{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T10:18:08Z","timestamp":1770459488322,"version":"3.49.0"},"reference-count":64,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T00:00:00Z","timestamp":1629849600000},"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":["41774014"],"award-info":[{"award-number":["41774014"]}],"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":["41574014"],"award-info":[{"award-number":["41574014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["XLYC2002082"],"award-info":[{"award-number":["XLYC2002082"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["XLYC2002101"],"award-info":[{"award-number":["XLYC2002101"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"publisher","award":["XLYC2008034"],"award-info":[{"award-number":["XLYC2008034"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Technology Commission of the Central Military Commission under Grant","award":["085015"],"award-info":[{"award-number":["085015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Dense Global Position System (GPS) arrays can be used to invert the terrestrial water-storage anomaly (TWSA) with higher accuracy. However, the uneven distribution of GPS stations greatly limits the application of GPS to derive the TWSA. Aiming to solve this problem, we grid the GPS array using regression to raise the reliability of TWSA inversion. First, the study uses the random forest (RF) model to simulate crustal deformation in unobserved grids. Meanwhile, the new Machine-Learning Loading-Inverted Method (MLLIM) is constructed based on the traditional GPS derived method to raise the truthfulness of TWSA inversion. Second, this research selects southwest China as the study region, the MLLIM and traditional GPS inversion methods are used to derive the TWSA, and the inverted results are contrasted with datasets of the Gravity Recovery and Climate Experiment (GRACE) Mascon and the Global Land Data Assimilation System (GLDAS) model. The comparison shows that values of Pearson Correlation Coefficient (PCC) between the MLLIM and GRACE and GRACE Follow-On (GRACE-FO) are equal to 0.91 and 0.88, respectively; and the values of R-squared (R2) are equal to 0.76 and 0.65, respectively; the values of PCC and R2 between MLLIM and GLDAS solutions are equal to 0.79 and 0.65. Compared with the traditional GPS inversion, the MLLIM improves PCC and R2 by 8.85% and 7.99% on average, which indicates that the MLLIM can improve the accuracy of TWSA inversion more than the traditional GPS method. Third, this study applies the MLLIM to invert the TWSA in each province of southwest China and combines the precipitation to analyze the change of TWSA in each province. The results are as follows: (1) The spatial distribution of TWSA and precipitation is coincident, which is highlighted in southwest Yunnan and southeast Guangxi; (2) this study compares TWSA of MLLIM with GRACE and GLDAS solutions in each province, which indicates that the maximum value of PCC is as high as 0.86 and 0.94, respectively, which indicates the MLLIM can be used to invert the TWSA in the regions with sparse GPS stations. The TWSA based on the MLLIM can be used to fill the vacancy between GRACE and GRACE-FO.<\/jats:p>","DOI":"10.3390\/rs13173358","type":"journal-article","created":{"date-parts":[[2021,8,25]],"date-time":"2021-08-25T04:24:27Z","timestamp":1629865467000},"page":"3358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Inverted Algorithm of Terrestrial Water-Storage Anomalies Based on Machine Learning Combined with Load Model and Its Application in Southwest China"],"prefix":"10.3390","volume":"13","author":[{"given":"Yifan","family":"Shen","sequence":"first","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"},{"name":"Qian Xuesen Laboratory of Technology, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"},{"name":"Qian Xuesen Laboratory of Technology, China Academy of Space Technology, Beijing 100094, China"},{"name":"School of Aeronautics and Astronautics, Taiyuan University of Technology, Jinzhong 030600, China"},{"name":"School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, China"},{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjie","family":"Yin","sequence":"additional","affiliation":[{"name":"Qian Xuesen Laboratory of Technology, China Academy of Space Technology, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aigong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huizhong","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5017-4832","authenticated-orcid":false,"given":"Shuai","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Su","sequence":"additional","affiliation":[{"name":"School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sun, A., Scanlon, B., Aghakouchak, A., and Zhang, Z. (2017). Using GRACE satellite gravimetry for assessing Large-Scale hydrologic extremes. Remote Sens., 9.","DOI":"10.3390\/rs9121287"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1038\/s41598-018-38148-4","article-title":"Water resources utilization and protection in the coal mining area of northern China","volume":"9","author":"Dong","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10584-016-1709-y","article-title":"Vulnerability of and risk to water resources in arid and semi-arid regions of west China under a scenario of climate change","volume":"144","author":"Xia","year":"2017","journal-title":"Clim. Chang."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"79","DOI":"10.3390\/rs13010079","article-title":"Spatiotemporal characteristics of drought and driving factors based on the GRACE-derived total storage deficit index: A case study in southwest China","volume":"13","author":"Wu","year":"2021","journal-title":"Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ma, S., Wu, Q., Wang, J., and Zhang, S. (2017). Temporal evolution of regional drought detected from GRACE TWSA and CCI SM in Yunnan Province, China. Remote Sens., 9.","DOI":"10.3390\/rs9111124"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5973","DOI":"10.1029\/2017JD027468","article-title":"Statistical downscaling of GRACE-derived groundwater storage using ET data in the North China Plain","volume":"123","author":"Yin","year":"2018","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jog.2011.07.003","article-title":"Efficient accuracy improvement of GRACE global gravitational field recovery using a new inter-satellite range interpolation method","volume":"53","author":"Zheng","year":"2012","journal-title":"J. Geodyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.3390\/rs12111835","article-title":"Surface mass variations from GPS and GRACE\/GFO: A case study in southwest China","volume":"12","author":"Zhong","year":"2020","journal-title":"Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8254824","DOI":"10.1155\/2017\/8254824","article-title":"Evaluation of groundwater storage variations in northern China using GRACE data","volume":"2017","author":"Yin","year":"2017","journal-title":"Geofluids"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhong, Y., Zhong, M., Mao, Y., and Ji, B. (2020). Evaluation of Evapotranspiration for Exorheic Catchments of China during the GRACE Era: From a Water Balance Perspective. Remote Sens., 12.","DOI":"10.3390\/rs12030511"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"125348","DOI":"10.1016\/j.jhydrol.2020.125348","article-title":"Improved water storage estimates within the North China Plain by assimilating GRACE data into the CABLE model","volume":"590","author":"Yin","year":"2020","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1002\/2013WR014581","article-title":"Uncertainty in evapotranspiration from land surface modeling, remote sensing, and GRACE satellites","volume":"50","author":"Long","year":"2014","journal-title":"Water Resour. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1002\/2017WR021521","article-title":"Accuracy of snow water equivalent estimated from GPS vertical displacements: A synthetic loading case study for western U.S. mountains","volume":"54","author":"Enzminger","year":"2018","journal-title":"Water Resour. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2110","DOI":"10.1002\/wrcr.20192","article-title":"Evaluation of groundwater depletion in North China using the Gravity Recovery and Climate Experiment (GRACE) data and ground-based measurements","volume":"49","author":"Feng","year":"2013","journal-title":"Water Resour. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sasgen, I., Konrad, H., Helm, V., and Grosfeld, K. (2019). High-resolution mass tends of the antarctic ice sheet through a spectral combination of satellite gravimetry and radar altimetry observations. Remote Sens., 11.","DOI":"10.3390\/rs11020144"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4144","DOI":"10.3390\/s19194144","article-title":"Bridging terrestrial water storage anomaly during GRACE\/GRACE-FO gap using SSA method: A case study in China","volume":"19","author":"Li","year":"2019","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tangdamrongsub, N., and \u0160prl\u00e1k, M. (2021). The assessment of hydrologic- and flood-induced land deformation in data-sparse regions using GRACE\/GRACE-FO data assimilation. Remote Sens., 13.","DOI":"10.3390\/rs13020235"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1029\/2011JB008925","article-title":"Seasonal and long-term vertical deformation in the Nepal Himalaya constrained by GPS and GRACE measurements","volume":"117","author":"Fu","year":"2012","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"He, M., Shen, W., Pan, Y., Chen, R., and Guo, G. (2017). Temporal\u2013Spatial surface seasonal mass changes and vertical crustal deformation in south china block from GPS and GRACE measurements. Sensors, 18.","DOI":"10.3390\/s18010099"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1002\/jgrb.50104","article-title":"The use of GPS horizontals for loading studies, with applications to northern California and southeast Greenland","volume":"118","author":"Wahr","year":"2013","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_21","first-page":"671","article-title":"Solute transport in heterogeneous porous formations","volume":"55","author":"Dagan","year":"2004","journal-title":"Water Resour. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1029\/RG010i003p00761","article-title":"Deformation of the earth by surface loads","volume":"10","author":"Farrell","year":"1972","journal-title":"Rev. Geophys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1002\/2014GL059570","article-title":"Seasonal variation in total water storage in California inferred from GPS observations of vertical land motion","volume":"41","author":"Argus","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1029\/2018EA000462","article-title":"LoadDef: A python-based toolkit to model elastic deformation caused by surface mass loading on spherically symmetric bodies","volume":"6","author":"Martens","year":"2019","journal-title":"Earth Space Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"13006","DOI":"10.1029\/2019GL085370","article-title":"A decade of water storage changes across the contiguous united states from GPS and satellite gravity","volume":"46","author":"Adusumilli","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s00024-018-2000-0","article-title":"Insight into the 2016 menyuan M w 5.9 earthquake with InSAR: A blind reverse event promoted by historical earthquakes","volume":"176","author":"Xiong","year":"2018","journal-title":"Pure Appl. Geophys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Drewes, H. (1998, January 12). Combination of VLBI, SLR and GPS determined station velocities for actual plate kinematic and crustal deformation models. Proceedings of the Geodesy on the Move, Berlin, Germany.","DOI":"10.1007\/978-3-642-72245-5_59"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.quaint.2017.05.043","article-title":"Continuous GPS measurements of crustal deformation in Garhwal-Kumaun Himalaya","volume":"462","author":"Gautam","year":"2017","journal-title":"Quat. Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"19861","DOI":"10.3390\/s141019861","article-title":"Earth surface deformation in the North China Plain detected by joint analysis of GRACE and GPS data","volume":"14","author":"Liu","year":"2014","journal-title":"Sensors"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"17507","DOI":"10.1109\/ACCESS.2021.3049118","article-title":"Feature extraction algorithm using a correlation coefficient combined with the VMD and its application to the GPS and GRACE","volume":"9","author":"Shen","year":"2021","journal-title":"IEEE Access"},{"key":"ref_31","first-page":"4777","article-title":"Determination of vertical surface displacements in Sichuan using GPS and GRACE measurements","volume":"061","author":"Ding","year":"2018","journal-title":"Chin. J. Geophy."},{"key":"ref_32","first-page":"332","article-title":"Seasonal variation of terrestrial water storage in Yunnan province inferred from GPS vertical observations","volume":"47","author":"He","year":"2018","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s00190-020-01445-w","article-title":"Atmospheric pressure loading in GPS positions: Dependency on GPS processing methods and effect on assessment of seasonal deformation in the contiguous USA and Alaska","volume":"94","author":"Martens","year":"2020","journal-title":"J. Geod."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6048","DOI":"10.1002\/2013GL058093","article-title":"Horizontal motion in elastic response to seasonal loading of rain water in the Amazon Basin and monsoon water in Southeast Asia observed by GPS and inferred from GRACE","volume":"40","author":"Fu","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"126349","DOI":"10.1016\/j.jhydrol.2021.126349","article-title":"Estimation of daily hydrological mass changes using continuous GNSS measurements in mainland China","volume":"598","author":"Jiang","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"L22310","DOI":"10.1029\/2005GL024104","article-title":"Atmospheric pressure loading corrections applied to GPS data at the observation level","volume":"32","author":"Tregoning","year":"2005","journal-title":"Geophys. Res. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"e2020JB020685","DOI":"10.1029\/2020JB020685","article-title":"Comparing non-tidal ocean loading around the southern north sea with subdaily GPS\/GLONASS data","volume":"126","author":"Geng","year":"2021","journal-title":"J. Geophys.Res. Solid Earth"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1029\/150GM15","article-title":"Dense gps array as a new sensor of seasonal changes of surface loads","volume":"150","author":"Heki","year":"2004","journal-title":"State Planet Front. Chall. Geophys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1002\/2014JB011415","article-title":"GPS as an independent measurement to estimate terrestrial water storage variations in Washington and Oregon","volume":"120","author":"Fu","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_40","unstructured":"Herring, T.A., King, R.W., and Mcclusky, S.C. (2006). GAMIT Reference Manual GPS Analysis at MIT Release 10.3, Department of Earth, Atmospheric, Massachusetts Institute of Technology."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"7547","DOI":"10.1002\/2016JB013007","article-title":"High-resolution CSR GRACE RL05 mascons","volume":"121","author":"Save","year":"2016","journal-title":"J. Geophys.Res. Solid Earth"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Breiman (2001). Random forests. Mach Learn., 45, 5\u201332.","DOI":"10.1023\/A:1010933404324"},{"key":"ref_43","first-page":"267","article-title":"The elements of statistical learning: Springer","volume":"1","author":"Hastie","year":"2009","journal-title":"Elements"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.epsl.2018.06.007","article-title":"Crustal structure and deformation beneath eastern and northeastern Tibet revealed by P-wave receiver functions","volume":"497","author":"Wang","year":"2018","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s00190-010-0437-8","article-title":"Vertical deformations from homogeneously processed GRACE and global GPS long-term series","volume":"85","author":"Tesmer","year":"2011","journal-title":"J. Geod."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.cageo.2012.06.022","article-title":"Load love numbers and Green\u2019s functions for elastic earth models PREM, iasp91, ak135, and modified models with refined crustal structure from Crust 2.0","volume":"49","author":"Wang","year":"2012","journal-title":"Comput. Geosci."},{"key":"ref_47","first-page":"235","article-title":"Determining the ridge parameter in a ridge estimation using L-curve method","volume":"29","author":"Wang","year":"2004","journal-title":"Editor. Board Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_48","unstructured":"Argus, D. (2015, January 18). Sustained water changes in California during drought and heavy precipitation inferred from GPS, InSAR, and GRACE. Proceedings of the Agu Fall Meeting, San Francisco, UCA, USA."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1007\/s10712-016-9385-z","article-title":"Terrestrial water storage anomalies associated with drought in southwestern USA from GPS observations","volume":"37","author":"Jin","year":"2016","journal-title":"Surv. Geophys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"L24605","DOI":"10.1029\/2004GL021435","article-title":"Climate-driven deformation of the solid Earth from GRACE and GPS","volume":"31","author":"Davis","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"0148","DOI":"10.1029\/2011JB009102","article-title":"Hydrological deformation induced by the west African Monsoon: Comparison of GPS, GRACE and loading models","volume":"117","author":"Nahmani","year":"2012","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.jog.2013.05.005","article-title":"Singular spectrum analysis for modeling seasonal signals from GPS time series","volume":"72","author":"Chen","year":"2013","journal-title":"J. Geodyn."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"150731131106004","DOI":"10.1175\/JHM-D-14-0230.1","article-title":"Evaluation of the global land data assimilation system (GLDAS) air temperature data products","volume":"16","author":"Ji","year":"2015","journal-title":"J. Hydrometeorol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s13351-021-0107-1","article-title":"The Asian subtropical westerly jet stream in CRA-40, ERA5, and CFSR reanalysis data: Comparative assessment","volume":"35","author":"Yu","year":"2021","journal-title":"J. Meteorol. Res."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1126\/science.1260279","article-title":"Ongoing drought-induced uplift in the western United States","volume":"345","author":"Borsa","year":"2014","journal-title":"Science"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.5194\/gmd-7-1247-2014","article-title":"Root mean square error (RMSE) or mean absolute error (MAE) aguments against avoiding RMSE in the literature","volume":"7","author":"Chai","year":"2014","journal-title":"Geosci. Model Dev."},{"key":"ref_57","first-page":"59","article-title":"Thirteen ways to look at the correlation coefficient","volume":"42","author":"Nicewander","year":"1988","journal-title":"Am. Stat."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0167-9473(03)00062-8","article-title":"Pseudo R-squared measures for poisson regression models with over- or underdispersion","volume":"44","author":"Heinzl","year":"2003","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Fok, H.S., and Liu, Y. (2019). An improved GPS-inferred seasonal terrestrial water storage using terrain-corrected vertical crustal displacements constrained by GRACE. Remote Sens., 11.","DOI":"10.3390\/rs11121433"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"4277","DOI":"10.1029\/2000JB900347","article-title":"Annual vertical crustal motions predicted from surface mass redistribution and observed by space geodesy","volume":"106","author":"Mangiarotti","year":"2001","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.jog.2009.09.003","article-title":"Crustal loading in vertical GPS time series in Fennoscandia","volume":"48","author":"Nordman","year":"2009","journal-title":"J. Geodyn."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"271","DOI":"10.2478\/v10156-011-0005-z","article-title":"Crustal deformation due to atmospheric pressure loading in new Zealand","volume":"1","author":"Gladkikh","year":"2011","journal-title":"J. Geod. Sci."},{"key":"ref_63","first-page":"79","article-title":"The international mass loading service","volume":"02","author":"Petrov","year":"2015","journal-title":"Physics"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/s10291-015-0478-9","article-title":"On the significance of periodic signals in noise analysis of GPS station coordinates time series","volume":"20","author":"Bogusz","year":"2016","journal-title":"GPS Solut."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3358\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:51:01Z","timestamp":1760165461000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3358"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,25]]},"references-count":64,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["rs13173358"],"URL":"https:\/\/doi.org\/10.3390\/rs13173358","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,25]]}}}