{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T12:49:44Z","timestamp":1784119784464,"version":"3.55.0"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"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":["41976190"],"award-info":[{"award-number":["41976190"]}],"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":["41976189"],"award-info":[{"award-number":["41976189"]}],"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":["2021B1212100006"],"award-info":[{"award-number":["2021B1212100006"]}],"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":["2022GDASZH-2022010202"],"award-info":[{"award-number":["2022GDASZH-2022010202"]}],"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":["2022010111"],"award-info":[{"award-number":["2022010111"]}],"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":["2022020402-01"],"award-info":[{"award-number":["2022020402-01"]}],"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":["AB20297037"],"award-info":[{"award-number":["AB20297037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Program of Guangdong","award":["41976190"],"award-info":[{"award-number":["41976190"]}]},{"name":"Science and Technology Program of Guangdong","award":["41976189"],"award-info":[{"award-number":["41976189"]}]},{"name":"Science and Technology Program of Guangdong","award":["2021B1212100006"],"award-info":[{"award-number":["2021B1212100006"]}]},{"name":"Science and Technology Program of Guangdong","award":["2022GDASZH-2022010202"],"award-info":[{"award-number":["2022GDASZH-2022010202"]}]},{"name":"Science and Technology Program of Guangdong","award":["2022010111"],"award-info":[{"award-number":["2022010111"]}]},{"name":"Science and Technology Program of Guangdong","award":["2022020402-01"],"award-info":[{"award-number":["2022020402-01"]}]},{"name":"Science and Technology Program of Guangdong","award":["AB20297037"],"award-info":[{"award-number":["AB20297037"]}]},{"name":"GDAS Project of Science and Technology Development","award":["41976190"],"award-info":[{"award-number":["41976190"]}]},{"name":"GDAS Project of Science and Technology Development","award":["41976189"],"award-info":[{"award-number":["41976189"]}]},{"name":"GDAS Project of Science and Technology Development","award":["2021B1212100006"],"award-info":[{"award-number":["2021B1212100006"]}]},{"name":"GDAS Project of Science and Technology Development","award":["2022GDASZH-2022010202"],"award-info":[{"award-number":["2022GDASZH-2022010202"]}]},{"name":"GDAS Project of Science and Technology Development","award":["2022010111"],"award-info":[{"award-number":["2022010111"]}]},{"name":"GDAS Project of Science and Technology Development","award":["2022020402-01"],"award-info":[{"award-number":["2022020402-01"]}]},{"name":"GDAS Project of Science and Technology Development","award":["AB20297037"],"award-info":[{"award-number":["AB20297037"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["41976190"],"award-info":[{"award-number":["41976190"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["41976189"],"award-info":[{"award-number":["41976189"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["2021B1212100006"],"award-info":[{"award-number":["2021B1212100006"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["2022GDASZH-2022010202"],"award-info":[{"award-number":["2022GDASZH-2022010202"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["2022010111"],"award-info":[{"award-number":["2022010111"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["2022020402-01"],"award-info":[{"award-number":["2022020402-01"]}]},{"name":"Science and Technology Key R&amp;D Program Project of Guangxi","award":["AB20297037"],"award-info":[{"award-number":["AB20297037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Knowledge of the precise water depth in shallow areas of the ocean is of great significance to the safe navigation of ships and hydrographic surveying. Compared with traditional bathymetry, satellite remote sensing for water depth determination makes it possible to cover large areas by dynamic observation. In this paper, we conducted an optically shallow water bathymetric inversion study using a Stumpf empirical model, random forest model, neural network model, and support vector machine model based on Sentinel-2 satellite images and Ganquan Dao measured bathymetry data. We compared and analyzed the inversion results based on the empirical model and different machine learning models. The results show that the Stumpf empirical and machine learning models are capable of inverting optically shallow water depth. Moreover, the machine learning models had better fitting ability than the Stumpf empirical model with a sufficient number of samples, especially when the water depth was greater than 15 m. In addition, the random forest model had the highest overall accuracy among these models, with a root mean square error (RMSE) of 1.41 m and a regression coefficient (R2) of 0.96 for the test data.<\/jats:p>","DOI":"10.3390\/rs15020393","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T04:47:08Z","timestamp":1673239628000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":63,"title":["A Comparison of Machine Learning and Empirical Approaches for Deriving Bathymetry from Multispectral Imagery"],"prefix":"10.3390","volume":"15","author":[{"given":"Wenneng","family":"Zhou","sequence":"first","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Water Quality Improvement and Ecological Restoration for Watersheds, School of Ecology, Environment and Resources, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yimin","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Geographic Science and Remote Sensing, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8021-3943","authenticated-orcid":false,"given":"Wenlong","family":"Jing","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Remote Sensing and Geographical Information System, Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangdong Engineering Technology Research Center of Remote Sensing Big Data Application, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China"},{"name":"Guangdong Provincial Laboratory of Southern Marine Science and Engineering (Guangzhou), Guangzhou 511458, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Remote Sensing and Geographical Information System, Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangdong Engineering Technology Research Center of Remote Sensing Big Data Application, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China"},{"name":"Guangdong Provincial Laboratory of Southern Marine Science and Engineering (Guangzhou), Guangzhou 511458, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4092-2264","authenticated-orcid":false,"given":"Ji","family":"Yang","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Remote Sensing and Geographical Information System, Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangdong Engineering Technology Research Center of Remote Sensing Big Data Application, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China"},{"name":"Guangdong Provincial Laboratory of Southern Marine Science and Engineering (Guangzhou), Guangzhou 511458, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0015-147X","authenticated-orcid":false,"given":"Yingbin","family":"Deng","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Remote Sensing and Geographical Information System, Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangdong Engineering Technology Research Center of Remote Sensing Big Data Application, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China"},{"name":"Guangdong Provincial Laboratory of Southern Marine Science and Engineering (Guangzhou), Guangzhou 511458, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yumeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Water Quality Improvement and Ecological Restoration for Watersheds, School of Ecology, Environment and Resources, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Goodman, J.A., Purkis, S.J., and Phinn, S.R. (2013). Coral Reef Remote Sensing: A Guide for Mapping, Monitoring and Management, Springer.","DOI":"10.1007\/978-90-481-9292-2"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/JSTARS.2012.2209864","article-title":"Potential of Space-Borne LiDAR Sensors for Global Bathymetry in Coastal and Inland Waters","volume":"6","author":"Abdallah","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_3","first-page":"92","article-title":"Progress in Water Depth Mapping from Visible Remote Sensing Data","volume":"26","author":"Wang","year":"2007","journal-title":"Mar. Sci. Bull."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1002\/arp.1823","article-title":"Exploration and reconstruction of a medieval harbour using hydroacoustics, 3-D shallow seismic and underwater photogrammetry: A case study from Puck, southern Baltic Sea","volume":"28","author":"Pydyn","year":"2021","journal-title":"Archaeol. Prospect."},{"key":"ref_5","first-page":"16","article-title":"Techniques of Water Depth Remote Sensing Retrieval and Underwater Obstacle Detection","volume":"35","author":"Huang","year":"2015","journal-title":"Hydrogr. Surv. Charting"},{"key":"ref_6","first-page":"53","article-title":"A Study of shallow water depth extraction using Landsat imagery","volume":"13","author":"Dang","year":"2001","journal-title":"Remote Sens. Land Resour."},{"key":"ref_7","unstructured":"Teng, H., MA, F., LI, H., YE, Q., and Xin, X. (2009, January 12\u201317). The Development and Model Analysis of The Retrieving Sounding Technology Using Satellite Remote Sensing. Proceedings of the 21st Comprehensive Symposium on Ocean Surveying and Mapping, Chengdu, China."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1364\/AO.17.000379","article-title":"Passive remote sensing techniques for mapping water depth and bottom features","volume":"17","author":"Lyzenga","year":"1978","journal-title":"Appl. Opt."},{"key":"ref_9","first-page":"331","article-title":"Progress in Shallow Water Depth Mapping from Optical Remote Sensing","volume":"36","author":"Ma","year":"2018","journal-title":"Adv. Mar. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7538","DOI":"10.1364\/AO.58.007538","article-title":"Rapid estimation of bathymetry from multispectral imagery without in situ bathymetry data","volume":"58","author":"Liu","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4349","DOI":"10.1109\/JSTARS.2018.2874684","article-title":"Multispectral Bathymetry via Linear Unmixing of the Benthic Reflectance","volume":"11","author":"Liu","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_12","first-page":"87","article-title":"Bathymetry Inversion Method Based on Adaptive Empricial Semi-Analytical Model without in situ Data-A Case Study in South China Sea","volume":"42","author":"Wang","year":"2022","journal-title":"Acta Opt. Sin."},{"key":"ref_13","unstructured":"Polcyn, F.C., and Lyzenga, D.R. (1973). Calculations of Water Depth from ERTS-MSS Data, Environmental Research Institute of Michigan."},{"key":"ref_14","unstructured":"Tanis, F.J., and Byrnes, H.J. (1985, January 21\u201325). Optimization of multispectral sensors for bathymetry applications. Proceedings of the 19th International Symposium on Remote Sensing of Enviroment, Ann Arbor, MI, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1364\/AO.22.001134","article-title":"Water depth mapping from passive remote sensing data under a generalized ratio assumption","volume":"22","author":"Paredes","year":"1983","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"547","DOI":"10.4319\/lo.2003.48.1_part_2.0547","article-title":"Determination of water depth with high-resolution satellite imagery over variable bottom types","volume":"48","author":"Stumpf","year":"2003","journal-title":"Limnol. Oceanogr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"16257","DOI":"10.3390\/rs71215829","article-title":"Derivation of High-Resolution Bathymetry from Multispectral Satellite Imagery: A Comparison of Empirical and Optimisation Methods through Geographical Error Analysis","volume":"7","author":"Hamylton","year":"2015","journal-title":"Remote Sens."},{"key":"ref_18","first-page":"373","article-title":"Study on Water Depth Extraction from Remote Sensing Imagery in Jiangsu Coastal Zone","volume":"11","author":"Tian","year":"2007","journal-title":"Natl. Remote Sens. Bull."},{"key":"ref_19","first-page":"55","article-title":"A Technique for Extracting Water Depth Information from Multispectral Scanner Data in the South China Sea","volume":"22","author":"Dang","year":"2003","journal-title":"Mar. Sci. Bull."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1007\/s11769-018-1013-z","article-title":"Comparative Study on Coastal Depth Inversion Based on Multi-source Remote Sensing Data","volume":"29","author":"Lu","year":"2019","journal-title":"Chin. Geogr. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2855","DOI":"10.1080\/01431161.2018.1533660","article-title":"Assessment of empirical algorithms for bathymetry extraction using Sentinel-2 data","volume":"40","author":"Casal","year":"2019","journal-title":"Int. J. Remote Sens."},{"key":"ref_22","first-page":"98","article-title":"Establishment of a RS-Fathoming Correlation Model","volume":"26","author":"Zhang","year":"1998","journal-title":"J. Hohai Univ."},{"key":"ref_23","first-page":"39","article-title":"An underwater bathymetry reversion in the radial sand ridge group region of the southern Huanghai Sea using the remote sensing technology","volume":"31","author":"Zhang","year":"2009","journal-title":"Acta Oceanol. Sin."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.petrol.2018.11.067","article-title":"The linear random forest algorithm and its advantages in machine learning assisted logging regression modeling","volume":"174","author":"Ao","year":"2018","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_25","first-page":"105","article-title":"A Summary of Machine Learning and Related Algorithms","volume":"22","author":"Cheng","year":"2007","journal-title":"Stat. Inf. Forum."},{"key":"ref_26","first-page":"37","article-title":"Study on remote sensing of water depth based on BP artificial neural networks","volume":"23","author":"Wang","year":"2005","journal-title":"Ocean. Eng."},{"key":"ref_27","first-page":"130","article-title":"Multiple kernel support vector regression based on fuzzy membership for remote sensing water depth fusion detection","volume":"37","author":"Wang","year":"2018","journal-title":"Mar. Environ. Sci."},{"key":"ref_28","first-page":"75","article-title":"Satellite-Derived Bathymetry Using Random Forest Model","volume":"34","author":"Qiu","year":"2019","journal-title":"J. Ocean. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2888","DOI":"10.1109\/JSTARS.2020.2993731","article-title":"Convolutional Neural Network to Retrieve Water Depth in Marine Shallow Water Area From Remote Sensing Images","volume":"13","author":"Ai","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhu, W., Ye, L., Qiu, Z., Luan, K., He, N., Wei, Z., Yang, F., Yue, Z., Zhao, S., and Yang, F. (2021). Research of the Dual-Band Log-Linear Analysis Model Based on Physics for Bathymetry without In-Situ Depth Data in the South China Sea. Remote Sens., 13.","DOI":"10.3390\/rs13214331"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1080\/01431169608948714","article-title":"The use of the Normalized Difference Water Index (NDWI) in the delineation of open water features","volume":"17","author":"McFeeters","year":"1996","journal-title":"Int. J. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1080\/01431160500034086","article-title":"Technical note: Simple and robust removal of sun glint for mapping shallow-ater benthos","volume":"26","author":"Hedley","year":"2005","journal-title":"Int. J. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.amc.2008.10.056","article-title":"A note on the Levenberg\u2013Marquardt parameter","volume":"207","author":"Fan","year":"2009","journal-title":"Appl. Math. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"012073","DOI":"10.1088\/1742-6596\/1437\/1\/012073","article-title":"Water Depth Inversion based on Landsat-8 Date and Random Forest Algorithm","volume":"1437","author":"Zhang","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.34133\/2022\/9831947","article-title":"A Portable Algorithm to Retrieve Bottom Depth of Optically Shallow Waters from Top-Of-Atmosphere Measurements","volume":"2022","author":"Lai","year":"2022","journal-title":"J. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_38","first-page":"1580","article-title":"Support Vector Machines for Regression","volume":"11","author":"Du","year":"2003","journal-title":"J. Syst. Simul."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"10875","DOI":"10.1109\/JSTARS.2021.3121446","article-title":"Determination of the initial value ranges of nonlinear solutions for a log ratio bathymetric inversion model and bathymetry retrieval","volume":"14","author":"Qi","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_40","first-page":"2","article-title":"An Overview on Theory and Algorithm of Support Vector Machines","volume":"40","author":"Ding","year":"2011","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"111302","DOI":"10.1016\/j.rse.2019.111302","article-title":"Adaptive bathymetry estimation for shallow coastal waters using Planet Dove satellites","volume":"232","author":"Li","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Sagawa, T., Yamashita, Y., Okumura, T., and Yamanokuchi, T. (2019). Satellite Derived Bathymetry Using Machine Learning and Multi-Temporal Satellite Images. Remote Sens., 11.","DOI":"10.3390\/rs11101155"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/2\/393\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:03:49Z","timestamp":1760119429000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/2\/393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,9]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15020393"],"URL":"https:\/\/doi.org\/10.3390\/rs15020393","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,9]]}}}