{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T14:04:08Z","timestamp":1769263448699,"version":"3.49.0"},"reference-count":76,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41604019"],"award-info":[{"award-number":["41604019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41871373"],"award-info":[{"award-number":["41871373"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"LIESMARS Special Research Funding","award":["202002"],"award-info":[{"award-number":["202002"]}]},{"name":"Beijing Key Laboratory of Urban Spatial Information Engineering","award":["2020201"],"award-info":[{"award-number":["2020201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles\u2014Tilting Mapping Function (TMF)\u2014was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg\u2013Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay\u2019s accuracy by 73%, 54% and 29% at the 5\u00b0 elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.<\/jats:p>","DOI":"10.3390\/rs13132568","type":"journal-article","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T02:44:39Z","timestamp":1625107479000},"page":"2568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9561-2047","authenticated-orcid":false,"given":"Di","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5427-6481","authenticated-orcid":false,"given":"Jiming","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Tianye","family":"Fang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1039-5937","authenticated-orcid":false,"given":"Na","family":"Wei","sequence":"additional","affiliation":[{"name":"GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Wensheng","family":"Mei","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}]},{"given":"Lv","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, China"}]},{"given":"Fei","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China"}]},{"given":"Yinzhi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"},{"name":"Beijing Key Laboratory of Urban Spatial Information Engineering, Beijing 100038, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"155028","DOI":"10.1109\/ACCESS.2019.2946916","article-title":"Determination of Weighted Mean Temperature (Tm) Lapse Rate and Assessment of Its Impact on Tm Calculation","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","unstructured":"Zhang, D. (2017). The Study of the GNSS Tropospheric Zenith Delay Model and Mapping Function. [Ph.D. Thesis, Wuhan University]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4487","DOI":"10.1029\/JC074i018p04487","article-title":"Two-quartic tropospheric refractivity profile for correcting satellite data","volume":"74","author":"Hopfield","year":"1969","journal-title":"J. Geophys. Res."},{"key":"ref_4","first-page":"247","article-title":"Atmospheric correction for the troposphere and stratosphere in radio ranging satellites","volume":"15","author":"Saastamoinen","year":"1972","journal-title":"Geophys. Monogr. Ser."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1029\/RS020i006p01593","article-title":"Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length","volume":"20","author":"Davis","year":"1985","journal-title":"Radio Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1029\/RS023i006p01023","article-title":"A model for the tropospheric excess path length of radio waves from surface meteorological measurements","volume":"23","author":"Gole","year":"1988","journal-title":"Radio Sci."},{"key":"ref_7","unstructured":"Ifadis, I.I. (1986). The Atmospheric Delay of Radio Waves: Modeling the Elevation Dependence on a Global Scale, Chalmers University of Technology. Technical Report 38L."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1029\/RS022i003p00379","article-title":"Estimation of tropospheric delay for microwaves from surface weather data","volume":"22","author":"Askne","year":"1987","journal-title":"Radio Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1016\/j.asr.2016.05.055","article-title":"Quantitative assessment of meteorological and tropospheric Zenith Hydrostatic Delay models","volume":"58","author":"Zhang","year":"2016","journal-title":"Adv. Space Res."},{"key":"ref_10","unstructured":"COESA (1966). U.S. Standard Atmosphere Supplements, 1966."},{"key":"ref_11","unstructured":"Kirchengast, G., Hafner, J., and Poetzi, W. (1999). The CIRA86aQ_UoG Model: An Extension of the CIRA-86 Monthly Tables Including Humidity Tables and a Fortran95 Global Moist Air Climatology Model, Institute for Meteorology and Geophysics, University of Graz."},{"key":"ref_12","first-page":"SIA 15-1","article-title":"NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues","volume":"107","author":"Picone","year":"2002","journal-title":"JGR Space Phys. (1978\u20132012)"},{"key":"ref_13","unstructured":"Leandro, R., Santos, M., and Langley, R.B. (2006, January 18\u201320). UNB neutral atmosphere models: Development and performance. Proceedings of the ION NTM, Monterey, CA, USA."},{"key":"ref_14","first-page":"22","article-title":"Standard Temperature and Pressure","volume":"80","author":"Morris","year":"2012","journal-title":"Ind. Heat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10291-014-0403-7","article-title":"Development of an improved empirical model for slant delays in the troposphere (GPT2w)","volume":"19","author":"Schindelegger","year":"2015","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1002\/j.2161-4296.2009.tb00444.x","article-title":"A North America wide area neutral atmosphere model for GNSS applications","volume":"56","author":"Leandro","year":"2009","journal-title":"Navigation"},{"key":"ref_17","unstructured":"RTCA (2006). Minimum Operational Performance Standards for Global Positioning System\/Wide Area Augmentation System Airborne Equipment, RTCA, Inc.. DO-229D."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10291-013-0316-x","article-title":"The TropGrid2 standard tropospheric correction model","volume":"18","year":"2014","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10273","DOI":"10.1038\/srep10273","article-title":"ITG: A New Global GNSS Tropospheric Correction Model","volume":"5","author":"Yao","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s00190-014-0761-5","article-title":"New versions of the BDS\/GNSS zenith tropospheric delay model IGGtrop","volume":"89","author":"Li","year":"2015","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, J.P., Wang, J.G., Wang, A.H., Ding, J.S., and Zhang, Y.Z. (2020). SHAtropE-A Regional Gridded ZTD Model for China and the Surrounding Areas. Remote Sens., 12.","DOI":"10.3390\/rs12010165"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF02520642","article-title":"Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements","volume":"64","author":"Tralli","year":"1990","journal-title":"Bull. G\u00e9od\u00e9sique"},{"key":"ref_23","unstructured":"Webb, S.R. (2015). Kinematic GNSS Tropospheric Estimation and Mitigation over a Range of Altitudes. [Ph.D. Thesis, Newcastle University]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.nrjag.2016.01.002","article-title":"Tropospheric wet delay estimation using GNSS: Case study of a permanent network in Egypt","volume":"5","author":"Mousa","year":"2016","journal-title":"NRIAG J. Astron. Geophys."},{"key":"ref_25","unstructured":"Dach, R., Lutz, S., Walser, P., and Fridez, P. (2015). Bernese GNSS Software Version 5.2, University of Bern."},{"key":"ref_26","unstructured":"Herring, T.A., King, R.W., Floyd, M.A., and McClusky, S.C. (2018). GAMIT Reference Manual Release 10.7, Massachusetts Institute of Technology."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.jastp.2018.11.004","article-title":"GNSS-derived PWV and comparison with radiosonde and ECMWF ERA-Interim data over mainland China","volume":"182","author":"Zhao","year":"2018","journal-title":"J. Atmos. Sol. Terr. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"87275","DOI":"10.1109\/ACCESS.2020.2991094","article-title":"Precipitable Water Vapor Converted From GNSS-ZTD and ERA5 Datasets for the Monitoring of Tropical Cyclones","volume":"8","author":"He","year":"2020","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Yang, F., Guo, J., Meng, X., Shi, J., Zhang, D., and Zhao, Y. (2020). An improved weighted mean temperature (T-m) model based on GPT2w with T-m lapse rate. GPS Solut., 24.","DOI":"10.1007\/s10291-020-0953-9"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Barriot, J.-P., and Peng, F. (2021). Beyond Mapping Functions and Gradients, IntechOpen.","DOI":"10.5772\/intechopen.96982"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1029\/RS007i002p00223","article-title":"Correction of Satellite Tracking Data for an Arbitrary Tropospheric Profile","volume":"7","author":"Marini","year":"1972","journal-title":"Radio Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"De Munck, J.C., and Spoelstra, T.A. (1992). Modeling Atmospheric Delays in the Analysis of Space Geodetic Data. Refraction of Transatmospheric Signals in Geodesy, The Netherlands Commission on Geodesy.","DOI":"10.54419\/9s7t55"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3227","DOI":"10.1029\/95JB03048","article-title":"Global mapping functions for the atmosphere delay at radio wavelengths","volume":"101","author":"Niell","year":"1996","journal-title":"J. Geophys. Res. [Solid Earth]"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/S1464-1895(01)00087-4","article-title":"Preliminary evaluation of atmospheric mapping functions based on numerical weather models","volume":"26","author":"Niell","year":"2001","journal-title":"Phys. Chem. Earth Part A"},{"key":"ref_35","unstructured":"Guo, J., and Langley, R.B. (2003, January 9\u201312). A New Tropospheric Propagation Delay Mapping Function for Elevation Angles Down to 2 degrees. Proceedings of the ION GPS 2003, Portland, OR, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1029\/2003GL018984","article-title":"Vienna mapping functions in VLBI analyses","volume":"31","author":"Boehm","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1029\/2005GL025546","article-title":"Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data","volume":"33","author":"Boehm","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"B02406","DOI":"10.1029\/2005JB003629","article-title":"Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data","volume":"111","author":"Boehm","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1002\/grl.50288","article-title":"GPT2: Empirical slant delay model for radio space geodetic techniques","volume":"40","author":"Lagler","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00190-017-1066-2","article-title":"VMF3\/GPT3: Refined discrete and empirical troposphere mapping functions","volume":"92","author":"Landskron","year":"2018","journal-title":"J. Geod."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10291-014-0386-4","article-title":"Systematic errors of mapping functions which are based on the VMF1 concept","volume":"19","author":"Zus","year":"2015","journal-title":"GPS Solut."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1007\/s00190-019-01263-9","article-title":"Assessment of forecast Vienna Mapping Function 1 for real-time tropospheric delay modeling in GNSS","volume":"93","author":"Yuan","year":"2019","journal-title":"J. Geod."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Qiu, C., Wang, X.M., Li, Z.S., Zhang, S.T., Li, H.B., Zhang, J.L., and Yuan, H. (2020). The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay. Remote Sens., 12.","DOI":"10.3390\/rs12010130"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"20489","DOI":"10.1029\/97JB01739","article-title":"Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data","volume":"102","author":"Chen","year":"1997","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"B\u00f6hm, J., Urquhart, L., Steigenberger, P., Heinkelmann, R., Nafisi, V., and Schuh, H. (2013). A Priori Gradients in the Analysis of Space Geodetic Observations. Reference Frames for Applications in Geosciences, Springer.","DOI":"10.1007\/978-3-642-32998-2_17"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1007\/s00190-018-1127-1","article-title":"Refined discrete and empirical horizontal gradients in VLBI analysis","volume":"92","author":"Landskron","year":"2018","journal-title":"J. Geod."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"5019","DOI":"10.1029\/97JB03534","article-title":"Estimating horizontal gradients of tropospheric path delay with a single GPS receiver","volume":"103","author":"Kroger","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rothacher, M., Springer, T.A., Schaer, S., and Beutler, G. (1998). Processing Strategies for Regional GPS Networks, Springer.","DOI":"10.1007\/978-3-662-03714-0_14"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"331","DOI":"10.2151\/jmsj.2004.331","article-title":"Tropospheric gradient estimation at CODE: Results from global solutions","volume":"82","author":"Meindl","year":"2004","journal-title":"J. Meteorol. Soc. Jpn."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1002\/2015JD024255","article-title":"GNSS tropospheric gradients with high temporal resolution and their effect on precise positioning","volume":"121","author":"Lu","year":"2016","journal-title":"J. Geophys. Res."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1029\/2002JD002214","article-title":"An impact of estimating tropospheric delay gradients on tropospheric delay estimations in the summer using the Japanese nationwide GPS array","volume":"108","author":"Iwabuchi","year":"2003","journal-title":"J. Geophys. Res."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Zus, F., Dou\u0161a, J., Ka\u010dma\u0159\u00edk, M., V\u00e1clavovic, P., Balidakis, K., Dick, G., and Wickert, J. (2019). Improving GNSS Zenith Wet Delay Interpolation by Utilizing Tropospheric Gradients: Experiments with a Dense Station Network in Central Europe in the Warm Season. Remote Sens., 11.","DOI":"10.3390\/rs11060674"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4173","DOI":"10.1002\/2015GL063856","article-title":"Retrieving high-resolution tropospheric gradients from multiconstellation GNSS observations","volume":"42","author":"Li","year":"2015","journal-title":"Geophys. Res. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1029\/93RS01917","article-title":"Ground-based measurement of gradients in the \u201cwet\u201d radio refractivity of air","volume":"28","author":"Davis","year":"1993","journal-title":"Radio Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s00190-007-0144-2","article-title":"Troposphere gradients from the ECMWF in VLBI analysis","volume":"81","author":"Boehm","year":"2007","journal-title":"J. Geod."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3615","DOI":"10.1002\/2013GL058721","article-title":"Real-time GPS sensing of atmospheric water vapor: Precise point positioning with orbit, clock and phase delay corrections","volume":"41","author":"Li","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_57","unstructured":"Zhang, D. (2016). A building method for a troposphere mapping function model representing atmospheric anisotropy (patent of China). (ZL201610831005.8)."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"7520","DOI":"10.1109\/TGRS.2020.2975458","article-title":"Modeling the Slant Wet Delays From One GPS Receiver as a Series Expansion With Respect to Time and Space: Theory and an Example of Application for the Tahiti Island","volume":"58","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2427","DOI":"10.1364\/AO.16.002427","article-title":"Correction of laser tracking data for the effects of horizontal refractivity gradients","volume":"16","author":"Gardner","year":"1977","journal-title":"Appl. Opt."},{"key":"ref_60","first-page":"182","article-title":"Using Ray-Tracing to Analyse the Precision of Three Classical Tropospheric Mapping Functions in China","volume":"40","author":"Guo","year":"2015","journal-title":"Geomat. Inf. Sci. Wuhan Uni."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","article-title":"The ERA5 global reanalysis","volume":"146","author":"Hersbach","year":"2020","journal-title":"Quart. J. R. Met. Soc."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1109\/JRPROC.1953.274297","article-title":"The constants in the equation for atmospheric refractive index at radio frequencies","volume":"41","author":"Smith","year":"1953","journal-title":"Proc. IRE"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"RS2020","DOI":"10.1029\/2011RS004918","article-title":"Ray-traced tropospheric delays in VLBI analysis","volume":"47","author":"Nafisi","year":"2012","journal-title":"Radio Sci."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TGRS.2011.2160952","article-title":"Comparison of ray-tracing packages for troposphere delays","volume":"50","author":"Nafisi","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_65","unstructured":"R\u00fceger, J.M. (2002, January 19\u201326). Refractive index formulae for radio waves. Proceedings of the FIG XXII International Congress, Washington, DC, USA."},{"key":"ref_66","unstructured":"Wallace, J.M., and Hobbs, P.V. (2006). Atmospheric Science: An Introductory Survey, Academic Press."},{"key":"ref_67","unstructured":"WMO (2008). Guide to Meteorological Instruments and Methods of Observation, Secretariat of the World Meteorological Organization. [7th ed.]."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Feng, P., Li, F., Yan, J., Zhang, F., and Barriot, J.-P. (2020). Assessment of the Accuracy of the Saastamoinen Model and VMF1\/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology. Remote Sens., 12.","DOI":"10.3390\/rs12203337"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/qj.828","article-title":"The ERA-Interim reanalysis: Configuration and performance of the data assimilation system","volume":"137","author":"Dee","year":"2011","journal-title":"Q. J. R. Met. Soc."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1029\/2008JD010503","article-title":"Fast and accurate ray-tracing algorithms for real-time space geodetic applications using numerical weather models","volume":"113","author":"Hobiger","year":"2008","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_71","unstructured":"Mendes, V. (1999). Modeling the Neutral-Atmospheric Propagation Delay in Radiometric Space Techniques. [Ph.D. Thesis, University of New Brunswick]."},{"key":"ref_72","unstructured":"Fleming, E.L., Chandra, S., Schoeberl, M., and Barnett, J.J. (1988). Monthly Mean Global Climatology of Temperature, Wind, Geopotential Height, and Pressure for 0\u2013120 km."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/14498596.2014.899932","article-title":"Improved dry tropospheric propagation delay mapping function for GPS measurements in Egypt","volume":"59","author":"Younes","year":"2014","journal-title":"J. Spat.Sci."},{"key":"ref_74","unstructured":"Hofmann-Wellenhof, B., and Moritz, H. (2005). Physical Geodesy, Springer."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00585-000-0223-7","article-title":"4D tropospheric tomography using GPS slant wet delays","volume":"18","author":"Flores","year":"2000","journal-title":"Ann. Geophys. Atmos. Hydrosph. Space Sci."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"4401","DOI":"10.1002\/2016JD026184","article-title":"A directional model of tropospheric horizontal gradients in Global Positioning System and its application for particular weather scenarios","volume":"122","author":"Masoumi","year":"2017","journal-title":"J. Geophys. Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/13\/2568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:20Z","timestamp":1760163860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/13\/2568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":76,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["rs13132568"],"URL":"https:\/\/doi.org\/10.3390\/rs13132568","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,30]]}}}