{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T16:35:07Z","timestamp":1771605307637,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T00:00:00Z","timestamp":1586822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Plan","award":["2016YFA0202200"],"award-info":[{"award-number":["2016YFA0202200"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61504092"],"award-info":[{"award-number":["61504092"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Tianjin Research Program of Application Foundation and Advanced Technology","award":["15JCQNJC01200"],"award-info":[{"award-number":["15JCQNJC01200"]}]},{"name":"National 973 Program of China","award":["61331901"],"award-info":[{"award-number":["61331901"]}]},{"name":"AoShan Talents outstanding scientist Program Supported by pilot Qingdao National Laboratory for Marine Science and Technology","award":["2017ASTCP-OS03"],"award-info":[{"award-number":["2017ASTCP-OS03"]}]},{"DOI":"10.13039\/501100010954","name":"Qingdao National Laboratory for Marine Science and Technology","doi-asserted-by":"publisher","award":["QNLM2016ORP0411"],"award-info":[{"award-number":["QNLM2016ORP0411"]}],"id":[{"id":"10.13039\/501100010954","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is critically meaningful to accurately predict the ionospheric F2 layer critical frequency (foF2), which greatly limits the efficiency of communications, radar, and navigation systems. This paper introduced the entropy weight method to develop the combination prediction model (CPM) for long-term foF2 at Darwin (12.4\u00b0 S, 131.5\u00b0 E) in Australia. The weight coefficient of each individual model in the CPM is determined by using the entropy weight method after completing the simulation of the individual model in the calibration period. We analyzed two sets of data to validate the method used in this study: One set is from 2000 and 2009, which are included in the calibration period (1998\u20132016), and the other set is outside the calibration cycle (from 1997 and 2017). To examine the performance, the root mean square error (RMSE) of the observed monthly median foF2 value, the proposed CPM, the Union Radio Scientifique Internationale (URSI), and the International Radio Consultative Committee (CCIR) are compared. The yearly RMSE average values calculated from CPM were less than those calculated from URSI and CCIR in 1997, 2000, 2009, and 2017. In 2000 and 2009, the average percentage improvement between CPM and URSI is 9.01%, and the average percentage improvement between CPM and CCIR is 13.04%. Beyond the calibration period, the average percentage improvement between CPM and URSI is 13.2%, and the average percentage improvement between CPM and CCIR is 12.6%. The prediction results demonstrated that the proposed CPM has higher precision of prediction and stability than that of the URSI and CCIR, both within the calibration period and outside the calibration period.<\/jats:p>","DOI":"10.3390\/e22040442","type":"journal-article","created":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T04:01:46Z","timestamp":1586923306000},"page":"442","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A Combination Prediction Model of Long-Term Ionospheric foF2 Based on Entropy Weight Method"],"prefix":"10.3390","volume":"22","author":[{"given":"Hongmei","family":"Bai","sequence":"first","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"},{"name":"School of Mathematics and Statistics, Hulunbuir College, Hulunbuir 021008, China"},{"name":"Tianjin Key Laboratory of Imaging and Sensing Microelectronic Technology, Tianjin University, Tianjin 300072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3569-8782","authenticated-orcid":false,"given":"Feng","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Electronics, Carleton University, Ottawa, ON K1S 5B6, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4361-8946","authenticated-orcid":false,"given":"Jian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"},{"name":"Qingdao Institute for Ocean Technology, Tianjin University, Qingdao 266237, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5743-0760","authenticated-orcid":false,"given":"Taosuo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Tianjin University, Tianjin 300072, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, J., Bai, H., Huang, X., Cao, Y., Chen, Q., and Ma, J. (2019). Simplified Regional Prediction Model of Long-Term Trend for Critical Frequency of Ionospheric F2 Region over East Asia. Appl. Sci., 9.","DOI":"10.3390\/app9163219"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1029\/2019RS006856","article-title":"Modeling of the ionospheric critical frequency of the F2 layer over Asia based on modified temporal-spatial reconstruction","volume":"54","author":"Wang","year":"2019","journal-title":"Radio Sci."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1029\/2018RS006622","article-title":"A prediction model of ionospheric foF2 based on extreme learning machine","volume":"53","author":"Bai","year":"2018","journal-title":"Radio Sci."},{"key":"ref_5","first-page":"395","article-title":"Twenty-four hour predictions of foF2 using time delay neural networks","volume":"35","author":"Wintoft","year":"2000","journal-title":"Radio Sci."},{"key":"ref_6","unstructured":"Rawer, K., Lincoln, J.V., and Conkright, R.O. (1981). International Reference Ionosphere\u2014IRI 79, World Data Center A for Solar-Terrestrial Physics. Report UAG-82."},{"key":"ref_7","unstructured":"Bilitza, D. (1990). International Reference Ionosphere: IRI-90, National Space Science Data Center."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1029\/2000RS002432","article-title":"International Reference Ionosphere 2000","volume":"36","author":"Bilitza","year":"2001","journal-title":"Radio Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.asr.2007.07.048","article-title":"International reference ionosphere 2007: Improvements and new parameters","volume":"42","author":"Bilitza","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"A07","DOI":"10.1051\/swsc\/2014004","article-title":"The International Reference Ionosphere 2012\u2014A model of international collaboration","volume":"4","author":"Bilitza","year":"2014","journal-title":"J. Space Weather Spac."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1002\/2016SW001593","article-title":"International Reference Ionosphere 2016: From ionospheric climate to real-time weather predictions","volume":"15","author":"Bilitza","year":"2017","journal-title":"Space Weather"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5194\/ars-16-1-2018","article-title":"IRI the International Standard for the Ionosphere","volume":"16","author":"Bilitza","year":"2018","journal-title":"Adv. Radio Sci."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1029\/1999RS900105","article-title":"On the predictability of foF2 using neural networks","volume":"35","author":"Poole","year":"2000","journal-title":"Radio Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1966","DOI":"10.1016\/j.asr.2004.06.010","article-title":"Towards the development of a new global foF2 empirical model using neural networks","volume":"34","author":"Oyeyemi","year":"2004","journal-title":"Adv. Space Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2004RS003223","article-title":"On the global model for foF2 using neural networks","volume":"40","author":"Oyeyemi","year":"2005","journal-title":"Radio Sci."},{"key":"ref_17","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_18","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/j.asr.2007.10.031","article-title":"A new global F2 peak electron density model for the International Reference Ionosphere (IRI)","volume":"42","author":"Oyeyemi","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2010RS004633","article-title":"Forecasting of low-latitude storm-time ionospheric foF2 using support vector machine","volume":"46","author":"Ban","year":"2011","journal-title":"Radio Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/j.jastp.2010.09.022","article-title":"Forecasting the ionospheric foF2, parameter one hour ahead using a support vector machine technique","volume":"72","author":"Chen","year":"2010","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_22","unstructured":"CCIR (1996). Comite Consultatif International des Radio Communications, International Telecommunication Union. Reports 340-1 and 340-6."},{"key":"ref_23","first-page":"179","article-title":"Ionospheric mapping\u2014An update of foF2 coefficients","volume":"56","author":"Rush","year":"1989","journal-title":"Telecommun. J."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1186\/s40623-015-0301-4","article-title":"Method for modeling of the components of ionospheric parameter time variations and detection of anomalies in the ionosphere","volume":"67","author":"Mandrikova","year":"2015","journal-title":"Earth Planets Space"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.jastp.2018.10.019","article-title":"Analysis of the dynamics of ionospheric parameters during periods of increased solar activity and magnetic storms","volume":"181","author":"Mandrikova","year":"2018","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.asr.2017.01.006","article-title":"Comparison of midlatitude ionospheric F region peak parameters and topside Ne profiles from IRI-2012 model prediction with ground-based ionosonde and alouette II observations","volume":"60","author":"Gordiyenko","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.asr.2009.08.002","article-title":"Ionospheric variation at Thailand equatorial latitude station: Comparison between observations and IRI-2001 model predictions","volume":"45","author":"Wichaipanich","year":"2010","journal-title":"Adv. Space Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.asr.2011.11.015","article-title":"Comparative study of fof2 measurements with IRI-2007 model predictions during extended solar minimum","volume":"51","author":"Zakharenkova","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.asr.2006.03.047","article-title":"Ionospheric behavior of the F2 peak parameters foF2 and hmF2 at Hainan and comparisons with IRI model predictions","volume":"39","author":"Zhang","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/j.asr.2003.07.013","article-title":"Comparative study of ionospheric characteristic parameters obtained by DPS-4 digisonde with IRI-2000 for low latitude station in China","volume":"33","author":"Zhang","year":"2004","journal-title":"Adv. Space. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1016\/j.asr.2019.06.013","article-title":"Nonlinear dependence study of ionospheric F2 layer critical frequency with respect to the solar activity indices using the mutual information method","volume":"64","author":"Bai","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3667","DOI":"10.1007\/s11269-017-1692-8","article-title":"A case study on a combination NDVI forecasting model based on the entropy weight method","volume":"31","author":"Huang","year":"2017","journal-title":"Water Resour. Manag."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cheng, L., Zhang, Y., Suo, L., Shen, S., Fang, F., and Jin, L. (2017, January 26\u201328). Short-term Cooling, Heating and Electrical Load Forecasting in Business Parks Based on Improved Entropy Method. Proceedings of the 36th Chinese Control Conference, Dalian, China.","DOI":"10.23919\/ChiCC.2017.8029046"},{"key":"ref_35","unstructured":"Zhang, Q.Y., Zhu, X.M., and Xu, K. (2011, January 12\u201314). Combination forecasting on software reliability based on entropy weight. Proceedings of the International Conference on Electronic and Mechanical Engineering and Information Technology, EMEIT 2011, Harbin, China."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_37","unstructured":"Li, Y., Wang, D.F., and Han, P. (2009, January 12\u201315). Selective ensemble using discrete differential evolution algorithm for short-term load forecasting. Proceedings of the IEEE 2009 International Conference on Machine Learning and Cybernetics, Baoding, China."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chen, Y., and Li, Y. (2009, January 10\u201311). Entropy-Based Combining Prediction of Grey Time Series and Its Application. Proceedings of the 12th International Conference on Intelligent Computation Technology & Automation, Xiangtan, China.","DOI":"10.1109\/ICICTA.2009.246"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1016\/j.jhydrol.2015.05.032","article-title":"Integrated index for drought assessment based on variable fuzzy set theory: A case study in the Yellow River Basin, China","volume":"527","author":"Huang","year":"2015","journal-title":"J. Hydrol."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Lu, J.P., Wei, C., Wu, J., and Wei, C.W. (2019). TOPSIS Method for Probabilistic Linguistic MAGDM with Entropy Weight and Its Application to Supplier Selection of New Agricultural Machinery Products. Entropy, 21.","DOI":"10.3390\/e21100953"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF00872281","article-title":"Evaluation of rainfall networks using entropy: I. Theoretical development","volume":"6","author":"Krstanovic","year":"1992","journal-title":"Water Resour. Manag."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/442\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:21:08Z","timestamp":1760361668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,14]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["e22040442"],"URL":"https:\/\/doi.org\/10.3390\/e22040442","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,14]]}}}