetic aperture radar (InSAR) atmospheric calibration and regional atmospheric water vapor analysis, which inevitably require the spatial interpolation of GNSS-PWV. This paper explored a PWV interpolation scheme based on the GPT2w model, which requires no meteorological data at an interpolation station and no regression analysis of the observation data. The PWV interpolation experiment was conducted in Hong Kong by different interpolation schemes, which differed in whether the impact of elevation was considered and whether the GPT2w model was added. In this paper, we adopted three skill scores, i.e., compound relative error (CRE), mean absolute error (MAE), and root mean square error (RMSE), and two approaches, i.e., station cross-validation and grid data validation, for our comparison. Numerical results showed that the interpolation schemes adding the GPT2w model could greatly improve the PWV interpolation accuracy when compared to the traditional schemes, especially at interpolation points away from the elevation range of reference stations. Moreover, this paper analyzed the PWV interpolation results under different weather conditions, at different locations, and on different days.<\/jats:p>","DOI":"10.3390\/rs11091127","type":"journal-article","created":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T03:57:07Z","timestamp":1557719827000},"page":"1127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Establishment and Assessment of a New GNSS Precipitable Water Vapor Interpolation Scheme Based on the GPT2w Model"],"prefix":"10.3390","volume":"11","author":[{"given":"Fei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Nottingham Geospatial Institute, University of Nottingham, Nottingham NG7 2TU, UK"},{"name":"Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation, Wuhan University, Wuhan 430079, China"}]},{"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2440-8054","authenticated-orcid":false,"given":"Xiaolin","family":"Meng","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Institute, University of Nottingham, Nottingham NG7 2TU, UK"}]},{"given":"Junbo","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"given":"Lv","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,10]]},"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":"2631","DOI":"10.1029\/93GL02935","article-title":"Sensing atmospheric water vapor with the global positioning system","volume":"20","author":"Rocken","year":"1993","journal-title":"Geophys. Res. Lett."},{"key":"ref_3","unstructured":"Nilsson, T., Gadinarsky, 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_4","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/s00190-011-0454-2","article-title":"4D GPS water vapor tomography: New parameterized approaches","volume":"85","author":"Perler","year":"2011","journal-title":"J. Geod."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"3347","DOI":"10.1029\/98GL02504","article-title":"Spatial interpolation of the atmospheric water vapor content between sites in a ground-based GPS Network","volume":"25","author":"Emardson","year":"1998","journal-title":"Geophys. Res. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.atmosres.2015.09.023","article-title":"Spatial interpolation of GPS PWV and meteorological variables over the west coast of Peninsular Malaysia during 2013 Klang Valley Flash Flood","volume":"168","author":"Suparta","year":"2016","journal-title":"Atmos. Res."},{"key":"ref_8","unstructured":"Barnett, V. (1981). A brief description of natural neighbour interpolation. Interpreting Multivariate Data, John Wiley."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/978-94-017-3048-8_7","article-title":"Computer Mapping: The SYMAP interpolation algorithm","volume":"40","author":"Shepard","year":"1984","journal-title":"Spat. Stat. Models"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.3354\/cr022013","article-title":"Self-organizing maps: Applications to synoptic climatology","volume":"22","author":"Hewitson","year":"2002","journal-title":"Clim. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1007\/s001900050174","article-title":"Strategies for spatial and temporal extrapolation and interpolation of zenith wet delay","volume":"72","author":"Jarlemark","year":"1998","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/s10291-004-0099-1","article-title":"Tropospheric correction to SAR interferometry from GPS observations","volume":"8","author":"Janssen","year":"2004","journal-title":"GPS Solut."},{"key":"ref_13","first-page":"155","article-title":"An interpolation method for zenith tropospheric delay based on higher taylor series expansion","volume":"33","author":"Yin","year":"2013","journal-title":"J. Geod. Geodyn."},{"key":"ref_14","first-page":"39","article-title":"Research on GPS water vapor interpolation by improved Kriging algorithm","volume":"25","author":"Yang","year":"2013","journal-title":"Remote Sens. Land Resour."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"161","DOI":"10.3354\/cr024161","article-title":"Comparative analysis of interpolation methods in the middle Ebro Valley (Spain): Application to annual precipitation and temperature","volume":"24","author":"Cuadrat","year":"2003","journal-title":"Clim. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"B02404","DOI":"10.1029\/2005JB003711","article-title":"Interferometric synthetic aperture radar atmospheric correction: GPS topography dependent turbulence model","volume":"111","author":"Li","year":"2006","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1016\/j.jastp.2006.03.002","article-title":"Modeling of atmospheric effects on InSAR measurements by incorporating terrain elevation information","volume":"68","author":"Li","year":"2006","journal-title":"J. Atoms. Sol. Terres. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s00190-011-0456-0","article-title":"Interpolating atmospheric water vapor delay by incorporating terrain elevation information","volume":"85","author":"Xu","year":"2011","journal-title":"J. Geod."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"B09102","DOI":"10.1029\/2005JB004012","article-title":"Correction for interferometric synthetic aperture radar atmospheric phase artifacts using time series of zenith wet delay observations from a GPS network","volume":"111","author":"Onn","year":"2006","journal-title":"J. Geophys. Res Solid Earth"},{"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","volume":"19","author":"Bohm","year":"2015","journal-title":"GPS Solut."},{"key":"ref_21","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":"1994","journal-title":"J. Appl. Meteorol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, F., Guo, J., Shi, J., 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_23","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_24","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1007\/s00190-012-0568-1","article-title":"A globally applicable, season-specific model for estimating the weighted mean temperature of the atmosphere","volume":"86","author":"Yao","year":"2012","journal-title":"J. Geod."},{"key":"ref_25","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. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1175\/1520-0450(1974)013<0760:PWAIRT>2.0.CO;2","article-title":"Precipitable Water and Its Relationship to Surface Dew Point and Vapor Pressure in Athens","volume":"13","author":"Karalis","year":"1974","journal-title":"J. Appl. Meteorol."},{"key":"ref_27","first-page":"181","article-title":"Direct solar radiation data as input into mathematical models describing the thermal performance of buildings\u2014II. Development of relationships","volume":"11","author":"Cole","year":"1976","journal-title":"Build. Sci."},{"key":"ref_28","first-page":"1170","article-title":"Statistics of Correlation of Integrated Water Vapor and Surface Vapor Pressure","volume":"33","author":"Li","year":"2008","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1322","DOI":"10.1175\/1520-0450(1972)011<1322:OTCOTT>2.0.CO;2","article-title":"On the correlation of the total precipitable water in a vertical column and absolute humidity at the surface","volume":"11","author":"Reber","year":"1972","journal-title":"J. Appl. Meteorol."},{"key":"ref_30","first-page":"2817","article-title":"An operational approach for estimating surface vapor pressure with satellite-derived parameter","volume":"5","author":"Huang","year":"2010","journal-title":"Afr. J. Agric. Res."},{"key":"ref_31","first-page":"9","article-title":"A relationship between precipitable water vapor and surface vapor pressure","volume":"30","author":"Zhang","year":"2004","journal-title":"Meteorol. Mon."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1002\/2013JD020611","article-title":"Evaluation of interpolation techniques for the creation of gridded daily precipitation (1 \u00d7 1 km2); Cyprus, 1980\u20132010","volume":"119","author":"Camera","year":"2014","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_33","first-page":"119","article-title":"A statistical approach to some basic mine valuation problems on the Witwatersrand","volume":"52","author":"Krige","year":"1951","journal-title":"J. Chem. Metall. Min. Soc. S. Afr."},{"key":"ref_34","first-page":"13","article-title":"Two-dimensional weighted moving average trend surfaces for ore evaluation","volume":"66","author":"Krige","year":"1966","journal-title":"J. S. Afr. Inst. Min. Metall."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.2113\/gsecongeo.58.8.1246","article-title":"Principles of geostatistics","volume":"58","author":"Matheron","year":"1963","journal-title":"Econ. Geol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"D21110","DOI":"10.1029\/2008JD010100","article-title":"Comparison of six methods for the interpolation of daily European climate data","volume":"113","author":"Hofstra","year":"2008","journal-title":"J. Geophys. Res."},{"key":"ref_37","unstructured":"Webster, R., and Oliver, M. (2001). Geostatistics for Environmental Scientists. Statistics in Practice, John Wiley and Sons."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wahba, G. (1990). Spline models for observational data. CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics. Book 59.","DOI":"10.1137\/1.9781611970128"},{"key":"ref_39","first-page":"152","article-title":"Interpolation of rainfall data with thin plate smoothing splines-Part I: Two-dimensional smoothing of data with short range correlation","volume":"2","author":"Hutchinson","year":"1998","journal-title":"J. Geogr. Inf. Decis. Anal."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1175\/1520-0450(1995)034<2577:SIOAAA>2.0.CO;2","article-title":"Smart interpolation of annually averaged air temperature in the United States","volume":"34","author":"Willmott","year":"1995","journal-title":"J. Appl. Meteorol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1002\/2015JD024181","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_42","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/joc.3370140405","article-title":"Estimating continental and terrestrial precipitation averages from rain-gauge networks","volume":"14","author":"Willmott","year":"1994","journal-title":"Int. J. Climatol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0168-1923(99)00169-0","article-title":"A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data","volume":"10","author":"Price","year":"2000","journal-title":"Agric. For. Meteorol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"99","DOI":"10.3354\/cr022099","article-title":"A knowledge-based approach to the statistical mapping of climate","volume":"22","author":"Daly","year":"2002","journal-title":"Clim. Res."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1175\/JCLI3246.1","article-title":"Gridded area-averaged daily precipitation via conditional interpolation","volume":"18","author":"Hewitson","year":"2005","journal-title":"J. Clim."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/9\/1127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:51:01Z","timestamp":1760187061000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/9\/1127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,10]]},"references-count":45,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["rs11091127"],"URL":"https:\/\/doi.org\/10.3390\/rs11091127","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,10]]}}}