{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:25:40Z","timestamp":1760145940292,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T00:00:00Z","timestamp":1726531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Project of China","award":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"],"award-info":[{"award-number":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"],"award-info":[{"award-number":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Laoshan Laboratory","award":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"],"award-info":[{"award-number":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"]}]},{"name":"High Performance Computing Center at the Institute of Oceanology, Chinese Academy of Sciences","award":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"],"award-info":[{"award-number":["2022YFC2808304","2019YFC1408405","2020YFA0608800","42076011","U1806214","LSKJ202202402"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This study employs the two-dimensional Legendre polynomial fitting (2-D LPF) method to fit M2 tidal harmonic constants from satellite altimetry data within the region of 53\u00b0E\u2013131\u00b0E, 34\u00b0S\u20136\u00b0N, extracting internal tide signals acting on the sea surface. The M2 tidal harmonic constants are derived from the sea surface height (SSH) data of the TOPEX\/Poseidon (T\/P), Jason-1, Jason-2, and Jason-3 satellites via t-tide analysis. We validate the 2-D LPF method against the 300 km moving average (300 km smooth) method and the one-dimensional Legendre polynomial fitting (1-D LPF) method. Through cross-validation across 42 orbits, the optimal polynomial orders are determined to be seven for 1-D LPF, and eight and seven for the longitudinal and latitudinal directions in 2-D LPF, respectively. The 2-D LPF method demonstrated superior spatial continuity and smoothness of internal tide signals. Further single-orbit correlation analysis confirmed generally higher correlation with topographic and density perturbations (correlation coefficients: 0.502, 0.620, 0.245; 0.420, 0.273, \u22120.101), underscoring its accuracy. Overall, the 2-D LPF method can use all regional data points, overcoming the limitations of single-orbit approaches and proving its effectiveness in extracting internal tide signals acting on the sea surface.<\/jats:p>","DOI":"10.3390\/rs16183447","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T00:51:43Z","timestamp":1726620703000},"page":"3447","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two-Dimensional Legendre Polynomial Method for Internal Tide Signal Extraction"],"prefix":"10.3390","volume":"16","author":[{"given":"Yunfei","family":"Zhang","sequence":"first","affiliation":[{"name":"Frontier Science Center for Deep Ocean Multispheres and Earth System (FDOMES) and Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China"}]},{"given":"Cheng","family":"Luo","sequence":"additional","affiliation":[{"name":"Frontier Science Center for Deep Ocean Multispheres and Earth System (FDOMES) and Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China"}]},{"given":"Haibo","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ocean Observation and Forecasting, Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China"},{"name":"Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0456-9002","authenticated-orcid":false,"given":"Wei","family":"Cui","sequence":"additional","affiliation":[{"name":"First Institute of Oceanography and Key Laboratory of Marine Science and Numerical Modeling, Ministry of Natural Resources, Qingdao 266061, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7994-7579","authenticated-orcid":false,"given":"Xianqing","family":"Lv","sequence":"additional","affiliation":[{"name":"Frontier Science Center for Deep Ocean Multispheres and Earth System (FDOMES) and Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1029\/RG013i001p00167","article-title":"Internal Tides in the Ocean","volume":"13","author":"Wunsch","year":"1975","journal-title":"Rev. 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