Abstract

We analyzed the observations of scintillations in a laser beam (532 nm, 200mW power) traveling along a 144 km path at an altitude of 2.2–2.4 km above sea level, just above the atmospheric boundary layer, between the islands of La Palma and Tenerife. The observations were performed during nighttime on 18 July 2011, by means of a telescope with an aperture diameter of 1 m. Strong scintillations were observed. The estimates of spatial spectra and correlation functions indicated that the observed intensity fields possess, statistically, a locally isotropic structure, which agrees with the idea of a locally isotropic turbulence. The estimates of spatial autospectra and autocorrelation functions of the intensity field indicated that the characteristic scale of the internal structure of the observed clusters is 6.5–8 mm, while the characteristic size of the clusters is 4–5 cm. The major contribution to the observed scintillations comes from the inhomogeneities of the intensity field with scales from 1–2 cm up to 10–12 cm. The analysis of the cross-spectra indicated that the hypothesis of frozen turbulence introduced by Taylor can be used for the description of spatiotemporal structure of intensity fluctuations of laser beams traveling through long paths in the atmosphere.

© 2012 Optical Society of America

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  2. S. Corrsin, “On the spectrum of isotropic temperature fluctuations in an isotropic turbulence,” J. Appl. Phys. 22, 469–473 (1951).
    [CrossRef]
  3. G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).
  4. L. R. Tsvang, “Some characteristics of the spectra of temperature pulsations in the boundary layer of the atmosphere,” Izv. Akad. Nauk. SSSR Ser. Geophys. 10, 1594–1600(1963).
  5. A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Atmos. Ocean. Phys. 16, 231–237 (1980).
  6. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, 1971).
  7. M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.
  8. A. S. Gurvich and V. Kan, “Structure of air density irregularities in the stratosphere from spacecraft observations of stellar scintillation: 1. Three-dimensional spectrum model and recovery of its parameters,” Izv. Atmos. Ocean. Phys. 39, 300–310 (2003).
  9. V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
    [CrossRef]
  10. V. I. Tatarskii, “Shortwave propagation in a medium with random heterogeneities in approximate Markovian random process,” Sov. Phys. JETP 29, 1133–1138 (1969).
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  12. J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).
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    [CrossRef]
  14. N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
    [CrossRef]
  15. A. Ishimaru, “The beam wave case and remote sensing,” in Topics in Applied PhysicsJ. W. Strohbehn, ed. (Springer-Verlag, 1978), pp. 129–170.
  16. M. E. Gracheva and A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the Earth,” Radiophys. Quantum Electron. 8, 511–515 (1965).
  17. G. R. Ochs and R. S. Lawrence, “Saturation of laser-beam scintillation under conditions of strong atmospheric turbulence,” J. Opt. Soc. Am. 59, 226–227 (1969).
    [CrossRef]
  18. G. R. Ochs, R. R. Bergmtan, and J. R. Snyder, “Laser-beam scintillation over horizontal paths from 5.5 to 145 kilometers,” J. Opt. Soc. Am. 59, 231–234 (1969).
    [CrossRef]
  19. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions (Springer-Verlag, 1987), Vols. 1 and 2.
  20. A. S. Gurvich, V. V. Pakhomov, and A. M. Cheremukhin, “The isotropy of refractive-index fluctuations of small-scale turbulence in the atmospheric surface layer,” Izv. Atmos. Ocean. Phys. 7, 49–52 (1971).

2011

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701(2011).
[CrossRef]

2007

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
[CrossRef]

2006

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

2003

A. S. Gurvich and V. Kan, “Structure of air density irregularities in the stratosphere from spacecraft observations of stellar scintillation: 1. Three-dimensional spectrum model and recovery of its parameters,” Izv. Atmos. Ocean. Phys. 39, 300–310 (2003).

1980

A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Atmos. Ocean. Phys. 16, 231–237 (1980).

1971

A. S. Gurvich, V. V. Pakhomov, and A. M. Cheremukhin, “The isotropy of refractive-index fluctuations of small-scale turbulence in the atmospheric surface layer,” Izv. Atmos. Ocean. Phys. 7, 49–52 (1971).

1969

1965

M. E. Gracheva and A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the Earth,” Radiophys. Quantum Electron. 8, 511–515 (1965).

1963

L. R. Tsvang, “Some characteristics of the spectra of temperature pulsations in the boundary layer of the atmosphere,” Izv. Akad. Nauk. SSSR Ser. Geophys. 10, 1594–1600(1963).

1951

S. Corrsin, “On the spectrum of isotropic temperature fluctuations in an isotropic turbulence,” J. Appl. Phys. 22, 469–473 (1951).
[CrossRef]

1949

A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk. SSSR Ser. Geogr. Geophys. 13, 58–69 (1949).

1938

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).

Beale, C. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Beresnev, L. A.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Bergmtan, R. R.

Bernath, P. F.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Brooke, J. S. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Carhart, G. W.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Cheremukhin, A. M.

A. S. Gurvich, V. V. Pakhomov, and A. M. Cheremukhin, “The isotropy of refractive-index fluctuations of small-scale turbulence in the atmospheric surface layer,” Izv. Atmos. Ocean. Phys. 7, 49–52 (1971).

Corrsin, S.

S. Corrsin, “On the spectrum of isotropic temperature fluctuations in an isotropic turbulence,” J. Appl. Phys. 22, 469–473 (1951).
[CrossRef]

Dalaudier, F.

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
[CrossRef]

Gerbig, C.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Giggenbach, D.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

González Abad, G.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Gracheva, M. E.

M. E. Gracheva and A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the Earth,” Radiophys. Quantum Electron. 8, 511–515 (1965).

Gurvich, A. S.

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
[CrossRef]

A. S. Gurvich and V. Kan, “Structure of air density irregularities in the stratosphere from spacecraft observations of stellar scintillation: 1. Three-dimensional spectrum model and recovery of its parameters,” Izv. Atmos. Ocean. Phys. 39, 300–310 (2003).

A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Atmos. Ocean. Phys. 16, 231–237 (1980).

A. S. Gurvich, V. V. Pakhomov, and A. M. Cheremukhin, “The isotropy of refractive-index fluctuations of small-scale turbulence in the atmospheric surface layer,” Izv. Atmos. Ocean. Phys. 7, 49–52 (1971).

M. E. Gracheva and A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the Earth,” Radiophys. Quantum Electron. 8, 511–515 (1965).

Hargreaves, R. J.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Harrison, J. J.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Henniger, H.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Horwath, J.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Ishimaru, A.

A. Ishimaru, “The beam wave case and remote sensing,” in Topics in Applied PhysicsJ. W. Strohbehn, ed. (Springer-Verlag, 1978), pp. 129–170.

Kan, V.

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
[CrossRef]

A. S. Gurvich and V. Kan, “Structure of air density irregularities in the stratosphere from spacecraft observations of stellar scintillation: 1. Three-dimensional spectrum model and recovery of its parameters,” Izv. Atmos. Ocean. Phys. 39, 300–310 (2003).

Kasyutich, V. L.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Kirchengast, G.

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701(2011).
[CrossRef]

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Knapek, M.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Kolle, O.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, 1987).

Lachinova, S. L.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Lawrence, R. S.

Liu, J.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Loescher, A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Martin, P. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Obukhov, A. M.

A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk. SSSR Ser. Geogr. Geophys. 13, 58–69 (1949).

Ochs, G. R.

Pakhomov, V. V.

A. S. Gurvich, V. V. Pakhomov, and A. M. Cheremukhin, “The isotropy of refractive-index fluctuations of small-scale turbulence in the atmospheric surface layer,” Izv. Atmos. Ocean. Phys. 7, 49–52 (1971).

Perlot, N.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142 km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Proschek, V.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Rao Gudimetla, V. S.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Rehder, K.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Riker, J. F.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, 1987).

Schweitzer, S.

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701(2011).
[CrossRef]

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Snyder, J. R.

Sofieva, V. F.

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, and V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).
[CrossRef]

Stevenson, E.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Tatarskii, V. I.

V. I. Tatarskii, “Shortwave propagation in a medium with random heterogeneities in approximate Markovian random process,” Sov. Phys. JETP 29, 1133–1138 (1969).

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Vol. 3: Elements of Random Fields (Springer-Verlag, 1987).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, 1971).

Taylor, G. I.

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).

Tereszchuk, K. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Thomas, C. B.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Tsvang, L. R.

L. R. Tsvang, “Some characteristics of the spectra of temperature pulsations in the boundary layer of the atmosphere,” Izv. Akad. Nauk. SSSR Ser. Geophys. 10, 1594–1600(1963).

Vorontsov, M. A.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Wang, J.-G.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144 km open path in the Canary Islands,” Atmos. Meas. Tech.5 (in press).

Weyrauch, T.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149 km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Yaglom, A. M.

A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions (Springer-Verlag, 1987), Vols. 1 and 2.

Zettl, K.

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Figures (12)

Fig. 1.
Fig. 1.

Consecutive distributions of intensity I(ρ;t), every about 5 ms, seen through the aperture of the OGS telescope. The distributions were observed on 18 July 2011 at 00:05:45 UTC+1h.

Fig. 2.
Fig. 2.

Fragment of the record of light flux J(t). The light-shaded area near 58.2 s indicates a 30 ms long interval corresponding to the six distributions I(ρ,t), shown in Fig. 1.

Fig. 3.
Fig. 3.

Left: intensity distributions (dimensionless) in the aperture, averaged over the study time interval of 120 s. Right: distribution of the ratio of the rms and mean values.

Fig. 4.
Fig. 4.

Estimates of PSD [mm4/rad2] normalized for the dispersion of scintillations, observed during the study time interval. Light-gray isolines correspond to rectangle 1, gray ones to rectangle 2, black ones to rectangle 3. The radius of the circle shown by a bold black dash-dotted line equals 0.8rad/mm. Isoline marks correspond to the level numbers in the legend.

Fig. 5.
Fig. 5.

Estimate of the normalized correlation function B(I)(δρ)/B(I)(0) for rectangle 1 during the study time interval. Isoline marks correspond to the level numbers in the legend.

Fig. 6.
Fig. 6.

Contribution of spectral components in the dispersion of scintillations as a scaled function of Λ=2π/κ. The correspondence between shades of gray and rectangles is the same as in Fig. 4.

Fig. 7.
Fig. 7.

Estimates of the correlation coefficient, b(δρ), of intensity fluctuations in the telescope aperture plane. The correspondence between shades of gray and rectangles is the same as in Fig. 4.

Fig. 8.
Fig. 8.

Estimates of 2D coherence spectra Coh(κ;δt) defined by Eq. (8). Left panel: δt=5ms (μ=1); right panel: δt=10ms (μ=2). The correspondence between shades of gray and rectangles is the same as in Fig. 4.

Fig. 9.
Fig. 9.

Estimates of 2D phase spectra φ(κ;δt). Left panel: δt=5ms (μ=1); right panel: δt=10ms (μ=2). The correspondence between shades of gray and rectangles is the same as in Fig. 4. Straight lines at κx=±0.3 in the left panel and at κx=±0.15 in the right-hand panel correspond to phase jumps of 2π.

Fig. 10.
Fig. 10.

Estimates of 1D phase spectra for δt=5ms evaluated for the three rectangles. The correspondence between shades of gray and rectangles is the same as in Fig. 4. The black dash-dotted line corresponds to φ¯(κx,δt)=u0κxδt, where u0 is the average drift velocity of the intensity clusters in the telescope aperture. The arrows mark the values of wave number κx=±0.3rad/mm, where the estimate of φ¯ has a jump of 2π.

Fig. 11.
Fig. 11.

Estimated wind speeds as a function of distance from the transmitter based on ECMWF analysis fields adjacent to the study time interval (18 July 2011, 00 UTC and 06 UTC analyses, linearly interpolated to the study time). Dashed line: along-beam component; solid line: transverse component.

Fig. 12.
Fig. 12.

2D PSD F(0)(κ;0) obtained from the observations during the study time interval. The correspondance between shades of gray and rectanges is the same as in Fig. 4. The radii of the circles shown by the black dash-dotted lines equal 0.8radmm1 and 0.1radmm1. Isoline marks correspond to the level numbers in the legend.

Equations (13)

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I(ρ,t)=12τtτt+τI(0)(ρ,t)dt,
I(0)(ρ,t)=f(0)(κ,t)exp(iκρ)d2κ,
I(ρ,t)=f(0)(κ,t)sinc(κuτ)exp(i(κρ))d2κ,sinc(x)sin(x)x,
F(I)(κ,0)=(sinc(κuτ))2F(0)(κ,0).
F(I)(κ,0)=1Gg|f(I)(κ,tg)|2,
B(I)(δρ)=F(I)(κ,0)exp(iκδρ)d2κ.
F(I)(κ,δt)=1Ggf(I)(κ,tg)f¯(I)(κ,tg+δt).
Coh(κ,δt)=|F(I)(κ,δt)|F(I)(κ,0),0Coh1.
F(I)(κ,δt)=F(I)(κ,0)exp(iφ(I)(κ,δt)).
(I(ρ,t)I(ρ,t))2d2ρ=14π2(F(I)(κ,0))2d2κ.
σI2=F(I)(κ,0)d2κ=2πV(I)(κ)κ2dlnκ,
V(I)(κ)=12π02πF(I)(κcosφ,κsinφ;0)dφ.
F(0)(κ;0)=F(I)(κ;0)/(sinc(κuτ))2,

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