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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 71, Iss. 4 — Apr. 1, 1981
  • pp: 397–405

Atmospheric modulation transfer function for desert and mountain locations: the atmospheric effects on r0

D. L. Walters and K. E. Kunkel  »View Author Affiliations

JOSA, Vol. 71, Issue 4, pp. 397-405 (1981)

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In conjunction with recent atmospheric modulation transfer function (MTF) measurements for desert and mountain locations, the distribution of optical turbulence within the planetary boundary layer was measured by using tower, aircraft, and acoustic sounder techniques. Diurnal variations in the atmospheric turbulence within 1–3 km above the surface dominate the MTF observations. During convective, daylight hours, desert and mountain boundary layers are found to be similar. The magnitudes of optical turbulence (CMn 2) are comparable, and similar thermal plume structures are observed. In addition, optical turbulence is found to have a simple (Δθ)4/3 dependence on the air-surface temperature difference. At night, the cool ground surface produces turbulent, stratified layers above a desert that are not observed for a mountain. The effects of tower height above the ground are investigated theoretically and experimentally. MTF measurements made 2 and 8 m above the desert during the day are in good agreement with theoretical models. We observe interrelationships between the turbulent boundary layer and the atmospheric MTF that can be applied to the selection of both astronomical and solar telescope site locations.

D. L. Walters and K. E. Kunkel, "Atmospheric modulation transfer function for desert and mountain locations: the atmospheric effects on r0," J. Opt. Soc. Am. 71, 397-405 (1981)

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  1. D. L. Walters, "Atmospheric modulation transfer function for desert and mountain locations—r0 measurements," J. Opt. Soc. Am. 71, 406–409 (1981).
  2. D. L. Fried, "Optical resolution looking down through a randomly homogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372–1379 (1966).
  3. R. F. Lutamirski and H. T. Yura, "Wave structure function and mutual coherence function of an optical wave in a turbulent atmosphere," J. Opt. Soc. Am. 61, 482–487 (1971).
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), pp. 40–58.
  5. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, Washington, D.C., 1971; available from National Technical Information Service, Springfield, Va. 22161), pp. 46–102.
  6. R. E. Hufnagel, "Propagation through atmospheric turbulence," in The Infrared Handbook (U.S. Government Printing Office, Washington, D.C., 1978), Chap. 6, pp. 6-1–6-56.
  7. S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Topics in Applied Physics—Laser Beam Propagation in the Atmosphere (Springer-Verlag, New York, 1978), Vol. 25, Chap. 2, pp. 9–43.
  8. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, "Measurements of atmospheric turbulence relevant to optical propagation," J. Opt. Soc. Am. 60, 826–830 (1970).
  9. C. A. Friehe et al., "Effects of temperature and humidity fluctuations on the optical refraction index in the marine boundary layer," J. Opt. Soc. Am. 65, 1502–1511 (1975).
  10. T. E. VanZandt et al., "Vertical profiles of refraction turbulence structure constant: comparison of observations by the sunset radar with a new theoretical model," Radio Sci. 13, 819–829 (1978).
  11. J. C. Kaimal et al., "Turbulent structure in the convective boundary layer," J. Atmos. Sci. 33, 2152–2169 (1976).
  12. L. F. Richardson, "The supply of energy from and to atmospheric eddies," Proc. Roy. Soc. London 97, 356–373 (1920).
  13. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972) pp. 98–99.
  14. J. D. Woods, "On Richardson's number as a criterion for laminar-turbulent-laminar transition in the ocean and atmosphere," Radio Sci. 4, 1289–1298 (1969).
  15. L. R. Tsuang, "Microstructure of temperature fields in the free atmosphere," Radio Sci. 4, 1175–1177 (1969).
  16. J. C. Wyngaard, Y. Izumi, and S. A. Collins, "Behavior of the refractive- index-structure parameter near the ground," J. Opt. Soc. Am. 61, 1646–1650 (1971).
  17. J. C. Wyngaard, "On surface-layer turbulence," in Workshop on Micrometeorology (American Meteorological Society, Boston, Mass., 1972), Chap. 3, pp. 101–149.
  18. The data in Figs. 1–4 are based on a log-normal average of 50-m spatial segments. An optical device performs a longer linear spatial average that has a different mean. This linear mean x¯ is obtained from the log-normal mean and standard deviation y¯, σy by x¯ = exp(y¯ + σy/2). For the standard deviations of Figs. 1–4, this corresponds to a multiplicative factor of about about 1.8 increase in the mean. See, for example, J. Aitchison and J. Brown, The Log Normal Distribution (Cambridge U. Press, New York, 1957), Chap. 2, pp. 7–9.
  19. Figure 1 shows a z-1.16 dependence for Cn 2, whereas most theories, such as Eq. (8), have a z-4/3 dependence for the unstable, midday convective period. The z-1.16 form we observe appears to be the result of the climatological averaging process, where Cn 2 data for several days are combined. Two effects occur that reduce the exponential coefficient. First, the inversion height has been neglected in compiling Fig. 1, and, from Fig. 15, Cn 2 increases as the inversion is approached. Second, the strength of the wind speed influences the thickness of the surface layer, which is of the order of a few meters to tens of meters. The high wind shear within the surface boundary layer forces Cn 2 toward a z-2/3 dependence (see Refs. 16 and 17). Depending on the wind speed, we have observed both the z-2/3 and z-4/3 forms. Thus, above the surface boundary layer, the z-4/3 dependence is the most representative form for the change in Cn 2 with altitude during the day up to about one half of the inversion height.
  20. A known wind-speed dependence discussed in Refs. 16 and 17 is ignored in Fig. 10. The significance of the wind-speed term is evident, in part, in the standard deviation of Fig. 10.
  21. L. G. McAllister et al., "Acoustic sounding—a new approach to the study of atmospheric structure," Proc. IEEE 57, 579–587 (1969).
  22. F. F. Hall, Jr., J. C. Edinger, and W. D. Neff, "Convective plumes in the planetary boundary layer, investigated with an acoustic echo sounder," J. Appl. Meteorol. 14, 513–523 (1975).
  23. F. F. Hall, Jr., "Temperature and wind structure studies by acoustic echo-sounding," in Remote Sensing of the Troposphere (U.S. Government Printing Office, Washington, D.C., 1972), Chap. 18, pp. 18-1–18-26.
  24. W. D. Neff, "An observational and numerical study, calibration techniques of the atmospheric boundary layer overlying the East Antarctic ice sheet," Ph.D. thesis (University of Colorado, Boulder, Colo., 1980).
  25. T. Beer, Atmospheric Waves (Halsted, New York, 1974), pp. 54–86.
  26. C. Fein, ARPA Maui Observatory Station, Maui, Hawaii, personal communication, September 20, 1979.
  27. J. L. Bufton et al., "Measurements of turbulence profiles in the troposphere," J. Opt. Soc. Am. 62, 1068–1070 (1972).
  28. R. Barletti et al., "Mean vertical profile of atmospheric turbulence relevant for astonomical seeing," J. Opt. Soc. Am. 66, 1380–1383 (1976).
  29. G. R. Ochs, T. Wang, and R. S. Lawrence, "Refraction-turbulence profiles measured by one-dimensional spatial filtering of scintillations," Appl. Opt. 15, 2504–2510 (1976).
  30. G. C. Loos and C. B. Hogge, "Turbulence of the upper atmosphere and isoplanatism" Appl. Opt. 18, 2654–2661 (1979).
  31. J. C. Wyngaard and M. A. Lemone, "Behavior of the refractive index structure parameter in the entraining convective boundary layer," J. Atmos. Sci. 37, 1573–1585 (1980).

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