{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T03:07:00Z","timestamp":1774148820789,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Autonomous and Controllable Special Project for Surveying and Mapping of China","award":["816-517"],"award-info":[{"award-number":["816-517"]}]},{"name":"Autonomous and Controllable Special Project for Surveying and Mapping of China","award":["2014TDJH101"],"award-info":[{"award-number":["2014TDJH101"]}]},{"name":"Autonomous and Controllable Special Project for Surveying and Mapping of China","award":["42274006"],"award-info":[{"award-number":["42274006"]}]},{"name":"SDUST Research Fund","award":["816-517"],"award-info":[{"award-number":["816-517"]}]},{"name":"SDUST Research Fund","award":["2014TDJH101"],"award-info":[{"award-number":["2014TDJH101"]}]},{"name":"SDUST Research Fund","award":["42274006"],"award-info":[{"award-number":["42274006"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["816-517"],"award-info":[{"award-number":["816-517"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2014TDJH101"],"award-info":[{"award-number":["2014TDJH101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42274006"],"award-info":[{"award-number":["42274006"]}],"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>The traditional altimetry satellites based on pulse-limited radar altimeter only calculate along-track deflection of the vertical (DOV), which results in poorer precision of the prime vertical component than that of the meridian component and limits the precision of the marine gravity field inversion. We expect an improvement in the higher precision prime vertical component using the Ice, Cloud and land Elevation Satellite 2 (ICESat-2) sea surface height (SSH) data. In this paper, the 2\u2032 \u00d7 2\u2032 gridded DOVs derived from along-beam DOVs, cross-beam DOVs, and joint along-cross beam DOVs in the South China Sea (SCS; 0\u00b0\u201323\u00b0N, 103\u00b0\u2013120\u00b0E) are calculated with the weighted least squares method, respectively. The inverse Vening\u2013Meinesz (IVM) formula is applied to derive 2\u2032 \u00d7 2\u2032 gravity anomalies over the SCS from ICESat-2-derived gridded DOVs. In addition, the XGM2019e_2159-DOV and SIO V31.1-DOV models are used to assess the precision of the gridded DOVs. The XGM2019e_2159-GRA, SIO V31.1-GRA models, and ship-borne gravity anomalies are also adopted to evaluate the quality of gravity anomalies. The results show that the gridded DOVs calculated by the joint along-cross beam DOVs have the highest precision among the three gridded DOVs determined by ICESat-2. The precision of difference between gravity anomalies derived from the joint along-cross beam DOV and the above verification data are higher than those derived from the along-beam and cross-beam DOVs. We conclude that the joint along-cross beam DOV can effectively improve the precision of the gridded DOV, which is conducive to the inversion of a high-precision marine gravity field.<\/jats:p>","DOI":"10.3390\/rs15010030","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T02:06:14Z","timestamp":1671674774000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Inversion of Deflection of the Vertical in the South China Sea Using ICESat-2 Sea Surface Height Data"],"prefix":"10.3390","volume":"15","author":[{"given":"Xin","family":"Liu","sequence":"first","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guihua","family":"Hui","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1817-1505","authenticated-orcid":false,"given":"Jinyun","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tinghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Menghao","family":"Song","sequence":"additional","affiliation":[{"name":"College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1179\/1752270613Y.0000000048","article-title":"Assessment of EGM2008 over Britain using vertical deflections, and problems with historical data","volume":"45","author":"Featherstone","year":"2013","journal-title":"Surv. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.jappgeo.2016.12.014","article-title":"Inversion of marine gravity anomalies over southeastern China seas from multi-satellite altimeter vertical deflections","volume":"137","author":"Zhang","year":"2017","journal-title":"J. Appl. Geophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"h1","DOI":"10.15446\/esrj.v20n2.54402","article-title":"Temporal-spatial distribution of oceanic vertical deflections determined by TOPEX\/Poseidon and Jason-1\/2 missions","volume":"20","author":"Guo","year":"2016","journal-title":"Earth Sci. Res. J."},{"key":"ref_4","first-page":"8025205","article-title":"A new DOV gridding method and its application in marine gravity recovery","volume":"19","author":"Liu","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.asr.2020.04.051","article-title":"Marine gravity anomaly mapping for the Gulf of Tonkin area (Vietnam) using Cryosat-2 and Saral\/AltiKa satellite altimetry data","volume":"66","author":"Nguyen","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1134\/S106935131006008X","article-title":"On calculation of the vertical deflection and the geoid undulation from gravity anomalies","volume":"46","author":"Boyarsky","year":"2010","journal-title":"Izv. Phys. Solid Earth"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s11001-014-9216-x","article-title":"Local normal height connection across sea with ship-borne gravimetry and GNSS techniques","volume":"35","author":"Guo","year":"2014","journal-title":"Mar. Geophys. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"730777","DOI":"10.3389\/feart.2021.730777","article-title":"Evaluation of marine gravity anomaly calculation accuracy by multi-source satellite altimetry data","volume":"9","author":"Liu","year":"2021","journal-title":"Front. Earth Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s11001-021-09461-x","article-title":"On performance of CryoSat-2 altimeter data in deriving marine gravity over the Bay of Bengal","volume":"42","author":"Ji","year":"2021","journal-title":"Mar. Geophys. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s00190-020-01378-4","article-title":"Marine gravity determined from multi-satellite GM\/ERM altimeter data over the South China Sea: SCSGA V1.0","volume":"94","author":"Zhu","year":"2020","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1111\/j.1365-246X.1992.tb00106.x","article-title":"Antarctic marine gravity field from high-density satellite altimetry","volume":"109","author":"Sandwell","year":"1992","journal-title":"Geophys. J. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1007\/BF00806737","article-title":"Gravity anomalies from satellite altimetry: Comparison between computation via geoid heights and via deflections of the vertica","volume":"69","author":"Olgiati","year":"1995","journal-title":"Bull. G\u00e9od\u00e9sique"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1111\/j.1365-246X.1998.tb07139.x","article-title":"Global derivation of marine gravity anomalies from Seasat, Geosat, ERS-1 and TOPEX\/POSEIDON altimeter data","volume":"134","author":"Hwang","year":"1998","journal-title":"Geophys. J. Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"670256","DOI":"10.3389\/feart.2021.670256","article-title":"Calculation of deflection of vertical and gravity anomalies over the South China Sea derived from ICESat-2 data","volume":"9","author":"Che","year":"2021","journal-title":"Front. Earth Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wan, X., Jin, S., Liu, B., Tian, S., Kong, W., and Annan, R.F. (2020). Effects of interferometric radar altimeter errors on marine gravity field inversion. Sensors, 20.","DOI":"10.3390\/s20092465"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"12048","DOI":"10.1109\/JSTARS.2021.3129273","article-title":"On deflections of vertical determined from HY-2A\/GM altimetry data in the Bay of Bengal","volume":"14","author":"Ji","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wan, X., Annan, R.F., Jin, S., and Gong, X. (2020). Vertical deflections and gravity disturbances derived from HY-2A data. Remote Sens., 12.","DOI":"10.3390\/rs12142287"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/s00190-022-01619-8","article-title":"Analysis of vertical deflections determined from one cycle of simulated SWOT wide-swath altimeter data","volume":"96","author":"Jin","year":"2022","journal-title":"J. Geod."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1109\/JPROC.2009.2034765","article-title":"The ICESat-2 laser altimetry mission","volume":"98","author":"Abdalati","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e2020EA001555","DOI":"10.1029\/2020EA001555","article-title":"ICESat-2 early mission synopsis and observatory performance","volume":"8","author":"Magruder","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2911","DOI":"10.1109\/TGRS.2017.2786659","article-title":"Performance analysis of airborne photon-counting lidar data in preparation for the ICESat-2 mission","volume":"56","author":"Magruder","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","unstructured":"Morison, J.H., Hancock, D., Dickinson, S., Robbins, J., Roberts, L., Kwok, R., Palm, S.P., Smith, B., Jasinski, M.F., and The ICESat-2 Science Team (2021). ATLAS\/ICESat-2 L3A Ocean Surface Height, Version 4, NASA National Snow and Ice Data Center Distributed Active Archive Center."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.rse.2016.12.029","article-title":"The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2): Science requirements, concept, and implementation","volume":"190","author":"Markus","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e2020EA001494","DOI":"10.1029\/2020EA001494","article-title":"ICESat-2 pointing calibration and geolocation performance","volume":"8","author":"Luthcke","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1093\/gji\/ggab084","article-title":"Assessment of ICESat-2 for the recovery of ocean topography","volume":"226","author":"Yu","year":"2021","journal-title":"Geophys. J. Int."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, Z., Guo, J., Ji, B., Wan, X., and Zhang, S. (2022). A Review of Marine Gravity Field Recovery from Satellite Altimetry. Remote Sens., 14.","DOI":"10.3390\/rs14194790"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1093\/gji\/ggz330","article-title":"How HY-2A\/GM altimeter performs in marine gravity derivation: Assessment in the South China Sea","volume":"219","author":"Zhu","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1016\/S0025-326X(01)00240-5","article-title":"South China Sea","volume":"42","author":"Morton","year":"2001","journal-title":"Mar. Pollut. Bull."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"e2021GL093425","DOI":"10.1029\/2021GL093425","article-title":"Deriving antarctic sea-ice thickness from satellite altimetry and estimating consistency for NASA\u2019s ICESat\/ICESat-2 missions","volume":"48","author":"Xu","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111325","DOI":"10.1016\/j.rse.2019.111325","article-title":"The Ice, Cloud, and Land Elevation Satellite-2 mission: A global geolocated photon product derived from the Advanced Topographic Laser Altimeter System","volume":"233","author":"Neumann","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_31","unstructured":"Zhu, X., Nie, S., Wang, C., and Xi, X. (October, January 26). The performance of ICESat-2\u2019s strong and weak beams in estimating ground elevation and forest height. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Waikoloa, HI, USA."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"e2020EA001538","DOI":"10.1029\/2020EA001538","article-title":"Quantifying surface-height change over a periglacial environment with ICESat-2 laser altimetry","volume":"8","author":"Michaelides","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lu, X., Hu, Y., and Yang, Y. (2019, January 17\u201320). Ocean subsurface study from ICESat-2 mission. Proceedings of the Photonics and Electromagnetics Research Symposium\u2014Fall (PIERS\u2014Fall), Xiamen, China.","DOI":"10.1109\/PIERS-Fall48861.2019.9021802"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1007\/s12145-020-00520-2","article-title":"OpenAltimetry\u2014Rapid analysis and visualization of Spaceborne altimeter data","volume":"15","author":"Khalsa","year":"2022","journal-title":"Earth Sci. Inform."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2754","DOI":"10.1109\/JSTARS.2016.2535281","article-title":"Reliable and stable radiometers for Jason-3","volume":"9","author":"Maiwald","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1002\/2014GL059510","article-title":"Mean dynamic topography estimates purely based on GOCE gravity field models and altimetry","volume":"41","author":"Becker","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"789","DOI":"10.5194\/os-17-789-2021","article-title":"The new CNES-CLS18 global mean dynamic topography","volume":"17","author":"Mulet","year":"2021","journal-title":"Ocean. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"008916","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_39","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s00190-020-01398-0","article-title":"The combined global gravity field model XGM2019e","volume":"94","author":"Zingerle","year":"2020","journal-title":"J. Geod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.asr.2019.09.011","article-title":"Gravity field recovery from geodetic altimeter missions","volume":"68","author":"Sandwell","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1111\/j.1365-246X.1995.tb07013.x","article-title":"Gravity anomalies derived from Seasat, Geosat, ERS-1 and TOPEX\/POSEIDON altimetry and ship gravity: A case study over the Reykjanes Ridge","volume":"122","author":"Hwang","year":"1995","journal-title":"Geophys. J. Int."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhang, S., Andersen, O.B., Kong, X., and Li, H. (2020). Inversion and validation of improved marine gravity field recovery in South China Sea by incorporating HY-2A altimeter waveform data. Remote Sens., 12.","DOI":"10.3390\/rs12050802"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"112650","DOI":"10.1016\/j.rse.2021.112650","article-title":"Gravity recovery from SWOT altimetry using geoid height and geoid gradient","volume":"265","author":"Yu","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4589","DOI":"10.5194\/essd-14-4589-2022","article-title":"SDUST2021GRA: Global marine gravity anomaly model recovered from Ka-band and Ku-band satellite altimeter data","volume":"14","author":"Zhu","year":"2022","journal-title":"Earth Syst. Sci. Data"},{"key":"ref_45","unstructured":"Wei, Q.Y. (2017). A Method for Location Determination of Intersections and Related Data Processing. [Master\u2019s Thesis, Henan University]."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:47:09Z","timestamp":1760147229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15010030"],"URL":"https:\/\/doi.org\/10.3390\/rs15010030","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,21]]}}}