Abstract

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 (Cn2) 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.

© 1981 Optical Society of America

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References

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  1. D. L. Walters, “Atmospheric modulation transfer function for desert and mountain locations—r0measurements,” J. Opt. Soc. Am. 71, 406–409 (1981).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef]
  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.
    [CrossRef]
  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).
    [CrossRef]
  9. C. A. Friehe and 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).
    [CrossRef]
  10. T. E. VanZandt and 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).
    [CrossRef]
  11. J. C. Kaimal and et al., “Turbulent structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
    [CrossRef]
  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).
    [CrossRef]
  15. L. R. Tsuang, “Microstructure of temperature fields in the free atmosphere,” Radio Sci. 4, 1175–1177 (1969).
    [CrossRef]
  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).
    [CrossRef]
  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−1.16dependence for Cn2, whereas most theories, such as Eq. (8), have a z−4/3dependence for the unstable, midday convective period. The z−1.16form we observe appears to be the result of the climatological averaging process, where Cn2data 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, Cn2increases 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 Cn2toward a z−2/3dependence (see Refs. 16 and 17). Depending on the wind speed, we have observed both the z−2/3and z−4/3forms. Thus, above the surface boundary layer, the z−4/3dependence is the most representative form for the change in Cn2with 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 and et al., “Acoustic sounding—a new approach to the study of atmospheric structure,” Proc. IEEE 57, 579–587 (1969).
    [CrossRef]
  22. F. F. Hall, 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).
    [CrossRef]
  23. F. F. Hall, “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, September20, 1979.
  27. J. L. Bufton and et al., “Measurements of turbulence profiles in the troposphere,” J. Opt. Soc. Am. 62, 1068–1070 (1972).
    [CrossRef]
  28. R. Barletti and et al., “Mean vertical profile of atmospheric turbulence relevant for astonomical seeing,” J. Opt. Soc. Am. 66, 1380–1383 (1976).
    [CrossRef]
  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).
    [CrossRef] [PubMed]
  30. G. C. Loos and C. B. Hogge, “Turbulence of the upper atmosphere and isoplanatism” Appl. Opt. 18, 2654–2661 (1979).
    [CrossRef] [PubMed]
  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).
    [CrossRef]

1981 (1)

1980 (1)

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).
[CrossRef]

1979 (1)

1978 (1)

T. E. VanZandt and 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).
[CrossRef]

1976 (3)

1975 (2)

C. A. Friehe and 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).
[CrossRef]

F. F. Hall, 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).
[CrossRef]

1972 (1)

1971 (2)

1970 (1)

1969 (3)

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).
[CrossRef]

L. R. Tsuang, “Microstructure of temperature fields in the free atmosphere,” Radio Sci. 4, 1175–1177 (1969).
[CrossRef]

L. G. McAllister and et al., “Acoustic sounding—a new approach to the study of atmospheric structure,” Proc. IEEE 57, 579–587 (1969).
[CrossRef]

1966 (1)

1920 (1)

L. F. Richardson, “The supply of energy from and to atmospheric eddies,” Proc. Roy. Soc. London 97, 356–373 (1920).

Aitchison, J.

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.

Barletti, R.

Beer, T.

T. Beer, Atmospheric Waves (Halsted, New York, 1974), pp. 54–86.

Brown, J.

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.

Bufton, J. L.

Clifford, S. F.

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).
[CrossRef]

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.
[CrossRef]

Collins, S. A.

Edinger, J. C.

F. F. Hall, 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).
[CrossRef]

Fein, C.

C. Fein, ARPA Maui Observatory Station, Maui, Hawaii, personal communication, September20, 1979.

Fried, D. L.

Friehe, C. A.

Hall, F. F.

F. F. Hall, 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).
[CrossRef]

F. F. Hall, “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.

Hogge, C. B.

Hufnagel, R. E.

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.

Izumi, Y.

Kaimal, J. C.

J. C. Kaimal and et al., “Turbulent structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

Lawrence, R. S.

Lemone, M. A.

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).
[CrossRef]

Loos, G. C.

Lumley, J. L.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972) pp. 98–99.

Lutamirski, R. F.

McAllister, L. G.

L. G. McAllister and et al., “Acoustic sounding—a new approach to the study of atmospheric structure,” Proc. IEEE 57, 579–587 (1969).
[CrossRef]

Neff, W. D.

F. F. Hall, 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).
[CrossRef]

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).

Ochs, G. R.

Richardson, L. F.

L. F. Richardson, “The supply of energy from and to atmospheric eddies,” Proc. Roy. Soc. London 97, 356–373 (1920).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), pp. 40–58.

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.

Tennekes, H.

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972) pp. 98–99.

Tsuang, L. R.

L. R. Tsuang, “Microstructure of temperature fields in the free atmosphere,” Radio Sci. 4, 1175–1177 (1969).
[CrossRef]

VanZandt, T. E.

T. E. VanZandt and 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).
[CrossRef]

Walters, D. L.

Wang, T.

Woods, J. D.

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).
[CrossRef]

Wyngaard, J. C.

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).
[CrossRef]

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).
[CrossRef]

J. C. Wyngaard, “On surface-layer turbulence,” in Workshop on Micrometeorology (American Meteorological Society, Boston, Mass., 1972), Chap. 3, pp. 101–149.

Yura, H. T.

Appl. Opt. (2)

J. Appl. Meteorol. (1)

F. F. Hall, 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).
[CrossRef]

J. Atmos. Sci. (2)

J. C. Kaimal and et al., “Turbulent structure in the convective boundary layer,” J. Atmos. Sci. 33, 2152–2169 (1976).
[CrossRef]

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).
[CrossRef]

J. Opt. Soc. Am. (8)

Proc. IEEE (1)

L. G. McAllister and et al., “Acoustic sounding—a new approach to the study of atmospheric structure,” Proc. IEEE 57, 579–587 (1969).
[CrossRef]

Proc. Roy. Soc. London (1)

L. F. Richardson, “The supply of energy from and to atmospheric eddies,” Proc. Roy. Soc. London 97, 356–373 (1920).

Radio Sci. (3)

T. E. VanZandt and 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).
[CrossRef]

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).
[CrossRef]

L. R. Tsuang, “Microstructure of temperature fields in the free atmosphere,” Radio Sci. 4, 1175–1177 (1969).
[CrossRef]

Other (13)

H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, Mass., 1972) pp. 98–99.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), pp. 40–58.

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.

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.

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.
[CrossRef]

J. C. Wyngaard, “On surface-layer turbulence,” in Workshop on Micrometeorology (American Meteorological Society, Boston, Mass., 1972), Chap. 3, pp. 101–149.

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.

Figure 1 shows a z−1.16dependence for Cn2, whereas most theories, such as Eq. (8), have a z−4/3dependence for the unstable, midday convective period. The z−1.16form we observe appears to be the result of the climatological averaging process, where Cn2data 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, Cn2increases 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 Cn2toward a z−2/3dependence (see Refs. 16 and 17). Depending on the wind speed, we have observed both the z−2/3and z−4/3forms. Thus, above the surface boundary layer, the z−4/3dependence is the most representative form for the change in Cn2with altitude during the day up to about one half of the inversion height.

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.

F. F. Hall, “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.

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).

T. Beer, Atmospheric Waves (Halsted, New York, 1974), pp. 54–86.

C. Fein, ARPA Maui Observatory Station, Maui, Hawaii, personal communication, September20, 1979.

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Figures (16)

Fig. 1
Fig. 1

Altitude dependence of the optical turbulence structure parameter Cn2 above the Tularosa basin for midday and clear weather conditions. The data represent a log-normal average of 50-m spatial segments collected during 15 flights in April–July, 1977 and 1978, by an aircraft-mounted microthermal probe and tower-mounted microthermal probes. Representative standard deviations of the data are shown and correspond to a factor of 2.5–3. The standard deviations of the means correspond to a factor of about 1.1 (10%). The least-squares line is represented by ( 7.7 ÷ × 1.2 ) × 10 - 13 ( z / z 0 ) - ( 1.16 ± 0.03 ) m - 2 / 3, where z0 = 1 m. (See Refs. 18 and 19.)

Fig. 2
Fig. 2

Altitude dependence of the optical turbulence structure parameter Cn2 above the Tularosa basis for ≈1800 h during clear weather. The data represent a log-normal average of 50-m spatial segments collected during 15 flights in April–July, 1977 and 1978, by an aircraft-mounted microthermal probe. The least-squares line is represented by ( 6.2 ÷ × 1.3 ) × 10 - 17 m - 2 / 3. (See Ref. 18.)

Fig. 3
Fig. 3

Altitude dependence of the optical turbulence structure parameter Cn2 above the Tularosa basin for ≈2400 h during clear weather. The data represent a log-normal average of 50-m spatial segments collected during 15 flights in April–July, 1977 and 1978, by an aircraft-mounted microthermal probe. The least-squares line is represented by ( 3.2 ÷ × 1.1 ) × 10 - 16 e - ( 0.00101 ± 0.00008 ) z m - 2 / 3. (See Ref. 18.)

Fig. 4
Fig. 4

Altitude dependence of the optical turbulence stucture parameter Cn2 above the Tularosa basin for 0500 h during clear weather. The data represent a log-normal average of 50-m spatial segments collected during 15 flights in April–July, 1977 and 1978, by an aircraft-mounted microthermal probe. The least-squares line is represented by ( 2.4 ÷ × 1.1 ) × 10 - 16 e - ( 0.00100 ± 0.00006 ) z m - 2 / 3. (See Ref. 18.)

Fig. 5
Fig. 5

Seasonally averaged Cn2 at 9 m above the Tularosa basin surface measured with microthermal resistance probes for the spring of 1977. The data are composed of a log normal average of 15-min linear average segments. A 15-min linear average point measurement is equivalent to a 3-km spatial average if a 3-m/sec average wind speed is assumed.

Fig. 6
Fig. 6

Seasonally averaged Cn2 at 33 m above the Tularosa basin surface measured with microthermal resistance probes for the springs of 1977–1979. The data processing is the same as for Fig. 5.

Fig. 7
Fig. 7

Seasonally averaged Cn2 at 8 m above a mountain surface measured with microthermal resistance probes for the summer of 1977. The data are for site B, a knoll that is 140 m above the surface, and are representative of all three mountain locations. The data processing is the same as for Fig. 5.

Fig. 8
Fig. 8

Seasonally averaged Cn2 at 16 m above a mountain surface measured with microthermal resistance probes for the summer of 1977. The data are for site B, a 140-m knoll, and are representative of all three mountain sites except that the magnitudes during both the day and the night are about a factor of 2 lower than for the other two larger mountains. The data processing is the same as for Fig. 5.

Fig. 9
Fig. 9

Diurnal variation in the surface temperature and the 9- and 34-m air temperatures for a typical clear summer day, August 15, 1978. Sunrise occurs at 0523 h, and sunset occurs at 1844 h.

Fig. 10
Fig. 10

The dependence of the temperature structure function CT2 on the surface and 9-m air temperature difference. These data are applicable under unstable conditions when the surface is warmer than the air. The average trend is represented by CT2(9 m) = 1.7 × 10−3θ)4/3 °C/m2/3.

Fig. 11
Fig. 11

Acoustic sounder facsimile recording above the Tularosa basin on March 23, 1978, during the day. The darker areas represent regions of higher atmospheric density fluctuations CT2. The vertical plumes are characteristic of daytime, unstable, convective activity. The height of the plumes extends beyond the 200–300-m altitude detected by the acoustic sounder.

Fig. 12
Fig. 12

Acoustic sounder facsimile recording above the Tularosa basin on March 24, 1978, during the night. The wavelike stratified layering is characteristic of nocturnal inversion activity that involves stable and unstable interactions between the local wind shear and the local temperature gradient.

Fig. 13
Fig. 13

Acoustic sounder facsimile recording for a large mountain escarpment, site C, on October 19, 1977, during the morning, day, and evening. Note that the time scale is different from that utilized in Figs. 11 and 12. The evening temperature transition occurs near sunset at 1722 h.

Fig. 14
Fig. 14

Acoustic sounder facsimile recording above the Tularosa basin on April 6, 1978, during the morning. The white band between 300 and 360 m is an artifact of the recording. The morning surface–air temperature crossover occurs near 0700 h. The characteristic daytime vertical plumes commence at the surface after 0700 h and grow in height with time, destroying the inversion layers from below.

Fig. 15
Fig. 15

Altitude dependence of the temperature structure function CT2 near 1200 h plotted with respect to the inversion height, compared with the empirical model of Kaimal.11 The data are a log normal average of 50-m spatial measurements and are normalized with respect to CT2 measured at 64 m.

Fig. 16
Fig. 16

The dependence of the vertical path transverse coherence length r0 on the altitude of the instrument above level ground is shown. The midday r0 data from Fig. 1 of Ref. 1 are compared with the prediction of the Kaimal model. The standard deviation comes from the measured standard deviation in the daytime Cn2 average of Fig. 5. The z1/5 curve is the theoretical consequence of a simple z−4/3 altitude dependence of Cn2(z).

Equations (9)

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r 0 = 2.1 [ 1.46 k 2 0 L C n 2 ( z ) d z ] - 3 / 5 ,
C n 2 = ( n 1 - n 2 ) 2 / r 12 2 / 3 ,
C n 2 = ( 79 × 10 - 6 P / T 2 ) 2 C T 2 ,
C T 2 = a α L 0 4 / 3 ( d θ / d z ) 2 ,
R i = ( g / θ ) ( d θ / d z ) / ( d u / d z ) 2 ,
z a C n 2 ( z ) d z = z a z b C n 2 ( z ) d z + z b C n 2 ( z ) d z .
z b C n 2 ( z ) d z = 2.36 ( z c - z b ) z c k 2 r 0 5 / 3 .
C T 2 ( g / T ) 2 / 3 3.2 ( Q 0 / z i ) 4 / 3 = { 0.83 ( z / z i ) - 4 / 3 z 0.5 z i 2.1 0.5 z i z 0.7 z i 6.1 ( z / z i ) 3 0.7 z i z z i ,
C n 2 ( z ) C n 2 ( z 0 ) = { ( z / z 0 ) - 4 / 3 z 0 , z 0.5 z i ( 0.5 z i / z 0 ) - 4 / 3 0.5 z i z 0.7 z i 2.9 ( 0.5 z i / z 0 ) - 4 / 3 ( z / z i ) 3 0.7 z i z z i ,