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A two-dimensional adjoint assimilation model is used for tidal numerical simulation and, as an improvement, trigonometric polynomials fitting (TPF) is applied in the inversion of OBCs. It is assumed that the linearized amplitudes\/phases in the open boundary are spatially varying and can be represented by nonlinear functions. Based on the discrete Fourier series, taking the trigonometric function as the basis function, the spatially varying OBCs are constructed by selecting the maximum truncation period. The independent points scheme used in previous studies was also compared in the experiments. Twin experiments show that the errors of simulations with TPF are the smallest in different schemes, and their results show the highest correlation with observations while maintaining the best performance in terms of observation errors. The mean absolute errors (MAEs) in amplitude\/phase between the simulated results using estimated OBCs and the satellite altimeter records are 2.82 cm and 2.26\u00b0, respectively.<\/jats:p>","DOI":"10.3390\/rs15020480","type":"journal-article","created":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T04:30:20Z","timestamp":1673584220000},"page":"480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Improved Estimation of the Open Boundary Conditions in Tidal Models Using Trigonometric Polynomials Fitting Scheme"],"prefix":"10.3390","volume":"15","author":[{"given":"Shengyi","family":"Jiao","sequence":"first","affiliation":[{"name":"Frontier Science Center for Deep Ocean Multispheres and Earth System (FDOMES), Ocean University of China, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, 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), Ocean University of China, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8804-7772","authenticated-orcid":false,"given":"Haidong","family":"Pan","sequence":"additional","affiliation":[{"name":"First Institute of Oceanography, and Key Laboratory of Marine Science and Numerical Modeling, Ministry of Natural Resources, Qingdao 266061, China"},{"name":"Shandong Key Laboratory of Marine Science and Numerical Modeling, 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), Ocean University of China, Qingdao 266100, China"},{"name":"Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1098\/rspa.1921.0088","article-title":"The harmonic development of the tide-generating potential","volume":"100","author":"Doodson","year":"1921","journal-title":"Proc. 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