Abstract

With measurements of the atmospheric microthermal field obtained from 67 independent radiosondes (balloon) scans up to 20–25 km above sea level, from three European sites, we have calculated an average vertical profile of the atmospheric refractive index structure coefficient CN2.

© 1976 Optical Society of America

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References

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  1. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  2. E. Moroder and A. Righini, Astron. Astrophys. 23, 307 (1973).
  3. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),
  4. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).
  5. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
    [CrossRef]
  6. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).
  7. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).
  8. R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).
  9. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).
  10. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
    [CrossRef]
  11. D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  12. D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).
    [CrossRef]
  13. R. E. Hufnagel, “Restoration of Atmospherically Degraded Images” (National Academy of Sciences-National Research Council, Washington, D. C.), 2, App. 3, (1966).
  14. R. E. Hufnagel, “Variations of Atmospheric Turbulence,” paper presented at “Topical Meeting on Optical Propagation through Turbulence” Wal-1, July 9–11, 1974, University of Colorado, Boulder, Colorado.
  15. J. Bufton, J. Atmos. Sci. 30, 83 (1973).
    [CrossRef]
  16. J. Bufton, Appl. Opt. 12, 1785 (1973).
    [CrossRef] [PubMed]
  17. J. Bufton, P. Minott, M. Fitzmaurice, and P. Titterton, J. Opt. Soc. Am. 62, 1068 (1972).
    [CrossRef]
  18. C. E. Coulman, Sol. Phys. 17, 122 (1969).
    [CrossRef]
  19. C. E. Coulman, Boundary Layer Meteorology 4, 169 (1973).
    [CrossRef]
  20. R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).
  21. R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
    [CrossRef]
  22. K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 15 (1972).
  23. K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 17 (1973).
  24. K. O. Kiepenheuer, JOSO Annual Report 1973, 4 (1974).
  25. J. Barat, “Transport Vertical associé a la Turbulence Stratosphérique,” paper presented at IUGG (1974), Grenoble.
  26. J. Vernin and F. Roddier, J. Opt. Soc. Am. 63, 270 (1973).
    [CrossRef]
  27. A. Rocca, F. Roddier, and J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
    [CrossRef]

1974 (5)

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
[CrossRef]

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
[CrossRef]

1973 (6)

C. E. Coulman, Boundary Layer Meteorology 4, 169 (1973).
[CrossRef]

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 17 (1973).

J. Vernin and F. Roddier, J. Opt. Soc. Am. 63, 270 (1973).
[CrossRef]

J. Bufton, J. Atmos. Sci. 30, 83 (1973).
[CrossRef]

J. Bufton, Appl. Opt. 12, 1785 (1973).
[CrossRef] [PubMed]

E. Moroder and A. Righini, Astron. Astrophys. 23, 307 (1973).

1972 (2)

1969 (1)

C. E. Coulman, Sol. Phys. 17, 122 (1969).
[CrossRef]

1966 (2)

1965 (1)

1964 (1)

Barat, J.

J. Barat, “Transport Vertical associé a la Turbulence Stratosphérique,” paper presented at IUGG (1974), Grenoble.

Barletti, R.

R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

Bufton, J.

Ceppatelli, G.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

Coulman, C. E.

C. E. Coulman, Boundary Layer Meteorology 4, 169 (1973).
[CrossRef]

C. E. Coulman, Sol. Phys. 17, 122 (1969).
[CrossRef]

Fitzmaurice, M.

Fried, D. L.

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
[CrossRef]

R. E. Hufnagel, “Restoration of Atmospherically Degraded Images” (National Academy of Sciences-National Research Council, Washington, D. C.), 2, App. 3, (1966).

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” paper presented at “Topical Meeting on Optical Propagation through Turbulence” Wal-1, July 9–11, 1974, University of Colorado, Boulder, Colorado.

Kiepenheuer, K. O.

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 17 (1973).

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 15 (1972).

K. O. Kiepenheuer, JOSO Annual Report 1973, 4 (1974).

Lemmetti, P.

R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
[CrossRef]

Minott, P.

Moroder, E.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

E. Moroder and A. Righini, Astron. Astrophys. 23, 307 (1973).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

Paternò, L.

R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

Righini, A.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

E. Moroder and A. Righini, Astron. Astrophys. 23, 307 (1973).

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

Rocca, A.

Roddier, F.

Schellenberger, W.

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 17 (1973).

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 15 (1972).

Speroni, N.

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

Stanley, N. R.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

Titterton, P.

Vernin, J.

Appl. Opt. (1)

Astron. Astrophys. (1)

E. Moroder and A. Righini, Astron. Astrophys. 23, 307 (1973).

Boundary Layer Meteorology (1)

C. E. Coulman, Boundary Layer Meteorology 4, 169 (1973).
[CrossRef]

J. Atmos. Sci. (1)

J. Bufton, J. Atmos. Sci. 30, 83 (1973).
[CrossRef]

J. Geophys. Res. (1)

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, J. Geophys. Res. 79, 4545 (1974).
[CrossRef]

J. Opt. Soc. Am. (7)

JOSO Sit 15 (1)

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 15 (1972).

JOSO Sit 17 (1)

K. O. Kiepenheuer and W. Schellenberger, JOSO Sit 17 (1973).

Rev. Sci. Instrum. (1)

R. Barletti, P. Lemmetti, and L. Paternò, Rev. Sci. Instrum. 45, 1563 (1974).
[CrossRef]

Riv. Ital. Geofisica (2)

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 207 (1974).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, Riv. Ital. Geofisica 23, 264 (1974).

Sol. Phys. (1)

C. E. Coulman, Sol. Phys. 17, 122 (1969).
[CrossRef]

Other (9)

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1972, 6 (1973).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Sit 21, Firenze (1974),

R. Barletti, G. Ceppatelli, E. Moroder, L. Paternò, and A. Righini, JOSO Annual Report 1973, 74 (1974).

R. Barletti, G. Ceppatelli, L. Paternò, A. Righini, and N. Speroni, JOSO Sit 27, Firenze (1975).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

R. E. Hufnagel, “Restoration of Atmospherically Degraded Images” (National Academy of Sciences-National Research Council, Washington, D. C.), 2, App. 3, (1966).

R. E. Hufnagel, “Variations of Atmospheric Turbulence,” paper presented at “Topical Meeting on Optical Propagation through Turbulence” Wal-1, July 9–11, 1974, University of Colorado, Boulder, Colorado.

K. O. Kiepenheuer, JOSO Annual Report 1973, 4 (1974).

J. Barat, “Transport Vertical associé a la Turbulence Stratosphérique,” paper presented at IUGG (1974), Grenoble.

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Figures (4)

FIG. 1
FIG. 1

C N 2 ( m - 2 / 3 ) vs height (km). Triangles refer to the data obtained in France, dots to Portugal, and squares to Tenerife. Standard deviations are indicated by vertical bars. Note that for Tenerife and France we report only data above 4000 m, since in these sites the atmospheric turbulence below 4000 m is affected by local disturbances. We report also the C N 2 profiles deduced by Hufnagel (curve 1 and curve 2) and Fried (curve 3). The dashed line represents the “lucky observer atmosphere” discussed in the text.

FIG. 2
FIG. 2

C N 2 ( m - 2 / 3 ) vs height (km) as measured in Portugal, August 17, 1974. Curve 1 represents Hufnagel’s model of 1966, and curve 2 Hufnagel’s model of 1974. In the tropopause a strong enhancement of turbulence can be observed in the experimental profile.

FIG. 3
FIG. 3

C N 2 ( m - 2 / 3 ) vs height (km) as measured in Tenerife, September 6, 1974. Curve 1 represents Hufnagel’s model of 1966, and curve 2 Hufnagel’s model of 1974. Highly stratified turbulence between 15 000 and 20 000 m can be observed in the experimental profile.

FIG. 4
FIG. 4

C N 2 ( m - 2 / 3 ) vs height (km) as measured in Tenerife, June 29, 1973. The dashed line represents the “lucky observer” model which can be compared with the dotted-dashed line, obtained by averaging the experimental profiles on the layers given in Table I. Below 4000 m the “lucky observer” model should be shifted to right since the launching site is 2400 m above sea level.

Tables (1)

Tables Icon

TABLE I Summary of results.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

r 0 = [ 0.06 λ 2 / I ( h ) ] 3 / 5 ,
I = 0 C N 2 ( h ) d h .
D T ( r ) = C T 2 ( h ) r 2 / 3 ,
C N 2 ( h ) = { 79.9 [ P ( h ) / T 2 ( h ) ] 10 - 6 } 2 C T 2 ( h ) ,
C ¯ N 2 = 1 h 2 - h 1 h 1 h 2 C N 2 ( h ) d h ,