{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:38:10Z","timestamp":1774021090411,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:00:00Z","timestamp":1759363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>Global Navigation Satellite System (GNSS) meteorology has emerged as a valuable tool for atmospheric monitoring, providing high-resolution, near-real-time data that can significantly improve precipitation nowcasting. This study aims to enhance short-term precipitation forecasting by integrating GNSS-derived Precipitable Water Vapor (PWV)\u2014a key indicator of atmospheric moisture\u2014with traditional meteorological observations. A novel two-step machine learning framework is proposed that combines a Random Forest (RF) model and a Long Short-Term Memory (LSTM) neural network. The RF model first estimates current precipitation based on PWV, surface weather parameters, and auxiliary atmospheric variables. Then, the LSTM network leverages temporal dependencies within the data to predict precipitation for the subsequent hour. This hybrid method capitalizes on the RF\u2019s ability to model complex nonlinear relationships and the LSTM\u2019s strength in handling time series data. The results demonstrate that the proposed approach improves forecasting accuracy, particularly during extreme weather events such as intense rainfall and thunderstorms, outperforming conventional models. By integrating GNSS meteorology with advanced machine learning techniques, this study offers a promising tool for meteorological services, early warning systems, and disaster risk management. The findings highlight the potential of GNSS-based nowcasting for real-time decision-making in weather-sensitive applications.<\/jats:p>","DOI":"10.3390\/e27101034","type":"journal-article","created":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T08:20:28Z","timestamp":1759393228000},"page":"1034","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Two-Step Machine Learning Approach Integrating GNSS-Derived PWV for Improved Precipitation Forecasting"],"prefix":"10.3390","volume":"27","author":[{"given":"Laura","family":"Profetto","sequence":"first","affiliation":[{"name":"Dipartimento Ingegneria dell\u2019Informazione e Scienze Matematiche (DIISM), Universit\u00e1 di Siena, 53100 Siena, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2013-1521","authenticated-orcid":false,"given":"Andrea","family":"Antonini","sequence":"additional","affiliation":[{"name":"Laboratory of Monitoring and Environmental Modelling for the Sustainable Development (LaMMA), 50019 Sesto Fiorentino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6985-6809","authenticated-orcid":false,"given":"Luca","family":"Fibbi","sequence":"additional","affiliation":[{"name":"Laboratory of Monitoring and Environmental Modelling for the Sustainable Development (LaMMA), 50019 Sesto Fiorentino, Italy"},{"name":"Institute for the Bioeconony (IBE), National Research Council (CNR), 50019 Sesto Fiorentino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3864-8411","authenticated-orcid":false,"given":"Alberto","family":"Ortolani","sequence":"additional","affiliation":[{"name":"Laboratory of Monitoring and Environmental Modelling for the Sustainable Development (LaMMA), 50019 Sesto Fiorentino, Italy"},{"name":"Institute for the Bioeconony (IBE), National Research Council (CNR), 50019 Sesto Fiorentino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2728-4272","authenticated-orcid":false,"given":"Giovanna Maria","family":"Dimitri","sequence":"additional","affiliation":[{"name":"Dipartimento SPS, Universit\u00e1 Degli Studi di Milano, Via Festa del Perdono 7, 20122 Milan, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6493","DOI":"10.1038\/s41467-024-49699-8","article-title":"Assessing flash flood erosion following storm Daniel in Libya","volume":"15","author":"Normand","year":"2024","journal-title":"Nat Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s43832-024-00185-8","article-title":"The impact of dam management and rainfall patterns on flooding in the Niger Delta: Using Sentinel-1 SAR data","volume":"4","author":"Eteh","year":"2024","journal-title":"Discov Water"},{"key":"ref_3","unstructured":"(2025, June 11). Climate Change Made Devastating Brazil Floods Twice as Likely, Scientists Say. Available online: https:\/\/www.reuters.com\/business\/environment\/climate-change-made-devastating-brazil-floods-twice-likely-scientists-say-2024-06-03\/."},{"key":"ref_4","unstructured":"European Environment Agency (2025, June 11). Economic Losses from Weather- and Climate-Related Extremes in Europe. Available online: https:\/\/www.eea.europa.eu\/en\/analysis\/indicators\/economic-losses-from-climate-related."},{"key":"ref_5","unstructured":"Rocca, M.L. (2025, June 11). Valencia Flood, Relatives of Victims Demand Truth and Justice from EU. Available online: https:\/\/www.eunews.it\/en\/2025\/05\/13\/valencia-flood-relatives-of-victims-demand-truth-and-justice-from-eu\/."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/nature14956","article-title":"The quiet revolution of numerical weather prediction","volume":"525","author":"Bauer","year":"2015","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e31648","DOI":"10.1016\/j.heliyon.2024.e31648","article-title":"Precision agriculture for wine production: A machine learning approach to link weather conditions and wine quality","volume":"10","author":"Dimitri","year":"2024","journal-title":"Heliyon"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"15787","DOI":"10.1029\/92JD01517","article-title":"GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System","volume":"97","author":"Bevis","year":"1992","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5385","DOI":"10.5194\/amt-9-5385-2016","article-title":"Review of the state of the art and future prospects of the ground-based GNSS meteorology in Europe","volume":"9","author":"Guerova","year":"2016","journal-title":"Atmos. Meas. Tech."},{"key":"ref_10","first-page":"76","article-title":"Real-time retrieval of precipitable water vapor from GPS precise point positioning","volume":"109","author":"Yuan","year":"2014","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_11","first-page":"60","article-title":"On the inclusion of GPS PWV in nowcasting models for precipitation prediction","volume":"220","author":"Benevides","year":"2019","journal-title":"Atmos. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3885","DOI":"10.1175\/MWR-D-18-0187.1","article-title":"Neural networks for postprocessing ensemble weather forecasts","volume":"146","author":"Rasp","year":"2018","journal-title":"Mon. Weather. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Srinu, N., and Bindu, B.H. (2022, January 8\u20139). A Review on Machine Learning and Deep Learning based Rainfall Prediction Methods. Proceedings of the 2022 International Conference on Power, Energy, Control and Transmission Systems (ICPECTS), Chennai, India.","DOI":"10.1109\/ICPECTS56089.2022.10047554"},{"key":"ref_14","first-page":"103946","article-title":"Machine learning for precipitation prediction: A review","volume":"226","author":"Camargo","year":"2022","journal-title":"Earth-Sci. Rev."},{"key":"ref_15","unstructured":"Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-K., and Woo, W.-C. (2015, January 7\u201312). Convolutional LSTM network: A machine learning approach for precipitation nowcasting. Proceedings of the Advances in Neural Information Processing Systems 28, Montreal, QC, Canada."},{"key":"ref_16","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_17","unstructured":"Tishby, N., Pereira, F.C., and Bialek, W. The information bottleneck method. Proceedings of the 37th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cao, J., Zhang, H., Liu, Y., Xu, X., Dong, X., and Zhang, R. (2023). Mutual Information Boosted Precipitation Nowcasting from Radar Images. Remote Sens., 15.","DOI":"10.3390\/rs15061639"},{"key":"ref_19","unstructured":"Alemi, A.A., Fischer, I., Dillon, J.V., and Murphy, K. (2017). Deep Variational Information Bottleneck. arXiv."},{"key":"ref_20","unstructured":"Grandvalet, Y., and Bengio, Y. (2004, January 13\u201318). Semi-supervised learning by entropy minimization. Proceedings of the 18th International Conference on Neural Information Processing Systems (NIPS\u201904), Vancouver, BC, Canada."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s10291-020-00976-1","article-title":"MG-APP: An open-source software for multi-GNSS precise point positioning and application analysis","volume":"24","author":"Xiao","year":"2020","journal-title":"GPS Solut."},{"key":"ref_22","first-page":"ACL 3-1","article-title":"Integrated atmospheric water vapor estimates from a regional GPS network","volume":"107","year":"2002","journal-title":"J. Geophys. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1175\/1520-0426(1995)012<0468:GSOAWV>2.0.CO;2","article-title":"GPS\/STORM\u2014GPS Sensing of Atmospheric Water Vapor for Meteorology","volume":"12","author":"Rocken","year":"1995","journal-title":"J. Atmos. Oceanic Technol."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"066138","DOI":"10.1103\/PhysRevE.69.066138","article-title":"Estimating mutual information","volume":"69","author":"Kraskov","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3157","DOI":"10.5194\/hess-24-3157-2020","article-title":"The accuracy of weather radar in heavy rain: A comparative study for Denmark, the Netherlands, Finland and Sweden","volume":"24","author":"Schleiss","year":"2020","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_27","unstructured":"Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Hor\u00e1nyi, A., Mu\u00f1oz Sabater, J., Nicolas, J., Peubey, C., Radu, R., and Rozum, I. (2025, July 30). ERA5 Hourly Data on Single Levels from 1940 to Present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS). Available online: https:\/\/cds.climate.copernicus.eu\/datasets\/reanalysis-era5-single-levels?tab=overview."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1034\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T08:23:11Z","timestamp":1759393391000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,2]]},"references-count":27,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["e27101034"],"URL":"https:\/\/doi.org\/10.3390\/e27101034","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,2]]}}}