{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:16:16Z","timestamp":1760235376439,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T00:00:00Z","timestamp":1629763200000},"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":["41604143"],"award-info":[{"award-number":["41604143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Key deployment projects of Chinese Academy of Sciences","award":["ZDRE-KT-2021-3"],"award-info":[{"award-number":["ZDRE-KT-2021-3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The energetic electrons in the Earth\u2019s radiation belt, known as \u201ckiller electrons\u201d, are one of the crucial factors for the safety of geostationary satellites. Geostationary satellites at different longitudes encounter different energetic electron environments. However, organizations of space weather prediction usually only display the real-time \u22652 MeV electron fluxes and the predictions of \u22652 MeV electron fluxes or daily fluences within the next 1\u20133 days by models at one location in GEO orbit. In this study, the relationship of \u22652 MeV electron fluxes at different longitudes is investigated based on observations from GOES satellites, and the relevant models are developed. Based on the observations from GOES-10 and GOES-12 after calibration verification, the ratios of the \u22652 MeV electron daily fluences at 135\u00b0 W to those at 75\u00b0 W are mainly in the range from 1.0 to 4.0, with an average of 1.92. The models with various combinations of two or three input parameters are developed by the fully connected neural network for the relationship between \u22652 MeV electron fluxes at 135\u00b0 W and 75\u00b0 W in GEO orbit. According to the prediction efficiency (PE), the model only using log10 (fluxes) and MLT from GOES-10 (135\u00b0 W), whose PE can reach 0.920, has the best performance to predict \u22652 MeV electron fluxes at the locations of GOES-12 (75\u00b0 W). Its PE is larger than that (0.882) of the linear model using log10 (fluxes four hours ahead) from GOES-10 (135\u00b0 W). We also develop models for the relationship between \u22652 MeV electron fluxes at 75\u00b0 W and at variable longitudes between 95.8\u00b0 W and 114.9\u00b0 W in GEO orbit by the fully connected neural network. The PE values of these models are larger than 0.90. These models realize the predictions of \u22652 MeV electron fluxes at arbitrary longitude between 95.8\u00b0 W and 114.9\u00b0 W in GEO orbit.<\/jats:p>","DOI":"10.3390\/rs13173347","type":"journal-article","created":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T22:09:39Z","timestamp":1629842979000},"page":"3347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Modeling the Relationship of \u22652 MeV Electron Fluxes at Different Longitudes in Geostationary Orbit by the Machine Learning Method"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8179-6407","authenticated-orcid":false,"given":"Xiaojing","family":"Sun","sequence":"first","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Ruilin","family":"Lin","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Siqing","family":"Liu","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Xinran","family":"He","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Liqin","family":"Shi","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7762-2786","authenticated-orcid":false,"given":"Bingxian","family":"Luo","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Qiuzhen","family":"Zhong","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"}]},{"given":"Jiancun","family":"Gong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Science and Technology on Environmental Space Situation Awareness, CAS, Beijing 100190, China"},{"name":"Innovation Academy for Microsatellites of CAS, Shanghai 20050, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,24]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"The status and prospect of orbital servicing in the geostationary orbit","volume":"31","author":"Liang","year":"2010","journal-title":"J. Astronaut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"687","DOI":"10.11728\/cjss2015.06.687","article-title":"Analysis of the Chinese GEO satellite anomaly on 9 March 2012","volume":"35","author":"Tian","year":"2015","journal-title":"Chin. J. Space Sci."},{"key":"ref_3","first-page":"201","article-title":"Influence of high energy electrons on geosynchronous orbit satellites","volume":"36","author":"Wang","year":"2017","journal-title":"J. Spacecr. TTC Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1109\/23.273511","article-title":"Spacecraft anomalies on the CRRES satellite correlated with the environment and insulator samples","volume":"40","author":"Violet","year":"1993","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0273-1177(97)01104-6","article-title":"Studies of spacecraft charging on a geosynchronous telecommunications satellite","volume":"22","author":"Lanzerotti","year":"1998","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/S0168-583X(03)00885-1","article-title":"Measurement of charge storage and leakage in polyimides","volume":"208","author":"Frederickson","year":"2003","journal-title":"Nucl. Instrum. Methods Phys. Res. B"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Baker, D. (2004). Characterizing the Earth\u2019s outer Van Allen zone using a radiation belt content index. Space Weather, 2.","DOI":"10.1029\/2003SW000026"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/swe.20023","article-title":"Space weather impacts on satellites and forecasting the Earth\u2019s electron radiation belts with SPACECAST","volume":"11","author":"Horne","year":"2013","journal-title":"Space Weather"},{"key":"ref_9","unstructured":"Bedingfield, K.L., Leach, R.D., and Alexander, M.B. (1996). NASA Reference Publication 1390, National Aeronautics and Space Administration."},{"key":"ref_10","unstructured":"AFRL Science Center USA, Koons, H.C., Mazur, J.E., Selesnick, R.S., and Blake, J.B. (1998). The Impact of the Space Environment on Space Systems. Proceedings of the 6th Spacecraft Charging Technology Conference, Hanscom AFB, MA, USA, 26\u201329 October 1998, AFRL Science Cente."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lucci, N. (2013). Space weather conditions and spacecraft anomalies in different orbits. Space Weather, 3.","DOI":"10.1029\/2003SW000056"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"953","DOI":"10.5194\/angeo-20-953-2002","article-title":"A solar cycle of spacecraft anomalies due to internal charging","volume":"20","author":"Wrenn","year":"2002","journal-title":"Ann. Geophys."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Turner, D. (2008). Quantitative forecast of relativistic electron flux at geosynchronous orbit based on low-energy electron flux. Space Weather, 6.","DOI":"10.1029\/2007SW000354"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-3886(87)90082-9","article-title":"Deep dielectric charging effects due to high energy electrons in the earth\u2019s outer magnetosphere","volume":"20","author":"Baker","year":"1987","journal-title":"J. Electrost."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"15133","DOI":"10.1029\/JA095iA09p15133","article-title":"Linear prediction filter analysis of relativistic electron properties at 6.6RE","volume":"95","author":"Baker","year":"1990","journal-title":"J. Geophys. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/S0964-2749(02)80193-7","article-title":"Prediction of relativistic electron fluence using magnetic observatory data","volume":"14","author":"Lam","year":"2002","journal-title":"COSPAR Colloq. Ser."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"S03003","DOI":"10.1029\/2003SW000036","article-title":"Adaptive linear prediction of radiation belt electrons using the Kalman fillter","volume":"2","author":"Rigler","year":"2004","journal-title":"Space Weather"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kataoka, R. (2006). Flux enhancement of radiation belt electrons during geomagnetic storms driven by coronal mass ejections and corotating interaction regions. Space Weather, 4.","DOI":"10.1029\/2005SW000211"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.jastp.2007.08.066","article-title":"Probabilistic space weather forecast of the relativistic electron flux enhancement at geosynchronous orbit","volume":"70","author":"Miyoshi","year":"2008","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20","DOI":"10.11728\/cjss2013.01.020","article-title":"Quantitative prediction of relativistic electron flux at geosynchronous orbit with geomagnetic pulsations parameters","volume":"33","author":"He","year":"2013","journal-title":"Chin. J. Space Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1002\/swe.20020","article-title":"Relativistic electron flux forecast at geostationary orbit using Kalman filter based on multivariate autoregressive model","volume":"11","author":"Sakaguchi","year":"2013","journal-title":"Space Weather"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.actaastro.2013.07.004","article-title":"Solar cycle variation of \u201ckiller\u201d electrons at geosynchronous orbit and electron flux correlation with the solar wind parameters and ULF waves intensity","volume":"95","author":"Potapova","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"298","DOI":"10.11728\/cjss2017.03.298","article-title":"Dynamic prediction model of relativistic electron differential fluxes at the geosynchronous orbit","volume":"37","author":"Li","year":"2017","journal-title":"Chin. J. Space Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18","DOI":"10.11728\/cjss2019.01.018","article-title":"Statistical model of the relativistic electron fluence forecast at geostationary orbit","volume":"39","author":"Zhong","year":"2019","journal-title":"Chin. J. Space Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Qian, Y. (2020). An hourly prediction model of relativistic electrons based on empirical mode decomposition. Space Weather, 17.","DOI":"10.1029\/2018SW002078"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ukhorskiy, A. (2004). Data-derived forecasting model for relativistic electron intensity at geosynchronous orbit. Geophys. Res. Lett., 31.","DOI":"10.1029\/2004GL019616"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"415","DOI":"10.5194\/angeo-29-415-2011","article-title":"Forecasting relativistic electron flux using dynamic multiple regression models","volume":"29","author":"Wei","year":"2011","journal-title":"Ann. Geophys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"405","DOI":"10.5194\/angeo-33-405-2015","article-title":"Online NARMAX model for electron fluxes at GEO","volume":"33","author":"Boynton","year":"2015","journal-title":"Ann. Geophys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1029\/2000GL012681","article-title":"Quantitative prediction of radiation belt electrons at geostationary orbit based on solar wind measurements","volume":"28","author":"Li","year":"2001","journal-title":"Geophys. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, X. (2004). Variations of 0.7\u20136.0 MeV electrons at geosynchronous orbit as a function of solar wind. Space Weather, 2.","DOI":"10.1029\/2003SW000017"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, X. (2006). Correlation between the inner edge of outer radiation belt electrons and the innermost plasmapause location. Geophys. Res. Lett., 33.","DOI":"10.1029\/2006GL026294"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, X. (2011). Behavior of MeV electrons at geosynchronous orbit during last two solar cycles. J. Geophys. Res., 116.","DOI":"10.1029\/2011JA016934"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"947","DOI":"10.5194\/angeo-20-947-2002","article-title":"Neural network prediction of relativistic electrons at geosynchronous orbit during the storm recovery phase: Effects of recurring substorms","volume":"20","author":"Fukata","year":"2002","journal-title":"Ann. Geophys."},{"key":"ref_34","first-page":"283","article-title":"Forcast of the enhancement of relativistic eletron at the GEO-synchronous orbit","volume":"24","author":"Xue","year":"2004","journal-title":"Chin. J. Space Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ling, A. (2010). A neural network-based geosynchronous relativistic electron flux forecasting model. Space Weather, 8.","DOI":"10.1029\/2010SW000576"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"418","DOI":"10.11728\/cjss2013.04.418","article-title":"Approach for predicting the energetic electron flux in geosynchronous earth orbit","volume":"33","author":"Guo","year":"2013","journal-title":"Chin. J. Space Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1002\/2015SW001359","article-title":"Artificial neural network prediction model for geosynchronous electron fluxes: Dependence on satellite position and particle energy","volume":"14","author":"Shin","year":"2016","journal-title":"Space Weather"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"354","DOI":"10.11728\/cjss2012.03.354","article-title":"Study on the forecasting method of relativistic electron flux at geostationary orbit based on support vector machine","volume":"32","author":"Wang","year":"2012","journal-title":"Chin. J. Space Sci."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wei, L.H. (2018). Study on the Prediction Model of High-Energy Electron Integral Flux at GEO Based on Deep Learning. [Master\u2019s Thesis, National Space Science Center, Chinese Academy of Sciences].","DOI":"10.1029\/2018SW001829"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"A05221","DOI":"10.1029\/2003JA010368","article-title":"The radial gradient of relativistic electrons at geosynchronous orbit","volume":"109","author":"Onsager","year":"2004","journal-title":"J. Geophys. Res."},{"key":"ref_41","first-page":"3604","article-title":"Influence of geomagnetic field structure on \u22652 MeV electron distribution at geostationary orbit","volume":"63","author":"Sun","year":"2020","journal-title":"Chin. J. Geophys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"A04207","DOI":"10.1029\/2009JA014235","article-title":"A three-dimensional asymmetric magnetopause model","volume":"115","author":"Lin","year":"2010","journal-title":"J. Geophys. Res."},{"key":"ref_43","first-page":"265","article-title":"The international geomagnetic reference field","volume":"2","author":"Macmillan","year":"2011","journal-title":"IAGA Spec. Sopr. Book"},{"key":"ref_44","first-page":"19","article-title":"International Geomagnetic Reference Field: The 12th generation","volume":"67","author":"Erwan","year":"2015","journal-title":"Earth Planets Space"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0032-0633(89)90066-4","article-title":"A magnetospheric magnetic field model with a warped tail current sheet","volume":"37","author":"Tsyganenko","year":"1989","journal-title":"Planet. Space Sci."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Chen, T.Q., and Guestrin, C. (2016). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13\u201317 August 2016, ACM Press.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_47","first-page":"358","article-title":"Classification and Regression Trees","volume":"40","author":"Breiman","year":"1984","journal-title":"Biometrics"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF00116037","article-title":"The strength of weak learnability","volume":"5","author":"Schapire","year":"1990","journal-title":"Mach. Learn."},{"key":"ref_49","first-page":"180","article-title":"Effects of the solar wind on magnetospheric dynamics-Energetic electrons at the synchronous orbit","volume":"1979","author":"Paulikas","year":"1979","journal-title":"Geophys. Monogr. Ser."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"17279","DOI":"10.1029\/97JA03329","article-title":"Coronal mass ejections, magnetic clouds, and relativistic magnetospheric electron events: ISTP","volume":"103","author":"Baker","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1023\/A:1005221108016","article-title":"The electron radiation belt","volume":"95","author":"Li","year":"2001","journal-title":"Space Sci. Rev."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1029\/2002GL016513","article-title":"Acceleration and loss of relativistic electron during geomagnetic storms","volume":"30","author":"Reeves","year":"2003","journal-title":"Geophys. Res. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.jastp.2006.06.019","article-title":"Review of radiation belt relativistic electron losses","volume":"69","author":"Millan","year":"2007","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Zhang, H. (2020). Relative electron flux prediction at geosynchronous orbit based on the neural network and the quantile regression method. Space Weather, 18.","DOI":"10.1029\/2020SW002445"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw."},{"key":"ref_57","first-page":"315","article-title":"Deep sparse rectifier neural networks","volume":"15","author":"Glorot","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"3827","DOI":"10.1029\/2001GL013586","article-title":"Long term measurements of radiation belts by SAMPEX and their variations","volume":"28","author":"Li","year":"2001","journal-title":"Geophys. Res. Lett."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1029\/2009JA014333","article-title":"Statistical roles of storms and substorms in changing the entire outer zone relativistic electron population","volume":"114","author":"Li","year":"2009","journal-title":"J. Geophys. Res."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Borovsky, J. (2009). Electron loss rates from the outer radiation belt caused by the fillvig of the outer plasmaspbere: The calm before the storm. J. Geophys. Res., 114.","DOI":"10.1029\/2009JA014063"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3347\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:50:50Z","timestamp":1760165450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/17\/3347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,24]]},"references-count":60,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["rs13173347"],"URL":"https:\/\/doi.org\/10.3390\/rs13173347","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,8,24]]}}}