Journal of Geodesy

, Volume 85, Issue 9, pp 623–635 | Cite as

Atmospheric range correction for two-frequency SLR measurements

  • Dudy D. Wijaya
  • Fritz K. Brunner
Original Article


It has been widely known that the use of two-frequency Satellite Laser Ranging (SLR) system is limited by stringent precision requirements of the range measurements and the proper atmospheric model. Owing to the stringent requirements, this SLR system is impractical for the current requirement of SLR measurements within the framework of global geodetic observing system (GGOS). If in the future this stringent requirement could be met, this SLR system would be an attractive tool to reduce atmospheric propagation effects of SLR and would be of great benefit for the next generation of GGOS design. To anticipate possible future developments of the two-frequency SLR systems, we have developed a new atmospheric correction formula for the two-frequency SLR measurements. The new formula eliminates the total atmospheric density effect including its gradient and provides two terms to calculate the curvature effect and the water vapor distribution effect. While the curvature effect can be calculated by an accurate model, the required information about the water vapor distribution along the propagation path can be calculated using previous developments of optical delay modeling or alternatively using results from microwave measurements. Theoretical simulations using the two-frequency systems of the Graz and TIGO-Concepción stations shows that the new formula completely reduces all propagation effects at any elevation angle above 3° with an accuracy better than 1 mm. However, the required precision for the difference of the two-frequency SLR measurements, i.e. better than 45 μm for a single epoch, exceeds the capability of the current state of the art SLR systems.


SLR Atmospheric propagation Dispersion effect Curvature effect Water vapor Perturbation 


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  1. Abshire JB, Gardner CS (1985) Atmospheric refractivity corrections in Satellite Laser Ranging. IEEE Trans Geosci Remote Sens GE-23(4): 414–425CrossRefGoogle Scholar
  2. Arnold D, Kirchner G, Koidl F (2004) Identifying single retro tracks with a 2 kHz SLR system. kHz SLR Meeting, 27–29 October, GrazGoogle Scholar
  3. Bar-Sever YE, Kroger PM, Borjesson JA (1998) Estimating horizontal gradients of tropospheric path delay with a single GPS receiver. J Geophys Res 103(B3): 5019–5035CrossRefGoogle Scholar
  4. Behrend D, Cucurull L, Vilá J, Haas R (2000) An inter-comparison study to estimate zenith wet delays using VLBI, GPS and NWP models. Earth Planets Space 52: 691–694Google Scholar
  5. Bendat JA, Piersol AG (1971) The effects of atmospheric turbulence on telescopic observations. Wiley, New YorkGoogle Scholar
  6. Bender PL, Owens JC (1965) Correction of optical distance measurements for the fluctuating atmospheric index of refraction. J Geophys Res 70(10): 2461CrossRefGoogle Scholar
  7. Böhm 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 111: B02406. doi: 10.1029/2005JB003629 CrossRefGoogle Scholar
  8. Borbás É (1998) Derivation of precipitable water vapor from GPS data: and application to meteorology. Phys Chem Earth 23(1): 87–90CrossRefGoogle Scholar
  9. Born M, Wolf E (1999) Principles of optics, 7th edn. Cambridge University Press, CambridgeGoogle Scholar
  10. Brunner FK (1982) The effects of atmospheric turbulence on telescopic observations. Bull Géod 56: 341–355CrossRefGoogle Scholar
  11. Ciddor PE (1996) Refractive index of air: new equations for the visible and near infrared. Appl Opt 35(9)Google Scholar
  12. Coster AJ, Niell AE, Solheim FS, Mendes VB, Toor PC, Buchmann KP, Upham CA (1996) Measurements of precipitable water vapor by GPS, Radiosondes and a Microwave Water Vapor Radiometer. Proceeding of ION-GPS, Kansas City, Kansas, September 17–20Google Scholar
  13. Davis JL, Herring TA, Shapiro II, Rogers AEE, Elgered G (1985) Geodesy by radio interferometry: effects of atmospheric modeling errors on estimates of baseline length. Radio Sci 20: 1593–1607CrossRefGoogle Scholar
  14. de Haan S, van der Marel H, Barlag S (2002) Comparison of GPS slant delay measurement to a numerical model: case study of a cold front passage. Phys Chem Earth 27: 317–322Google Scholar
  15. Degnan JJ, Mc Garry JT (1997) SLR2000: eyesafe and autonomous single photoelectron satellite laser ranging at kilohertz rates, SPIE Vol 3218. Laser Radar Ranging and Atmospheric Lidar Techniques, LondonGoogle Scholar
  16. Edlen B (1966) The refractive index of air. Metrologia 2(2): 71–80CrossRefGoogle Scholar
  17. Elgered G, Johansson JM, Rönnäng BO (1990) Characterizing atmospheric water vapour fluctuations using microwave radiometry. Department of Radio and Space Science with Onsala Space Observatory, Chalmers University of Technology, Göteborg, Sweden, Reseacrh Report 165Google Scholar
  18. Greene BA, Herring TA (1986) Multiple wavelength laser ranging. The 6th international workshop on laser ranging instrumentation, Antibes FranceGoogle Scholar
  19. Gu M, Brunner FK (1990) Theory of the two frequency dispersive range correction. Manuscr Geod 15: 357–361Google Scholar
  20. Gurtner W, Pop E, Utzinger J (2002) Zimmerwald dual-wavelength observations: first experiences. The 13th international workshop on laser ranging instrumentation. Washington DC, USAGoogle Scholar
  21. Gurtner W, Pop E, Utzinger J (2006) Two-color calibration of the Zimmerwald SLR system. The 15th international workshop on laser ranging instrumentation, Canbera, AustraliaGoogle Scholar
  22. Hamal K, Prochazka I, Kirchner G, Koidl F (2005) Satellite laser ranging normal point precision limit. CTU Workshop, Prague Czech RepublicGoogle Scholar
  23. Hase H, Böer A, Riepl S, Schlüter W, Cecioni A, Bataille K, Amthauer E, Baradit E, Narvaez A, Cifuentes O (2003) The TIGO project, Next Technology in VLBI. Astron Soc Pacific Conf 306: 347–360Google Scholar
  24. Hulley GC, Pavlis EC (2007) A ray-tracing technique for improving satellite laser ranging atmospheric delay corrections including the effects of horizontal refractivity gradients. J Geophys Res 112: B06417. doi: 10.1029/2006JB004834 CrossRefGoogle Scholar
  25. Hulley GC (2007) Improved refraction corrections for satellite laser ranging (SLR) by ray tracing through meteorological data. PhD thesis, The Faculty of the Graduate School of the University of Maryland, USAGoogle Scholar
  26. Linfield R, Bar-Server Y, Kroger P, Keihm S (1997) Comparison of global positioning system and water vapor radiometer wet tropospheric delay estimates. TDA Progress Report, pp 42–130Google Scholar
  27. Lukas K, Prochazka I, Hamal K (2005) Optical signal path delay fluctuations caused by atmospheric turbulence. Opt Lett 30: 1767–1769CrossRefGoogle Scholar
  28. MacMillan DS (1995) Atmospheric gradients from very long baseline interferometry observations. Geophys Res Lett 22(9): 1041–1044. doi: 10.1029/95GL00887 CrossRefGoogle Scholar
  29. Marini JW, Murray CW (1973) Correction of laser range tracking data for atmospheric refraction at elevations above 10 degrees. NASA Goddard Space Flight Center, x-591-73-351Google Scholar
  30. Mendes VB, Pavlis EC (2004) High-accuracy zenith delay prediction at optical wavelengths. Geophys Res Lett 31: L14602. doi: 10.1029/2004GL020308 CrossRefGoogle Scholar
  31. Mendes VB, Pavlis EC, Pavlis DE, Langley RB (2002) Improved mapping functions for atmospheric refraction correction in SLR. Geophys Res Lett 29(10): 1414. doi: 10.1029/2001GL014394 CrossRefGoogle Scholar
  32. NASA (1991) Standard atmosphere 1976. National Oceanic and Atmospheric Administration, NASAGoogle Scholar
  33. Niell AE, Coster AJ, Solheim FS, Mendes VB, Toor PC, Langley RB, Ruggles CA (1996) Measurements of water vapor by GPS, WVR and Radiosonde. In: Proceedings 11th working meeting on European VLBI for geodesy and astrometry, Department of Radio and Space Science with Onsala Space Observatory, Chalmers University of Technology, Göteborg, SwedenGoogle Scholar
  34. Pany T (2002) Measuring and modeling the slant wet delay with GPS and the ECMWF NWP model. Phys Chem Earth 27: 347–354Google Scholar
  35. Reigber C, Tapley B (2000) A new class of satellites for Earth system sciences: CHAMP and GRACE. The 12th international workshop on laser ranging, Matera, ItalyGoogle Scholar
  36. Riepl S, Schlüter W (2001) Normal point algorithm for reduction of two colour SLR observations. Surv Geophys 22: 558–581CrossRefGoogle Scholar
  37. Riepl S (2000) Experimental verification of the Marini–Murray model by two colour SLR. The 12th international workshop on laser ranging instrumentation, Matera, ItalyGoogle Scholar
  38. Rothacher M, Beutler G, Donnellan A, Hinderer J, Ma Noll C, Oberts J, Pearlman M, Plag HP, Richter B, Schöne T, Tavernier G, Woodworth PL (2009) The future global geodetic observing system. In: Plag H-P, Pearlman M (eds) Global geodetic observing system, meeting the requierements of a global society on a changing planet in 2020. Springer, Berlin, pp 237–272Google Scholar
  39. Rothacher M (2005) Role of the existing IAG services for GGOS. Dynamic Planet 2005, Cairns, AustraliaGoogle Scholar
  40. Rüeger JM (2002) Refractive indices of light, infrared and radio waves in the atmosphere. UNISURV S-68, School of Surveying and Spatial Information Systems, The University of New South Wales, AustraliaGoogle Scholar
  41. Snajdrova K, Böhm J, Willis P, Haas R, Schuh H (2006) Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign. J Geod 79: 613–623. doi: 10.1007/s00190-005-0010-z CrossRefGoogle Scholar
  42. Teke K, Böhm J, Nilsson T, Schuh H, Steigenberger P, Dach R, Heinkelmann R, Willis P, Haas R, Garcia-Espada S, Hobiger T, Ichikawa R, Shimizu S (2010) Multi-technique comparison of troposphere zenith delays and gradients during CONT08. J Geod. doi: 10.1007/s00190-010-0434-y
  43. Tregoning P, Boers R, O’Brien D, Hendy M (1998) Accuracy of absolute precipitable water vapor estimates from GPS observations. J Geophys Res 103(D22): 28701–28710CrossRefGoogle Scholar
  44. Ware RH, Fulker DW, Stein SA, Anderson DN, Avery SK, Clark RD, Droegemeier KK, Kuettner JP, Minster JB, Sorooshian S (2001) Real-time national GPS networks for atmospheric sensing. J Atmos Sollar-Terrestrial Phys 63: 1315–1330CrossRefGoogle Scholar
  45. Wijaya DD (2010) Atmospheric correction formulae for space geodetic techniques. PhD thesis, Institute of Engineering Geodesy and Measurements Systems, Graz University of Technology, Shaker VerlagGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institute of Geodesy and GeophysicsVienna University of TechnologyViennaAustria
  2. 2.Geodesy Research GroupBandung Institute of TechnologyBandungIndonesia
  3. 3.Institute of Engineering Geodesy and Measurements SystemsGraz University of TechnologyGrazAustria

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