{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T12:52:35Z","timestamp":1774443155293,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T00:00:00Z","timestamp":1774396800000},"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":["42075001"],"award-info":[{"award-number":["42075001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The inhomogeneity of the evaporation duct significantly influences electromagnetic propagation. Based on observation data from four buoy stations in the northern South China Sea (SCS) and European Centre for Medium-Range Weather Forecasts (ECMWF) data, the Naval Postgraduate School (NPS) model is employed to calculate the evaporation duct height (EDH). The concept of information entropy is used to assess the horizontal inhomogeneity of the evaporation duct and the evaporation duct height entropy (EDHE) is defined as the assessment index. The research findings are as follows: (1) The probability of EDH differences based on statistical methods between stations falling within the range of \u22122 m to 2 m remains above 60%, with uniformity characteristics showing minimal variation throughout the day. (2) The EDHE can better quantify the horizontal inhomogeneous characteristics of EDH between buoy stations compared to statistical methods. (3) The monthly variation characteristics of EDHE between buoy stations based on ECMWF reanalysis data are quite consistent with actual observations, but it overestimates the EDHE values. Therefore, the EDH derived from ECMWF data leads to an overestimation of inhomogeneity characteristics compared to buoy observations.<\/jats:p>","DOI":"10.3390\/e28040368","type":"journal-article","created":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:07:13Z","timestamp":1774433233000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Inhomogeneous Characteristics of Evaporation Ducts in the Northern South China Sea Based on Information Entropy"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4072-892X","authenticated-orcid":false,"given":"Ning","family":"Yang","sequence":"first","affiliation":[{"name":"College of Electronic Engineering, Chengdu University of Information Technology, Chengdu 610225, China"},{"name":"Key Laboratory of Atmospheric Sounding, China Meteorological Administration, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debin","family":"Su","sequence":"additional","affiliation":[{"name":"College of Electronic Engineering, Chengdu University of Information Technology, Chengdu 610225, China"},{"name":"Key Laboratory of Atmospheric Sounding, China Meteorological Administration, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuduo","family":"Feng","sequence":"additional","affiliation":[{"name":"College of Electronic Engineering, Chengdu University of Information Technology, Chengdu 610225, China"},{"name":"Key Laboratory of Atmospheric Sounding, China Meteorological Administration, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3485","DOI":"10.1109\/TAP.2023.3240998","article-title":"Prediction of Over-the-Horizon Electromagnetic Wave Propagation in Evaporation Ducts Based on the Gated Recurrent Unit Network Model","volume":"71","author":"Wang","year":"2023","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1007\/s13351-015-4127-6","article-title":"A New Evaporation Duct Climatology over the South China Sea","volume":"29","author":"Shi","year":"2015","journal-title":"J. Meteorol. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1306","DOI":"10.1109\/LAWP.2023.3241159","article-title":"Comparison of Evaporation Duct Height Statistics Based on Surface Bulk Measurements Over Yongxing Island","volume":"22","author":"Zhao","year":"2023","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10865","DOI":"10.1109\/TAP.2022.3191160","article-title":"The Diurnal Variation of the Evaporation Duct Height and Its Relationship with Environmental Variables in the South China Sea","volume":"70","author":"Huang","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1175\/BAMS-D-16-0046.1","article-title":"CASPER: Coupled Air\u2013Sea Processes and Electromagnetic Ducting Research","volume":"99","author":"Wang","year":"2018","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/LAWP.2022.3153389","article-title":"Observations of Anomalous Over-the-Horizon Propagation in the Evaporation Duct Induced by Typhoon Kompasu (202118)","volume":"21","author":"Wang","year":"2022","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5322","DOI":"10.1109\/TAP.2023.3263212","article-title":"Observed Over-the-Horizon Propagation Characteristics and Evaporation Duct Inversion During the Entire Process of Tropical Cyclone Mulan (202207)","volume":"71","author":"Wang","year":"2023","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1109\/TAP.2021.3090828","article-title":"Frequency Diversity in Electromagnetic Remote Sensing of Lower Atmospheric Refractivity","volume":"70","author":"Xu","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/MCOM.002.00508","article-title":"Long-Range Microwave Links Guided by Evaporation Ducts","volume":"60","author":"Ma","year":"2022","journal-title":"IEEE Commun. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2674","DOI":"10.1109\/TAP.2022.3209664","article-title":"Measurements and Analysis of Maritime Wireless Channel at 8 GHz in the South China Sea Region","volume":"71","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/MCOM.2014.6917399","article-title":"Beyond-line-of-sight Communications with Ducting Layer","volume":"52","author":"Dinc","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"E2286","DOI":"10.1175\/BAMS-D-23-0113.1","article-title":"Anomalous Propagation and the Sinking of the Russian Warship Moskva","volume":"104","author":"Norin","year":"2023","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ippolito, L.J. (2017). Introduction to Satellite Communications. Satellite Communications Systems Engineering: Atmospheric Effects, Satellite Link Design and System Performance, John Wiley & Sons Ltd.","DOI":"10.1002\/9781119259411"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/COMST.2020.3028247","article-title":"Satellite Communications in the New Space Era: A Survey and Future Challenges","volume":"23","author":"Kodheli","year":"2021","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Majumdar, A.K. (2022). Basics of Satellite Wireless Communications: Single Satellite and a Constellation of Satellites. Laser Communication with Constellation Satellites, UAVs, HAPs and Balloons: Fundamentals and Systems Analysis for Global Connectivity, Springer International Publishing.","DOI":"10.1007\/978-3-031-03972-0"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6948","DOI":"10.3390\/s100706948","article-title":"Wireless Sensor Networks for Oceanographic Monitoring: A Systematic Review","volume":"10","author":"Albaladejo","year":"2010","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Xu, G., Shi, Y., Sun, X., and Shen, W. (2019). Internet of Things in Marine Environment Monitoring: A Review. Sensors, 19.","DOI":"10.3390\/s19071711"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"RS0F01","DOI":"10.1029\/2011RS004818","article-title":"Refractivity estimation from sea clutter: An invited review","volume":"46","author":"Karimian","year":"2011","journal-title":"Radio Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Huang, L., Liu, C., Wang, H., Zhu, Q., Zhang, L., Han, J., Zhang, Y., and Wang, Q. (2022). Experimental Analysis of Atmospheric Ducts and Navigation Radar Over-the-Horizon Detection. Remote Sens., 14.","DOI":"10.3390\/rs14112588"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.23919\/JCIN.2021.9475120","article-title":"Atmospheric Ducting Effect in Wireless Communications: Challenges and Opportunities","volume":"6","author":"Liu","year":"2021","journal-title":"J. Commun. Inf. Netw."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Rosson, P., Estavoyer, J., Lombard, L., Miscopein, B., Popon, X., Dore, J., Ktenas, D., Coquen, V., and Jegou-Le Bris, R. (October, January 27). Long-range broadband wireless system for maritime communications in the 3.5 GHz band. Proceedings of the 2021 IEEE 94th Vehicular Technology Conference (VTC2021-Fall), Virtual.","DOI":"10.1109\/VTC2021-Fall52928.2021.9625164"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10228","DOI":"10.1109\/TVT.2022.3187753","article-title":"Statistical Modeling of Evaporation Duct Channel for Maritime Broadband Communications","volume":"71","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1109\/LAWP.2021.3136044","article-title":"Exploration of X-Band Communication for Maritime Applications in the South China Sea","volume":"21","author":"Yang","year":"2022","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4677","DOI":"10.1007\/s11276-021-02730-y","article-title":"Simulation of the effects of evaporation ducts on maritime wireless communication","volume":"27","author":"Cruz","year":"2021","journal-title":"Wirel. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1175\/1520-0450(1997)036<0193:ANMOTO>2.0.CO;2","article-title":"A New Model of the Oceanic Evaporation Duct","volume":"36","author":"Babin","year":"1997","journal-title":"J. Appl. Meteorol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1029\/2000GL012751","article-title":"Air-sea Interaction and Spatial Variability of the Surface Evaporation Duct in a Coastal Environment","volume":"28","author":"Brooks","year":"2001","journal-title":"Geophys. Res. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"044102","DOI":"10.1088\/1674-1056\/24\/4\/044102","article-title":"Experimental Verification of Effect of Horizontal Inhomogeneity of Evaporation Duct on Electromagnetic Wave Propagation","volume":"24","author":"Shi","year":"2015","journal-title":"Chin. Phys. B"},{"key":"ref_28","first-page":"210","article-title":"Electromagnetic Wave Propagation Simulation in Horizontally Inhomogeneous Evaporation Duct","volume":"Volume 645","author":"Shi","year":"2016","journal-title":"2016 Asian Simulation Conference SCS Autumn Simulation Multi-Conference"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1007\/978-3-642-21697-8_117","article-title":"Study on the Propagation Characteristics of Electromagnetic Waves in Horizontally Inhomogeneous Environment","volume":"Volume 97","author":"Wang","year":"2011","journal-title":"Lecture Notes in Electrical Engineering; Lecture Notes in Electrical Engineering"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, N., Zou, X., Sun, L., Su, D., and Wang, T. (2023). The non-uniformity characteristics of the evaporation duct in the South China Sea based on CLDAS data. Front. Mar. Sci., 10.","DOI":"10.3389\/fmars.2023.1326975"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"29792","DOI":"10.3402\/tellusa.v68.29792","article-title":"Spatial and Temporal Variability of the Evaporation Duct in the Gulf of Aden","volume":"68","author":"Zhang","year":"2016","journal-title":"Tellus A Dyn. Meteorol. Oceanogr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s13131-016-0903-0","article-title":"On Analyzing Space-time Distribution of Evaporation Duct Height over the Global Ocean","volume":"35","author":"Yang","year":"2016","journal-title":"Acta Oceanol. Sin."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Yang, N., Su, D., and Wang, T. (2023). Atmospheric Ducts and Their Electromagnetic Propagation Characteristics in the Northwestern South China Sea. Remote Sens., 15.","DOI":"10.20944\/preprints202305.0604.v1"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"e2022RS007456","DOI":"10.1029\/2021RS007345","article-title":"Refractivity Inversions from Point-To-Point X-Band Radar Propagation Measurements","volume":"57","author":"Pastore","year":"2022","journal-title":"Radio Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.1109\/TAP.2018.2814060","article-title":"X-Band Beacon-Receiver Array Evaporation Duct Height Estimation","volume":"66","author":"Pozderac","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1002\/2014RS005642","article-title":"Evaluation of simplified evaporation duct refractivity models for inversion problems","volume":"50","author":"Saeger","year":"2015","journal-title":"Radio Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7916","DOI":"10.1109\/TAP.2024.3438360","article-title":"The Horizontal Inhomogeneity of the Evaporation Duct Based on Surface Bulk Measurements Over the South China Sea","volume":"72","author":"Yang","year":"2024","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","article-title":"The ERA5 global reanalysis","volume":"146","author":"Hersbach","year":"2020","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1175\/JCLI-D-12-00823.1","article-title":"The NCEP Climate Forecast System Version 2","volume":"27","author":"Saha","year":"2014","journal-title":"J. Clim."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107454","DOI":"10.1016\/j.cpc.2020.107454","article-title":"PETOOL v2.0: Parabolic Equation Toolbox with Evaporation Duct Models and Real Environment Data","volume":"256","author":"Ozgun","year":"2020","journal-title":"Comput. Phys. Commun."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1007\/s11802-019-3971-x","article-title":"A Comparison Study of Sensitivity on PJ and NPS Models in China Seas","volume":"18","author":"Guo","year":"2019","journal-title":"J. Ocean Univ. China"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF00120756","article-title":"Potential refractivity as a similarity variable","volume":"58","author":"Cook","year":"1992","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1134\/S0001433807010045","article-title":"Determination of the Evaporation Duct Height from Standard Meteorological Data","volume":"43","author":"Ivanov","year":"2007","journal-title":"Izv. Atmos. Ocean. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10546-007-9177-6","article-title":"SHEBA Flux\u2013profile Relationships in the Stable Atmospheric Boundary Layer","volume":"124","author":"Grachev","year":"2007","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"109111","DOI":"10.1109\/ACCESS.2019.2932969","article-title":"Impact of Typhoon on Evaporation Duct in the Northwest Pacific Ocean","volume":"7","author":"Shi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_46","first-page":"379","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Acta Ecol. Sin."},{"key":"ref_47","first-page":"4444","article-title":"Information entropy-based analysis of spatial and temporal variation in precipitation in Xinjiang","volume":"37","author":"Huang","year":"2017","journal-title":"Bell Syst. Tech. J."},{"key":"ref_48","first-page":"1071","article-title":"Stochastic characteristics of daily precipitation and its spatiotemporal difference over China based on information entropy","volume":"29","author":"Li","year":"2018","journal-title":"Chin. J. Appl. Ecol."},{"key":"ref_49","first-page":"26","article-title":"Spatio-temporal changes of precipitation in Chengdu from 1980 to 2016 based on Mann\u2013Kendall test and information entropy","volume":"17","author":"Wang","year":"2019","journal-title":"Sci. Soil Water Conserv."},{"key":"ref_50","first-page":"119201","article-title":"Spatiotemporal analysis of information entropy of the global temperature","volume":"60","author":"Feng","year":"2011","journal-title":"Acta Phys. Sin."},{"key":"ref_51","first-page":"37","article-title":"CORA Data-Based Analysis of Sea-Surface Temperature Field Variation in the South China Sea","volume":"37","author":"Wu","year":"2018","journal-title":"J. Ocean Technol."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"8591","DOI":"10.1002\/joc.7749","article-title":"Information entropy-based projection of temperature variability under the warming trend in China","volume":"42","author":"Sun","year":"2022","journal-title":"Int. J. Climatol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1175\/JTECH-D-23-0111.1","article-title":"Lower Atmospheric Ducts over the South China Sea Related to the Monsoon, Atmospheric, and Ocean Conditions Based on ECMWF Reanalysis Data","volume":"41","author":"Yang","year":"2024","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_54","first-page":"59","article-title":"Statistical analysis of the impact of cold air on the daily variation of the South China Sea","volume":"18","author":"Yang","year":"2001","journal-title":"Mar. Forecast."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"270","DOI":"10.2112\/SI99-039.1","article-title":"Validation of 558 Evaporation Duct Model in Coastal Regions with ASIT Data","volume":"99","author":"Ding","year":"2020","journal-title":"J. Coast. Res."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Yang, S., Li, X., Wu, C., He, X., and Zhong, Y. (2017). Application of the PJ and NPS Evaporation Duct Models Over the South China Sea (SCS) in Winter. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0172284"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Wang, Q., Li, X., Li, H., Yang, S., Yang, S., Ma, L., and Zhao, J. (2022). A Novel System for the Measurement of an Evaporation Duct Using the Magnetic Coupling Principle for Power Feeding and Data Transmission. Sensors, 22.","DOI":"10.3390\/s22197376"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Yang, F., Yang, K., Shi, Y., Wang, S., Zhang, H., and Zhao, Y. (2022). The Effects of Rainfall on Over-the-Horizon Propagation in the Evaporation Duct over the South China Sea. Remote Sens., 14.","DOI":"10.3390\/rs14194787"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/4\/368\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:12:53Z","timestamp":1774433573000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/4\/368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,25]]},"references-count":58,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["e28040368"],"URL":"https:\/\/doi.org\/10.3390\/e28040368","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,25]]}}}