Abstract
Tibet presents significant elevation changes, thus leading to extraordinary tropospheric conditions. This eventually forms complicated and diverse delays in satellite data (such as global navigation satellite system (GNSS) observations), particularly for the wet component. Such delays cause non-negligible errors in microwave-dependent techniques. As infrastructure development progresses, GNSS applications (such as real-time kinematic and unmanned aerial vehicles) require a reliable tropospheric model that works not only on the surface but also over broader operating heights to pre-correct delays. However, the existing models, even the widely used global pressure and temperature 3 (GPT3) model, exhibit low performance in Tibet due to insufficient spatiotemporal resolution and limited vertical correction capability. We thereby proposed a refined Tibetan zenith wet delay (ZWD) model (TZ) established using pressure-level ERA5 datasets with a horizontal resolution of 0.25° released by the European Centre for Medium-Range Weather Forecasts. The core of the TZ is the optimized vertical correction, i.e., the cubic polynomial with two more parameters than the commonly used exponential function, whose underlying parameters are determined by a least-squares function refined up to semidiurnal harmonics. TZ achieves ZWD estimates for an arbitrary time and height in the Tibetan region with the above structure. ERA5- and radiosonde-derived ZWDs validated the TZ performance. Validation results show that the TZ model achieved a lower bias and root-mean-square error than the GPT3 model, regardless of the surface or other height layers. It demonstrates that the TZ performs better in Tibet than the widely adopted GPT3. The required MATLAB scripts and coefficient matrix of the TZ are available at https://zenodo.org/record/7063960.
Similar content being viewed by others
Data availability
The ECMWF ERA5 data used in this paper can be accessed at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels?tab=form. The SRTM DEM data are now available at https://earthexplorer.usgs.gov/. The radiosonde records for three stations in Tibet can be found at http://weather.uwyo.edu/upperair/sounding.html. The GPT3 model’s codes and coefficients can be downloaded at https://vmf.geo.tuwien.ac.at/codes/.
References
Boehm J, Schuh H (2004) Vienna mapping functions in VLBI analyses. Geophys Res Lett 31:L01603
Boehm J, Werl B, Schuh H (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European centre for medium-range weather forecasts operational analysis data. J Geophys Res-Sol Ea 111:B02406
Böhm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33:L07304
Böhm J, Heinkelmann R, Schuh H (2007) Short note: a global model of pressure and temperature for geodetic applications. J Geodesy 81:679–683
Böhm J, Möller G, Schindelegger M, Pain G, Weber R (2015) Development of an improved empirical model for slant delays in the troposphere (GPT2w). GPS Solut 19:433–441
Collins JP, Langley RB (1997) A tropospheric delay model for the user of the wide area augmentation system vol 20. Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, NB, Canada
Compo GP et al (2011) The twentieth century reanalysis project. Q J R Meteorol Soc 137:1–28
Dee DP et al (2011) The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597
Gegout P, Biancale R, Soudarin L (2011) Adaptive mapping functions to the azimuthal anisotropy of the neutral atmosphere. J Geodesy 85:661–677
Gupta L, Jain R, Vaszkun G (2016) Survey of important issues in UAV communication networks. IEEE Commun Surv Tut 18:1123–1152
Hersbach H et al (2020) The ERA5 global reanalysis. Q J R Meteorol Soc 146:1999–2049
Hocke K (1998) Phase estimation with the Lomb-Scargle periodogram method. Ann Geophys 16:356–358
Hofmeister A, Böhm J (2017) Application of ray-traced tropospheric slant delays to geodetic VLBI analysis. J Geodesy 91:945–964
Kouba J (2008) Implementation and testing of the gridded Vienna mapping function 1 (VMF1). J Geodesy 82:193–205
Krueger E, Schueler T, Hein GW, Martellucci A, Blarzino G (2004) Galileo tropospheric correction approaches developed within GSTB-V1. Paper presented at the Proceedings of ENC-GNSS 2004, Rotterdam, the Netherlands
Lagler K, Schindelegger M, Böhm J, Krásná H, Nilsson T (2013) GPT2: Empirical slant delay model for radio space geodetic techniques. Geophys Res Lett 40:1069–1073
Landskron D, Böhm J (2018) VMF3/GPT3: refined discrete and empirical troposphere mapping functions. J Geodesy 92:349–360
Leandro RF, Langley RB, Santos MC (2008) UNB3m_pack: a neutral atmosphere delay package for radiometric space techniques. GPS Solut 12:65–70
Leandro R, Santos M, Langley R (2006) UNB neutral atmosphere models: development and performance. Paper presented at the Proceedings ION NTM 2006, Institute of Navigation, Monterey, California
Li W, Yuan Y, Ou J, Li H, Li Z (2012) A new global zenith tropospheric delay model IGGtrop for GNSS applications. Chin Sci Bull 57:2132–2139
Li W, Yuan Y, Ou J, Chai Y, Li Z, Liou Y-A, Wang N (2015) New versions of the BDS/GNSS zenith tropospheric delay model IGGtrop. J Geodesy 89:73–80
Li T et al (2021) Refining the empirical global pressure and temperature model with the ERA5 reanalysis and radiosonde data. J Geodesy 95:1–17
Liu Y et al (2021) Untangling the effects of management measures, climate and land use cover change on grassland dynamics in the Qinghai-Tibet Plateau, China. Land Degrad Dev 32:4974–4987
Liu C, Yao Y, Xu C (2022) Conventional and neural network-based water vapor density model for GNSS troposphere tomography. GPS Solut 26:1–12
Mooney PA, Mulligan FJ, Fealy R (2011) Comparison of ERA-40, ERA-Interim and NCEP/NCAR reanalysis data with observed surface air temperatures over Ireland. Int J Climatol 31:545–557
Niell AE (1996) Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res-Sol Ea 101:3227–3246
Niell A (2000) Improved atmospheric mapping functions for VLBI and GPS. Earth Planets Space 52:699–702
Nilsson T, Böhm J, Wijaya DD, Tresch A, Nafisi V, Schuh H (2013) Path delays in the neutral atmosphere. In: Bohm J, Schuh H (eds) Atmospheric effects in space geodesy. Springer, Berlin, pp 73–136
Reuter HI, Nelson A, Jarvis A (2007) An evaluation of void-filling interpolation methods for SRTM data. Int J Geogr Inform Sci 21:983–1008
Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. Bull Géodésique 15:247–251
Schüler T (2014) The TropGrid2 standard tropospheric correction model. GPS Solut 18:123–131
Thayer GD (1974) An improved equation for the radio refractive index of air. Radio Sci 9:803–807
Tregoning P, Herring TA (2006) Impact of a priori zenith hydrostatic delay errors on GPS estimates of station heights and zenith total delays. Geophys Res Lett 33:L23303
Uppala SM et al (2005) The ERA-40 re-analysis. Q J R Meteorol Soc 131:2961–3012
Xu C, Yao Y, Shi J, Zhang Q, Peng W (2020) Development of global tropospheric empirical correction model with high temporal resolution. Remote Sens 12:721
Yao Y, Xu C, Shi J, Cao N, Zhang B, Yang J (2015) ITG: a new global GNSS tropospheric correction model. Sci Rep 5:1–9
Yao Y, Peng W, Xu C, Cheng S (2016) Enhancing real-time precise point positioning with zenith troposphere delay products and the determination of corresponding tropospheric stochastic models. Geophys J Int 208:1217–1230
Yu C, Zhang Y, Claus H, Zeng R, Zhang X, Wang J (2012) Ecological and environmental issues faced by a developing Tibet. Environ Sci Technol 46:1979–1980
Zhang B, Yao Y, Xin L, Xu X (2019) Precipitable water vapor fusion: an approach based on spherical cap harmonic analysis and Helmert variance component estimation. J Geodesy 93:2605–2620
Zus F, Dick G, Douša J, Heise S, Wickert J (2014) The rapid and precise computation of GPS slant total delays and mapping factors utilizing a numerical weather model. Radio Sci 49:207–216
Acknowledgements
We would like to thank the European Centre for Medium-Range Weather Forecasts (ECMWF) for providing the ERA5 reanalysis data, the United States Geological Survey (USGS) for providing the Shuttle Radar Topography Mission (SRTM) DEM data, the University of Wyoming for providing radiosonde data, and the TU Vienna for providing the GPT3 model. This work is supported by the National Natural Science Foundation of China (42004019; 42142037). Our deepest gratitude goes to three anonymous reviewers for their careful work and valuable comments that have helped improve this paper substantially.
Author information
Authors and Affiliations
Contributions
CX, CL, and YY together designed the research. CL, QW, and XW performed computations and numerical analysis. CX and CL wrote the paper. YY provided valuable suggestions.
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xu, C., Liu, C., Yao, Y. et al. Tibetan zenith wet delay model with refined vertical correction. J Geod 97, 31 (2023). https://doi.org/10.1007/s00190-023-01719-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00190-023-01719-z