Skip to main content
SpringerLink
Log in

Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

  • Published:
Bulletin géodésique Aims and scope Submit manuscript

Abstract

Range and range rate measurements play an important role in geodetic applications of electromagnetic waves (terrestrial as well as from space, including Very Long Baseline Interferometry (VLBI)) Recent developments of measuring, techniques have led to the situation that the measuring accuracy is no longer the limiting factor in the final accuracies of range and range rate measurements. The main error stems now from the influence of the atmosphere and from assumptions and approximations in context with the derivation of refractive index used to describe the wave propagation properties of the atmosphere. Only in the case that the geometrical optics approximation holds is it possible to calculate or to measure range error for wave propagation in the atmosphere of the earth (troposphereand ionosphere) from knowledge of the refractive index as a function of space (location) and time. Otherwise we have to consides additionally scattering and/or diffraction effects.

A discussion of the formulae for the refractive indices in the troposphere and in the ionosphere is followed by a review of the propagation of electromagnetic waves described by the geometrical optics approximation and on the limitations, of geometrical optics. A comprehensive discussion of range errors in the non-ionized atmosphere (troposphere) and in the ionosphere follows. For this purpose we use the elevation of the “ray” at a ground station for division into four domains: a) vertical incidence (as a special case), b) elevation between 90° and 30°, c)elevation between 30° and 5°, d) elevation smaller than 5°.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • H.J. ALBRECHT (editor): Propagation Effects in Space/Earth Paths. AGARD Conference Proceedings No. 284, 7 Rue Ancelle, F-92200 Neuilly sur Seine, France, 1980 (AGARD-CP-284).

  • G. O. AJAYI, A. HEDBERG, G. HAMBERG: Accurate determination of ionospheric effects on satellite based positioning systems using a versatile 3-dimensional ray tracing program. Radio Science, vol. 15, no. 5, pp. 1009–1016, 1980.

    Article  Google Scholar 

  • A.L. BARGHAUSEN, J.W. FINNER, L.L. PROCTOR and L.D. SCHULTZ: Predicting long-term operational parameters of high-frequency sky-wave telecommunications systems. ESSA Tech. Report, ERL 110-ITS 78, 1969.

  • H. BARREL: The dispersion of air between 2500 A and 6500 A. J. Opt. Soc. Amer.41, 195, 1951.

    Google Scholar 

  • B.R. BEAN: The Radio Refractive Index of Air. Proceedings of the IRE, vol. 50, 1962.

  • H.D. BLACK: The Transit System, 1977: performance, plans and potential. Phil. Trans. R. Soc. Lond.A 294, pp. 217–236, 1980.

    Article  Google Scholar 

  • M. BORN, E. WOLF: Principles of Optics, 4th Editior Pergamon Press, Oxfor, London, New York, 1970.

    Google Scholar 

  • K.G. BUDDEN: Radio waves in the ion osphere. Cambridge University Press, 1961.

  • J. CAMPBELL: Die Radiointerferometrie of langen Basen als geodätisches Messprinzip hoher Genauigkeit. Verlag der Bayerischen Akademie der Wiss., München, ISSN 0065-5325, ISBN 37696 9306X, 1979.

  • J.E. CHAMBBERLAIN, F.D. FINDLAY, H.A. GEBBIE: Refractive index of air at 0.337 mm wave length. Nature, vol.206, no. 4987, pp. 886–887, 1965.

    Article  Google Scholar 

  • B.K. CHING and Y.T. CHIU. A phenomenological model of global ionospheric electron density in the E, F1, and F2 regions. J. atmos. terr. Phys.35, 1615, 1973.

    Article  Google Scholar 

  • Y.T. CHIU: An improved phenomenological model of ionospheric density. J. atmos. terr. Phys.37, 341, 1975.

    Article  Google Scholar 

  • K. DAVIES: Ionospheric Radio Propagation: Washington, D.C., Supt. of Documents, U.S. Government Printing Office, 1965.

    Google Scholar 

  • K. DAVIES: Recent progress in satellite ratio beacon studies with particular emphasis on the ATS-6 radio beacon experiment. Space Science Reviews 25, pp. 357–430, 1980.

    Article  Google Scholar 

  • P. DEBYE: Handbuch der Radiologie, Leipzig, 1925.

  • D.E. DONATELLI, R.S. ALLEN: Temporal variability of ionospheric refraction correction. In: Proceedings of the Symposium on the Effect of the lonosphere on Space and Terrestrial Systems, edited by J.M. Goodman, pp. 490–496, U.S. Government Printing Office, Washington, D.C., 1978.

    Google Scholar 

  • D.E. DONATELLI, R.S. ALLEN: Ionospheric refractive corrections using an adaptive procedure. In: Solar-Terrestrial Predictions Proceedings, IV, SD 003-017-00479-1, pp. D1-65–D1-80. U.S. Government Printing Office, Washington, D.C., 1979.

    Google Scholar 

  • D.E. DONATELLI, R.S. ALLEN: Time cells for adaptive prediction of total electron content. Radio Science, vol. 16, no. 2, pp. 261–269, 1981.

    Article  Google Scholar 

  • L. ESSEN, K.D. FROOME: The refractive index and dielectric constants of air and its principal constituents at 24.000 Mc/s. Proc. Phys. Soc. B 64, 862, 1951.

    Article  Google Scholar 

  • K.D. FROOME: The refractive indices of water, air oxygen, nitrogen argon at 72 KMc/s. Proc. Phys. Soc. London, 833, November 1955

  • R.N. GRUBB: Radio Beacon Modulation Schemes for Differential Group Detay Measurements. In: Proceedings of the Symposium of the COSPAR Satellite Beacon Group “Beacon Satellite Measurements of Plasmaspheric and lonospheric Properties”, 22–25 May 1978, Firenze Italy, (1), pp. 51-1–51-6, 1978.

  • Handbook of Chemistry and Physics, ed. by R.C. Weast, p. E-233, 50th ed. 1969-1970, The Chemical Rubber Co., Cleland, Ohio, 44128, USA.

    Google Scholar 

  • G.K. HARTMANN: HF and UHF propagation studies of the mid-latitude ionosphere. (Review). Ann. Geophys., vol. 31, no. 1, pp. 39–52, 1975.

    Google Scholar 

  • G.K. HARTMANN: The Zeeman-effect of O2 and its application to the investigation of the Earth's atmosphere. MPAE-W-66-81-22. Max-Planck-Institut für Aeronomie. P.O. Box 20, 3411 Katlenburg-Lindau, Germany, 1981.

    Google Scholar 

  • P.A. HICKS: Measurements of Total Electron Content Using NAVSTAR GPS-Signal. In: Proceedings of the Symposium of the COSPAR Satellite Beacon Group “Beacon Satellite Measurements of Plasmaspheric and ion ospheric Properties”, 22–25 May 1978, Firenze, Italy, (1), pp. 52-1–52-8, 1978.

  • H.S. HOPFIELD: The Effect of Tropospheric Refraction on the Doppler Shift of a Satellite Signal. J. Geophys. Res., vol. 68, no. 18, pp. 5157–5168, 1963.

    Google Scholar 

  • H.S. HOPFIELD: Two-Quartic Tropospheric Refractivity Profile for Correcting Satellite Data. J. Geophys. Res., vol. 74, no 18, pp. 4487–4499, 1969.

    Article  Google Scholar 

  • H.S. HOPFIELD: Tropospheric effect on electromagnetically measured range: prediction from surface weather data. Radio Science, vol.6, pp. 357–367, 1971.

    Article  Google Scholar 

  • Institute of Navigation: 1980 Global Positioning System, The Institute of Navigation, 815 Fifteenth Str., Washington, D.C. 20005, USA. ISBN 0-936406-00-3.

    Google Scholar 

  • W. KÖHNLEIN: Electron density models of the ionosphere. Rev. Geophys. Space Phys., vol.16, 341, 1978.

    Article  Google Scholar 

  • J. A. KLOBUCHAR: Present state of ionospheric time delay prediction. In: Scientific and Engineering Uses of Satellite Radio Beacons. Proceedings of the COSPAR/URSI Symposium Warszawa, Poland May 19–23, 1980. Polish Scientific Publishers, Warszawa-Lodz, 1981, (ed.: A.W. Wernik), pp. 357–377.

    Google Scholar 

  • I.G. KOLCHINSKII: Some problems in the investigation of Light refraction in the Earth's Atmosphere. In: Atmospheric Optics, vol. 2, edited by Nikolai B. Divari, translated into English by F.L. Sinclair, pp. 56–61, Consultants Bureau, New York, London, 1972.

    Google Scholar 

  • G. KRUSPE: Der atmosphärische Brechungsindex und seine Messung mit Mikrowellen-Refraktometern. Technische Mitteilung Nr. 1, Inst. für Radiometerologie und Maritime Meteorologie der Universität Hamburg, 1965.

  • LANDOLT-BÖRNSTEIN: Zahlenwerte und Funktionen aus vol. II, part 6, pp. 874–908, Springer-Verlag, Berlin, Göttingen, Heidelberg, 1959.

    Google Scholar 

  • LANDOLT-BÖRNSTEIN, ed. by. K.H Hellwege and H.H. Voigt, vol. 1, Astronomy and Astrophysics, “Influence of the Earth's atmosphere”, pp. 48–61, Springer Verlag, Berlin, Heidelberg, New York, 1965.

    Google Scholar 

  • LANDOLT-BÖRNSTEIN, ed. by K.H. hellwege and A.M. hellwege, Part 8, Optical Constants, pp. 871–901 (878), Springer Verlag, Berlin, Göttingen, Heidelberg, 1962.

    Google Scholar 

  • R. LEITINGER: Der Einfluss ionosphärischer Ausbreitungsfehler bei der geodätischen Anwendung von Navigationssatelliten. Kleinheubacher Berichte. Bd. Nr. 17, pp. 321–332, 1974.

    Google Scholar 

  • R. LEITINGER, G.K. HARTMANN: Zeit- und Breitenabhängigkeit von transionosphärischen Ausbreitungsfehlern. Kleinheubacher Berichte. Bd. Nr. 20, 267–276, 1977.

    Google Scholar 

  • R. LEITINGER, R.S. ALLEN, D.E. DONATELLI, G.K. HARTMANN: Adaptive mapping of ionospheric features. In: Proceedings of the Symposium on the Effect of the Ionosphere on Space and Terrestrial Systems, edited by J.M. Goodman, pp. 530–537, U.S. Government Printing Office, Washington, D.C., 1978.

    Google Scholar 

  • H.J. LIEBE, G.G. GIMMESTAD, J.D. HOPPONEN: Atmospheric Oxygen Microwave Spectrum Experiment versus Theory. IEEE Ant. and Prob., vol. Ap-25, no. 3, pp. 327–335, 1977.

    Article  Google Scholar 

  • H.J. LIEBE, G.G. GIMMESTAD: Calculation of clear air EHF refractivity. Radio Science, vol. 13, no. 2, pp. 245–251, 1978b.

    Article  Google Scholar 

  • H.J. LIEBE, J.D. HOPPONEN: Atmospheric Medium Characterizations and Modelling of EHF propagation in air. In: operational Modelling of the Aerospace propagation environment, pp. 45-1–45-18, 1978 a.

  • H.J. LIEBE: Modelling attenuation and phase of radio waves in air at frequencies below 1000 GHz. Radio Science, vol. 10, no. 6, pp. 1183–1199, 1981.

    Article  Google Scholar 

  • Linke's meteorologisches Taschenbuch, Vol. II (Ed.: F. Baur), Akademische Verlagsges, Geest & Portig, Leipzig, 1953.

    Google Scholar 

  • S.K. LLWELLYN, R.B. BENT: Documentation and Description of the Bent ionospheric, Model. AFCRL-TR-73-0657, 1973.

  • J.M. MORAN, B.R. ROSEN: Estimation of the propagation delay through the troposphere from microwave radiometer data. Radio Science, vol. 16, no. 2, pp. 235–244, 1981.

    Article  Google Scholar 

  • J.A. RATCLIFFE: The Magneto-Ionic Theory and its Application to the Ionosphere. Cambridge at the University Press, 1959.

  • K. RAWER, K. SUCHY: Radio observations of the ionosphere. In: Encyclopedia of Physics, ed. by S. Flügge, vol. XLIX/2—geophysics 11/2—pp. 1–537, Springer-Verlag, Berlin, Hwidelberg, New York, 1967.

    Google Scholar 

  • K. RAWER: In: International Reference Ionosphere—IRI 79 Editors: J. V. Lincoln, R.O. Conkright, World Data Center A for STP, NOAA, Boulder, CO, 1981.

    Google Scholar 

  • C.L. RINO, R.C. LIVINGSTONE, M.D. COUSINS, B.C. FAIR: Wideband Satellite Phase Coherent Beacon Observations at Auroral and Equatorial Latitudes A Review. In: Proceedings of the Symposium of the COSPAR Satellite Beacon Group “Beacon Satellite Measurements of Plasmaspheric and Ionospheric Properties”, 22–25 May 1978, Firenze, Italy, (1), pp. 37-1–37-8, 1978.

  • P.W. ROSENKRANZ, M.J.KOMICHAK, D.H. STAELIN: A Method for Estimation of Atmospheric Water Vapour Profiles by Microwave Radiometry. To be published in Journal of Applied Meteorology, 1981.

  • SIEN-CHONG WU: Optimum frequencies of a passive microwave radiometer for tropospheric path length correction.. IEEE Transactions on Antennas and Propagation,AP27, pp. 233–239, 1979.

    Article  Google Scholar 

  • E.K. SMITH, S. WEINTRAUB: The constants in the equation, for atmospheric refractive index at radio frequencies. J. Res. NBS, vol. 50, RP 2385, 39 1953.

    Google Scholar 

  • A. SOMMERFELD: Optik, 2. Aufl. Akademische Verlagsgesellschaft, Geest & Portig KG, Leipzig, 1959.

    Google Scholar 

  • D.H. STAELIN: Passive Microwave Techniques for Geophysical Sensing of the Earth from Satellites. IEEE Transactions on Antennas and Propagation, von. AP-29, no. 4, pp. 683–687, 1981.

    Article  Google Scholar 

  • V.E. TATARSKI: The Effects of the Turbulent Atmosphere on Wave propagation. (translated from Russian) Springfield, V.A., National Technical Information Service, U.S. Dept. of Commerce, 1971.

    Google Scholar 

  • B.E. TATARSKI: Wave Propagation in a Turbulent Medium, New York, Mc Graw-Hill, 1961.

    Google Scholar 

  • S. WEISBROD, L.J. ANDERSON: Simple methods for computing tropospheric and ionospheric refractive effects on radio waves. Proc. IRE, vol. 47, pp. 1770–1777, 1959.

    Article  Google Scholar 

  • Ed. R. WESTWATER: The accuracy of water vapour and cloud liquid determination by dual frequency ground-based microwave radiometry. Radio Science, vol. 13, no. 4, pp. 677–685, 1978.

    Article  Google Scholar 

  • E.R. WESTWATER, N.C. GRODY: Combined Surface and Satellite Temperature Profile Retrieval. Journal of Applied Meteorology, vol. 19, no. 12, pp. 1438–1444, 1980.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Aeronomie, 3411, Katlenburg-Lindau, Germany

    G. K. Hartmann

  2. Institut für Meterologie und Geophysik, Universität Graz, Halbärthgasse 1, 8010, Graz, Austria

    R. Leitinger

Authors
  1. G. K. Hartmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Leitinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hartmann, G.K., Leitinger, R. Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz. Bull. Geodesique 58, 109–136 (1984). https://doi.org/10.1007/BF02520897

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02520897

Keywords

Search

Navigation