{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T20:51:05Z","timestamp":1770238265992,"version":"3.49.0"},"reference-count":53,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T00:00:00Z","timestamp":1648857600000},"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":["41801389"],"award-info":[{"award-number":["41801389"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42004013"],"award-info":[{"award-number":["42004013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Science and Technology Plan Project","award":["2020YJ0115"],"award-info":[{"award-number":["2020YJ0115"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the Global Navigation Satellite System, ionospheric delay is a significant source of error. The magnitude of the ionosphere total electron content (TEC) directly impacts the magnitude of the ionospheric delay. Correcting the ionospheric delay and improving the accuracy of satellite navigation positioning can both benefit from the accurate modeling and forecasting of ionospheric TEC. The majority of current ionospheric TEC forecasting research only considers the temporal or spatial dimensions, ignoring the ionospheric TEC\u2019s spatial and temporal autocorrelation. Therefore, we constructed a spatiotemporal network model with two modules: (i) global spatiotemporal characteristics extraction via forwarding spatiotemporal characteristics transfer and (ii) regional spatiotemporal characteristics correction via reverse spatiotemporal characteristics transfer. This model can realize the complementarity of TEC global spatiotemporal characteristics and regional spatiotemporal characteristics. It also ensures that the global spatiotemporal characteristics of the global ionospheric TEC are transferred to each other in both temporal and spatial domains at the same time. The spatiotemporal network model thus achieves a spatiotemporal prediction of global ionospheric TEC. The Huber loss function is also used to suppress the gross error and noise in the ionospheric TEC data to improve the forecasting accuracy of global ionospheric TEC. We compare the results of the spatiotemporal network model with the Center for Orbit Determination in Europe (CODE), the convolutional Long Short-Term Memory (convLSTM) model and the Predictive Recurrent Neural Network (PredRNN) model for one-day forecasts of global ionospheric TEC under different conditions of time and solar activity, respectively. With internal data validation, the average root mean square error (RMSE) of our proposed algorithm increased by 21.19, 15.75, and 9.67%, respectively, during the maximum solar activity period. During the minimum solar activity period, the RMSE improved by 38.69, 38.02, and 13.54%, respectively. This algorithm can effectively be applied to ionospheric delay error correction and can improve the accuracy of satellite navigation and positioning.<\/jats:p>","DOI":"10.3390\/rs14071717","type":"journal-article","created":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:04:01Z","timestamp":1648965841000},"page":"1717","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9402-5329","authenticated-orcid":false,"given":"Xu","family":"Lin","sequence":"first","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]},{"given":"Hongyue","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]},{"given":"Qingqing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]},{"given":"Chaolong","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Natural Resources and Environment, South China Agricultural University, Guangzhou 510642, China"}]},{"given":"Changxin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]},{"given":"Lin","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]},{"given":"Zhaoxiong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Earth Science, Chengdu University of Technology, Chengdu 610059, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,2]]},"reference":[{"key":"ref_1","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_2","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. Chin. Ed."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.actaastro.2020.11.027","article-title":"Regional application of ANFIS in ionosphere time series prediction at severe solar activity period","volume":"179","author":"Inyurt","year":"2021","journal-title":"Acta Astronaut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1029\/RS021i003p00343","article-title":"International reference ionosphere: Recent developments","volume":"21","author":"Bilitza","year":"1986","journal-title":"Radio Sci."},{"key":"ref_5","unstructured":"Bent, R.B., Llewellyn, S.K., Nesterczuk, G., and Schmid, P.E. (1975). The development of a highly-successful worldwide empirical ionospheric model and its use in certain aspects of space communications and worldwide total electron content investigations, Effect of the Ionosphere on Space Systems and Communications."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1109\/TAES.1987.310829","article-title":"Ionospheric time-delay algorithm for single-frequency GPS users","volume":"3","author":"Klobuchar","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","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. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s00190-018-1175-6","article-title":"Assessment of spatial and temporal TEC variations derived from ionospheric models over the polar regions","volume":"93","author":"Jiang","year":"2019","journal-title":"J. Geod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"48-1","DOI":"10.1029\/2002GL014678","article-title":"Regional and local ionospheric models based on Millstone Hill incoherent scatter radar data","volume":"29","author":"Holt","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_10","first-page":"321","article-title":"Specifications of the F-region variations for quiet and disturbed conditions","volume":"24","author":"Kouris","year":"1999","journal-title":"Phys. Chem. Earth C Sol. Terr. Planet. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5049","DOI":"10.1002\/2015JA021140","article-title":"A regional ionospheric TEC mapping technique over China and adjacent areas on the basis of data assimilation","volume":"120","author":"Aa","year":"2015","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_12","first-page":"550","article-title":"Ionospheric parameter modelling and anomaly discovery by combining the wavelet transform with autoregressive models","volume":"58","author":"Mandrikova","year":"2015","journal-title":"Ann. Geophys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1016\/j.asr.2018.03.024","article-title":"Development of multivariate ionospheric TEC forecasting algorithm using linear time series model and ARMA over low-latitude GNSS station","volume":"63","author":"Ratnam","year":"2019","journal-title":"Adv. Space Res."},{"key":"ref_14","first-page":"3090856","article-title":"Deep recurrent neural networks for ionospheric variations estimation using gnss measurements","volume":"60","author":"Kaselimi","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"An, X., Meng, X., Chen, H., Jiang, W., Xi, R., and Chen, Q. (2020). Modelling Global Ionosphere Based on Multi-Frequency, Multi-Constellation GNSS Observations and IRI Model. Remote Sens., 12.","DOI":"10.3390\/rs12030439"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Krypiak-Gregorczyk, A., Wielgosz, P., and Borkowski, A. (2017). Ionosphere model for European region based on multi-GNSS data and TPS interpolation. Remote Sens., 9.","DOI":"10.3390\/rs9121221"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, J., Huang, G., Zhou, P., Yang, Y., Zhang, Q., and Gao, Y. (2020). Advantages of Uncombined Precise Point Positioning with Fixed Ambiguity Resolution for Slant Total Electron Content (STEC) and Differential Code Bias (DCB) Estimation. Remote Sens., 12.","DOI":"10.3390\/rs12020304"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"33499","DOI":"10.1038\/srep33499","article-title":"Global ionospheric modelling using multi-GNSS: BeiDou, Galileo, GLONASS and GPS","volume":"6","author":"Ren","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s00190-021-01487-8","article-title":"Integrity investigation of global ionospheric TEC maps for high-precision positioning","volume":"95","author":"Zhao","year":"2021","journal-title":"J. Geod."},{"key":"ref_20","unstructured":"Schaer, S. (1999). Mapping and Predicting the Earth\u2019s Ionosphere Using the Global Positioning System, Institut f\u00fcr Geod\u00e4sie und Photogrammetrie, Eidg. Technische Hochschule Z\u00fcrich."},{"key":"ref_21","first-page":"1","article-title":"Global prediction of the vertical total electron content of the ionosphere based on GPS data","volume":"46","author":"Monte","year":"2011","journal-title":"Radio Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10291-018-0721-2","article-title":"Performance of various predicted GNSS global ionospheric maps relative to GPS and JASON TEC data","volume":"22","author":"Li","year":"2018","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0925-2312(01)00702-0","article-title":"Time series forecasting using a hybrid ARIMA and neural network model","volume":"50","author":"Zhang","year":"2003","journal-title":"Neurocomputing"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103","DOI":"10.4401\/ag-7297","article-title":"TEC Regional Modeling and prediction using ANN method and single frequency receiver over IRAN","volume":"61","author":"Sabzehee","year":"2018","journal-title":"Ann. Geophys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1016\/j.asr.2008.08.020","article-title":"Application of Neural Networks to South African GPS TEC Modelling","volume":"43","author":"Habarulema","year":"2009","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"105052","DOI":"10.1016\/j.jastp.2019.05.016","article-title":"Feed forward neural network based ionospheric model for the East African region","volume":"191","author":"Tebabal","year":"2019","journal-title":"J. Atmos. Sol. Terr. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Adolfs, M., and Hoque, M.M. (2021). A Neural Network-Based TEC Model Capable of Reproducing Nighttime Winter Anomaly. Remote Sens., 13.","DOI":"10.3390\/rs13224559"},{"key":"ref_28","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_29","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Pan, S., Gao, C., Zhao, T., and Gao, W. (2019). Support vector machine for regional ionospheric delay modeling. Sensors, 19.","DOI":"10.3390\/s19132947"},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"7068349","DOI":"10.1155\/2018\/7068349","article-title":"Deep learning for computer vision: A brief review","volume":"2018","author":"Voulodimos","year":"2018","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_32","first-page":"925","article-title":"Deep Learning for Spatio-Temporal Sequence Forecasting:A Survey","volume":"47","author":"Liu","year":"2021","journal-title":"J. Beijing Univ. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kaselimi, M., Voulodimos, A., Doulamis, N., Doulamis, A., and Delikaraoglou, D.J.R.S. (2020). A Causal Long Short-Term Memory Sequence to Sequence Model for TEC Prediction Using GNSS Observations. Remote Sens., 12.","DOI":"10.3390\/rs12091354"},{"key":"ref_35","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_36","doi-asserted-by":"crossref","unstructured":"Sun, W., Xu, L., Huang, X., Zhang, W., Yuan, T., Chen, Z., and Yan, Y. (2017, January 9\u201312). Forecasting of ionospheric vertical total electron content (TEC) using LSTM networks. Proceedings of the 2017 International Conference on Machine Learning and Cybernetics (ICMLC), Ningbo, China.","DOI":"10.1109\/ICMLC.2017.8108945"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"e2020SW002706","DOI":"10.1029\/2020SW002706","article-title":"Long Short-Term Memory Neural Network for Ionospheric Total Electron Content Forecasting Over China","volume":"19","author":"Xiong","year":"2021","journal-title":"Space Weather"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1029\/2018JA026167","article-title":"Improvement of a deep learning algorithm for total electron content maps: Image completion","volume":"124","author":"Chen","year":"2019","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2020SW002600","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_40","first-page":"802","article-title":"Convolutional LSTM network: A machine learning approach for precipitation nowcasting","volume":"28","author":"Xingjian","year":"2015","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e2021GL095561","DOI":"10.1029\/2021GL095561","article-title":"Machine Learning Prediction of Storm-Time High-Latitude Ionospheric Irregularities From GNSS-Derived ROTI Maps","volume":"48","author":"Liu","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_42","first-page":"553","article-title":"Global ionospheric TEC prediction based on deep learning","volume":"36","author":"Zhang","year":"2021","journal-title":"Chin. J. Radio Sci."},{"key":"ref_43","unstructured":"Wang, Y., Long, M., Wang, J., Gao, Z., and Yu, P.S. (2017, January 4\u20139). Predrnn: Recurrent neural networks for predictive learning using spatiotemporal lstms. Proceedings of the 31st International Conference on Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_44","first-page":"666","article-title":"Short-Term Ionospheric TEC Prediction Using EWT-Elman Combination Model","volume":"41","author":"Lu","year":"2021","journal-title":"J. Geod. Geodyn."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Huber, P.J. (1992). Robust estimation of a location parameter. Breakthroughs in Statistics, Springer.","DOI":"10.1007\/978-1-4612-4380-9_35"},{"key":"ref_46","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_47","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_48","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.2514\/3.3166","article-title":"Maximum likelihood estimates of linear dynamic systems","volume":"3","author":"Rauch","year":"1965","journal-title":"AIAA J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3796","DOI":"10.1109\/TSMC.2019.2931723","article-title":"Location-Aware Deep Collaborative Filtering for Service Recommendation","volume":"51","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"950","DOI":"10.1109\/34.877518","article-title":"Robust linear and support vector regression","volume":"22","author":"Mangasarian","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_51","unstructured":"Hern\u00e1ndez-Pajares, M. (2004). IGS Ionosphere WG Status Report: Performance of IGS Ionosphere TEC Maps-Position Paper, IGS Workshop."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1007\/s00190-017-1032-z","article-title":"Methodology and consistency of slant and vertical assessments for ionospheric electron content models","volume":"91","author":"Krankowski","year":"2017","journal-title":"J. Geod."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s00190-016-0988-4","article-title":"Positive and negative ionospheric responses to the March 2015 geomagnetic storm from BDS observations","volume":"91","author":"Jin","year":"2017","journal-title":"J. Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/7\/1717\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:48:54Z","timestamp":1760136534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/7\/1717"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,2]]},"references-count":53,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["rs14071717"],"URL":"https:\/\/doi.org\/10.3390\/rs14071717","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,2]]}}}