Articles | Volume 18, issue 15
https://doi.org/10.5194/gmd-18-4951-2025
© 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/gmd-18-4951-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
DNS (v1.0): an open-source ray-tracing tool for space geodetic techniques
Florian Zus
CORRESPONDING AUTHOR
GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Kyriakos Balidakis
GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Federal Agency for Cartography and Geodesy (BKG), 60598 Frankfurt am Main, Germany
Ali Hasan Dogan
Department of Geomatics Engineering, Gaziosmanpasa University, 60150, Tokat, Türkiye
Rohith Thundathil
GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Technische Universität Berlin, 10623 Berlin, Germany
Galina Dick
GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Jens Wickert
GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Technische Universität Berlin, 10623 Berlin, Germany
Related authors
Rohith Thundathil, Florian Zus, Galina Dick, and Jens Wickert
Atmos. Meas. Tech., 18, 4907–4922, https://doi.org/10.5194/amt-18-4907-2025, https://doi.org/10.5194/amt-18-4907-2025, 2025
Short summary
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.
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.
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).
Rohith Thundathil, Florian Zus, Galina Dick, and Jens Wickert
Atmos. Meas. Tech., 18, 4907–4922, https://doi.org/10.5194/amt-18-4907-2025, https://doi.org/10.5194/amt-18-4907-2025, 2025
Short summary
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.
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).
Chaiyaporn Kitpracha, Robert Heinkelmann, Markus Ramatschi, Kyriakos Balidakis, Benjamin Männel, and Harald Schuh
Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2021-87, https://doi.org/10.5194/amt-2021-87, 2021
Preprint withdrawn
Short summary
Short summary
In this study, we expected to learn what are the potential effects of GNSS atmospheric delays from this unique experiment. The results show that the instrument effects on GNSS zenith delays were mitigated by using the same instrument. The radome causes unexpected bias of GNSS zenith delays in this study. Additionally, multipath effects at low-elevation observations degraded the tropospheric east gradients.
Cited articles
Alken, P., Thébault, E., Beggan, C. D., Amit, H., Aubert, J., Baerenzung, J., Bondar, T. N., Brown, W. J., Califf, S., Chambodut, A., Chulliat, A., Cox, G. A., Finlay, C. C., Fournier, A., Gillet, N., Grayver, A., Hammer, M. D., Holschneider, M., Huder, L., Hulot, G., Jager, T., Kloss, C., Korte, M., Kuang, W., Kuvshinov, A., Langlais, B., Léger, J.-M., Lesur, V., Livermore, P. W., Lowes, F. J., Macmillan, S., Magnes, W., Mandea, M., Marsal, S., Matzka, J., Metman, M. C., Minami, T., Morschhauser, A., Mound, J. E., Nair, M., Nakano, S., Olsen, N., Pavón-Carrasco, F. J., Petrov, V. G., Ropp, G., Rother, M., Sabaka, T. J., Sanchez, S., Saturnino, D., Schnepf, N. R., Shen, X., Stolle, C., Tangborn, A., Tøffner-Clausen, L., Toh, H., Torta, J. M., Varner, J., Vervelidou, F., Vigneron, P., Wardinski, I., Wicht, J., Woods, A., Yang, Y., Zeren, Z., and Zhou, B.: International Geomagnetic Reference Field: the thirteenth generation, Earth Planets Space, 73, 49, https://doi.org/10.1186/s40623-020-01288-x, 2021.
Bilitza, D.: International Reference Ionosphere 2000, Radio Sci., 36, 261–275, https://doi.org/10.1029/2000RS002432, 2001.
Bock, O., Pacione, R., Ahmed, F., Araszkiewicz, A., Bałdysz, Z., Balidakis, K., Barroso, C., Bastin, S., Beirle, S., Berckmans, J., Böhm, J., Bogusz, J., Bos, M., Brockmann, E., Cadeddu, M., Chimani, B., Douša, J., Elgered, G., Eliaš, M., Fernandes, R., Figurski, M., Fionda, E., Gruszczynska, M., Guerova, G., Guijarro, J., Hackman, C., Heinkelmann, R., Jones, J., Kazancı, S. Z., Klos, A., Landskron, D., Martins, J. P., Mattioli, V., Mircheva, B., Nahmani, S., Nilsson, R. T., Ning, T., Nykiel, G., Parracho, A., Pottiaux, E., Ramos, A., Rebischung, P., Sá, A., Dorigo, W., Schuh, H., Stankunavicius, G., Stępniak, K., Valentim, H., Van Malderen, R., Viterbo, P., Willis, P., and Xaver, A.: Use of GNSS Tropospheric Products for Climate Monitoring (Working Group 3), Springer International Publishing, 267–402, ISBN 9783030139018, https://doi.org/10.1007/978-3-030-13901-8_5, 2019.
Boehm, J., Werl, B., and Schuh, H.: Troposphere mapping functions for GPS and VLBI from European centre for medium-range weather forecasts operational analysis data, J. Geophys. Res., 111, B02406, https://doi.org/10.1029/2005JB003629, 2006.
Boisits, J., Landskron, D., and Böhm, J.: VMF3o: the Vienna Mapping Functions for optical frequencies, J. Geodesy, 94, 57, https://doi.org/10.1007/s00190-020-01385-5, 2020.
Chou, M.-Y., Yue, J., Wang, J., Huba, J. D., El Alaoui, M., Kuznetsova, M. M., Rastätter, L., Shim, J. S., Fang, T.-W., Meng, X., Fuller-Rowell, D., John, M., and Retterer, J. M.: Validation of ionospheric modeled TEC in the equatorial ionosphere during the 2013 March and 2021 November geomagnetic storms, Space Weather, 21, e2023SW003480, https://doi.org/10.1029/2023SW003480, 2023.
Davis, J. L., Herring, T. A., Shapiro, I. I., Rogers, A. E., and Elgered, G.: Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length, Radio Sci., 20, 1593–1607, 1985.
Dogan, A. H., Zus, F., Dick, G., Wickert, J., Schuh, H., Durdag, U. M., and Erdogan, B.: Improving the wet mapping function by numerical weather models, Adv. Space Res., 73, 404–413, https://doi.org/10.1016/j.asr.2023.07.060, 2024.
Drożdżewski, M. and Sośnica, K.: Troposphere delay modeling in SLR based on PMF, VMF3o, and meteorological data, Prog. Earth. Planet. Sci., 11, 12, https://doi.org/10.1186/s40645-024-00613-2, 2024.
Fan, H., Li, S., Sun, Z., Xiao, G., Li, X., and Liu, X.: Analysis of systematic biases in tropospheric hydrostatic delay models and construction of a correction model, Geosci. Model Dev., 16, 1345–1358, https://doi.org/10.5194/gmd-16-1345-2023, 2023.
Hobiger, T., Ichikawa, R., Koyama, Y., and Kondo, T.: Fast and accurate ray-tracing algorithms for real-time space geodetic applications using numerical weather models, J. Geophys. Res., 113, D20302, https://doi.org/10.1029/2008JD010503, 2008.
Hofmeister, A. and Böhm, J.: Application of ray-traced tropospheric slant delays to geodetic VLBI analysis, J. Geodesy, 91, 945–964, https://doi.org/10.1007/s00190-017-1000-7, 2017.
Hoque, M. M. and Jakowski, N.: Estimate of higher order ionospheric errors in GNSS positioning, Radio Sci., 43, RS5008, https://doi.org/10.1029/2007RS003817, 2008.
Hoque, M. M. and Jakowski, N.: New Correction Approaches for Mitigating Ionospheric Higher Order Effects in GNSS Applications, Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, 3444–3453, 2012.
Hulley, G. C and Pavlis, E. C.: A ray-tracing technique for improving Satellite Laser Ranging atmospheric delay corrections, including the effects of horizontal refractivity gradients, J. Geophys. Res., 112, B06417, https://doi.org/10.1029/2006JB004834, 2007.
Kashcheyev, A., Nava, B., and Radicella, S. M.: Estimation of higher-order ionospheric errors in GNSS positioning using a realistic 3-D electron density model, Radio Sci., 47, RS4008, https://doi.org/10.1029/2011RS004976, 2012.
Kedar, S., Hajj, G. A., Wilson, B. D., and Heflin, M. B.: The effect of the second order GPS ionospheric correction on receiver positions, Geophys. Res. Lett., 30, 1829, https://doi.org/10.1029/2003GL017639, 2003.
Landskron, D.: VieVS Ray-tracer RADIATE, https://github.com/TUW-VieVS/RADIATE (last access: 10 August 2025), 2018.
Landskron, D. and Böhm, J.: Refined discrete and empirical horizontal gradients in VLBI analysis, J. Geodesy, 92, 1387–1399, 2018a.
Landskron, D. and Böhm, J.: VMF3/GPT3: Refined discrete and empirical troposphere mapping functions, J. Geodesy, 92, 349–360, 2018b.
MacMillan, D. S. and Ma, C.: Atmospheric gradients and the VLBI terrestrial and celestial reference frames, Geophys. Res. Lett., 24, 453–456, https://doi.org/10.1029/97gl00143, 1997.
Mendes, V. B. and Pavlis, E. C.: High-accuracy zenith delay prediction at optical wavelengths, Geophys. Res. Lett., 31, L14602, https://doi.org/10.1029/2004GL020308, 2004.
Nafisi, V., Madzak, M., Boehm, J., Ardalan, A. A., and Schuh, H.: Ray-traced tropospheric delays in VLBI analysis, Radio Sci., 47, RS2020, https://doi.org/10.1029/2011RS004918, 2012a.
Nafisi, V., Urquhart, L., Santos, M. S., Nievinski, F. G., Böhm, J., Wijaya, D. D., Schuh, H., Ardalan, A. A., Hobiger, T., Ichikawa, R., Zus, F., Wickert, J., and Gegout, P.: Comparison of ray-tracing packages for troposphere delays, IEEE T. Geosci. Remote, 50, 469–481, 2012b.
Nava, B., Coisson, P., and Radicella, S. M.: A new version of the NeQuick ionosphere electron density model, J. Atmos. Sol.-Terr. Phy., 70, 1856–1862, https://doi.org/10.1016/j.jastp.2008.01.015, 2008.
Nilsson, T., Soja, B., Balidakis, K., Karbon, M., Heinkelmann, R., Deng, Z., and Schuh, H.: Improving the modeling of the atmospheric delay in the data analysis of the Intensive VLBI sessions and the impact on the UT1 estimates, J. Geodesy, 91, 857–866, https://doi.org/10.1007/s00190-016-0985-7, 2017.
Petrie, E. J., King, M. A., Moore, P., and Lavallee, D. A.: A first look at the effects of ionospheric signal bending on a globally processed GPS network, J. Geodesy, 84, 491–499, https://doi.org/10.1007/s00190-010-0386-2, 2010.
Petrie, E. J., Hernández-Pajares, M., Spalla, P., Moore, P., and King, M. A.: A Review of Higher Order Ionospheric Refraction Effects on Dual Frequency GPS, Surv. Geophys., 32, 197–253, https://doi.org/10.1007/s10712-010-9105-z, 2011.
Petrov, L.: Modeling of propagation in the neutral atmosphere for radio astronomy data analysis: a paradigm shift, Proceedings of Science, 230, https://doi.org/10.22323/1.230.0035, 2015.
Rothacher, M., Springer, T. A., Schaer, S., and Beutler, G.: Processing Strategies for Regional GPS Networks, Springer Berlin Heidelberg, 93–100, ISBN 9783662037140, https://doi.org/10.1007/978-3-662-03714-0_14, 1998.
Shampine, L. F., Reichelt, M. W., and Kierzenka, J.: Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c, MATLAB File Exchange, 2004.
Strasser, S., Mayer-Gürr, T., and Zehentner, N.: Processing of GNSS constellations and ground station networks using the raw observation approach, J. Geodesy, 93, 1045–1057, https://doi.org/10.1007/s00190-018-1223-2, 2019.
Thayer, G. D.: An improved equation for the radio refractive index of air, Radio Sci., 9, 803–807, 1974.
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, 2024.
Urquhart, L., Nievinski, F. G., and Santos, M.: Ray-traced slant factors for mitigating the tropospheric delay at the observation level, J. Geodesy, 86, 149–160, https://doi.org/10.1007/s00190-011-0503-x, 2012.
Zus, F.: DNS(v1.0): An open source ray-tracing tool for space geodetic techniques, Zenodo [code], https://doi.org/10.5281/zenodo.15044588, 2025a.
Zus, F.: Numerical(Space-)Weather Model dataset for the ray-tracing tool DNS, Zenodo [data set], https://doi.org/10.5281/zenodo.15187660, 2025b.
Zus, F.: RADIATE ray-tracing code, Zenodo [code], https://doi.org/10.5281/zenodo.15180888, 2025c.
Zus, F., Dick, G., Dousa, J., Heise, S., and Wickert, J.: The rapid and precise computation of GPS slant total delays and mapping factors utilizing a numerical weather model, Radio Sci., 49, 207–216, https://doi.org/10.1002/2013RS005280, 2014.
Zus, F., Deng, Z., Heise, S., and Wickert, J.: Ionospheric mapping functions based on electron density fields, GPS Solut., 21, 873–885, https://doi.org/10.1007/s10291-016-0574-5, 2017a.
Zus, F., Deng, Z., and Wickert, J.: The impact of higher-order ionospheric effects on estimated tropospheric parameters in Precise Point Positioning, Radio Sci., 52, 963–971, https://doi.org/10.1002/2017RS006254, 2017b.
Zus, F., Balidakis, K., Dick, G., Wilgan, K., and Wickert, J.: Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM, Remote Sens.-Basel, 13, 3944, https://doi.org/10.3390/rs13193944, 2021.
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.
Atmospheric signal propagation effects are one of the largest error sources in the analysis of...