Articles | Volume 18, issue 19
https://doi.org/10.5194/amt-18-4907-2025
© 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-18-4907-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
30 Sep 2025
Research article |
| 30 Sep 2025
| 30 Sep 2025
Assimilation of global navigation satellite system (GNSS) zenith delays and tropospheric gradients: a sensitivity study utilizing sparse and dense station networks
Rohith Thundathil
CORRESPONDING AUTHOR
Institute of Geodesy and Geoinformation Sciences, Technische Universität, Berlin, Kaiserin-Augusta-Allee 104, 10553 Berlin, Germany
Section 1.1 Space Geodetic Techniques, GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Florian Zus
Section 1.1 Space Geodetic Techniques, GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Galina Dick
Section 1.1 Space Geodetic Techniques, GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Jens Wickert
Institute of Geodesy and Geoinformation Sciences, Technische Universität, Berlin, Kaiserin-Augusta-Allee 104, 10553 Berlin, Germany
Section 1.1 Space Geodetic Techniques, GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Related authors
Florian Zus, Kyriakos Balidakis, Ali Hasan Dogan, Rohith Thundathil, Galina Dick, and Jens Wickert
Geosci. Model Dev., 18, 4951–4964, https://doi.org/10.5194/gmd-18-4951-2025, https://doi.org/10.5194/gmd-18-4951-2025, 2025
Short summary
Short summary
Atmospheric signal propagation effects are one of the largest error sources in the analysis of space geodetic techniques. Inaccuracies in the modelling map into errors in positioning, navigation and timing. We describe the open-source ray-tracing tool DNS and show the two outstanding features of this tool compared to previous model developments: it can handle both the troposphere and the ionosphere, and it does so efficiently. This makes the tool perfectly suited for geoscientific applications.
Rohith Thundathil, Florian Zus, Galina Dick, and Jens Wickert
Geosci. Model Dev., 17, 3599–3616, https://doi.org/10.5194/gmd-17-3599-2024, https://doi.org/10.5194/gmd-17-3599-2024, 2024
Short summary
Short summary
Global Navigation Satellite Systems (GNSS) provides moisture observations through its densely distributed ground station network. In this research, we assimilate a new type of observation called tropospheric gradient observations, which has never been incorporated into a weather model. We develop a forward operator for gradient-based observations and conduct an assimilation impact study. The study shows significant improvements in the model's humidity fields.
Florian Zus, Kyriakos Balidakis, Ali Hasan Dogan, Rohith Thundathil, Galina Dick, and Jens Wickert
Geosci. Model Dev., 18, 4951–4964, https://doi.org/10.5194/gmd-18-4951-2025, https://doi.org/10.5194/gmd-18-4951-2025, 2025
Short summary
Short summary
Atmospheric signal propagation effects are one of the largest error sources in the analysis of space geodetic techniques. Inaccuracies in the modelling map into errors in positioning, navigation and timing. We describe the open-source ray-tracing tool DNS and show the two outstanding features of this tool compared to previous model developments: it can handle both the troposphere and the ionosphere, and it does so efficiently. This makes the tool perfectly suited for geoscientific applications.
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.
Rohith Thundathil, Florian Zus, Galina Dick, and Jens Wickert
Geosci. Model Dev., 17, 3599–3616, https://doi.org/10.5194/gmd-17-3599-2024, https://doi.org/10.5194/gmd-17-3599-2024, 2024
Short summary
Short summary
Global Navigation Satellite Systems (GNSS) provides moisture observations through its densely distributed ground station network. In this research, we assimilate a new type of observation called tropospheric gradient observations, which has never been incorporated into a weather model. We develop a forward operator for gradient-based observations and conduct an assimilation impact study. The study shows significant improvements in the model's humidity fields.
Ladina Steiner, Holger Schmithüsen, Jens Wickert, and Olaf Eisen
The Cryosphere, 17, 4903–4916, https://doi.org/10.5194/tc-17-4903-2023, https://doi.org/10.5194/tc-17-4903-2023, 2023
Short summary
Short summary
The present study illustrates the potential of a combined Global Navigation Satellite System reflectometry and refractometry (GNSS-RR) method for accurate, simultaneous, and continuous estimation of in situ snow accumulation, snow water equivalent, and snow density time series. The combined GNSS-RR method was successfully applied on a fast-moving, polar ice shelf. The combined GNSS-RR approach could be highly advantageous for a continuous quantification of ice sheet surface mass balances.
Karina Wilgan, Galina Dick, Florian Zus, and Jens Wickert
Atmos. Meas. Tech., 15, 21–39, https://doi.org/10.5194/amt-15-21-2022, https://doi.org/10.5194/amt-15-21-2022, 2022
Short summary
Short summary
The assimilation of GNSS data in weather models has a positive impact on the forecasts. The impact is still limited due to using only the GPS zenith direction parameters. We calculate and validate more advanced tropospheric products from three satellite systems: the US American GPS, Russian GLONASS and European Galileo. The quality of all the solutions is comparable; however, combining more GNSS systems enhances the observations' geometry and improves the quality of the weather forecasts.
Benjamin Männel, Florian Zus, Galina Dick, Susanne Glaser, Maximilian Semmling, Kyriakos Balidakis, Jens Wickert, Marion Maturilli, Sandro Dahlke, and Harald Schuh
Atmos. Meas. Tech., 14, 5127–5138, https://doi.org/10.5194/amt-14-5127-2021, https://doi.org/10.5194/amt-14-5127-2021, 2021
Short summary
Short summary
Within the MOSAiC expedition, GNSS was used to monitor variations in atmospheric water vapor. Based on 15 months of continuously tracked data, coordinates and hourly zenith total delays (ZTDs) were determined using kinematic precise point positioning. The derived ZTD values agree within few millimeters with ERA5 and terrestrial GNSS and VLBI stations. The derived integrated water vapor corresponds to the frequently launched radiosondes (0.08 ± 0.04 kg m−2, rms of the differences of 1.47 kg m−2).
Cited articles
Bar-Sever, Y. E., Kroger, P. M., and Borjesson, J. A.: Estimating horizontal gradients of tropospheric path delay with a single GPS receiver, J. Geophys. Res.-Sol. Ea., 103, 5019–5035, https://doi.org/10.1029/97JB03534, 1998.
Bennitt, G. V. and Jupp, A.: Operational assimilation of GPS zenith total delay observations into the Met Office numerical weather prediction models, Mon. Weather Rev., 140, 2706–2719, https://doi.org/10.1175/MWR-D-11-00156.1, 2012.
Bevis, M., Businger, S., Herring, T. A., Rocken, C., Anthes, R. A., and Ware, R. H.: GPS meteorology: Remote sensing of atmospheric water vapor using the global positioning system, J. Geophys. Res.-Atmos., 97, 15787–15801, https://doi.org/10.1029/92JD01517, 1992.
Boniface, K., Ducrocq, V., Jaubert, G., Yan, X., Brousseau, P., Masson, F., Champollion, C., Chéry, J., and Doerflinger, E.: Impact of high-resolution data assimilation of GPS zenith delay on Mediterranean heavy rainfall forecasting, Ann. Geophys., 27, 2739–2753, https://doi.org/10.5194/angeo-27-2739-2009, 2009.
Brenot, H., Neméghaire, J., Delobbe, L., Clerbaux, N., De Meutter, P., Deckmyn, A., Delcloo, A., Frappez, L., and Van Roozendael, M.: Preliminary signs of the initiation of deep convection by GNSS, Atmos. Chem. Phys., 13, 5425–5449, https://doi.org/10.5194/acp-13-5425-2013, 2013.
Caldas-Alvarez, A. and Khodayar, S.: Assessing atmospheric moisture effects on heavy precipitation during HyMeX IOP16 using GPS nudging and dynamical downscaling, Nat. Hazards Earth Syst. Sci., 20, 2753–2776, https://doi.org/10.5194/nhess-20-2753-2020, 2020.
Chen, F. and Dudhia, J.: Coupling an advanced land surface-hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity, Mon. Weather Rev., 129, 569–585, https://doi.org/10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2, 2001.
Davis, J. L., Elgered, G., Niell, A. E., and Kuehn, C. E.: Ground-based measurement of gradients in the “wet” radio refractivity of air, Radio Sci., 28, 1003–1018, https://doi.org/10.1029/93RS01917, 1993.
Douša, J., Dick, G., Kačmařík, M., Brožková, R., Zus, F., Brenot, H., Stoycheva, A., Möller, G., and Kaplon, J.: Benchmark campaign and case study episode in central Europe for development and assessment of advanced GNSS tropospheric models and products, Atmos. Meas. Tech., 9, 2989–3008, https://doi.org/10.5194/amt-9-2989-2016, 2016.
Gendt, G., Dick, G., Reigber, C., Tomassini, M., Liu, Y., and Ramatschi, M.: Near real time GPS water vapor monitoring for numerical weather prediction in Germany, J. Meteorol. Soc. Jpn. Ser. II, 82, 361–370, https://doi.org/10.2151/jmsj.2004.361, 2004.
Giannaros, C., Kotroni, V., Lagouvardos, K., Giannaros, T. M., and Pikridas, C.: Assessing the impact of GNSS ZTD data assimilation into the WRF modeling system during high-impact rainfall events over Greece, Remote Sens., 12, 383, https://doi.org/10.3390/rs12030383, 2020.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J. N.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020.
Grell, G. A. and Freitas, S. R.: A scale and aerosol aware stochastic convective parameterization for weather and air quality modeling, Atmos. Chem. Phys., 14, 5233–5250, https://doi.org/10.5194/acp-14-5233-2014, 2014.
Hong, S.-Y. and Lim, J.-O. J.: The WRF single-moment 6-class microphysics scheme (WSM6), Asia-Pac. J. Atmos. Sci., 42, 129–151, https://www.dbpia.co.kr/journal/articleDetail?nodeId=node00937254 (last access: 25 September 2025), 2006.
Hong, S.-Y., Lim, K.-S. S., Lee, Y.-H., Ha, J.-C., Kim, H.-W., Ham, S.-J., and Dudhia, J.: Evaluation of the WRF double-moment 6-class microphysics scheme for precipitating convection, Adv. Meteorol., 2010, 707253, https://doi.org/10.1155/2010/707253, 2010.
Iacono, M. J., Delamere, J. S., Mlawer, E. J., Shephard, M. W., Clough, S. A., and Collins, W. D.: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models, J. Geophys. Res.-Atmos., 113, D13103, https://doi.org/10.1029/2008JD009944, 2008.
Iwabuchi, T., Miyazaki, S. I., Heki, K., Naito, I., and Hatanaka, Y.: An impact of estimating tropospheric delay gradients on tropospheric delay estimations in the summer using the Japanese nationwide GPS array, J. Geophys. Res.-Atmos., 108, https://doi.org/10.1029/2002JD002214, 2003.
Kačmařík, M., Douša, J., Zus, F., Václavovic, P., Balidakis, K., Dick, G., and Wickert, J.: Sensitivity of GNSS tropospheric gradients to processing options, Ann. Geophys., 37, 429–446, https://doi.org/10.5194/angeo-37-429-2019, 2019.
Lagasio, M., Pulvirenti, L., Parodi, A., Boni, G., Pierdicca, N., Venuti, G., Realini, E., Tagliaferro, G., Barindelli S., and Rommen, B.: Effect of the ingestion in the WRF model of different Sentinel-derived and GNSS-derived products: analysis of the forecasts of a high impact weather event, Eur. J. Remote Sens., 52, 16–33, https://doi.org/10.1080/22797254.2019.1642799, 2019.
Lauer, A., Devaney, J., Kieu, C., Kravitz, B., O'Brien, T. A., Robeson, S. M., Staten, P. W., and Vu, T. A.: A convection-permitting dynamically downscaled dataset over the Midwestern United States, Geosci. Data J., 10, 429–446, https://doi.org/10.1002/gdj3.188, 2023.
Li, X., Zus, F., Lu, C., Ning, T., Dick, G., Ge, M., Wickert, J., and Schuh, H.: Retrieving high-resolution tropospheric gradients from multiconstellation GNSS observations, Geophys. Res. Lett., 42, 4173–4181, https://doi.org/10.1002/2015GL063856, 2015.
Lindskog, M., Ridal, M., Thorsteinsson, S., and Ning, T.: Data assimilation of GNSS zenith total delays from a Nordic processing centre, Atmos. Chem. Phys., 17, 13983–13998, https://doi.org/10.5194/acp-17-13983-2017, 2017.
Mahfouf, J. F., Ahmed, F., Moll, P., and Teferle, F. N.: Assimilation of zenith total delays in the AROME France convective scale model: a recent assessment, Tellus A, 67, 26106, https://doi.org/10.3402/tellusa.v67.26106, 2015.
Mascitelli, A., Federico, S., Fortunato, M., Avolio, E., Torcasio, R. C., Realini, E., Mazzoni, A., Transerici, C., Crespi, M., and Dietrich, S.: Data assimilation of GPS-ZTD into the RAMS model through 3D-Var: preliminary results at the regional scale, Meas. Sci. Technol., 30, 055801, https://doi.org/10.1088/1361-6501/ab0b87, 2019.
Mascitelli, A., Federico, S., Torcasio, R. C., and Dietrich, S.: Assimilation of GPS Zenith Total Delay estimates in RAMS NWP model: Impact studies over central Italy, Adv. Space Res., 68, 4783–4793, https://doi.org/10.1016/j.asr.2020.08.031, 2021.
Morel, L., Pottiaux, E., Durand, F., Fund, F., Boniface, K., de Oliveira Junior, P. S., and Van Baelen, J.: Validity and behaviour of TGs estimated by GPS in Corsica, Adv. Space Res., 55, 135–149, https://doi.org/10.1016/j.asr.2014.10.004, 2015.
Parrish, D. F. and Derber, J. C.: The National Meteorological Center's spectral statistical-interpolation analysis system, Mon. Weather Rev., 120, 1747–1763, https://repository.library.noaa.gov/view/noaa/11449 (last access: 23 September 2025), 1992.
Poli, P., Moll, P., Rabier, F., Desroziers, G., Chapnik, B., Berre, L., Healy, S. B., Andersson, E., and El Guelai, F. Z.: Forecast impact studies of zenith total delay data from European near real-time GPS stations in Météo France 4DVAR, J. Geophys. Res.-Atmos., 112, https://doi.org/10.1029/2006JD007430, 2007.
Powers, J. G., Klemp, J. B., Skamarock, W. C., Davis, C. A., Dudhia, J., Gill, D. O., Coen, J. L., Gochis, D. J., Ahmadov, R., Peckham, S. E., Grell, G. A., Michalakes, J., Trahan, S., Benjamin, S. G., Alexander, C. R., Dimego, G. J., Wang, W., Schwartz, C. S., Romine, G. S., Liu, Z., Snyder, C., Chen, F., Barlage, M. J., Yu, W., and Duda, M. G.: The weather research and forecasting model: Overview, system efforts, and future directions, B. Am. Meteorol. Soc., 98, 1717–1737, https://doi.org/10.1175/BAMS-D-15-00308.1, 2017.
Risanto, C. B., Castro, C. L., Arellano, A. F., Moker, J. M., and Adams, D. K.: The impact of assimilating GPS precipitable water vapor in convective-permitting WRF-ARW on North American Monsoon precipitation forecasts over Northwest Mexico, Mon. Weather Rev., 149, 3013–3035, https://doi.org/10.1175/MWR-D-20-0394.1, 2021.
Rohm, W., Guzikowski, J., Wilgan, K., and Kryza, M.: 4DVAR assimilation of GNSS zenith path delays and precipitable water into a numerical weather prediction model WRF, Atmos. Meas. Tech., 12, 345–361, https://doi.org/10.5194/amt-12-345-2019, 2019.
Singh, R., Ojha, S. P., Puviarasan, N., and Singh, V.: Impact of GNSS signal delay assimilation on short range weather forecasts over the Indian region, J. Geophys. Res.-Atmos., 124, 9855–9873, https://doi.org/10.1029/2019JD030866, 2019.
Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Duda, M. G., Huang, X., Wang, W., Powers, J. G.: A Description of the Advanced Research WRF Version 3, NCAR Tech. Note, https://doi.org/10.5065/D68S4MVH, 2008.
Thayer, G. D.: An improved equation for the radio refractive index of air, Radio Sci., 9, 803–807, https://doi.org/10.1029/RS009i010p00803, 1974.
Thompson, G., Field, P. R., Rasmussen, R. M., and Hall, W. D.: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization, Mon. Weather Rev., 136, 5095–5115, https://doi.org/10.1175/2008MWR2387.1, 2008.
Thundathil, R., Zus, F., Dick, G., and Wickert, J.: Assimilation of GNSS tropospheric gradients into the Weather Research and Forecasting (WRF) model version 4.4.1, Geosci. Model Dev., 17, 3599–3616, https://doi.org/10.5194/gmd-17-3599-2024, 2024a.
Thundathil, R., Zus, F., Dick, G., and Wickert, J.: Assimilation of GNSS Zenith Delays and Tropospheric Gradients: A Sensitivity Study utilizing sparse and dense station networks, Zenodo [data set and code], https://doi.org/10.5281/zenodo.13734634, 2024b.
Václavovic, P., Douša, J., and Györi, G.: G-Nut software library – State of development and first results, Acta Geodyn. Geomater., 10, 431–436, https://doi.org/10.13168/AGG.2013.0042, 2014.
Vedel, H. and Huang, X. Y.: Impact of ground based GPS data on numerical weather prediction, J. Meteorol. Soc. Jpn. Ser. II, 82, 459–472, https://doi.org/10.2151/jmsj.2004.459, 2004.
Walpersdorf, A., Calais, E., Haase, J., Eymard, L., Desbois, M., and Vedel, H.: Atmospheric gradients estimated by GPS compared to a high resolution numerical weather prediction (NWP) model, Phys. Chem. Earth A, 26, 147–152, https://doi.org/10.1016/S1464-1895(01)00038-2, 2001.
Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P.: Image quality assessment: from error visibility to structural similarity, IEEE Trans. Image Process., 13, 600–612, https://doi.org/10.1109/TIP.2003.819861, 2004.
Wickert, J., Dick, G., Schmidt, T., Asgarimehr, M., Antonoglou, N., Arras, C., Brack, A., Ge, M., Kepkar, A., Männel, B., Nguyen, C., Oluwadare, T. S., Schuh, H., Semmling, M., Simeonov, T., Vey, S., Wilgan, K., and Zus, F.:GNSS Remote Sensing at GFZ: Ove: GNSS remote sensing at GFZ: Overview and recent results, ZfV-Z. Geod. Geoinf. Landmanag., 5/2020, https://doi.org/10.12902/zfv-0320-2020, 2020.
Yan, X., Ducrocq, V., Poli, P., Hakam, M., Jaubert, G., and Walpersdorf, A.: Impact of GPS zenith delay assimilation on convective-scale prediction of Mediterranean heavy rainfall, J. Geophys. Res.-Atmos., 114, https://doi.org/10.1029/2008JD011036, 2009.
Yang, S. C., Huang, Z. M., Huang, C. Y., Tsai, C. C., and Yeh, T. K.: A case study on the impact of ensemble data assimilation with GNSS-zenith total delay and radar data on heavy rainfall prediction, Mon. Weather Rev., 148, 1075–1098, https://doi.org/10.1175/MWR-D-18-0418.1, 2020.
Zus, F., Douša, J., Kačmařík, M., Václavovic, P., Dick, G., and Wickert, J.: Estimating the impact of GNSS horizontal delay gradients in variational data assimilation, Remote Sens., 11, 41, https://doi.org/10.3390/rs11010041, 2019.
Zus, F., Thundathil, R., Dick, G., and Wickert, J.: Fast Observation Operator for Global Navigation Satellite System TGs, Remote Sens., 15, 5114, https://doi.org/10.3390/rs15215114, 2023.
Zus, F., Balidakis, K., Dogan, A. H., Thundathil, R., Dick, G., and Wickert, J.: DNS (v1.0): An open source ray-tracing tool for space geodetic techniques, Geosci. Model Dev. Discuss. [preprint], https://doi.org/10.5194/gmd-2024-237, in review, 2025.
Short summary
Tropospheric gradients provide information on the moisture distribution, whereas zenith total delays provide the overall moisture information along the zenith. When both observations are used together, the model can actuate the moisture fields, correcting their dynamics. Our research shows that, in regions with very few stations, assimilating tropospheric gradients on top of zenith total delay observations can enhance the performance of existing improvements.
Tropospheric gradients provide information on the moisture distribution, whereas zenith total...
