{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T20:30:35Z","timestamp":1776457835393,"version":"3.51.2"},"reference-count":45,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T00:00:00Z","timestamp":1648166400000},"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":["41761089"],"award-info":[{"award-number":["41761089"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Accurate corrections for ionospheric total electron content (TEC) and early warning information are crucial for global navigation satellite system (GNSS) applications under the influence of space weather. In this study, we propose to use a new machine learning model\u2014the Prophet model, to predict the global ionospheric TEC by establishing a short-term ionospheric prediction model. We use 15th-order spherical harmonic coefficients provided by the Center for Orbit Determination in Europe (CODE) as the training data set. Historical spherical harmonic coefficient data from 7 days, 15 days, and 30 days are used as the training set to model and predict 256 spherical harmonic coefficients. We use the predicted coefficients to generate a global ionospheric TEC forecast map based on the spherical harmonic function model and select a year with low solar activity (63.4 &lt; F10.7 &lt; 81.8) and a year with the high solar activity (79.5 &lt; F10.7 &lt; 255.0) to carry out a sliding 2-day forecast experiment. Meanwhile, we verify the model performance by comparing the forecasting results with the CODE forecast product (COPG) and final product (CODG). The results show that we obtain the best predictions by using 15 days of historical data as the training set. Compared with the results of CODE\u2019S 1-Day (C1PG) and CODE\u2019S 2-Day (C2PG). The number of days with RMSE better than COPG on the first and second day of the low-solar-activity year is 151 and 158 days, respectively. This statistic for high-solar-activity year is 183 days and 135 days.<\/jats:p>","DOI":"10.3390\/rs14071585","type":"journal-article","created":{"date-parts":[[2022,3,27]],"date-time":"2022-03-27T21:29:36Z","timestamp":1648416576000},"page":"1585","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["An Approach for Predicting Global Ionospheric TEC Using Machine Learning"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1292-6746","authenticated-orcid":false,"given":"Jun","family":"Tang","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0715-3574","authenticated-orcid":false,"given":"Yinjian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6167-408X","authenticated-orcid":false,"given":"Dengpan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2256-9663","authenticated-orcid":false,"given":"Mingfei","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,25]]},"reference":[{"key":"ref_1","unstructured":"Komjathy, A. (1997). Global Ionospheric Total Electron Content Mapping Using the Global Positioning System. [Ph.D. Thesis, University of New Brunswick Fredericton]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4596","DOI":"10.1109\/TGRS.2015.2402598","article-title":"A worldwide ionospheric model for fast precise point positioning","volume":"53","author":"Juan","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-007-0152-2","article-title":"The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS","volume":"82","author":"Yuan","year":"2008","journal-title":"J. Geod."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e2020JA028108","DOI":"10.1029\/2020JA028108","article-title":"Observation of postsunset OI 135.6 nm radiance enhancement over south America by the GOLD Mission","volume":"126","author":"Cai","year":"2021","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e2020JA028510","DOI":"10.1029\/2020JA028510","article-title":"Longitudinal variation of postsunset plasma depletions from the global-scale observations of the limb and disk (GOLD) mission","volume":"126","author":"Martinis","year":"2021","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7686","DOI":"10.1029\/2018JA025422","article-title":"Nighttime enhancements in the midlatitude ionosphere and their relation to the plasmasphere","volume":"123","author":"Li","year":"2018","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1029\/2018SW002143","article-title":"Simulation and observations of the polar tongue of ionization at different heights during the 2015 St. Patrick\u2019s day storms","volume":"17","author":"Klimenko","year":"2019","journal-title":"Space Weather"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1002\/2016JA023727","article-title":"GPS detection of ionospheric rayleigh wave and its source following the 2012 Haida Gwaii earthquake","volume":"122","author":"Jin","year":"2017","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8587","DOI":"10.1029\/2017JA025001","article-title":"Two-mode ionospheric disturbances following the 2005 Northern California offshore earthquake from GPS measurements","volume":"123","author":"Jin","year":"2018","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1007\/s00190-018-1118-2","article-title":"Real-time precise point positioning (RTPPP) with raw observations and its application in real-time regional ionospheric VTEC modeling","volume":"92","author":"Liu","year":"2018","journal-title":"J. Geod."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, Y., Yao, Y., Zhang, L., and Fang, M. (2020). A refinement method of real-time ionospheric model for China. Remote Sens., 12.","DOI":"10.3390\/rs12203354"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jin, S., Gao, C., Yuan, L., Guo, P., Calabia, A., Ruan, H., and Luo, P. (2021). Long-term variations of plasmaspheric total electron content from topside GPS observations on LEO satellites. Remote Sens., 13.","DOI":"10.3390\/rs13040545"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, W., Huo, X., Yuan, Y., Li, Z., and Wang, N. (2021). Algorithm research using GNSS-TEC data to calibrate TEC calculated by the IRI-2016 model over China. Remote Sens., 13.","DOI":"10.3390\/rs13194002"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"He, X., Bos, M.S., Montillet, J.P., Fernandes, R., Melbourne, T., Jiang, W., and Li, W. (2021). Spatial variations of stochastic noise properties in GPS time series. Remote Sens., 13.","DOI":"10.3390\/rs13224534"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/TAES.1987.310829","article-title":"Ionospheric time-delay algorithms for single-frequency GPS users","volume":"AES-23","author":"Klobuchar","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1109\/TAES.2008.4667725","article-title":"Refining the Klobuchar ionospheric coefficients based on GPS observations","volume":"44","author":"Yuan","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s10291-019-0871-x","article-title":"Midlatitude Klobuchar correction model based on the K-means clustering of ionospheric daily variations","volume":"23","author":"Pongracic","year":"2019","journal-title":"GPS Solut."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.1016\/j.jastp.2008.01.015","article-title":"A new version of the NeQuick ionosphere electron density model","volume":"70","author":"Nava","year":"2008","journal-title":"J. Atmos. Sol.-Terr. Phy."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1002\/navi.292","article-title":"The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results","volume":"66","author":"Yuan","year":"2019","journal-title":"Navigation"},{"key":"ref_20","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_21","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s001900100182","article-title":"An improvement to ionospheric delay correction for single-frequency GPS users\u2014The APR-I scheme","volume":"75","author":"Yuan","year":"2001","journal-title":"J. Geod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/BF02907577","article-title":"Differential Areas for Differential Stations (DADS): A new method of establishing grid ionospheric model","volume":"47","author":"Yuan","year":"2002","journal-title":"Chin. Sci. Bull."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/S0273-1177(03)00029-2","article-title":"The international GPS service (IGS) ionosphere working group","volume":"31","author":"Feltens","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s00190-008-0266-1","article-title":"The IGS VTEC Maps: A reliable source of ionospheric information since 1998","volume":"83","author":"Juan","year":"2009","journal-title":"J. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s00190-008-0300-3","article-title":"The international GNSS service in a changing landscape of global navigation satellite systems","volume":"83","author":"Dow","year":"2009","journal-title":"J. Geod."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"A10319","DOI":"10.1029\/2010JA015432","article-title":"Assessment of GPS global ionosphere maps (GIM) by comparison between CODE GIM and TOPEX\/Jason TEC data: Ionospheric perspective","volume":"115","author":"Jee","year":"2010","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s00190-017-1088-9","article-title":"Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle","volume":"92","author":"Krankowski","year":"2018","journal-title":"J. Geod."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"RS4016","DOI":"10.1029\/2005RS003285","article-title":"Forecasting total electron content maps by neural network technique","volume":"41","author":"Tulunay","year":"2006","journal-title":"Radio Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1016\/j.asr.2021.03.021","article-title":"Ionospheric TEC forecast model based on Ssupport vector machine with GPU acceleration in the China region","volume":"68","author":"Xia","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_31","first-page":"144","article-title":"Machine learning methodology for ionosphere total electron content nowcasting","volume":"16","author":"Zhukov","year":"2018","journal-title":"Int. J. Artif. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s10291-020-01055-1","article-title":"GIMLi: Global ionospheric total electron content model based on machine learning","volume":"25","author":"Zhukov","year":"2021","journal-title":"GPS Solut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/2013RS005247","article-title":"Ionospheric single-station TEC short-term forecast using RBF neural network","volume":"49","author":"Huang","year":"2014","journal-title":"Radio Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"e2020SW002600","DOI":"10.1029\/2020SW002600","article-title":"One-day forecasting of global TEC using a novel deep learning model","volume":"19","author":"Lee","year":"2021","journal-title":"Space Weather"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1109\/LGRS.2019.2895112","article-title":"A Deep Learning-based approach to forecast ionospheric delays for GPS signals","volume":"16","author":"Srivani","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/LGRS.2020.2992633","article-title":"Implementation of hybrid deep learning model (LSTM-CNN) for ionospheric TEC forecasting using GPS data","volume":"18","author":"Ruwali","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1002\/cjg2.1038","article-title":"A study of prediction models for ionosphere","volume":"50","author":"Li","year":"2007","journal-title":"Chin. J. Geophys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40623-017-0762-8","article-title":"Prediction of global ionospheric VTEC maps using an adaptive autoregressive model","volume":"70","author":"Wang","year":"2018","journal-title":"Earth Planets Space"},{"key":"ref_39","first-page":"1271","article-title":"Prediction of global ionospheric TEC using the semiparametric kernel estimation method","volume":"63","author":"Wang","year":"2020","journal-title":"Chin. J. Geophys."},{"key":"ref_40","first-page":"3021","article-title":"Global ionospheric TEC prediction model integrated with semiparametric kernel estimation and autoregressive compensation","volume":"64","author":"Qiu","year":"2021","journal-title":"Chin. J. Geophys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e2020SW002501","DOI":"10.1029\/2020SW002501","article-title":"Forecasting global ionospheric TEC using deep learning approach","volume":"18","author":"Liu","year":"2020","journal-title":"Space Weather"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/00031305.2017.1380080","article-title":"Forecasting at scale","volume":"72","author":"Taylor","year":"2018","journal-title":"Am. Stat."},{"key":"ref_43","unstructured":"Schaer, S. (1999). Mapping and Predicting the Earth\u2019s Ionosphere Using the Global Positioning System. [Ph.D. Thesis, University of Bern]."},{"key":"ref_44","first-page":"610","article-title":"Ionosphere VTEC prediction model fused with wavelet decomposition and Prophet framework","volume":"43","author":"Tian","year":"2021","journal-title":"Syst. Eng. Electron."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"e2020SW002639","DOI":"10.1029\/2020SW002639","article-title":"Data-driven forecasting of low-latitude ionospheric total electron content using the random forest and LSTM machine learning methods","volume":"19","author":"Zewdie","year":"2021","journal-title":"Space Weather"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/7\/1585\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:43:24Z","timestamp":1760136204000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/7\/1585"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":45,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["rs14071585"],"URL":"https:\/\/doi.org\/10.3390\/rs14071585","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,25]]}}}