{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T06:24:56Z","timestamp":1775024696565,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T00:00:00Z","timestamp":1686873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information Systems","award":["CEMEE2022G0201"],"award-info":[{"award-number":["CEMEE2022G0201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The ionospheric F2 layer is the essential layer in the propagation of high-frequency radio waves, and the peak electron density height of the ionospheric F2 layer (hmF2) is one of the important parameters. To improve the predicted accuracy of hmF2 for further improving the ability of HF skywave propagation prediction and communication frequency selection, we present an interpretable long-term prediction model of hmF2 using the statistical machine learning (SML) method. Taking Moscow station as an example, this method has been tested using the ionospheric observation data from August 2011 to October 2016. Only by inputting sunspot number, month, and universal time into the proposed model can the predicted value of hmF2 be obtained for the corresponding time. Finally, we compare the predicted results of the proposed model with those of the International Reference Ionospheric (IRI) model to verify its stability and reliability. The result shows that, compared with the IRI model, the predicted average statistical RMSE decreased by 5.20 km, and RRMSE decreased by 1.78%. This method is expected to provide ionospheric parameter prediction accuracy on a global scale.<\/jats:p>","DOI":"10.3390\/rs15123154","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T08:56:01Z","timestamp":1686905761000},"page":"3154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Prediction Method of Ionospheric hmF2 Based on Machine Learning"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4361-8946","authenticated-orcid":false,"given":"Jian","family":"Wang","sequence":"first","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"},{"name":"Qingdao Institute for Ocean Technology, Tianjin University, Qingdao 266200, China"},{"name":"Shandong Engineering Technology Research Center of Ocean Information Awareness and Transmission, Qingdao 266200, China"}]},{"given":"Qiao","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"}]},{"given":"Yafei","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"},{"name":"Qingdao Institute for Ocean Technology, Tianjin University, Qingdao 266200, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4173-6060","authenticated-orcid":false,"given":"Cheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"},{"name":"Qingdao Institute for Ocean Technology, Tianjin University, Qingdao 266200, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5264","DOI":"10.1109\/TAP.2013.2275153","article-title":"Estimation of hmF2 and foF2 Communication Parameters of Ionosphere F2-Layer Using GPS Data and IRI-Plas Model","volume":"61","author":"Sezen","year":"2013","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1029\/2018SW002035","article-title":"Assessment of current capabilities in modeling the ionospheric climatology for space weather applications: foF2 and hmF2","volume":"16","author":"Tsagouri","year":"2018","journal-title":"Space Weather"},{"key":"ref_3","unstructured":"ITU (2015). ITU-R P.1240, ITU-R Methods of Basic MUF, Operational MUF and Ray-Path Prediction, ITU."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3321","DOI":"10.1109\/TAP.2013.2249571","article-title":"Prediction of the HF Ionospheric Channel Stability Based on the Modified ITS Model","volume":"61","author":"Yan","year":"2013","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1109\/TAP.2011.2122237","article-title":"The HF Channel EM Parameters Estimation Under a Complex Environment Using the Modified IRI and IGRF Model","volume":"59","author":"Yan","year":"2011","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2106","DOI":"10.1016\/j.asr.2014.10.016","article-title":"Online, automatic, ionospheric maps: IRI-PLAS-MAP","volume":"55","author":"Arikan","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1029\/RS025i005p00757","article-title":"Modeling the F2 layer peak height in terms of atmospheric pressure","volume":"25","author":"Rishbeth","year":"1990","journal-title":"Radio Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LGRS.2020.3045702","article-title":"A Bidirectional Long Short-Term Memory-Based Ionospheric foF2 and hmF2 Models for a Single Station in the Low Latitude Region","volume":"19","author":"Rao","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1109\/LGRS.2020.3007362","article-title":"Testing of the Method Retrieving a Consistent Set of Aeronomic Parameters with Millstone Hill ISR Noontime hmF2 Observations","volume":"18","author":"Perrone","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"860","DOI":"10.3390\/rs14040860","article-title":"Evaluation of foF2 and hmF2 Parameters of IRI-2016 Model in Different Latitudes over China under High and Low Solar Activity Years","volume":"14","author":"Zhang","year":"2022","journal-title":"Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, J., Shi, Y., and Yang, C. (2022). Investigation of Two Prediction Models of Maximum Usable Frequency for HF Communication Based on Oblique- and Vertical-Incidence Sounding Data. Atmosphere, 13.","DOI":"10.3390\/atmos13071122"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1007\/s00190-010-0427-x","article-title":"The international reference ionosphere today and in the future","volume":"85","author":"Bilitza","year":"2011","journal-title":"J. Geod."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3203","DOI":"10.5194\/angeo-27-3203-2009","article-title":"A global model of the ionospheric F2 peak height based on EOF analysis","volume":"27","author":"Zhang","year":"2009","journal-title":"Ann. Geophys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1016\/j.asr.2010.06.004","article-title":"Evaluation of global modeling of M(3000)F2 and hmF2 based on alternative empirical orthogonal function expansions","volume":"46","author":"Zhang","year":"2010","journal-title":"Adv. Space Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1002\/2014SW001159","article-title":"Modeling Chinese ionospheric layer parameters based on EOF analysis","volume":"13","author":"Yu","year":"2015","journal-title":"Space Weather"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9015","DOI":"10.1002\/2017JA024398","article-title":"The Empirical Canadian High Arctic Ionospheric Model (E-CHAIM): NmF2 and hmF2","volume":"122","author":"Themens","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_17","first-page":"11743","article-title":"An Artificial Neural Network based Ionospheric Model to predict NmF2 and hmF2 using long-term data set of FORMOSAT-3\/COSMIC radio occultation observations: Preliminary results","volume":"122","author":"Sai","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5807","DOI":"10.1029\/2018JA025559","article-title":"The improved two-dimensional artificial neural network-based ionospheric model (ANNIM)","volume":"123","author":"Tulasi","year":"2018","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, W., Zhao, D., He, C., Hu, A., and Zhang, K. (2020). Advanced Machine Learning Optimized by The Genetic Algorithm in Ionospheric Models Using Long-Term Multi-Instrument Observations. Remote Sens., 12.","DOI":"10.3390\/rs12050866"},{"key":"ref_20","first-page":"2","article-title":"Model Selection for Optimal Prediction in Statistical Machine Learning","volume":"67","year":"2020","journal-title":"Not. Am. Math. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4040","DOI":"10.1109\/TAP.2021.3111634","article-title":"Regional Refined Long-term Predictions Method of Usable Frequency for HF Communication Based on Machine Learning over Asia","volume":"70","author":"Wang","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, J., Yu, Q., Shi, Y., Liu, Y., and Yang, C. (2023). An Explainable Dynamic Prediction Method for Ionospheric foF2 Based on Machine Learning. Remote Sens., 15.","DOI":"10.3390\/rs15051256"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1928","DOI":"10.1002\/grl.50448","article-title":"Annual\/semiannual variation of the ionosphere","volume":"40","author":"Qian","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","unstructured":"Zhou, Z.H. (2016). Machine Learning, Tsinghua University Press. [2nd ed.]."},{"key":"ref_25","unstructured":"(2022, October 28). National Oceanic and Atmospheric Administration (NOAA), Available online: https:\/\/www.ngdc.noaa.gov\/stp\/space-weather\/solar-data\/."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"335","DOI":"10.5194\/angeo-26-335-2008","article-title":"Global electron content: A new conception to track solar activity","volume":"26","author":"Afraimovich","year":"2008","journal-title":"Ann. Geophys."},{"key":"ref_27","unstructured":"(2022, October 28). Sunspot Number. Available online: https:\/\/www.sidc.be\/silso\/datafiles."},{"key":"ref_28","unstructured":"(2022, April 27). Data of Hydrogen Emission at 121.6 nm. Available online: https:\/\/lasp.colorado.edu\/lisird\/composite_timeseries.html."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/swe.20064","article-title":"The 10.7cm solar radio flux (F10.7)","volume":"11","author":"Tapping","year":"2013","journal-title":"Space Weather"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6524","DOI":"10.1002\/jgra.50561","article-title":"The anomalous ionosphere between solar cycles 23 and 24","volume":"118","author":"Solomon","year":"2013","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_31","unstructured":"Bai, H.M. (2022). Ionospheric Model Research Based on Intelligent Information Processing Technology, Tianjin University."},{"key":"ref_32","unstructured":"Sun, W. (2015). Study on Regional Ionospheric Characteristics Based on Ground-Based GPS and Occultation Technology, Wuhan University."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"850","DOI":"10.54097\/hset.v38i.5969","article-title":"Comparison of Different Detection Scenarios of Lyman-\u03b1","volume":"Volume 38","author":"Zeng","year":"2023","journal-title":"Highlights in Science, Engineering and Technology"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jastp.2016.08.003","article-title":"foF2 vs solar indices for the Rome station: Looking for the best general relation which is able to describe the anomalous minimum between cycles 23 and 24","volume":"148","author":"Perna","year":"2016","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2036","DOI":"10.1016\/j.asr.2020.01.026","article-title":"A regional model for the prediction of M(3000)F2 over East Asia","volume":"65","author":"Wang","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_36","unstructured":"(2022, April 18). International Reference Ionosphere. Available online: http:\/\/IRImodel.org\/IRI-2016."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3154\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:56:40Z","timestamp":1760126200000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3154"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,16]]},"references-count":36,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["rs15123154"],"URL":"https:\/\/doi.org\/10.3390\/rs15123154","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,16]]}}}