{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T08:48:47Z","timestamp":1783414127871,"version":"3.54.6"},"reference-count":55,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,24]],"date-time":"2022-07-24T00:00:00Z","timestamp":1658620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"German Academic Exchange Service"},{"name":"Technical University of Munich (TUM)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Space weather describes varying conditions between the Sun and Earth that can degrade Global Navigation Satellite Systems (GNSS) operations. Thus, these effects should be precisely and timely corrected for accurate and reliable GNSS applications. That can be modeled with the Vertical Total Electron Content (VTEC) in the Earth\u2019s ionosphere. This study investigates different learning algorithms to approximate nonlinear space weather processes and forecast VTEC for 1 h and 24 h in the future for low-, mid- and high-latitude ionospheric grid points along the same longitude. VTEC models are developed using learning algorithms of Decision Tree and ensemble learning of Random Forest, Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost). Furthermore, ensemble models are combined into a single meta-model Voting Regressor. Models were trained, optimized, and validated with the time series cross-validation technique. Moreover, the relative importance of input variables to the VTEC forecast is estimated. The results show that the developed models perform well in both quiet and storm conditions, where multi-tree ensemble learning outperforms the single Decision Tree. In particular, the meta-estimator Voting Regressor provides mostly the lowest RMSE and the highest correlation coefficients as it averages predictions from different well-performing models. Furthermore, expanding the input dataset with time derivatives, moving averages, and daily differences, as well as modifying data, such as differencing, enhances the learning of space weather features, especially over a longer forecast horizon.<\/jats:p>","DOI":"10.3390\/rs14153547","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T01:42:13Z","timestamp":1658713333000},"page":"3547","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":150,"title":["Ensemble Machine Learning of Random Forest, AdaBoost and XGBoost for Vertical Total Electron Content Forecasting"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9497-7570","authenticated-orcid":false,"given":"Randa","family":"Natras","sequence":"first","affiliation":[{"name":"Deutsches Geod\u00e4tisches Forschungsinstitut (DGFI-TUM), TUM School of Engineering and Design, Technical University of Munich, 80333 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7010-2147","authenticated-orcid":false,"given":"Benedikt","family":"Soja","sequence":"additional","affiliation":[{"name":"Institute of Geodesy and Photogrammetry, ETH Zurich, 8093 Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Deutsches Geod\u00e4tisches Forschungsinstitut (DGFI-TUM), TUM School of Engineering and Design, Technical University of Munich, 80333 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2008SW000400","article-title":"Space Weather and the Global Positioning System","volume":"6","author":"Coster","year":"2008","journal-title":"Space Weather"},{"key":"ref_2","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":"AES-23","author":"Klobuchar","year":"1987","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_3","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":"Roma","year":"2017","journal-title":"J. Geod."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","unstructured":"Cander, L.R. (2019). Ionospheric Variability. Ionospheric Space Weather, Springer.","DOI":"10.1007\/978-3-319-99331-7"},{"key":"ref_6","unstructured":"Nishimura, Y., Verkhoglyadova, O., Deng, Y., and Zhang, S.R. (2021). Cross-Scale Coupling and Energy Transfer in the Magnetosphere-Ionosphere-Thermosphere SYSTEM, Elsevier."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.jseaes.2010.03.005","article-title":"Lithosphere\u2013Atmosphere\u2013Ionosphere Coupling (LAIC) model\u2014An unified concept for earthquake precursors validation","volume":"41","author":"Pulinets","year":"2011","journal-title":"J. Asian Earth Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e2021SW002908","DOI":"10.1029\/2021SW002908","article-title":"A Method to Mitigate the Effects of Strong Geomagnetic Storm on GNSS Precise Point Positioning","volume":"20","author":"Luo","year":"2022","journal-title":"Space Weather"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Luo, X., Gu, S., Lou, Y., Xiong, C., Chen, B., and Jin, X. (2018). Assessing the Performance of GPS Precise Point Positioning Under Different Geomagnetic Storm Conditions during Solar Cycle 24. Sensors, 18.","DOI":"10.3390\/s18061784"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42452-018-0040-9","article-title":"Strong solar flare detection and its impact on ionospheric layers and on coordinates accuracy in the Western Balkans in October 2014","volume":"1","author":"Natras","year":"2019","journal-title":"SN Appl. Sci."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1126\/science.aaa8415","article-title":"Machine learning: Trends, perspectives, and prospects","volume":"349","author":"Jordan","year":"2015","journal-title":"Science"},{"key":"ref_13","unstructured":"Natras, R., and Schmidt, M. (2021, January 1\u20135). Machine Learning Model Development for Space Weather Forecasting in the Ionosphere. Proceedings of the CEUR Workshop, Gold Coast, Australia."},{"key":"ref_14","unstructured":"Camporeale, E., Wing, S., and Johnson, J. (2018). Machine Learning Techniques for Space Weather, Elsevier."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Natras, R., Goss, A., Halilovic, D., Magnet, N., Mulic, M., Schmidt, M., and Weber, R. (Navig. J. Inst. Navig., 2022). Regional ionosphere delay models based on CORS data and machine learning, Navig. J. Inst. Navig., in review.","DOI":"10.33012\/navi.577"},{"key":"ref_17","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_18","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_19","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_20","doi-asserted-by":"crossref","unstructured":"Tang, R., Zeng, F., Chen, Z., Wang, J.S., Huang, C.M., and Wu, Z. (2020). The Comparison of Predicting Storm-Time Ionospheric TEC by Three Methods: ARIMA, LSTM, and Seq2Seq. Atmosphere, 11.","DOI":"10.3390\/atmos11040316"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2021.3090856","article-title":"Deep Recurrent Neural Networks for Ionospheric Variations Estimation Using GNSS Measurements","volume":"60","author":"Kaselimi","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","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":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1051\/swsc\/2020013","article-title":"Neural network based model for global Total Electron Content forecasting","volume":"10","author":"Cesaroni","year":"2020","journal-title":"J. Space Weather Space Clim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1016\/j.asr.2021.11.033","article-title":"A novel hybrid Machine learning model to forecast ionospheric TEC over Low-latitude GNSS stations","volume":"69","author":"Sivavaraprasad","year":"2022","journal-title":"Adv. Space Res."},{"key":"ref_26","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":"2020","journal-title":"Space Weather"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/JSTARS.2021.3132049","article-title":"Machine Learning-Based Short-Term GPS TEC Forecasting During High Solar Activity and Magnetic Storm Periods","volume":"15","author":"Han","year":"2022","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_28","first-page":"1","article-title":"Ionosphere time series modeling using adaptive neuro-fuzzy inference system and principal component analysis","volume":"24","author":"Voosoghi","year":"2020","journal-title":"GPS Solut."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10291-020-01063-1","article-title":"Correction to: GIMLi: Global Ionospheric total electron content model based on machine learning","volume":"25","author":"Zhukov","year":"2021","journal-title":"GPS Solut."},{"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 support vector machine with GPU acceleration in the China region","volume":"68","author":"Xia","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Monte-Moreno, E., Yang, H., and Hern\u00e1ndez-Pajares, M. (2022). Forecast of the Global TEC by Nearest Neighbour Technique. Remote Sens., 14.","DOI":"10.3390\/rs14061361"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10509-020-03907-1","article-title":"Ionospheric TEC prediction using Long Short-Term Memory deep learning network","volume":"366","author":"Wen","year":"2021","journal-title":"Astrophys. Space Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Natras, R., Soja, B., and Schmidt, M. (June, January 30). Machine Learning Ensemble Approach for Ionosphere and Space Weather Forecasting with Uncertainty Quantification. Proceedings of the 2022 3rd URSI Atlantic and Asia Pacific Radio Science Meeting (AT-AP-RASC), Gran Canaria, Spain.","DOI":"10.23919\/AT-AP-RASC54737.2022.9814334"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11000","DOI":"10.1002\/2015JA021961","article-title":"Modelling total electron content during geomagnetic storm conditions using empirical orthogonal functions and neural networks","volume":"120","author":"Uwamahoro","year":"2015","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer. [2nd ed.].","DOI":"10.1007\/978-0-387-84858-7"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Blum, A., Kalai, A., and Langford, J. (1999). Beating the Hold-out: Bounds for K-Fold and Progressive Cross-Validation. Proceedings of the Twelfth Annual Conference on Computational Learning Theory, Santa Cruz, CA, USA, 7\u20139 July 1999, Association for Computing Machinery.","DOI":"10.1145\/307400.307439"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1214\/09-SS054","article-title":"A survey of cross-validation procedures for model selection","volume":"4","author":"Arlot","year":"2010","journal-title":"Stat. Surv."},{"key":"ref_38","unstructured":"Hyndman, R.J., and Athanasopoulos, G. (2021). Forecasting: Principles and Practice, OTexts. [3rd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2004JA010649","article-title":"Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data","volume":"110","author":"King","year":"2005","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/jcss.1997.1504","article-title":"A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting","volume":"55","author":"Freund","year":"1997","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_43","unstructured":"Breiman, L., Friedman, J., Stone, C., and Olshen, R. (1984). Classification and Regression Trees, Taylor & Francis."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1109\/TKDE.2019.2912815","article-title":"Reliable Accuracy Estimates from k-Fold Cross Validation","volume":"32","author":"Wong","year":"2020","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","article-title":"Greedy Function Approximation: A Gradient Boosting Machine","volume":"29","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"ref_46","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_47","unstructured":"Esposito, D. (2020). Introducing Machine Learning, Safari. [1st ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1016\/j.asr.2018.04.010","article-title":"Empirical forecast of quiet time ionospheric Total Electron Content maps over Europe","volume":"61","author":"Badeke","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_49","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_50","doi-asserted-by":"crossref","first-page":"e2020SW002452","DOI":"10.1029\/2020SW002452","article-title":"Evaluation of Total Electron Content Prediction Using Three Ionosphere-Thermosphere Models","volume":"18","author":"Verkhoglyadova","year":"2020","journal-title":"Space Weather"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"359","DOI":"10.5194\/angeo-38-359-2020","article-title":"Response of the low- to mid-latitude ionosphere to the geomagnetic storm of September 2017","volume":"38","author":"Imtiaz","year":"2020","journal-title":"Ann. Geophys."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Wang, G., Yin, Z., Hu, Z., Chen, G., Li, W., and Bo, Y. (2021). Analysis of the BDGIM Performance in BDS Single Point Positioning. Remote Sens., 13.","DOI":"10.3390\/rs13193888"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s00190-021-01483-y","article-title":"Influence of temporal resolution on the performance of global ionospheric maps","volume":"95","author":"Liu","year":"2021","journal-title":"J. Geod."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"699","DOI":"10.5194\/angeo-37-699-2019","article-title":"High-resolution vertical total electron content maps based on multi-scale B-spline representations","volume":"37","author":"Goss","year":"2019","journal-title":"Ann. Geophys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"e2021SW002858","DOI":"10.1029\/2021SW002858","article-title":"Real-Time Monitoring of Ionosphere VTEC Using Multi-GNSS Carrier-Phase Observations and B-Splines","volume":"19","author":"Erdogan","year":"2021","journal-title":"Space Weather"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3547\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:55:45Z","timestamp":1760140545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3547"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,24]]},"references-count":55,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153547"],"URL":"https:\/\/doi.org\/10.3390\/rs14153547","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,24]]}}}