Articles | Volume 18, issue 1
https://doi.org/10.5194/amt-18-57-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-18-57-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 Jan 2025
Research article |
| 07 Jan 2025
| 07 Jan 2025
Global Navigation Satellite System (GNSS) radio occultation climatologies mapped by machine learning and Bayesian interpolation
Endrit Shehaj
CORRESPONDING AUTHOR
STAR Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Stephen Leroy
Atmospheric and Environmental Research, Lexington, MA 02421, USA
Kerri Cahoy
STAR Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Alain Geiger
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Laura Crocetti
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Gregor Moeller
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Department of Geodesy and Geoinformation, TU Wien, Vienna, Austria
Benedikt Soja
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Markus Rothacher
Institute of Geodesy and Photogrammetry, ETH Zürich, Zurich, 8093, Switzerland
Related authors
Endrit Shehaj, Stephen Leroy, Kerri Cahoy, Juliana Chew, and Benedikt Soja
EGUsphere, https://doi.org/10.5194/egusphere-2025-1516, https://doi.org/10.5194/egusphere-2025-1516, 2025
Short summary
Short summary
This work investigates the capability of machine learning models, trained with space and ground GNSS observations, to produce fields of refractivity and IWV that describe the spatiotemporal morphology of atmospheric rivers (ARs) and quantify moisture associated with them to a degree sufficient for atmospheric studies. The reconstructed fields can be used to monitor ARs. It studies what LEO radio occultation (RO) constellation is appropriate to quantify the structure, location and timing of ARs.
Benjamin Fersch, Andreas Wagner, Bettina Kamm, Endrit Shehaj, Andreas Schenk, Peng Yuan, Alain Geiger, Gregor Moeller, Bernhard Heck, Stefan Hinz, Hansjörg Kutterer, and Harald Kunstmann
Earth Syst. Sci. Data, 14, 5287–5307, https://doi.org/10.5194/essd-14-5287-2022, https://doi.org/10.5194/essd-14-5287-2022, 2022
Short summary
Short summary
In this study, a comprehensive multi-disciplinary dataset for tropospheric water vapor was developed. Geodetic, photogrammetric, and atmospheric modeling and data fusion techniques were used to obtain maps of water vapor in a high spatial and temporal resolution. It could be shown that regional weather simulations for different seasons benefit from assimilating these maps and that the combination of the different observation techniques led to positive synergies.
Sara Vannah, Stephen S. Leroy, Chi O. Ao, E. Robert Kursinski, Kevin J. Nelson, Kuo-Nung Wang, and Feiqin Xie
Atmos. Meas. Tech., 18, 4293–4310, https://doi.org/10.5194/amt-18-4293-2025, https://doi.org/10.5194/amt-18-4293-2025, 2025
Short summary
Short summary
Uncertainty estimation for Global Navigation Satellite System (GNSS) radio occultation (RO) soundings in the planetary boundary layer (PBL) depends on the algorithms used to process the RO data. We compare the refractivity retrievals from three RO processing centers – each with their own retrieval algorithm – in the PBL, finding a strong underestimation of refractivity in regions with the strongest refractivity gradients, especially in Jet Propulsion Laboratory (JPL) processing, as well as areas of weak overestimation of refractivity near the poles.
Endrit Shehaj, Stephen Leroy, Kerri Cahoy, Juliana Chew, and Benedikt Soja
EGUsphere, https://doi.org/10.5194/egusphere-2025-1516, https://doi.org/10.5194/egusphere-2025-1516, 2025
Short summary
Short summary
This work investigates the capability of machine learning models, trained with space and ground GNSS observations, to produce fields of refractivity and IWV that describe the spatiotemporal morphology of atmospheric rivers (ARs) and quantify moisture associated with them to a degree sufficient for atmospheric studies. The reconstructed fields can be used to monitor ARs. It studies what LEO radio occultation (RO) constellation is appropriate to quantify the structure, location and timing of ARs.
Yuanxin Pan, Grzegorz Kłopotek, Laura Crocetti, Rudi Weinacker, Tobias Sturn, Linda See, Galina Dick, Gregor Möller, Markus Rothacher, Ian McCallum, Vicente Navarro, and Benedikt Soja
Atmos. Meas. Tech., 17, 4303–4316, https://doi.org/10.5194/amt-17-4303-2024, https://doi.org/10.5194/amt-17-4303-2024, 2024
Short summary
Short summary
Crowdsourced smartphone GNSS data were processed with a dedicated data processing pipeline and could produce millimeter-level accurate estimates of zenith total delay (ZTD) – a critical atmospheric variable. This breakthrough not only demonstrates the feasibility of using ubiquitous devices for high-precision atmospheric monitoring but also underscores the potential for a global, cost-effective tropospheric monitoring network.
Nicholas Belsten, Mary Knapp, Rebecca Masterson, Cadence Payne, Kristen Ammons, Frank D. Lind, and Kerri Cahoy
Geosci. Instrum. Method. Data Syst., 12, 201–213, https://doi.org/10.5194/gi-12-201-2023, https://doi.org/10.5194/gi-12-201-2023, 2023
Short summary
Short summary
AERO and VISTA spacecraft will use commercial magnetometers to measure space weather events near Earth’s aurora. The small size of AERO and VISTA necessitate the use of magnetometers with small size, weight, and power. The magnetometers selected exhibit good precision, but additional calibration is needed to achieve good accuracy. This work evaluates a method for calibration by regression which has reduced the magnetic observed error by a factor of ca. 50, meeting mission requirements.
Alex Meredith, Stephen Leroy, Lucy Halperin, and Kerri Cahoy
Atmos. Meas. Tech., 16, 3345–3361, https://doi.org/10.5194/amt-16-3345-2023, https://doi.org/10.5194/amt-16-3345-2023, 2023
Short summary
Short summary
We developed a new efficient algorithm leveraging orbital dynamics to collocate radio occultation soundings with microwave radiance soundings. This new algorithm is 99 % accurate and is much faster than traditional collocation-finding approaches. Speeding up collocation finding is useful for calibrating and validating microwave radiometers and for data assimilation into numerical weather prediction models. Our algorithm can also be used to predict collocation yield for new satellite missions.
Benjamin Fersch, Andreas Wagner, Bettina Kamm, Endrit Shehaj, Andreas Schenk, Peng Yuan, Alain Geiger, Gregor Moeller, Bernhard Heck, Stefan Hinz, Hansjörg Kutterer, and Harald Kunstmann
Earth Syst. Sci. Data, 14, 5287–5307, https://doi.org/10.5194/essd-14-5287-2022, https://doi.org/10.5194/essd-14-5287-2022, 2022
Short summary
Short summary
In this study, a comprehensive multi-disciplinary dataset for tropospheric water vapor was developed. Geodetic, photogrammetric, and atmospheric modeling and data fusion techniques were used to obtain maps of water vapor in a high spatial and temporal resolution. It could be shown that regional weather simulations for different seasons benefit from assimilating these maps and that the combination of the different observation techniques led to positive synergies.
Matthias Aichinger-Rosenberger, Elmar Brockmann, Laura Crocetti, Benedikt Soja, and Gregor Moeller
Atmos. Meas. Tech., 15, 5821–5839, https://doi.org/10.5194/amt-15-5821-2022, https://doi.org/10.5194/amt-15-5821-2022, 2022
Short summary
Short summary
This study develops an innovative approach for the detection and prediction of foehn winds. The approach uses products generated from GNSS (Global Navigation Satellite Systems) in combination with machine learning-based classification algorithms to detect and predict foehn winds at Altdorf, Switzerland. Results are encouraging and comparable to similar studies using meteorological data, which might qualify the method as an additional tool for short-term foehn forecasting in the future.
Roberto Villalobos-Herrera, Emanuele Bevacqua, Andreia F. S. Ribeiro, Graeme Auld, Laura Crocetti, Bilyana Mircheva, Minh Ha, Jakob Zscheischler, and Carlo De Michele
Nat. Hazards Earth Syst. Sci., 21, 1867–1885, https://doi.org/10.5194/nhess-21-1867-2021, https://doi.org/10.5194/nhess-21-1867-2021, 2021
Short summary
Short summary
Climate hazards may be caused by events which have multiple drivers. Here we present a method to break down climate model biases in hazard indicators down to the bias caused by each driving variable. Using simplified fire and heat stress indicators driven by temperature and relative humidity as examples, we show how multivariate indicators may have complex biases and that the relationship between driving variables is a source of bias that must be considered in climate model bias corrections.
Cited articles
Aichinger-Rosenberger, M., Brockmann, E., Crocetti, L., Soja, B., and Moeller, G.: Machine learning-based prediction of Alpine foehn events using GNSS troposphere products: first results for Altdorf, Switzerland, Atmos. Meas. Tech., 15, 5821–5839, https://doi.org/10.5194/amt-15-5821-2022, 2022.
Crocetti, L., Schartner, M., and Soja, B.: Discontinuity Detection in GNSS Station Coordinate Time Series Using Machine Learning, Remote Sens., 13, 3906, https://doi.org/10.3390/rs13193906, 2021.
Crocetti, L., Schartner, M., Zus, F., Zhang, W., Moeller, G., Navarro, V., See, L., Schindler, K., and Soja, B.: Global, spatially explicit modelling of zenith wet delay with XGBoost, J. Geod., 98, 23, https://doi.org/10.1007/s00190-024-01829-2, 2024.
ECMWF: IFS documentation, https://www.ecmwf.int/en/publications/ifs-documentation (last access: 31 July 2023), 2023.
Foelsche, U., Borsche, M., Steiner, A., Gobiet, A., Pirscher, B., Kirchengast, G., Wickert, J., and Schmidt, T.: Observing upper troposphere–lower stratosphere climate with radio occultation data from the CHAMP satellite, Clim. Dynam., 31, 49–65, https://doi.org/10.1007/s00382-007-0337-7, 2008.
Foelsche, U., Scherllin-Pirscher, B., Ladstädter, F., Steiner, A. K., and Kirchengast, G.: Refractivity and temperature climate records from multiple radio occultation satellites consistent within 0.05 %, Atmos. Meas. Tech., 4, 2007–2018, https://doi.org/10.5194/amt-4-2007-2011, 2011.
Gou, J., Rösch, C., Shehaj, E., Chen, K., Kiani Shahvandi, M., Soja, B., and Rothacher, M.: Modelling the differences between ultra-rapid and final orbit products of GPS satellites using machine learning approaches, Remote Sens., 15, 5585, https://doi.org/10.3390/rs15235585, 2023.
Gou, J., Soja, B.: Global high-resolution total water storage anomalies from self-supervised data assimilation using deep learning algorithms, Nat. Water, 2, 139–150, https://doi.org/10.1038/s44221-024-00194-w, 2024.
Hassanien, A. E.: Machine Learning Paradigms: Theory and Application, Springer, https://doi.org/10.1007/978-3-030-02357-7, 2018.
Hastie, T., Tibshirani, R., and Friedman, J.: The Elements of Statistical Learning (2nd edition), Springer-Verlag, https://doi.org/10.1007/978-0-387-84858-7, 2009.
Haykin, S.O.: Neural Networks and Learning Machines, Pearson, https://dai.fmph.uniba.sk/courses/NN/haykin.neural-networks.3ed.2009.pdf (last access: 10 December 2024), 2009.
Ho, S. P., Zhou, X., Shao, X., Zhang, B., Adhikari, L., Kireev, S., He, Y., Yoe, J. G., Xia-Serafino, W., and Lynch, E.: Initial Assessment of the COSMIC-2/FORMOSAT-7 Neutral Atmosphere Data Quality in NESDIS/STAR Using In Situ and Satellite Data, Remote Sens., 12, 4099, https://doi.org/10.3390/rs12244099, 2020.
Kiani Shahvandi, M., Schartner, M., and Soja, B.: Neural ODE Differential Learning and Its Application in Polar Motion Prediction, JGR Solid Earth, 127, e2022JB024775, https://doi.org/10.1029/2022JB024775, 2022.
Kiani Shahvandi, M., Dill, R., Dobslaw, H., Kehm, A., Bloßfeld, M., Schartner, M., Mishra, S., and Soja, B.: Geophysically informed machine learning for improving rapid estimation and short-term prediction of Earth orientation pa-rameters, JGR Solid Earth, 128, e2023JB026720, https://doi.org/10.1029/2023JB026720, 2023.
Kitpracha, C., Modiri, S., Asgarimchr, M., Heinkelmann, R., and Schuh, H.: Machine Learning based prediction of atmospheric zenith wet delay: A study using GNSS measurements in Wettzell and co-located VLBI observations, Vol. 21, EGU2019-4127, 2019.
Kursinski, E., Hajj, G., Schofield, J., Linfield, R., and Hardy, K.: Observing Earth's atmosphere with radio occultation measurements using the Global Positioning System, J. Geophys. Res., 102 (D19), 23429–23465, https://doi.org/10.1029/97JD01569, 1997.
Kursinski, E., Hajj, G., Leroy, S., and Herman, B.: The GPS radio occultation technique, Terr. Atmos. Ocean. Sci., 11, 53–114, https://doi.org/10.3319/TAO.2000.11.1.53(COSMIC), 2000.
Leroy, S.: The measurement of geopotential heights by GPS radio occultation, J. Geophys. Res., 102, 6971–6986, 1997.
Leroy, S., Ao, C., and Verkhoglyadova, O.: Mapping GPS Radio Occultation Data by Bayesian Interpolation, J. Atmos. Ocean. Technol., 29, 1062–1074, https://doi.org/10.1175/JTECH-D-11-00179.1, 2012.
Leroy, S., Ao, C., Verkhoglyadova, O., and Oyola, M.: Analyzing the Diurnal Cycle by Bayesian Interpolation on a Sphere for Mapping GNSS Radio Occultation Data, J. Atmos. Oceab. Technol., 38, 951–961, https://doi.org/10.1175/JTECH-D-20-0031.1, 2021.
MacKay, D.: Bayesian Interpolation, Neural Comput., 4, 415–447, 1992.
Mannucci, A. J., Ao, C., and Williamson, W.: GNSS Radio Occultation, in Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, Volume 1, 1st Edition, edited by: Morton, J. Y., van Diggelen, Fm., Spilker, Jr. J. J., and Parkinson, B. W., 1168 pp., John Wiley & Sons, https://doi.org/10.1002/9781119458449, 2021.
Melbourne, W. G.: Radio Occultations Using Earth Satellites: A Wave Theory Treatment, Deep Space Communications and Navigation Series, Monograph 6, Jet Proupulison Laboratory, California Institute of Technology, https://descanso.jpl.nasa.gov/monograph/series6/Full_Version_rev2.pdf (last access: 10 December 2024), 2004.
Miotti, L., Shehaj, E., Geiger, A., D'Aronco, S., Wegner, J. D., Moeller, G., and Rothacher, M.: Tropospheric delays derived from ground meteorological parameters: comparison between machine learning and empirical model approaches, 2020 European Navigation Conference (ENC), Dresden, Germany, 1–10 pp., https://doi.org/10.23919/ENC48637.2020.9317442, 2020.
Muir, J. and Tkalcic, H.: A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference, Geophys. J. Int., 203, 1164–1171, 2015.
Natras, R., Soja, B., and Schmidt, M.: Ensemble Machine Learning of Random Forest, AdaBoost and XGBoost for Vertical Total Electron Content Forecasting, Remote Sens., 14, 3547, https://doi.org/10.3390/rs14153547, 2022.
Nwankpa, C., Ijomah, W., Gachagan, A., and Marshall, S.: Activation Functions: Comparison of Trends in Practice and Research for Deep Learning, https://doi.org/10.48550/arXiv.1811.03378, 2018.
Rueger, J. M.: Refractive index formulae for radio waves. Proceedings of the FIG XXII International Congress, Washington D.C., USA, paper in JS28, 12 pp., https://api.semanticscholar.org/CorpusID:126525251 (last access: 10 December 2024), 2002.
Schreiner, W. S., Weiss, J. P., Anthes, R. A., Braun, J., Chu, V., Fong, J., Hunt, D., Kuo, Y.-H., Meehan, T., Serafino, W., Sjoberg, J., Sokolovskiy, S., Talaat, E., Wee, T. K., and Zeng, Z.: COSMIC-2 Radio Occultation Constellation: First Results, Geophys. Res. Lett., 47 , e2019GL086841, https://doi.org/10.1029/2019GL086841, 2020.
Shamshiri, R., Motagh, M., and Nahavandchi, H.: A machine learning-based regression technique for prediction of tropospheric phase delay on large-scale Sentinel-1 InSAR time-series, EGU, https://meetingorganizer.copernicus.org/EGU2019/EGU2019-10739.pdf (last access: 10 December 2024), 2019.
Shehaj, E.: Space Geodetic Techniques for Retrieval of High-Resolution Atmospheric Water Vapor Fields, PhD thesis, ETH Zurich, https://doi.org/10.3929/ethz-b-000618346, 2023.
Shehaj, E.: GNSS Radio Occultation Climatologies mapped by Machine Learning and Bayesian Interpolation (dataset and code example), ETH Zurich [data set, code], https://doi.org/10.3929/ethz-b-000670139, 2024.
Shehaj, E., Miotti, L., Geiger, A., D'Aronco, S., Wegner, J.D., Moeller, G., Soja, B., and Rothacher, M.: High-Resolution Tropospheric Refractivity Fields by Combining Machine Learning and Collocation Methods to Correct Earth Observation Data, Acta Astronaut., 204, 591–598, https://doi.org/10.1016/j.actaastro.2022.10.007, 2023.
Shi, J., Li, X., Li, L., Ouyang, C., and Xu, C.: An Efficient Deep Learning-Based Troposphere ZTD Dataset Generation Method for Massive GNSS CORS Stations, IEEE T. Geosci. Remote Sens., 61, 1–11, https://doi.org/10.1109/TGRS.2023.3276874, 2023.
Stanford CS: CS231n Convolutional Neural Networks for Visual Recognition, https://cs231n.github.io/ (last access: 15 February 2023), 2023.
UCAR: Constellation Observing System for Meteorology, Ionosphere and Climate, https://www.cosmic.ucar.edu/global-navigation-satellite-system-gnss-background/cosmic-2 (last access: 7 November 2022), 2022a.
UCAR: COSMIC-2 Data, Index of /gnss-ro/cosmic2/nrt/level2/, https://data.cosmic.ucar.edu/gnss-ro/cosmic2/nrt/level2/ (last acess: 7 November 2022), 2022b.
Wang, J. X., Wu, J. L., and Xiao, H.: Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data, Phys. Rev. Fluids, 2, 034603, https://doi.org/10.1103/PhysRevFluids.2.034603, 2017.
Zhang, B. and Yao, Y.: Precipitable water vapor fusion based on a generalized regression neural network, J. Geod., 95, 36, https://doi.org/10.1007/s00190-021-01482-z, 2021.
Short summary
This work investigates whether machine learning (ML) can offer an alternative to existing methods to map radio occultation (RO) products, allowing the extraction of information not visible in direct observations. ML can further improve the results of Bayesian interpolation, a state-of-the-art method to map RO observations. The results display improvements in horizontal and temporal domains, at heights ranging from the planetary boundary layer up to the lower stratosphere, and for all seasons.
This work investigates whether machine learning (ML) can offer an alternative to existing...
