{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T05:54:20Z","timestamp":1773381260105,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T00:00:00Z","timestamp":1623110400000},"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":["42071374, 41930647"],"award-info":[{"award-number":["42071374, 41930647"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program of Frontier Sciences of Chinese Academy of Sciences","award":["ZDBS-LY-DQC005"],"award-info":[{"award-number":["ZDBS-LY-DQC005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Dissolved oxygen (DO) is a direct indicator of water pollution and an important water quality parameter that affects aquatic life. Based on the fundamental theorem of surfaces in differential geometry, the present study proposes a new modeling approach to estimate DO concentrations with high accuracy by assessing the spatial correlation and heterogeneity of DO with respect to explanatory variables. Specifically, a regularization penalty term is integrated into the high-accuracy surface modeling (HASM) method by applying geographically weighted regression (GWR) with some covariates. A modified version of HASM, namely HASM_MOD, is illustrated through a case study of Poyang Lake, China, by comparing the results of HASM, a support vector machine (SVM), and cokriging. The results indicate that HASM_MOD yields the best performance, with a mean absolute error (MAE) that is 38%, 45%, and 42% lower than those of HASM, the SVM, and cokriging, respectively, by using the cross-validation method. The introduction of a regularization penalty term by using GWR with respect to covariates can effectively improve the quality of the DO estimates. The results also suggest that HASM_MOD is able to effectively estimate nonlinear and nonstationary time series and outperforms three other methods using cross-validation, with a root-mean-square error (RMSE) of 0.20 mg\/L and R2 of 0.93 for the two study sites (Sanshan and Outlet_A stations). The proposed method, HASM_MOD, provides a new way to estimate the DO concentration with high accuracy.<\/jats:p>","DOI":"10.3390\/s21123954","type":"journal-article","created":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T21:16:58Z","timestamp":1623187018000},"page":"3954","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A New Approach for Estimating Dissolved Oxygen Based on a High-Accuracy Surface Modeling Method"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4434-1726","authenticated-orcid":false,"given":"Na","family":"Zhao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100101, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographic Information Resource Development and Application, Nanjing 210023, China"}]},{"given":"Zemeng","family":"Fan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China"},{"name":"College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100101, China"}]},{"given":"Miaomiao","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.5194\/bg-6-1273-2009","article-title":"Coastal hypoxia and sediment biogeochemistry","volume":"6","author":"Middelburg","year":"2009","journal-title":"Biogeosciences"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6565","DOI":"10.1007\/s12665-014-3876-3","article-title":"Modeling stream dissolved oxygen concentration using teaching-learning based optimization algorithm","volume":"73","author":"Bayram","year":"2015","journal-title":"Environ. 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