{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T23:18:16Z","timestamp":1771456696013,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T00:00:00Z","timestamp":1693440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013209","name":"Hellenic Foundation for Research and Innovation","doi-asserted-by":"publisher","award":["1550"],"award-info":[{"award-number":["1550"]}],"id":[{"id":"10.13039\/501100013209","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the present study, we first examine the contribution of different, satellite-only or combined, global geopotential models in geoid computation employing the remove\u2013compute\u2013restore approach. For this reason, two test areas of about 100 km2 each, one in northern and one in central Greece, were selected, and gravity measurements were conducted. These new gravity measurements were used along with the selected geopotential models to produce the reduced gravity field for the study areas. The classical and spectral residual terrain modeling effect is also removed to derive the residual gravity field. The latter is used for geoid computation using the 1D fast Fourier transform. The validation of the geoid models is carried out with gravity\/GNSS\/leveling measurements, which were conducted in two traverses located in the study areas. Special attention is given to the tidal approach, the geoid separation term as well as the coordinate reference system. Next, the northern study area is extended by incorporating gravity measurements obtained during the last five decades, and geoid models are recomputed. Lastly, using the geoid models computed, reference geopotential values are computed for both areas. From the results achieved for both study areas, the combined model XGM2019 provides the best overall statistical results with differences of 0.065 m and 0.036 m in terms of root mean square error. The incorporation of not recent data into the solutions leads to a degradation in accuracy by about 1.2 cm in terms of standard deviation. Lastly, the computed reference geopotential values present discrepancies between the two study areas, revealing network inconsistencies as well as the dependency on the geopotential model used for the geoid computations.<\/jats:p>","DOI":"10.3390\/rs15174282","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T11:41:18Z","timestamp":1693482078000},"page":"4282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Geoid Studies in Two Test Areas in Greece Using Different Geopotential Models towards the Estimation of a Reference Geopotential Value"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1486-8284","authenticated-orcid":false,"given":"Vassilios N.","family":"Grigoriadis","sequence":"first","affiliation":[{"name":"Laboratory of Gravity Field Research and Applications (GravLab), Department of Geodesy and Surveying, Aristotle University of Thessaloniki, University Box 440, GR-54124 Thessaloniki, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2709-963X","authenticated-orcid":false,"given":"Vassilios D.","family":"Andritsanos","sequence":"additional","affiliation":[{"name":"Geospatial Technologies Lab, Department of Surveying and Geoinformatics Engineering, University of West Attica, GR-12243 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3943-1767","authenticated-orcid":false,"given":"Dimitrios A.","family":"Natsiopoulos","sequence":"additional","affiliation":[{"name":"Laboratory of Gravity Field Research and Applications (GravLab), Department of Geodesy and Surveying, Aristotle University of Thessaloniki, University Box 440, GR-54124 Thessaloniki, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2475-2568","authenticated-orcid":false,"given":"Georgios S.","family":"Vergos","sequence":"additional","affiliation":[{"name":"Laboratory of Gravity Field Research and Applications (GravLab), Department of Geodesy and Surveying, Aristotle University of Thessaloniki, University Box 440, GR-54124 Thessaloniki, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3797-8016","authenticated-orcid":false,"given":"Ilias N.","family":"Tziavos","sequence":"additional","affiliation":[{"name":"Laboratory of Gravity Field Research and Applications (GravLab), Department of Geodesy and Surveying, Aristotle University of Thessaloniki, University Box 440, GR-54124 Thessaloniki, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10712-017-9409-3","article-title":"Definition and proposed realization of the International Height Reference System (IHRS)","volume":"38","author":"Ihde","year":"2017","journal-title":"Surv. Geophys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1007\/s00190-016-0913-x","article-title":"A conventional value for the geoid reference potential W0","volume":"90","author":"Sanchez","year":"2016","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/1345_2017_12","article-title":"GOCE Variance and Covariance Contribution to Height System Unification","volume":"Volume 148","author":"Vergos","year":"2017","journal-title":"International Symposium on Gravity, Geoid and Height Systems 2016"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/978-3-319-10837-7_32","article-title":"Estimation of the geopotential value Wo for the local vertical datum of continental Greece using EGM08 and GPS\/leveling data","volume":"Volume 141","author":"Marti","year":"2014","journal-title":"Gravity, Geoid and Height Systems"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/1345_2017_1","article-title":"Assessment of the Greek Vertical Datum: A Case Study in Central Greece","volume":"Volume 148","author":"Vergos","year":"2017","journal-title":"International Symposium on Gravity, Geoid and Height Systems 2016"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s00190-011-0530-7","article-title":"Estimation of the zero-height geopotential level WoLVD in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: A case study in the Hellenic islands","volume":"86","author":"Kotsakis","year":"2012","journal-title":"J. Geod."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s40328-017-0204-x","article-title":"Preliminary results of GOCE-based height system unification between Greece and Turkey over marine and land areas","volume":"53","author":"Vergos","year":"2018","journal-title":"Acta Geod. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Forsberg, R. (1984). A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling, Department of Geodetic Science, The Ohio State University. Technical Report OSU Report 1984, No 355.","DOI":"10.21236\/ADA150788"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1007\/s00190-017-1086-y","article-title":"Solution to the spectral filter problem of residual terrain modelling (RTM)","volume":"92","author":"Rexer","year":"2018","journal-title":"J. Geod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1126\/science.1099192","article-title":"GRACE Measurements of Mass Variability in the Earth System","volume":"305","author":"Tapley","year":"2004","journal-title":"Science"},{"key":"ref_11","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. Chang."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2514\/1.A34326","article-title":"GRACE-FO: The Gravity Recovery and Climate Experiment Follow-On Mission","volume":"56","author":"Kornfeld","year":"2019","journal-title":"J. Spacecr. Rocket."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e2020GL088306","DOI":"10.1029\/2020GL088306","article-title":"Extending the global mass change data record: GRACE Follow-On instrument and science data performance","volume":"47","author":"Landerer","year":"2020","journal-title":"Geophys. Res. Lett."},{"key":"ref_14","unstructured":"Siry, J.W. (2021, May 21). The LAGEOS System, Available online: https:\/\/ntrs.nasa.gov\/api\/citations\/19760006091\/downloads\/19760006091.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/0094-5765(89)90119-7","article-title":"IRIS-LAGEOS 2 mission","volume":"19","author":"Ibba","year":"1989","journal-title":"Acta Astronaut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/1345_2015_160","article-title":"Validation of GOCE\/GRACE Satellite Only and Combined Global Geopotential Models over Greece in the Frame of the GOCESeaComb Project","volume":"Volume 143","author":"Rizos","year":"2015","journal-title":"IAG 150 Years"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"B04406","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_18","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1007\/s11600-017-0085-y","article-title":"Validation of recent geopotential models in Tierra Del Fuego","volume":"65","author":"Gomez","year":"2017","journal-title":"Acta Geophys."},{"key":"ref_19","unstructured":"F\u00f6rste, C., Bruinsma, S., Abrikosov, O., Flechtner, F., Marty, J.-C., Lemoine, J.-M., Dahle, C., Neumayer, H., Barthelmes, F., and K\u00f6nig, R. (2014, January 25\u201328). EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. Proceedings of the 5th GOCE User Workshop, Paris, France."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/s11200-015-1114-4","article-title":"GECO: A global gravity model by locally combining GOCE data and EGM2008","volume":"60","author":"Gilardoni","year":"2016","journal-title":"Stud. Geophys. Geod."},{"key":"ref_21","unstructured":"Ries, J.B., Bettadpur, S., Eanes, R., Kang, Z., Ko, U., McCullough, C., Nagel, P., Pie, N., Poole, S., and Richter, T. (2016). The Combined Gravity Model GGM05C, GFZ Data Services."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s10712-016-9406-y","article-title":"GOCO05c: A new combined gravity field model based on full normal equations and regionally varying weighting","volume":"38","author":"Fecher","year":"2017","journal-title":"Surv. Geophys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.jappgeo.2018.03.002","article-title":"The use of absolute gravity data for the validation of Global Geopotential Models and for improving quasigeoid heights determined from satellite-only Global Geopotential Models","volume":"152","author":"Godah","year":"2018","journal-title":"J. Appl. Geophys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"749611","DOI":"10.3389\/feart.2021.749611","article-title":"An Assessment of Recently Released High-Degree Global Geopotential Models Based on Heterogeneous Geodetic and Ocean Data","volume":"9","author":"Wu","year":"2021","journal-title":"Front. Earth Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"104612","DOI":"10.1016\/j.jafrearsci.2022.104612","article-title":"Rigorous evaluation of global geopotential models for geoid modelling: A case study in Kenya","volume":"194","author":"Nyoka","year":"2022","journal-title":"J. Afr. Earth Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Isik, M.S., \u00c7evikalp, M.R., Erol, B., and Erol, S. (2022). Improvement of GOCE-Based Global Geopotential Models for Gravimetric Geoid Modeling in Turkey. Geosciences, 12.","DOI":"10.3390\/geosciences12120432"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF03655315","article-title":"Fast evaluation of convolution integrals on the sphere using 1D FFT, and a com- parison with existing methods for Stokes\u2019 integral","volume":"18","author":"Haagmans","year":"1993","journal-title":"Manuscripta Geod."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lyszkowicz, A., Nastula, J., Zielinski, J.B., and Birylo, M. (2021). A New Model of Quasigeoid for the Baltic Sea Area. Remote Sens., 13.","DOI":"10.3390\/rs13132580"},{"key":"ref_29","unstructured":"Kvas, A., Mayer-G\u00fcrr, T., Krauss, S., Brockmann, J.M., Schubert, T., Schuh, W.-D., Pail, R., Gruber, T., J\u00e4ggi, A., and Meyer, U. (2019). GFZ Data Services, GFZ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"99","DOI":"10.5194\/essd-13-99-2021","article-title":"GOCO06s\u2014A satellite-only global gravity field model","volume":"13","author":"Kvas","year":"2021","journal-title":"Earth Syst. Sci. Data"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7508","DOI":"10.1002\/2014GL062045","article-title":"ESA\u2019s satellite-only gravity field model via the direct approach based on all GOCE data","volume":"41","author":"Bruinsma","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10712-020-09626-0","article-title":"An improved model of the Earth\u2019s static gravity field solely derived from reprocessed GOCE data","volume":"42","author":"Brockmann","year":"2021","journal-title":"Surv. Geophys."},{"key":"ref_33","unstructured":"Zingerle, P., Brockmann, J.M., Pail, R., Gruber, T., and Willberg, M. (2019). GFZ Data Services, GFZ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s00190-017-1089-8","article-title":"The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor","volume":"92","author":"Lu","year":"2017","journal-title":"J. Geod."},{"key":"ref_35","unstructured":"Mayer-G\u00fcrr, T., Behzadpur, S., Ellmer, M., Kvas, A., Klinger, B., Strasser, S., and Zehentner, N. (2018). GFZ Data Services, GFZ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9332","DOI":"10.1029\/2019JB017415","article-title":"ITSG-Grace2018: Overview and evaluation of a new GRACE-only gravity field time series","volume":"124","author":"Kvas","year":"2019","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1016\/j.eng.2020.05.008","article-title":"A High-Resolution Earth\u2019s Gravity Field Model SGG-UGM-2 from GOCE, GRACE, Satellite Altimetry, and EGM2008","volume":"6","author":"Liang","year":"2020","journal-title":"Engineering"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chen, J., Zhang, X., Chen, Q., Shen, Y., and Nie, Y. (2022, January 23\u201327). Static Gravity Field Recovery and Accuracy Analysis Based on Reprocessed GOCE Level 1b Gravity Gradient Observations. Proceedings of the EGU General Assembly 2022, Vienna, Austria. EGU22-6771.","DOI":"10.5194\/egusphere-egu22-6771"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6111","DOI":"10.1029\/2018JB015641","article-title":"Tongji-Grace02s and Tongji-Grace02k: High-precision static GRACE-only global Earth\u2019s gravity field models derived by refined data processing strategies","volume":"123","author":"Chen","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_40","unstructured":"Zingerle, P., Pail, R., Thomas, G., and Oikonomidou, X. (2019). GFZ Data Services, GFZ."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"64","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_42","unstructured":"DLR e.V.; Airbus Defense and Space GmbH. Copernicus DEM GLO-30. Provided under COPERNICUS by the European Union and ESA; all rights reserved, 2018."},{"key":"ref_43","unstructured":"Hellenic Navy Hydrographic Service (2021, March 24). Digital Terrain Model (DTM) of the Greek Seas. Available online: https:\/\/www.hnhs.gr\/."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Grigoriadis, V.N., Andritsanos, V.D., and Natsiopoulos, D.A. (2023). Validation of Recent DSM\/DEM\/DBMs in Test Areas in Greece Using Spirit Leveling, GNSS, Gravity and Echo Sounding Measurements. ISPRS Int. J. Geo-Inf., 12.","DOI":"10.3390\/ijgi12030099"},{"key":"ref_45","unstructured":"Grigoriadis, V.N., Andritsanos, V.D., and Natsiopoulos, D. (2022). International Association of Geodesy Symposia, Springer."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s00190-021-01541-5","article-title":"The permanent tide and the International Height Reference Frame IHRF","volume":"95","year":"2021","journal-title":"J. Geod."},{"key":"ref_47","unstructured":"Grigoriadis, V.N. (2009). Geodetic and Geophysical Approach of the Earth\u2019s Gravity Field and Applications in the Hellenic Area. [Ph.D. Dissertation, Department of Geodesy & Surveying, School of Rural and Surveying Engineering, Aristotle University of Thessaloniki]. (In Greek)."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Heiskanen, W.A., and Moritz, H. (1967). Physical Geodesy, W.H. Freeman and Co.","DOI":"10.1007\/BF02525647"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s00190-009-0302-9","article-title":"On the geoid\u2013quasigeoid separation in mountain areas","volume":"83","author":"Flury","year":"2009","journal-title":"J. Geod."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Rapp, R.H. (1982). A FORTRAN Program for the Computation of Gravimetric Quantities from High-Degree Spherical Harmonic Expansions, Department of Geodetic Science, The Ohio State University. Technical Report OSU Report 1982, No 334.","DOI":"10.21236\/ADA123406"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1007\/s10712-016-9382-2","article-title":"Layer-based modelling of the Earth\u2019s gravitational potential up to 10km scale in spherical harmonics and ellipsoidal approximation","volume":"37","author":"Rexer","year":"2016","journal-title":"Surv. Geophys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.cageo.2014.09.001","article-title":"Study of the Earth\u2019s short scale gravity field using the ERTM2160 gravity model","volume":"73","author":"Hirt","year":"2014","journal-title":"Comput. Geosci."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Sans\u00f2, F., and Sideris, M.G. (2013). Geoid Determination: Theory and Methods, Springer.","DOI":"10.1007\/978-3-540-74700-0"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF02520477","article-title":"Impacts of geodynamic phenomena on systems for height and gravity","volume":"63","author":"Ekman","year":"1989","journal-title":"Bull. Geod."},{"key":"ref_55","first-page":"1","article-title":"The 1st order leveling net of Greece (in Greek)","volume":"50","year":"1990","journal-title":"Bull. Hell. Mil. Geogr. Serv."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/17\/4282\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:43:47Z","timestamp":1760129027000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/17\/4282"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,31]]},"references-count":55,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["rs15174282"],"URL":"https:\/\/doi.org\/10.3390\/rs15174282","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,31]]}}}