{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T10:03:16Z","timestamp":1782036196224,"version":"3.54.5"},"reference-count":85,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing Municipality","doi-asserted-by":"publisher","award":["8184092"],"award-info":[{"award-number":["8184092"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDA17010304"],"award-info":[{"award-number":["XDA17010304"]}]},{"name":"CAS Pioneer Hundred Talents Program","award":["XiaomingWang"],"award-info":[{"award-number":["XiaomingWang"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41904033"],"award-info":[{"award-number":["41904033"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global navigation satellite systems (GNSSs) have become an important tool for remotely sensing water vapor in the atmosphere. In GNSS data processing, mapping functions and gradient models are needed to map the zenith tropospheric delay (ZTD) to the slant total tropospheric delay (STD) along a signal path. Therefore, it is essential to investigate the spatial\u2013temporal performance of various mapping functions and gradient models in the determination of STD. In this study, the STDs at nine elevations were first calculated by applying the ray-tracing method to the atmospheric European Reanalysis-Interim (ERA\u2014Interim) dataset. These STDs were then used as the reference to study the accuracy of the STDs that determined the ZTD together with mapping functions and gradient models. The performance of three mapping functions (i.e., Niell mapping function (NMF), global mapping function (GMF), and Vienna mapping function (VMF1)) and three gradient models (i.e., Chen, MacMillan, and Meindl) in six regions (the temperate zone, Qinghai\u2013Tibet Plateau, Equator, Sahara Desert, Amazon Rainforest, and North Pole) in determining slant tropospheric delay was investigated in this study. The results indicate that the three mapping functions have relatively similar performance above a 15\u00b0 elevation, but below a 15\u00b0 elevation, VMF1 clearly performed better than the GMF and NMF. The results also show that, if no gradient model is included, the root-mean-square (RMS) of the STD is smaller than 2 mm above the 30\u00b0 elevation and smaller than 9 mm above the 15\u00b0 elevation but shows a significant increase below the 15\u00b0 elevation. For example, in the temperate zone, the RMS increases from approximately 35 mm at the 10\u00b0 elevation to approximately 160 mm at the 3\u00b0 elevation. The inclusion of gradient models can significantly improve the accuracy of STDs by 50%. All three gradient models performed similarly at all elevations and in all regions. The bending effect was also investigated, and the results indicate that the tropospheric delay caused by the bending effect is normally below 13 mm above a 15\u00b0 elevation, but this delay increases dramatically from approximately 40 mm at a 10\u00b0 elevation to approximately 200 mm at a 5\u00b0 elevation, and even reaches 500\u2013700 mm at a 3\u00b0 elevation in most studied regions.<\/jats:p>","DOI":"10.3390\/rs12010130","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T04:43:03Z","timestamp":1578026583000},"page":"130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay"],"prefix":"10.3390","volume":"12","author":[{"given":"Cong","family":"Qiu","sequence":"first","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing 100094, China"},{"name":"School of Electronic, Electrical and Communicating Engineering, University of Chinese Academy of Sciences, No.19A Yuquan Road, Shijingshan District, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1720-6630","authenticated-orcid":false,"given":"Xiaoming","family":"Wang","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3911-3059","authenticated-orcid":false,"given":"Zishen","family":"Li","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaotian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing 100094, China"},{"name":"School of Electronic, Electrical and Communicating Engineering, University of Chinese Academy of Sciences, No.19A Yuquan Road, Shijingshan District, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haobo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology (Xuzhou), No.1 Daxue Road, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinglei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Land Science and Technology, China University of Geosciences (Beijing), 29 Xue Yuan Road, Haidian District, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Yuan","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, No.9 Dengzhuang South Road, Haidian District, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,1]]},"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. 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