{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:11:31Z","timestamp":1760148691141,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"LUH\u2019s open-access publishing fund"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This study focuses on the development of a time-variable regional geo-potential model for Antarctica using the spherical cap harmonic analysis (SCHA) basis functions. The model is derived from line-of-sight gravity difference (LGD) measurements obtained from the GRACE-Follow-On (GFO) mission. The solution of a Laplace equation for the boundary values over a spherical cap is used to expand the geo-potential coefficients in terms of Legendre functions with a real degree and integer order suitable for regional modelling, which is used to constrain the geo-potential coefficients using LGD measurements. To validate the performance of the SCHA, it is first utilized with LGD data derived from a L2 JPL (Level 2 product of the Jet Propulsion Laboratory). The obtained LGD data are used to compute the local geo-potential model up to Kmax = 20, corresponding to the SH degree and order up to 60. The comparison of the radial gravity on the Earth\u2019s surface map across Antarctica with the corresponding radial gravity components of the L2 JPL is carried out using local geo-potential coefficients. The results of this comparison provide evidence that these basis functions for Kmax = 20 are valid across the entirety of Antarctica. Subsequently, the analysis proceeds using LGD data obtained from the Level 1B product of GFO by transforming these LGD data into the SCHA coordinate system and applying them to constrain the SCHA harmonic coefficients up to Kmax = 20. In this case, several independent LGD profiles along the trajectories of the satellites are devised to verify the accuracy of the local model. These LGD profiles are not employed in the inverse problem of determining harmonic coefficients. The results indicate that using regional harmonic basis functions, specifically spherical cap harmonic analysis (SCHA) functions, leads to a close estimation of LGD compared to the L2 JPL. The regional harmonic basis function exhibits a root mean square error (RMSE) of 3.71 \u00d7 10\u22124 mGal. This represents a substantial improvement over the RMSE of the L2 JPL, which is 6.36 \u00d7 10\u22124 mGal. Thus, it can be concluded that the use of local geo-potential coefficients obtained from SCHA is a reliable method for extracting nearly the full gravitational signal within a spherical cap region, after validation of this method. The SCHA model provides significant realistic information as it addresses the mass gain and loss across various regions in Antarctica.<\/jats:p>","DOI":"10.3390\/rs15112815","type":"journal-article","created":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T07:49:23Z","timestamp":1685346563000},"page":"2815","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Antarctic Time-Variable Regional Gravity Field Model Derived from Satellite Line-of-Sight Gravity Differences and Spherical Cap Harmonic Analysis"],"prefix":"10.3390","volume":"15","author":[{"given":"Mohsen","family":"Feizi","sequence":"first","affiliation":[{"name":"Faculty of Geodesy and Geomatics Engineering, Department of Geodesy, K. N. Toosi University of Technology, Tehran 19967-15433, Iran"},{"name":"Institut f\u00fcr Erdmessung, Leibniz Universit\u00e4t Hannover, 30167 Hannover, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6118-8228","authenticated-orcid":false,"given":"Mehdi","family":"Raoofian Naeeni","sequence":"additional","affiliation":[{"name":"Faculty of Geodesy and Geomatics Engineering, Department of Geodesy, K. N. Toosi University of Technology, Tehran 19967-15433, Iran"},{"name":"School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia"}]},{"given":"Jakob","family":"Flury","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Erdmessung, Leibniz Universit\u00e4t Hannover, 30167 Hannover, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"ref_1","unstructured":"Eicker, A. (2008). Gravity Field Refinement by Radial Basis Functions from In-Situ Satellite Data, Citeseer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"L08403","DOI":"10.1029\/2005GL025509","article-title":"Regional high-resolution spatiotemporal gravity modeling from GRACE data using spherical wavelets","volume":"33","author":"Schmidt","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6875","DOI":"10.1002\/2016JB013633","article-title":"Passive-ocean radial basis function approach to improve temporal gravity recovery from GRACE observations","volume":"122","author":"Yang","year":"2017","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Han, S.C., and Simons, F.J. (2008). Spatiospectral localization of global geopotential fields from the Gravity Recovery and Climate Experiment (GRACE) reveals the coseismic gravity change owing to the 2004 Sumatra-Andaman earthquake. J. Geophys. Res. Solid Earth, 113.","DOI":"10.1029\/2007JB004927"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s00190-007-0196-3","article-title":"A data-driven approach to local gravity field modelling using spherical radial basis functions","volume":"82","author":"Klees","year":"2008","journal-title":"J. Geod."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wittwer, T. (2009). Regional Gravity Field Modelling with Radial Basis Functions, Neighborhood Cinema Group.","DOI":"10.54419\/hboxky"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00190-006-0101-5","article-title":"Regional gravity modeling in terms of spherical base functions","volume":"81","author":"Schmidt","year":"2007","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1007\/s10712-015-9344-0","article-title":"Global and regional gravity field determination from GOCE kinematic orbit by means of spherical radial basis functions","volume":"36","author":"Bucha","year":"2015","journal-title":"Surv. Geophys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1093\/gji\/ggv210","article-title":"On the regularization of regional gravity field solutions in spherical radial base functions","volume":"202","author":"Naeimi","year":"2015","journal-title":"Geophys. J. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1093\/gji\/ggx041","article-title":"Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: A case study for central Europe","volume":"209","author":"Tenzer","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_11","first-page":"559","article-title":"Contribution of the GOCE gradiometer components to regional gravity solutions","volume":"209","author":"Naeimi","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00190-020-01395-3","article-title":"GRACE gravitational measurements of tsunamis after the 2004, 2010, and 2011 great earthquakes","volume":"94","author":"Han","year":"2020","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9186","DOI":"10.1029\/2018JB016088","article-title":"A transfer function between line-of-sight gravity difference and GRACE intersatellite ranging data and an application to hydrological surface mass variation","volume":"123","author":"Han","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e2021JB022983","DOI":"10.1029\/2021JB022983","article-title":"Along-orbit analysis of GRACE Follow-On inter-satellite laser ranging measurements for sub-monthly surface mass variations","volume":"127","author":"Han","year":"2022","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_15","unstructured":"M\u00fcller, J., Riedel, S., Scheinert, M., Howath, M., Dietrich, R., Steinhage, D., Ansch\u00fctz, H., and Jokat, W. (2023, May 19). Regional Geoid and Gravity Field from a Combination of Airborne and Satellite Data in Dronning Maud Land, East Antarctica. Available online: https:\/\/epic.awi.de\/id\/eprint\/16885\/."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s00190-007-0189-2","article-title":"Regional geoid determination in Antarctica utilizing airborne gravity and topography data","volume":"82","author":"Scheinert","year":"2008","journal-title":"J. Geod."},{"key":"ref_17","unstructured":"Scheinert, M. (2012). Geodesy for Planet Earth: Proceedings of the 2009 IAG Symposium, Buenos Aires, Argentina, 31 August\u20134 September 2009, Springer."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.jog.2013.12.002","article-title":"Regional geoid modeling in the area of subglacial Lake Vostok, Antarctica","volume":"75","author":"Schwabe","year":"2014","journal-title":"J. Geodyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1007\/s00190-014-0724-x","article-title":"Regional geoid of the Weddell Sea, Antarctica, from heterogeneous ground-based gravity data","volume":"88","author":"Schwabe","year":"2014","journal-title":"J. Geod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s00190-015-0857-6","article-title":"A new degree-2190 (10 km resolution) gravity field model for Antarctica developed from GRACE, GOCE and Bedmap2 data","volume":"90","author":"Hirt","year":"2016","journal-title":"J. Geod."},{"key":"ref_21","first-page":"1","article-title":"A spherical cap harmonic model of the crustal magnetic anomaly field","volume":"261","author":"Kerridge","year":"2012","journal-title":"Geomagn. Palaeomagnetism"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"163","DOI":"10.25131\/sajg.122.0012","article-title":"Application of Spherical Cap Harmonic Analysis on CHAMP satellite data to develop a lithospheric magnetic field model over southern Africa at satellite altitude","volume":"122","author":"Nahayo","year":"2019","journal-title":"S. Afr. J. Geol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF02225927","article-title":"Spherical cap harmonic analysis applied to the Scandinavian geomagnetic field 1985.0","volume":"41","author":"Nevanlinna","year":"1988","journal-title":"Dtsch. Hydrogr. Z."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1007\/s11430-013-4580-y","article-title":"A high resolution lithospheric magnetic field model over China","volume":"56","author":"Ou","year":"2013","journal-title":"Sci. China Earth Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1016\/j.pce.2008.02.024","article-title":"Initial SCHA. DI. 00 regional archaeomagnetic model for Europe for the last 2000 years","volume":"33","author":"Osete","year":"2008","journal-title":"Phys. Chem. Earth Parts A\/B\/C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1186\/BF03352875","article-title":"Spherical cap harmonic analysis of magnetic variations data from mainland Australia","volume":"60","author":"Stening","year":"2008","journal-title":"Earth Planets Space"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.pepi.2016.11.008","article-title":"Evaluation of using R-SCHA to simultaneously model main field and secular variation multilevel geomagnetic data for the North Atlantic","volume":"263","author":"Talarn","year":"2017","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_28","unstructured":"Taylor, P., Kis, K.I., Puszta, S., Wittmann, G., and Kim, H.R. (2009, January 23\u201330). Interpretation of CHAMP magnetic anomaly data over the Pannonian Basin region using lower altitude and gradient data. Proceedings of the International Association of Geomagnetism and Aeronomy IAGA 11. Scientific Assembly, Sopron, Hungary."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Th\u00e9bault, E., and Gaya-Piqu\u00e9, L. (2008). Applied comparisons between SCHA and R-SCHA regional modeling techniques. Geochem. Geophys. Geosystems, 9.","DOI":"10.1029\/2008GC001953"},{"key":"ref_30","first-page":"B05102","article-title":"Modeling the lithospheric magnetic field over France by means of revised spherical cap harmonic analysis (R-SCHA)","volume":"111","author":"Mandea","year":"2006","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_31","unstructured":"Torta, J.M., Gaya-Piqu\u00e9, L.R., and De Santis, A. (2006). Geomagnetics for Aeronautical Safety: A Case Study in and Around the Balkans, Springer."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0021-9169(89)90106-2","article-title":"Spherical cap harmonic modelling of high latitude magnetic activity and equivalent sources with sparse observations","volume":"51","author":"Walker","year":"1989","journal-title":"J. Atmos. Terr. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1111\/j.1365-246X.1994.tb03981.x","article-title":"Determination of equivalent current sources from spherical cap harmonic models of geomagnetic field variations","volume":"118","author":"Haines","year":"1994","journal-title":"Geophys. J. Int."},{"key":"ref_34","first-page":"27","article-title":"Modelling the geomagnetic field by the method of spherical cap harmonic analysis","volume":"21","author":"Haines","year":"1987","journal-title":"HHI Rep."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s11770-016-0567-8","article-title":"Spherical cap harmonic analysis of regional magnetic anomalies based on CHAMP satellite data","volume":"13","author":"Feng","year":"2016","journal-title":"Appl. Geophys."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"De Santis, A., Kerridge, D., and Barraclough, D. (1989). A Spherical Cap Harmonic Model of the Crustal Magnetic Anomaly Field in Europe Observed by Magsat, Springer.","DOI":"10.1007\/978-94-009-0905-2_1"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1029\/JB090iB03p02583","article-title":"Spherical cap harmonic analysis","volume":"90","author":"Haines","year":"1985","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1093\/gji\/ggab280","article-title":"Comparison of spherical cap and rectangular harmonic analysis of airborne vector gravity data for high-resolution (1.5 km) local geopotential field models over Tanzania","volume":"227","author":"Feizi","year":"2021","journal-title":"Geophys. J. Int."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1515\/jag-2018-0040","article-title":"Construction of regional geoid using a virtual spherical harmonics model","volume":"13","author":"Wang","year":"2019","journal-title":"J. Appl. Geod."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1007\/s001900050120","article-title":"Spherical cap harmonic analysis: A comment on its proper use for local gravity field representation","volume":"71","author":"Torta","year":"1997","journal-title":"J. Geod."},{"key":"ref_41","first-page":"107","article-title":"Determination of short-wavelength components of the gravity field from satellite-to-satellite tracking or satellite gradiometry","volume":"4","author":"Rummel","year":"1979","journal-title":"Manuscr. Geod."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1016\/j.asr.2019.10.015","article-title":"Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field","volume":"65","author":"Han","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02149761","article-title":"Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems","volume":"6","author":"Hansen","year":"1994","journal-title":"Numer. Algorithms"},{"key":"ref_44","unstructured":"Schenkels, N., and Vanroose, W. (2018). Projected Newton method for a system of Tikhonov-Morozov equations. arXiv."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/0019-1035(92)90183-8","article-title":"Estimation of local planetary gravity fields using line of sight gravity data and an integral operator","volume":"99","author":"Barriot","year":"1992","journal-title":"Icarus"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1038\/s41558-019-0456-2","article-title":"Contributions of GRACE to understanding climate change","volume":"9","author":"Tapley","year":"2019","journal-title":"Nat. Clim. Change"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1914","DOI":"10.1093\/gji\/ggac033","article-title":"Extraction of GRACE\/GRACE-FO observed mass change patterns across Antarctica via independent component analysis (ICA)","volume":"229","author":"Shi","year":"2022","journal-title":"Geophys. J. Int."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.epsl.2015.01.029","article-title":"Accelerated West Antarctic ice mass loss continues to outpace East Antarctic gains","volume":"415","author":"Harig","year":"2015","journal-title":"Earth Planet. Sci. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/11\/2815\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:44:20Z","timestamp":1760125460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/11\/2815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,29]]},"references-count":48,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["rs15112815"],"URL":"https:\/\/doi.org\/10.3390\/rs15112815","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,5,29]]}}}