{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T06:31:30Z","timestamp":1772605890269,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,3,7]],"date-time":"2020-03-07T00:00:00Z","timestamp":1583539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The ionospheric delay is of paramount importance to radio communication, satellite navigation and positioning. It is necessary to predict high-accuracy ionospheric peak parameters for single frequency receivers. In this study, the state-of-the-art artificial neural network (ANN) technique optimized by the genetic algorithm is used to develop global ionospheric models for predicting foF2 and hmF2. The models are based on long-term multiple measurements including ionospheric peak frequency model (GIPFM) and global ionospheric peak height model (GIPHM). Predictions of the GIPFM and GIPHM are compared with the International Reference Ionosphere (IRI) model in 2009 and 2013 respectively. This comparison shows that the root-mean-square errors (RMSEs) of GIPFM are 0.82 MHz and 0.71 MHz in 2013 and 2009, respectively. This result is about 20%\u201335% lower than that of IRI. Additionally, the corresponding hmF2 median errors of GIPHM are 20% to 30% smaller than that of IRI. Furthermore, the ANN models present a good capability to capture the global or regional ionospheric spatial-temporal characteristics, e.g., the equatorial ionization anomaly and Weddell Sea anomaly. The study shows that the ANN-based model has a better agreement to reference value than the IRI model, not only along the Greenwich meridian, but also on a global scale. The approach proposed in this study has the potential to be a new three-dimensional electron density model combined with the inclusion of the upcoming Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC-2) data.<\/jats:p>","DOI":"10.3390\/rs12050866","type":"journal-article","created":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T05:37:34Z","timestamp":1583732254000},"page":"866","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Advanced Machine Learning Optimized by The Genetic Algorithm in Ionospheric Models Using Long-Term Multi-Instrument Observations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6526-1509","authenticated-orcid":false,"given":"Wang","family":"Li","sequence":"first","affiliation":[{"name":"School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"SPACE Research Center, School of Science, RMIT University, Melbourne 3001, Australia"}]},{"given":"Dongsheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Changyong","family":"He","sequence":"additional","affiliation":[{"name":"SPACE Research Center, School of Science, RMIT University, Melbourne 3001, Australia"},{"name":"IGN, ENSG, Cit\u00e9 Descartes, Champs-sur-Marne, 77455 Marne la Vall\u00e9e, France"}]},{"given":"Andong","family":"Hu","sequence":"additional","affiliation":[{"name":"SPACE Research Center, School of Science, RMIT University, Melbourne 3001, Australia"},{"name":"Multi-scale Group, Centrum Wiskunde &amp; Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands"}]},{"given":"Kefei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"SPACE Research Center, School of Science, RMIT University, Melbourne 3001, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9183","DOI":"10.1002\/2017JA024464","article-title":"A neural network model of three-dimensional dynamic electron density in the inner magnetosphere","volume":"122","author":"Chu","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2934","DOI":"10.1016\/j.asr.2017.03.023","article-title":"A comparison of neural network-based predictions of foF2 with the IRI-2012 model at conjugate points in southeast asia","volume":"59","author":"Wichaipanich","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1002\/2016RS006192","article-title":"A neural network-based foF2 model for a single station in the polar cap","volume":"52","author":"Athieno","year":"2017","journal-title":"Radio Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.1029\/1999RS900070","article-title":"Temporal and spatial forecasting of ionospheric critical frequency using neural networks","volume":"34","author":"Kumluca","year":"1999","journal-title":"Radio Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Yue, X., Wan, W., Liu, L., Ning, B., and Zhao, B. (2006). Applying artificial neural network to derive long-term foF2 trends in the Asia\/Pacific sector from ionosonde observations. J. Geophys. Res. Space Phys., 111.","DOI":"10.1029\/2005JA011577"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hoque, M., and Jakowski, N. (2012). A new global model for the ionospheric F2 peak height for radio wave propagation. Annales Geophysicae, Copernicus GmbH.","DOI":"10.5194\/angeo-30-797-2012"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.asr.2013.12.001","article-title":"A prediction model of short-term ionospheric foF2 based on AdaBoost","volume":"53","author":"Zhao","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1016\/j.jastp.2006.07.002","article-title":"Near-real time foF2 predictions using neural networks","volume":"68","author":"Oyeyemi","year":"2006","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11141-005-0043-4","article-title":"Artificial neural network technique for predicting the critical frequency of the ionospheric F 2 layer","volume":"48","author":"Barkhatov","year":"2005","journal-title":"Radiophys. Quantum Electron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.jastp.2012.09.010","article-title":"Predicting foF2 in the China region using the neural networks improved by the genetic algorithm","volume":"92","author":"Wang","year":"2013","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3659","DOI":"10.1029\/96GL03472","article-title":"Neural networks, foF2, sunspot number and magnetic activity","volume":"23","author":"Williscroft","year":"1996","journal-title":"Geophys. Res. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1016\/j.asr.2010.06.003","article-title":"Equatorial predictions from a new neural network based global foF2 model","volume":"46","author":"McKinnell","year":"2010","journal-title":"Adv. Space Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"477","DOI":"10.5194\/npg-9-477-2002","article-title":"Neural-network-based prediction techniques for single station modeling and regional mapping of the foF2 and M (3000) F2 ionospheric characteristics","volume":"9","author":"Xenos","year":"2002","journal-title":"Nonlinear Process. Geophys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1016\/j.jastp.2007.05.003","article-title":"A neural network-based ionospheric model for the auroral zone","volume":"69","author":"McKinnell","year":"2007","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Oyeyemi, E., Poole, A., and McKinnell, L. (2005). On the global model for foF2 using neural networks. Radio Sci., 40.","DOI":"10.1029\/2004RS003223"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, J.-Y., Lin, C., Lin, C., Tsai, H., Solomon, S., Sun, Y., Lee, I., Schreiner, W., and Kuo, Y. (2010). Artificial plasma cave in the low-latitude ionosphere results from the radio occultation inversion of the FORMOSAT-3\/COSMIC. J. Geophys. Res. Space Phys., 115.","DOI":"10.1029\/2009JA015079"},{"key":"ref_17","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":"Mitra","year":"2018","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s00190-011-0481-z","article-title":"Ionospheric electron density observed by FORMOSAT-3\/COSMIC over the European region and validated by ionosonde data","volume":"85","author":"Krankowski","year":"2011","journal-title":"J. Geod."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.asr.2014.07.015","article-title":"Validation of COSMIC values of foF2 and M (3000) F2 using ground-based ionosondes","volume":"55","author":"McNamara","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1016\/j.asr.2011.12.029","article-title":"Radio occultation electron density profiles from the FORMOSAT-3\/COSMIC satellites over the Brazilian region: A comparison with Digisonde data","volume":"49","author":"Ely","year":"2012","journal-title":"Adv. Space Res."},{"key":"ref_21","first-page":"3625","article-title":"Comparison between ionospheric character parameters retrieved from FORMOSAT3 measurement and ionosonde observation over China","volume":"57","author":"Sun","year":"2014","journal-title":"Chin. J. Geophys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2011RS004807","article-title":"A new global empirical NmF2 model for operational use in radio systems","volume":"46","author":"Hoque","year":"2011","journal-title":"Radio Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bilitza, D., Reinisch, B.W., Radicella, S.M., Pulinets, S., Gulyaeva, T., and Triskova, L. (2006). Improvements of the International Reference Ionosphere model for the topside electron density profile. Radio Sci., 41.","DOI":"10.1029\/2005RS003370"},{"key":"ref_24","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":"Gowtam","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.asr.2009.10.014","article-title":"A global survey of COSMIC ionospheric peak electron density and its height: A comparison with ground-based ionosonde measurements","volume":"46","author":"Chu","year":"2010","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1016\/j.asr.2014.05.012","article-title":"Comparison between ionospheric peak parameters retrieved from COSMIC measurement and ionosonde observation over Sanya","volume":"54","author":"Hu","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lei, J., Syndergaard, S., Burns, A.G., Solomon, S.C., Wang, W., Zeng, Z., Roble, R.G., Wu, Q., Kuo, Y.H., and Holt, J.M. (2007). Comparison of COSMIC ionospheric measurements with ground-based observations and model predictions: Preliminary results. J. Geophys. Res. Space Phys., 112.","DOI":"10.1029\/2006JA012240"},{"key":"ref_28","unstructured":"Haykin, S. (1994). Neural Networks: A Comprehensive Foundation, Prentice Hall."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.asr.2016.04.029","article-title":"Regional application of multi-layer artificial neural networks in 3-D ionosphere tomography","volume":"58","author":"Razin","year":"2016","journal-title":"Adv. Space Res."},{"key":"ref_30","unstructured":"Montana, D.J., and Davis, L. (1989, January 20\u201325). Training Feedforward Neural Networks Using Genetic Algorithms. Proceedings of the IJCAI, Detroit, MI, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.asr.2018.03.043","article-title":"Predicting TEC in China based on the neural networks optimized by genetic algorithm","volume":"62","author":"Song","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/j.asr.2010.10.025","article-title":"Storm time behavior of topside scale height inferred from the ionosphere\u2013plasmasphere model driven by the F2 layer peak and GPS-TEC observations","volume":"47","author":"Gulyaeva","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"8865","DOI":"10.1029\/2018JA025700","article-title":"Ionospheric and Thermospheric Responses to the Recent Strong Solar Flares on 6 September 2017","volume":"123","author":"Li","year":"2018","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10291-018-0722-1","article-title":"Ionospheric responses to typhoons in Australia during 2005\u20132014 using GNSS and FORMOSAT-3\/COSMIC measurements","volume":"22","author":"Li","year":"2018","journal-title":"GPS Solut."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1016\/j.asr.2017.12.013","article-title":"Statistical seismo-ionospheric precursors of M7. 0+ earthquakes in Circum-Pacific seismic belt by GPS TEC measurements","volume":"61","author":"Li","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3319\/TAO.2018.07.09.03","article-title":"Analysis of the melting glaciers in Southeast Tibet by ALOS-PALSAR data","volume":"30","author":"Du","year":"2019","journal-title":"Terr. Atmos. Ocean. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1002\/2014SW001133","article-title":"Space weather observations by GNSS radio occultation: From FORMOSAT-3\/COSMIC to FORMOSAT-7\/COSMIC-2","volume":"12","author":"Yue","year":"2014","journal-title":"Space Weather"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/5\/866\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:05:10Z","timestamp":1760173510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/5\/866"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,7]]},"references-count":37,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["rs12050866"],"URL":"https:\/\/doi.org\/10.3390\/rs12050866","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,7]]}}}