{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T03:26:11Z","timestamp":1768015571944,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T00:00:00Z","timestamp":1687478400000},"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":["2019YFC1408405"],"award-info":[{"award-number":["2019YFC1408405"]}]},{"name":"National Key Research and Development Project of China","award":["U2006210"],"award-info":[{"award-number":["U2006210"]}]},{"name":"National Natural Science Foundation of China","award":["2019YFC1408405"],"award-info":[{"award-number":["2019YFC1408405"]}]},{"name":"National Natural Science Foundation of China","award":["U2006210"],"award-info":[{"award-number":["U2006210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The harmonic constants of long-period tidal constituents are critical for simulating the tide process, obtaining theoretical datum sounding reduction, and conducting further ocean research. In this paper, the equidistant node orthogonal polynomial fitting (ENOPF) method is employed to fit the harmonic constants of the T\/P satellite altimeter data and the gridded altimeter data from the Data Unification and Altimeter Combination System (DUACS) to obtain the full-field harmonic constants of the long-period tidal constituents (Sa and Ssa) in the Bohai Sea, Yellow Sea, and East China Sea (BYECS). To verify the validity of the ENOPF method, the long-period tidal harmonic constants of the ENOPF method, the Finite Element Solutions 2014 (FES2014) model, the Empirical Ocean Tide 20 (EOT20) model, and the DUACS data were compared with the observations of the X-TRACK products and the tide gauges. In addition, the root-mean-square errors (RMSEs), amplitude differences (\u0394H), and phase-lag differences (\u0394G) of the comparison results were calculated. According to the error analysis and the cotidal charts, the ENOPF method is better than the other three methods or models for comparing tide gauges (6.19 cm, 5.85 cm, 25.44\u00b0; 1.10 cm, 0.72 cm, 59.09\u00b0, respectively. The cotidal charts obtained by the ENOPF method are smoother and have better consistency with the actual track data. The results indicate that, due to the polynomial fitting method adopted in ENOPF method, which has the characteristics of improving the resolution infinitely, it is easier to obtain the harmonic constant of full field than with other models or methods. This study proves that the ENOPF method is a reasonable and simple tool in extracting the harmonic constants of the BYECS.<\/jats:p>","DOI":"10.3390\/rs15133246","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T03:14:56Z","timestamp":1687749296000},"page":"3246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Equidistant Nodes Orthogonal Polynomial Fitting for Harmonic Constants of Long-Period Tides Based on Satellite Altimeter Data"],"prefix":"10.3390","volume":"15","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0457-1893","authenticated-orcid":false,"given":"Qixiang","family":"Wang","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4227-7708","authenticated-orcid":false,"given":"Yibo","family":"Zhang","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":"Minjie","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Ocean, Yantai University, Yantai 264005, China"}]},{"given":"Yonggang","family":"Wang","sequence":"additional","affiliation":[{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China"},{"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":[[2023,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1016\/S0967-0637(98)00070-3","article-title":"Abyssal Recipes II: Energetics of Tidal and Wind Mixing","volume":"45","author":"Munk","year":"1998","journal-title":"Deep. 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