Calibration of Empirical Models of Thermospheric Density Using Satellite Laser Ranging Observations to Near-Earth Orbiting Spherical Satellites

  • Sergei RudenkoEmail author
  • Michael Schmidt
  • Mathis Bloßfeld
  • Chao Xiong
  • Hermann Lühr
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 149)


The thermosphere causes by far the largest non-gravitational perturbing acceleration of near-Earth orbiting satellites. Especially between 80 km and 1,000 km, the thermospheric density distribution and variations are required to model accurately this acceleration for precise orbit determination (POD), ephemeris computation and re-entry prediction of the Low-Earth Orbiting (LEO) satellites. So far, mostly on-board accelerometers are used to measure the thermospheric density. However, such type of satellite is usually of complex shape and any error or mismodelling in the satellite drag coefficient and satellite effective cross-sectional area will directly propagate into the derived thermospheric density values. At GFZ, an empirical model of the thermospheric mass density denoted as “CH-Therm-2018” has been developed by using 9 years (2001–2009) of CHAMP observations.

A completely different approach for thermospheric density determination is based on using satellite laser ranging (SLR) measurements to LEO satellites equipped with retro-reflectors to determine an accurate satellite orbit. These measurements are sensitive to small perturbations acting on the satellite. In order to minimize the error induced by imprecise satellite macro-models, we use in our investigation SLR observations to satellites with a simple spherical shape and thus, relate estimated scaling factors to the thermospheric density.

In this paper, we use SLR observations to two ANDE-2 satellites – ANDE-Castor and ANDE-Pollux – as well as SpinSat with altitudes between 248 km and 425 km to calibrate the CH-Therm-2018 model, as well as four other empirical models of thermospheric density, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. For our tests, we chose a period from 16 August 2009 to 26 March 2010 of low solar activity and a period from 29 December 2014 to 29 March 2015 of high solar activity. Using data of a few geodetic satellites obtained at the same and different time intervals allows us to investigate the reliability of the scaling factors of the thermospheric densities provided by the models. We have found that CIRA86 and NRLMSISE00 most significantly overestimate the thermospheric density at the period of low solar activity among the models tested. The JB2008 model is the least scaled model and provides reliable values of the thermospheric density for the periods of both low and high solar activity. The GFZ CH-Therm-2018 model, on the contrary, underestimates the thermospheric density at the time interval of low solar activity. Using SLR observations at longer time intervals should allow to investigate temporal evolution of the scaling factors of these models more precisely.


ANDE-2 Empirical thermosphere models Precise orbit determination Satellite Laser Ranging (SLR) SpinSat Thermospheric drag 



This study was performed within the project “Interactions of Low-orbiting Satellites with the Surrounding Ionosphere and Thermosphere (INSIGHT)” funded by the German Research Foundation (DFG) in the framework of the Special Priority Programme 1788 “Dynamic Earth”. We are grateful to two anonymous reviewers and Editor-in-Chief for their comments that allowed us to improve this paper.


  1. Afonso G, Barlier F, Mignard F, Carpino M, Farinella P (1989) Orbital effects of LAGEOS seasons and eclipses. Ann Geophys 7:501–514Google Scholar
  2. Bloßfeld M (2015) The key role of Satellite Laser Ranging towards the integrated estimation of geometry, rotation and gravitational field of the Earth. PhD Dissertation, Technische Universität München (TUM), MunichGoogle Scholar
  3. Bowman BR, Tobiska WK, Marcos FA, Huang CY, Lin CS, Burke WJ (2008) A new empirical thermospheric density model JB2008 using new solar and geomagnetic indices. In: AIAA/AAS astrodynamics specialist conference and exhibit, AIAA 2008-6438Google Scholar
  4. Bruinsma SL (2015) The DTM-2013 thermosphere model. J Space Weather Space Clim 5(A1).
  5. Bruinsma S, Arnold D, Jäggi A, Sánchez-Ortiz N (2017) Semi-empirical thermosphere model evaluation at low altitude with GOCE densities. J Space Weather Space Clim 7(A4).
  6. Combrinck L (2010) Satellite laser ranging. In: Xu G (ed) Sciences of geodesy - I. Springer, Berlin/Heidelberg. Google Scholar
  7. Doornbos E, Klinkrad H, Visser P (2005) Atmospheric density calibration using satellite drag observations. Adv Space Res 36(3):515–521. CrossRefGoogle Scholar
  8. Drob DP, Emmert JT, Meriwether JW, Makela JJ, Doornbos E, Conde M, Hernandez G, Noto J, Zawdie KA, McDonald SE, Huba JD, Klenzing JH (2015) An update to the Horizontal Wind Model (HWM): the quiet time thermosphere. Earth Space Sci 2(7):301–319. CrossRefGoogle Scholar
  9. Emmert JT (2015) Thermospheric mass density: a review. Adv Space Res 56:773–824. CrossRefGoogle Scholar
  10. Emmert JT, Lean JL, Picone JM (2010) Record-low thermospheric density during the 2008 solar minimum. Geophys Res Lett 37:L12102. CrossRefGoogle Scholar
  11. Fleming EL, Chandra S, Shoeberl M-R, Barnett JJ (1988) Monthly mean global climatology of temperature, wind, geopotential height and pressure for 0–120 km. National Aeronautics and Space Administration, Technical Memorandum 100697, Washington, DCGoogle Scholar
  12. Floberghagen, R, Fehringer, M, Lamarre, D, et al (2011) Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J Geod 85:749–758. CrossRefGoogle Scholar
  13. Gerstl M (1997) Parameterschätzung in DOGS-OC. In: DGFI Interner Bericht, MG/01/1996/DGFI, 2nd edn (in German)Google Scholar
  14. Hedin AE, Spencer NW, Killeen TL (1988) Empirical global model of upper thermosphere winds based on Atmosphere and Dynamics Explorer satellite data. J Geophys Res 93:9959–9978. CrossRefGoogle Scholar
  15. Liu H, Hirano T, Watanabe S (2013) Empirical model of the thermosphereic mass density based on CHAMP satellite observation. J Geophys Res Space Phys 118:843–848. CrossRefGoogle Scholar
  16. Milani A, Nobili AM, Farinella P (1987) Non-gravitational perturbations and satellite geodesy. Adam Hilger, Bristol, 125 pagesGoogle Scholar
  17. Nicholas AC, Finne T, Davis MA, Kessel R (2009) Atmospheric Neutral density Experiment (ANDE-2) flight hardware details, 26 May 2009.
  18. Nicholas A, Finne T, Galysh I, Mai A, Yen J, Sawka W, Ransdell J, Williams S (2013) SpinSat mission overview. In: Proceedings of the 27th AIAA/USU conference, small satellite constellations, Logan, UT, 10–15 Aug 2013, paper: SSC13-I-3.
  19. Panzetta F, Bloßfeld M, Erdogan E, Rudenko S, Schmidt M, Müller H (2018) Towards thermospheric density estimation from SLR observations of LEO satellites - a case study with ANDE-Pollux satellite. J Geod,
  20. Petit G, Luzum B (2010) IERS conventions (2010), Technical note 36. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt. ISBN 3-89888-884-3Google Scholar
  21. Picone JM, Hedin AE, Drob DP, Aikin AC (2002) NRLMSISE-00 empirical model of the atmosphere: statistical comparisons and scientific issues. J Geophys Res Space.
  22. Reigber C, Lühr H, Schwintzer P (2002) CHAMP mission status. Adv Space Res 30:129–134.
  23. Rubincam D (1987) LAGEOS orbit decay due to Infrared radiation from Earth. J Geophys Res Solid Earth 92(B2):1287–1294. CrossRefGoogle Scholar
  24. Rudenko S, Neumayer K-H, Dettmering D, Esselborn S, Schöne T, Raimondo J-C (2017) Improvements in precise orbits of altimetry satellites and their impact on mean sea level monitoring. IEEE Trans Geosci Remote Sens 55(6):3382–3395. CrossRefGoogle Scholar
  25. Rudenko S, Bloßfeld M, Müller H, Dettmering D, Angermann D, Seitz M (2018) Evaluation of DTRF2014, ITRF2014 and JTRF2014 by precise orbit determination of SLR satellites. IEEE Trans Geosci Remote 56(6):3148–3158. CrossRefGoogle Scholar
  26. Seitz M, Bloßfeld M, Angermann D, Schmid R, Gerstl M, Seitz F (2016) The new DGFI-TUM realization of the ITRS: DTRF2014 (data). Deutsches Geodätisches Forschungsinstitut, Munich. (Open Access)
  27. Sośnica K (2015) Impact of the atmospheric drag on Starlette, Stella, Ajisai, and Lares orbits. Artif. Satell. 50(1):1–18. CrossRefGoogle Scholar
  28. Tapley BD, Bettadpur S, Watkins M, et al (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31:L09607. CrossRefGoogle Scholar
  29. Vallado DA, Finkleman D (2014) A critical assessment of satellite drag and atmospheric density modeling. Acta Astronaut 95:141–165. CrossRefGoogle Scholar
  30. Xiong C, Lühr H, Schmidt M, Bloßfeld M, Rudenko S (2018) An empirical model (CH-Therm-2018) of the thermospheric mass density derived from CHAMP. Ann Geophys Discuss., in review

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sergei Rudenko
    • 1
    Email author
  • Michael Schmidt
    • 1
  • Mathis Bloßfeld
    • 1
  • Chao Xiong
    • 2
  • Hermann Lühr
    • 2
  1. 1.Deutsches Geodätisches Forschungsinstitut at the Technische Universität München (DGFI-TUM)MunichGermany
  2. 2.Deutsches GeoForschungsZentrum (GFZ) PotsdamPotsdamGermany

Personalised recommendations