Path Delays in the Neutral Atmosphere

  • Tobias Nilsson
  • Johannes Böhm
  • Dudy D. Wijaya
  • Ana Tresch
  • Vahab Nafisi
  • Harald Schuh
Part of the Springer Atmospheric Sciences book series (SPRINGERATMO)


This part describes the effects of the troposphere—strictly speaking the neutral atmosphere—on the propagation delay of space geodetic signals. A theoretical description of this tropospheric propagation delay is given as well as strategies for correcting for it in the data analysis of the space geodetic observations. The differences between the tropospheric effects for microwave techniques, like the Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI), and those for optical techniques, like Satellite Laser Ranging (SLR), are discussed. Usually, residual tropospheric delays are estimated in the data analysis, and the parameterization needed to do so is presented. Other possibilities of correcting for the tropospheric delays are their calculation by ray-tracing through the fields of numerical weather models and by utilizing water vapor radiometer measurements. Finally, we shortly discuss how space geodetic techniques can be used in atmospheric analysis in meteorology and climatology.



First of all we would like to thank the reviewer, Gunnar Elgered, for providing very valuable suggestions to improve the quality of this part of the book. We are grateful for the financial support from the German Science Foundation (DFG, SCHU 1103/3-2), and from the Austrian Science Fund (FWF, P20902-N10).


  1. J. B. Abshire and C. S. Gardner. Atmospheric refractivity corrections in Satellite Laser Ranging. IEEE Trans. Geosc. Rem. Sens., GE-23(4):414–425, 1985. doi: 10.1109/TGRS.1985.289431.Google Scholar
  2. C. Alber, R. Ware, C. Rocken, and J. Braun. Obtaining single path delays from GPS double differences. Geoph. Res. Lett., 27:2661–2664, 2000. doi:  10.1029/2000GL011525.Google Scholar
  3. M. Alizadeh, D. D. Wijaya, T. Hobiger, R. Weber, and H. Schuh. Ionospheric effects on microwave signals. In Atmospheric Effects in Space Geodesy. Springer-Verlag, 2013. this book.Google Scholar
  4. T. Alkhalifah and S. Fomel. Implementing the fast marching Eikonal solver: Spherical versus cartesian coordinates. Geophys. Prospect., 49:165 178, 2001. doi:  10.1046/j.1365-2478.2001.00245.x.
  5. J. I. H. Askne and E. R. Westwater. A review of ground-based remote sensing of temperature and moisture by passive microwave radiometers. IEEE Trans. Geosci. Remote Sensing, GE-24 (3):340–352, 1986. doi:  10.1109/TGRS.1986.289591.
  6. B. R. Bean and G. D. Thayer. CRPL exponential reference atmosphere. Technical report, U.S. Government Printing Office, 1959. URL
  7. P. L. Bender and J. C. Owens. Correction of optical distance measurements for the fluctuating atmospheric index of refraction. J. Geophys. Res., 70:2461, 1965. doi:  10.1029/JZ070i010p02461.Google Scholar
  8. L. Bengtsson, S. Hagemann, and K. I. Hodges. Can climate trends be calculated from reanalysis data? J. Geophys. Res., 109:D11111, 2004. doi:  10.1029/2004JD004536.
  9. H. Berg. Allgemeine Meteorologie. Dümmlers Verlag, Bonn, 1948.Google Scholar
  10. M. Bevis, S. Businger, S. Chiswell, T. A. Herring, R. A. Anthes, C. Rocken, and R. H. Ware. GPS meteorology: Mapping zenith wet delays onto precipitable water. J. Appl. Meteorology, 33(3):379–386, 1994. doi: 10.1175/1520-0450(1994)033<0379:GMMZWD>2.0.CO;2.Google Scholar
  11. M. Bevis, S. Businger, T.A. Herring, C. Rocken, R.A. Anthes, and R.H. Ware. GPS meteorology: remote sensing of atmospheric water vapor using the global positioning system. J. Geophys. Res., 97(D14):15787–801, 1992. ISSN 0148–0227. doi:  10.1029/92JD01517.Google Scholar
  12. J. Böhm. Troposphärische Laufzeitverzögerungen in der VLBI. PhD thesis, Technische Universität Wien, 2004.Google Scholar
  13. J. Böhm, R. Heinkelmann, and H. Schuh. Short Note: A global model of pressure and temperature for geodetic applications.J. Geodesy, 81(10):679–683, OCT 2007. doi: 10.1007/s00190-007-0135-3.
  14. J. Böhm, R. Heinkelmann, and H. Schuh. Neutral atmosphere delays: Empirical models versus discrete time series from numerical weather models. In H. Drewes, editor, Geodetic Reference Frames - IAG Symposium, volume 134 of IAG Symposia, pages 317–321, Munich, Germany, 2009a. doi:10.1007/978-3-642-00860-3_49.Google Scholar
  15. J. Böhm, J. Kouba, and H. Schuh. Forecast Vienna mapping functions 1 for real-time analysis of space geodetic observations. J. Geodesy, 83(5), 2009b. doi:  10.1007/s00190-008-0216-y.
  16. J. Böhm, P.J. Mendes Cerveira, H. Schuh, and P. Tregoning. The impact of mapping functions for the neutral atmosphere based on numerical weather models in GPS data analysis. In P. Tregoning and C. Rizos, editors, Dynamic Planet, volume 130 of IAG Symposia Series, pages 837–843. Springer-Verlag, 2007. doi:10.1007/978-3-540-49350-1_118.Google Scholar
  17. J. Böhm, A. Niell, P. Tregoning, and H. Schuh. Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys. Res. Lett., 33:L07304, 2006a. doi:  10.1029/2005GL025546.
  18. J. Böhm, D. Salstein, M. Alizadeh, and D. D. Wijaya. Geodetic and atmospheric background. In Atmospheric effects in space geodesy. Springer-Verlag, Berlin, Germany, 2013. this book.Google Scholar
  19. J. Böhm and H. Schuh. Vienna mapping functions. In Proc. 16th Working Meeting on European VLBI for Geodesy and Astrometry, page 131 143, Leipzig, Germany, 2003. Verlag des Bundesamtes für Kartographie und Geodäsie.Google Scholar
  20. J. Böhm and H. Schuh. Vienna mapping functions in VLBI analyses. Geophys. Res. Lett., 31:L01603, 2004. doi:  10.1029/2003GL018984.
  21. J. Böhm and H. Schuh. Tropospheric gradients from the ECMWF in VLBI analysis. J. Geodesy, 81(6–8):409–421, 2007. doi:  10.1007/s00190-006-0126-9.Google Scholar
  22. J. Böhm, B. Werl, and H. Schuh. Troposphere mapping functions for GPS and very long baseline interferometry from european centre for medium-range weather forecasts operational analysis data. J. Geophys. Res., 111:B02406, 2006b. doi: 10.1029/2005JB003629.
  23. M. Born and E. Wolf. Principles of optics. Cambridge Univ. Press, New York, 7\(^{{\rm th}}\) edition, 1999.Google Scholar
  24. A. V. Bosisio and C. Mallet. Infuence of cloud temperature on brightness temperature and consequences for water retrieval. Radio Sci., 33(4):929–939, 1998. doi:  10.1029/98RS00949.Google Scholar
  25. G. Boudouris. On the index of refraction of air, the absorption and dispersion of centimeter waves in gases. J. Res. Natl. Bur. Stand., 67D:631–684, 1963.Google Scholar
  26. K. G. Budden. The propagation of radio waves. Cambridge University Press, New York, 1 edition, 1985.Google Scholar
  27. V. Cerveny. Seismic ray theory. Cambridge University Press, New York, 2005.Google Scholar
  28. V. Cerveny, L. Klimes, and I. Psencik. Complete seismic-ray tracing in three-dimensional structures. In D. J. Doornbos, editor, Seismological algorithms, page 89–168. Academic Press, New York, 1988.Google Scholar
  29. C. Champollion, F. Mason, M.-N. Bouin, A. Walpersdorf, E. Doerflinger, O. Bock, and J. van Baelen. GPS water vapour tomography: preliminary results from the ESCOMPTE field experiment. Atmospheric Research, 74:253–274, 2005. doi:  10.1016/j.atmosres.2004.04.003.Google Scholar
  30. C.C. Chao. The troposphere calibration model for mariner mars 1971. Technical Report 32–1587, NASA JPL, Pasadena, CA, 1974.Google Scholar
  31. G. Chen and T. A. Herring. Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data. J. Geophys. Res., 102(B9):20489–20502, 1997. doi:  10.1029/97JB01739.Google Scholar
  32. P. E. Ciddor. Refractive index of air: new equations for the visible and near infrared. Appl. Opt., 35(9):1566–1573, 1996. doi:  10.1364/AO.35.001566.
  33. P. E. Ciddor and R. J. Hill. The refractive index of air \(2\). Group index. Appl. Opt., 38:1663–1667, 1999. doi:  10.1364/AO.38.001663.
  34. G. d’Auria, F. S. Marzano, and U. Merlo. Model for estimating the refractive-index stucture constant in clear-air intermittent turbulence. Applied Optics, 32:2674–2680, 1993. doi: 10.1364/AO.32.002674.Google Scholar
  35. J. L. Davis, G. Elgered, A. E. Niell, and C. E. Kuehn. Ground-based measurement of gradients in the “wet” radio refractivity of air. Radio Sci., 28(6):1003–1018, 1993. doi:  10.1029/93RS01917.Google Scholar
  36. J. L. Davis, T. A. Herring, I. I. Shapiro, A. E. E. Rogers, and G. Elgered. Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length. Radio Sci., 20(6):1593–1607, 1985. doi:  10.1029/RS020i006p01593.Google Scholar
  37. J.L. Davis. Atmospheric propagation effects on radio interferometry. Technical Report AFGL-TR-86-0243, Scientific Report No. 1, Air Force Geophysics Laboratory, 1986.Google Scholar
  38. P. Debye. Polar Molecules. Dover, New York, 1929.Google Scholar
  39. B. Edlén. The refractive index of air. Metrologia, 2(2):71–80, 1966. doi:  10.1088/0026-1394/2/2/002.Google Scholar
  40. G. Elgered. Tropospheric radio-path delay from ground based microwave radiometry. In M. Janssen, editor, Atmospheric Remote Sensing by Microwave Radiometry, chapter 5. Wiley & Sons, Inc., N.Y., 1993.Google Scholar
  41. G. Elgered, J. L. Davis, T. A. Herring, and I. I. Shapiro. Geodesy by radio interferometry: Water vapor radiometry for estimation of the wet delay. J. Geophys. Res., 95(B4):6541–6555, 1991. doi: 10.1029/90JB00834.Google Scholar
  42. G. Elgered, H.-P. Plag, H. van der Marel, S. Barlag, and J. Nash, editors. Exploitation of ground-based GPS for operational numerical weather prediction and climate applications. COST action 716: Final Report. European Union, Brussels, Belgium, 2005.Google Scholar
  43. T. R. Emardson and H. J. P. Derks. On the relation between the wet delay and the integrated precipitable water vapour in the European atmosphere. Meteorol. Appl., 7(1):61–68, 2000. doi:  10.1017/S1350482700001377.Google Scholar
  44. T. R. Emardson, G. Elgered, and J. M. Johansson. External atmospheric corrections in geodetic very-long-baseline interferometry. J. Geodesy, 73:375–383, 1999. doi:  10.1007/s001900050256.Google Scholar
  45. L. Essen and K. D. Froome. The refractive indices and dielectric constants of air and its principal constituents at 24,000 Mc/s. Proc. Phys Soc. B, 64(10):862–875, 1951. doi:  10.1088/0370-1301/64/10/303.
  46. A. Flores, G. Ruffini, and A. Rius. 4D tropospheric tomography using GPS slant delays. Ann. Geophysicae, pages 223–234, 2000. doi:  10.1007/s00585-000-0223-7.
  47. U. Fölsche. Tropospheric water vapor imaging by combination of spaceborne and ground-based GNSS sounding data. PhD thesis, Univ. Graz, Graz, Austria, 1999.Google Scholar
  48. P. J. Fowler. Finite-difference solutions of the 3d eikonal equation in spherical coordinates. In Proc. 64th SEG meeting, pages 1394–1397, Los Angeles, USA, 1994.Google Scholar
  49. C. S. Gardner. Effects of horizontal refractivity gradients on the accuracy of laser ranging to satellites. Radio Sci., 11(12):1037–1044, 1976. doi:  10.1029/RS011i012p01037.Google Scholar
  50. P. Gegout, R. Biancale, and L. Soudarin. Adaptive mapping functions to the azimuthal anisotropy of the neutral-atmosphere. J. Geodesy, 85(10):661–677, 2011. doi:  10.1007/s00190-011-0474-y.Google Scholar
  51. L. Gradinarsky and P. Jarlemark. Ground-based GPS tomography of water vapor: Analysis of simulated and real data. J. Meteorol. Soc. Japan, 82:551–560, 2004. doi:  10.2151/jmsj.2004.551.
  52. L. P. Gradinarsky, J. M. Johansson, H. R. Bouma, H.-G. Scherneck, and G. Elgered. Climate monitoring using GPS. Physics and Chemistry of the Earth, 27:335–340, 2002. doi:  10.1016/S1474-7065(02)00009-8.
  53. B. A. Greene and T. A. Herring. Multiple wavelength laser ranging. In The 6th International Workshop on Laser Ranging Instrumentation, 1986.Google Scholar
  54. S. I. Gutman and S. G. Benjamin. The role of ground-based GPS meteorological observations in numerical weather prediction. GPS Solutions, 4(4):16–24, 2001. doi:  10.1007/PL00012860.
  55. R. Heinkelmann, J. Böhm, H. Schuh, S. Bolotin, G. Engelhardt, D. S. MacMillan, M. Negusini, E. Skurikhina, V. Tesmer, and O. Titov. Combination of long time-series of troposphere zenith delays observed by VLBI. J. Geodesy, 81(6–8):483–501, 2007. doi: 10.1007/s00190-007-0147-z.Google Scholar
  56. T. A. Herring. Modeling atmospheric delays in the analysis of space geodetic data. In J.C. De Munk and T. A. Spoelstra, editors, Symposium on Refraction of Transatmospheric Signals in Geodesy, pages 157–164. Netherlands Geod. Comm., Delft, 1992.Google Scholar
  57. T. A. Herring, J. L. Davis, and I. I. Shapiro. Geodesy by radio interferometry: The application of Kalman filtering to the analysis of Very Long Baseline Interferometry data. J. Geophys. Res., 95(B8):12,561–12,581, 1990. 90JB00683.Google Scholar
  58. R. J. Hill, R. S. Lawrence, and J. T. Priestley. Theoretical and calculational aspects of the radio refractive index of water vapor. Radio Sci., 17(5):1251–1257, 1982. doi:  10.1029/RS017i005p01251.Google Scholar
  59. T. Hobiger, R. Ichikawa, Y. Koyama, and T. Kondo. Fast and accurate ray-tracing algorithms for real-time space geodetic applications using numerical weather models. J. Geophys. Res., 113:D20302, 2008. doi:  10.1029/2008JD010503.
  60. H.S. Hopfield. Two-quartic tropospheric refractivity profile for correcting satellite data. J. Geophys. Res., 74:4487–4499, 1969. doi:  10.1029/JC074i018p04487.Google Scholar
  61. C. G. Hulley. Improved Refraction Corrections for Satellite Laser Ranging (SLR) by Ray Tracing through Meteorological Data. PhD thesis, University of Maryland, 2007.Google Scholar
  62. G. C. Hulley and E. C. Pavlis. A ray-tracing technique for improving Satellite Laser Ranging atmospheric delay corrections, including the effects of horizontal refractivity gradients. J. Geophys. Res., 112(B06417):1–19, 2007. doi:  10.1029/2006JB004834.Google Scholar
  63. I. Ifadis. The atmospheric delay of radio waves: Modeling the elevation dependence on a global scale. Technical Report 38L, School Electrical Computer Engineering, Chalmers University of Technology, Göteborg, Sweden, 1986. ISBN:99-0605353-4.Google Scholar
  64. K. Iizuka. Engineering optics, volume 35 of Springer Series in Optical Sciences. Springer-Verlag, New York, 3rd edition, 2008.Google Scholar
  65. A. Ishimaru. Wave Propagation and Scattering in Random Media. Academic Press, New York, 1978.Google Scholar
  66. J. D. Jackson. Classical electrodynamics. Wiley & Sons, Inc., N.Y., 3rd edition, 1998.Google Scholar
  67. P. O. J. Jarlemark. Analysis of temporal and spatial variations in atmospheric water vapor using microwave radiometry. PhD Thesis, Tech. Rep. 308, School Electrical Computer Engineering, Chalmers Univ. Tech., 1997. Göteborg, Sweden.Google Scholar
  68. H. Jeske. Meteorological optics and radiometeorology. In Landolt-Börnstein, editor, Numerical data and functional relationships in science and technology, volume 4b of Group V. Springer, 1988.Google Scholar
  69. S. Jin, J.-U. Park, J.-H. Cho, and P.-H. Park. Seasonal variability of GPS-derived zenith tropospheric delay (1994–2006) and climate implications. J. Geophys. Res., 112:D09110, 2007. doi:  10.1029/2006JD007772.
  70. A. Karabatić, R. Weber, and T. Haiden. Near real-time estimation of tropospheric water vapour content from ground based GNSS data and its potential contribution to weather now-casting in Austria. Adv. Space Res., 47(10):1691–1703, 2011. doi:  10.1016/j.asr.2010.10.028.
  71. A. N. Kolmogorov. Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR, 32(1):16–18, 1941a. English translation in: Proc R. Soc. Lond. A, 434:15–17.Google Scholar
  72. A. N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30(4):299–303, 1941b. English translation in: Proc R. Soc. Lond. A, 434:9–13.Google Scholar
  73. J. Kouba. Implementation and testing of the gridded vienna mapping function 1 (VMF1). J. Geodesy, 82(4–5):193–205, 2008. doi:  10.1007/s00190-007-0170-0.
  74. C. E. Kuehn, W. E. Himwich, T. A. Clark, and C. Ma. An evaluation of water vapor radiometer data for calibration of the wet path delay in very long baseline interferometry experiments. Radio Sci., 26(6):1381–1391, 1991. doi:  10.1029/91RS02020.Google Scholar
  75. R.F. Leandro, M.C. Santos, and R.B. Langley. UNB neutral atmosphere models: Development and performance. In National Technical Meeting of The Institute of Navigation, Monterey, California, 18–20 January 2006, pages 564–573, 2006.Google Scholar
  76. H. J. Liebe. An updated model for millimeter wave propagation in moist air. Radio Sci., 20(5): 1069–1089, 1985. doi: 10.1029/RS020i005p0106.
  77. H. J. Liebe. MPMan atmospheric millimeter-wave propagation model. Int. J. Infrared Millimeter Waves, 10(6): 631–650, 1989. doi:  10.1007/BF01009565.Google Scholar
  78. H. J. Liebe, G. A. Hufford, and M. G. Cotton. Propagation modeling of moist air and suspended water/ice particles at frequencies below 1000 GHz. In Proc. AGARD 52d Specialists Meeting of the Electromagnetic Wave Propagation Panel, pages 3.1–3.10, Palam de Mallorca, Spain, 1993. AGARD.Google Scholar
  79. D. S. MacMillan. Atmospheric gradients from very long baseline interferometry observations. Geophys. Res. Lett., 22(9):1041–1044, 1995. doi:  10.1029/95GL00887.Google Scholar
  80. D. S. MacMillan and C. Ma. Evaluation of very long baseline interferometry atmospheric modeling improvements. J. Geophys. Res., 99(B1):637–651, 1994. doi:  10.1029/93JB02162.Google Scholar
  81. D. S. MacMillan and C. Ma. Atmospheric gradients and the VLBI terrestrial and celestial reference frames. Geophys. Res. Lett., 24(4):453–456, 1997. doi: 10.1029/97GL00143.
  82. J.W. Marini. Correction of satellite tracking data for an arbitrary tropospheric profile. Radio Science, 7(2):223–231, 1972. doi:  10.1029/RS007i002p00223.Google Scholar
  83. J.W. Marini and C.W. Murray. Correction of laser range tracking data for atmospheric refraction at elevation angles above 10 degrees. Technical Report X-591-73-351, NASA, 1973.Google Scholar
  84. V. B. Mendes. Modeling of the neutral-atmosphere propagation delay in radiometric space techniques. PhD dissertation, Department of Geodesy and Geomatics Engineering Tech. Report No. 199, University of New Brunswick, Fredericton, New Brunswick, Canada, 1999. General definitions of IWV, relative humidity etc.Google Scholar
  85. V. B. Mendes and R. Langley. Tropospheric zenith delay prediction accuracy for airborne GPS high-precision positioning. In Proc. of ION GPS-98, pages 337–347, Nashville, TN, USA, 1998.Google Scholar
  86. V. B. Mendes and E. C. Pavlis. High-accuracy zenith delay prediction at optical wavelengths. Geophys. Res. Lett., 31, 2004. doi:  10.1029/2004GL020308.L14602.
  87. V. B. Mendes, G. Prates, E. C. Pavlis, D. E. Pavlis, and R. B. Langley. Improved mapping functions for atmospheric refraction correction in SLR. Geophys. Res. Lett., 29(10):10.1029-10.1032, 2002. doi: 10.1029/2001GL014394.
  88. V. Nafisi, M. Madzak, J. Böhm, A. A. Ardalan, and H. Schuh. Ray-traced tropospheric delays in VLBI analysis. Radio Sci., 47:RS2020, 2012a. doi:  10.1029/2011RS004918.
  89. V. Nafisi, L. Urquhart, M. C. Santos, F. G. Nievinski, J. Böhm, D. D. Wijaya, H. Schuh, A. A. Ardalan, T. Hobiger, R. Ichikawa, F. Zus, J. Wickert, and P. Gegout. Comparison of ray-tracing packages for troposphere delays. IEEE Trans. Geosci. Remote Sensing, 50(2):469–481, 2012b. doi: 10.1109/TGRS.2011.2160952.
  90. A. Niell. Global mapping functions for the atmosphere delay at radio wavelengths. J. Geophys. Res., 101(B2):3227–3246, 1996. doi:  10.1029/95JB03048.Google Scholar
  91. A. E. Niell. Improved atmospheric mapping functions for VLBI and GPS. Earth Planets Space, 52:699–702, 2000.Google Scholar
  92. A. E. Niell. Preliminary evaluation of atmospheric mapping functions based on numerical weather models. Phys. Chem. Earth (A), 26:475–480, 2001. doi:  10.1016/S1464-1895(01)00087-4.Google Scholar
  93. A. E. Niell, A. J. Coster, F. S. Solheim, V. B. Mendes, P. C. Toor, R. B. Langley, and C. A. Upham. Comparison of measurements of atmospheric wet delay by Radiosonde, Water Vapor Radiometer, GPS, and VLBI. J. Atmos. Oceanic Technol., 18(6):830–850, 2001. doi: 10.1175/1520-0426(2001)018<0830:COMOAW>2.0.CO;2.Google Scholar
  94. A. E. Niell. Interaction of atmosphere modeling and vlbi analysis strategy. In D. Behrend and K. Baver, editors, International VLBI Service for Geodesy and Astrometry 2006 General Meeting Proceedings, number NASA/CP-2006-214140, 2006.Google Scholar
  95. F. G. Nievinski. Ray-tracing options to mitigate the neutral atmosphere delay in GPS. Master’s thesis, University of New Brunswick, Department of Geodesy and Geomatics Engineering, 2009. URL Technical Report No. 262.
  96. T. Nilsson. Improving GNSS tropospheric tomography by better knowledge of atmospheric turbulence. In Proc. 1:st Colloquium Scientific and Fundamental Aspects of the Galileo Programme, Toulouse, France, 2007. European Space Agency.Google Scholar
  97. T. Nilsson and G. Elgered. Long-term trends in the atmospheric water vapor content estimated from ground-based GPS data. J. Geophys. Res., 113:D19101, 2008. doi:  10.1029/2008JD010110.
  98. T. Nilsson and L. Gradinarsky. Water vapor tomography using GPS phase observations: Simulaton results. IEEE Trans. Geosci. Remote Sensing, 44(10):2927–2941, 2006. doi: 10.1109/TGRS.2006.877755.Google Scholar
  99. T. Nilsson, L. Gradinarsky, and G. Elgered. Correlations between slant wet delays measured by microwave radiometry. IEEE Trans. Geosci. Remote Sensing, 43(5):1028–1035, 2005. doi: 10.1109/TGRS.2004.840659.Google Scholar
  100. T. Nilsson, L. Gradinarsky, and G. Elgered. Water vapour tomography using GPS phase observations: Results from the ESCOMPTE experiment. Tellus A, 59:574–682, 2007. doi:  10.1111/j.1600-0870.2007.00247.x.
  101. T. Nilsson and R. Haas. Impact of atmospheric turbulence on geodetic very long baseline interferometry. J. Geophys. Res., 115:B03407, 2010. doi:  10.1029/2009JB006579.
  102. T. Ning and G. Elgered. Trends in the atmospheric water vapor content from ground-based GPS: The impact of the elevation cutoff angle. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5:744–751, 2012. doi:  10.1109/JSTARS.2012.2191392.Google Scholar
  103. A. Nothnagel, J. Cho, A. Roy, and R. Haas. WVR calibration applied to European VLBI observing sessions. In P. Tregoning and C. Rizos, editors, Dynamic Planet, volume 130 of IAG Symposia, pages 152–157. Springer, Berlin, Germany, 2007. doi:10.1007/978-3-540-49350-1_24 Google Scholar
  104. J. C. Owens. Optical refractive index of air: Dependence on pressure, temperature and composition. Appl. Opt., 6(1):51–59, 1967. doi:  10.1364/AO.6.000051.Google Scholar
  105. T. K. Pany. Development and application of tropospheric GPS slant delay models based on numerical weather prediction models and turbulence theory. PhD thesis, Institute of Engineering Geodesy and Measurements Systems, Graz University of Technology, 2002.Google Scholar
  106. D. Perler, A. Geiger, and F. Hurter. 4D GPS water vapor tomography: new parameterized approaches. J. Geodesy, 85(8):539–550, 2011. doi:  10.1007/s00190-011-0454-2.Google Scholar
  107. P. Poli, P. Moll, F. Rabier, G. Desroziers, B. Chapnik, L. Berre, S. B. Healy, E. Andersson, and F.-Z. El Guelai. Forecast impact studies of zenith total delay data from European near real-time GPS stations in météo france 4DVAR. J. Geophys. Res., 112:D06114, 2007. doi: 10.1029/2006JD007430.
  108. M. T. Prilepin. Light modulating method for determining average index of refraction of air along a line. Tr. Tsentr. Nauchno-Issled. Inst. Geod. Aero. Kartog., 114:127, 1957.Google Scholar
  109. L. F. Richardson. The supply of energy from and to atmospheric eddies. Proc. Roy. Soc. Lond. A, 97(686):354–373, 1920.Google Scholar
  110. P. W. Rosenkranz. Water vapor microwave continuum absorption: a comparison of measurements and models. Radio Sci., 33(4):919–928, 1998. doi:  10.1029/98RS01182.
  111. M. Rothacher, T.A. Springer, S. Schaer, and G. Beutler. Processing strategies for regional GPS networks. In F.K. Brunner, editor, Advances in Positioning and Reference Frames, volume 118 of IAG Symposia Series, pages 93–100. Springer-Verlag, 1998.Google Scholar
  112. J. M. Rüeger. Refractive index formulae for radio waves. In Proc. XXII FIG International Congress, Washington DC, USA, 2002a. FIG. URL
  113. J. M. Rüeger. Refractive indices of light, infrared and radio waves in the atmosphere. Technical report, UNISURV S-68, School of Surveying and Spatial Information Systems, The University of New South Wales, Australia, 2002b.Google Scholar
  114. J. Saastamoinen. Atmospheric correction for the troposphere and stratosphere in radio ranging of satellites. In S. W. Henriksen et al., editors, The Use of Artificial Satellites for Geodesy, volume 15, pages 247–251, AGU, Washington, D.C., 1972b.Google Scholar
  115. J. Saastamoinen. Introduction to practical computation of astronomical refraction. Bull. Géod., 106:383–397, 1972a. doi:  10.1007/BF02522047.
  116. T. M. Scheve and C. T. Swift. Profiling atmospheric water vapor with a K-band spectral radiometer. IEEE Trans. Geosci. Remote Sensing, 37(3):1719–1729, 1999. doi: 10.1109/36.763294.Google Scholar
  117. W. A. Schneider, Jr. Robust, efficient upwind finite-difference traveltime calculations in 3d. In Proc. 63rd SEG meeting, pages 1036–1039, Washington, DC, USA, 1993.Google Scholar
  118. S. D. Schubert, J. Pjaendtner, and R. Rood. An assimilated data set for earth science applications. Bull. American. Meteo. Soc., 74:2331–2342, 1993. doi:  10.1175/1520-0477(1993)074<2331:AADFES>2.0.CO;2.Google Scholar
  119. K. Snajdrova, J. Böhm, P. Willis, R. Haas, and H. Schuh. Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign. J. Geodesy, 79(10–11):613–623, 2006. doi:  10.1007/s00190-005-0010-z.Google Scholar
  120. F. S. Solheim, J. Vivekanandan, R. H. Ware, and C. Rocken. Propagation delays induced in GPS signals by dry air, water vapor, hydrometeors, and other particulates. J. Geophys. Res., 104(D8):9663–9670, 1999. doi:  10.1029/1999JD900095.Google Scholar
  121. P. Steigenberger, J. Böhm, and V. Tesmer. Comparison of GMF/GPT with VMF1/ECMWF and implications for atmospheric loading. J. Geodesy, 83:943–951, 2009. doi: 10.1007/s00190-009-0311-8.
  122. P. Steigenberger, V. Tesmer, M. Krügel, D. Thaller, R. Schmid, S. Vey, and M. Rothacher. Comparisons of homogeneously reprocessed GPS and VLBI long time-series of troposphere zenith delays and gradients. J. Geodesy, 81(6–8):503–514, 2007. doi: 10.1007/s00190-006-0124-y.Google Scholar
  123. V. I. Tatarskii. The Effects of the Turbulent Atmosphere on Wave Propagation. Israel Program for Scientific Translations, Jerusalem, 1971.Google Scholar
  124. G. I. Taylor. The spectrum of turbulence. Proc. Roy. Soc. Lond. A, 164(919):476–490, 1938. URL
  125. K. Teke, J. Böhm, T. Nilsson, H. Schuh, P. Steigenberger, R. Dach, R. Heinkelmann, P. Willis, R. Haas, S. Garcia-Espada, T. Hobiger, R. Ichikawa, and S. Shimizu. Multi-technique comparison of troposphere zenith delays and gradients during CONT08. J. Geodesy, 85(7):395–413, 2011. doi: 10.1007/s00190-010-0434-y.Google Scholar
  126. V. Tesmer, J. Böhm, R. Heinkelmann, and H. Schuh. Effect of different tropospheric mapping functions on the TRF, CRF and position time-series estimated from VLBI. J. Geodesy, 81(6–8): 409–421, 2007. doi: 10.1007/s00190-006-0126-9.
  127. G. D. Thayer. A rapid and accurate ray tracing algorithm for a horizontally stratified atmosphere. Radio Sci., 1(2):249–252, 1967.Google Scholar
  128. G. D. Thayer. An improved equation for the radio refractive index of air. Radio Sci., 9(10):803–807, 1974. doi:  10.1029/RS009i010p00803.Google Scholar
  129. R. N. Thessin. Atmospheric signal delay affecting GPS measurements made by space vehicles during launch, orbit and reentry. Master’s thesis, Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, Cambridge, Mass., 2005. URL
  130. D. M. Tralli and S. M. Lichten. Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements. Bull. Geod., 64:127–159, 1990. doi:  10.1007/BF02520642.Google Scholar
  131. P. Tregoning and T.A. Herring. Impact of a priori zenith hydrostatic delay errors on GPS estimates of station heights and zenith total delays. Geophys. Res. Lett., 33(L23303), 2006. doi: 10.1029/2006GL027706.
  132. K. E. Trenberth, A. Dai, R.M. Rasmussen, and D.B. Parsons. The changing character of precipitation. Bull. Amer. Meteor. Soc., 84(9):12051217, 2003. doi: 10.1175/BAMS-84-9-1205.Google Scholar
  133. R. N. Treuhaft and G. E. Lanyi. The effect of the dynamic wet troposphere on radio interferometric measurements. Radio Sci., 22(2):251–265, 1987. doi:  10.1029/RS022i002p00251.
  134. M. Troller, A. Geiger, E. Brockmann, J.-M. Bettems, B. Bürki, and H.-G. Kahle. Tomographic determination of the spatial distribution of water vapor using GPS observations. Adv. Space Res., 37(12):2211–2217, 2006. doi:  10.1016/j.asr.2005.07.002.
  135. H. Vedel. Targeting optimal use of GPS humidity measurements in meteorology: Final report of the TOUGH project, 2006. URL
  136. H. Vedel and X.-Y. Huang. Impact of ground based GPS data on numerical weather prediction. J. Met. Soc. Japan, 82(1B):459–472, 2004. doi: 10.2151/jmsj.2004.459.Google Scholar
  137. J. Wang, L. Zhang, and A. Dai. Global estimates of water-vapor-weighted mean temperature of the atmosphere for GPS applications. J. Geophys. Res., 110(D21101), 2005. doi: 10.1029/2005JD006215.
  138. R. Ware, C. Rocken, F. Solheim, T. van Hove, C. Alber, and J. Johnson. Pointed water vapor radiometer corrections for accurate global positioning system surveying. Geophys. Res. Lett., 20(23): 2635–2638, 1993. doi:  10.1029/93GL02936.Google Scholar
  139. E. R. Westwater, M. J. Falls, and I. A. Popa-Fotin. Ground-based microwave radiometric observations of precipitable water vapor: A comparison with ground truth from two radiosonde observing systems. J. Atmos. Oceanic Technol., 6(4):724–730, 1989. doi: 10.1175/1520-0426(1989)006.
  140. A. D. Wheelon. Electromagnetic scintillation: Geometrical optics. Cambridge University Press, 2001.Google Scholar
  141. D. D. Wijaya. Atmospheric correction formulae for space geodetic techniques. PhD thesis, Graz University of Technology, Institute of Engineering Geodesy and Measurements Systems, Graz, Austria, 2010.Google Scholar
  142. D. D. Wijaya, J. Böhm, M. Karbon, and H. Schuh. Atmospheric pressure loading. In Atmospheric Effects in Space Geodesy. Springer-Verlag, 2013. this book.Google Scholar
  143. D.D. Wijaya and F.K. Brunner. Atmospheric range correction for two-frequency SLR measurements. J. Geodesy, 85(9):623–635, 2011. doi:  10.1007/s00190-011-0469-8.Google Scholar
  144. S.-C. Wu. Optimum frequencies of a passive microwave radiometer for tropospheric path-length correction. IEEE Trans. Antennas Propagat., 27:233–239, 1979. doi: 10.1109/TAP.1979.1142066.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tobias Nilsson
    • 1
  • Johannes Böhm
    • 2
  • Dudy D. Wijaya
    • 3
  • Ana Tresch
    • 4
  • Vahab Nafisi
    • 5
  • Harald Schuh
    • 6
  1. 1.Section 1.1 GPS/Galileo Earth ObservationsHelmholtz Centre Potsdam GFZ German Research Centre for GeosciencesPotsdamGermany
  2. 2.Department of Geodesy and GeoinformationVienna University of TechnologyViennaAustria
  3. 3.Geodesy Research GroupInstitute of Technology BandungBandung-West JavaIndonesia
  4. 4.Monitoring SolutionsLeica Geosystems AGHeerbruggSwitzerland
  5. 5.Department of Surveying Engineering, Faculty of EngineeringUniversity of IsfahanIsfahanIran
  6. 6.Department 1 Geodesy and Remote SensingHelmholtz Centre Potsdam GFZ German Research Centre for GeosciencesPotsdamGermany

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