Abstract

Because turbulent fluctuations in the atmospheric refractive index (n) at a wavelength λ are related to fluctuations in the temperature (t) and the humidity (q) by n = A(λ, P, T, Q)t + B(λ, P, T, Q)q it is possible to estimate the refractive-index structure parameter Cn2 from meteorological quantities. I describe and evaluate two such estimation procedures,one based on the velocity, temperature and humidity scales u*, t*, and q*and a second based on the routine meteorological quantities Uh, TsTh and QsQh. The subscript h here denotes the wind speed (Uh), temperature (Th), or humidity (Qh) at a reference height h; the subscript s indicates the surface value. I also develop analytical expressions for the coefficients A and B as functions of λ, the atmospheric pressure (P), and the temperature and the humidity in four wavelength regions: visible (including near infrared), an infrared window, near millimeter, and radio. In a sensitivity analysis of the two estimation procedures, the core of the paper, I demonstrate that the accuracy of the Cn2 estimate is a strong function of the Bowen ratio (Bo). At two Bo values within the interval [−10, 10], one dependent on λ and the other dependent on meteorological conditions, the uncertainty in the Cn2 estimate becomes infinite.

© 1988 Optical Society of America

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  3. S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
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  5. R. J. Hill, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
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  7. M. A. Kallistratova, D. F. Timanovskiy, “The distribution of the structure constant of refractive index fluctuations in the atmospheric surface layer,” Izv. Atmos. Oceanic Phys. 7, 46–48 (1971).
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  9. E. L. Andreas, “Spectral measurements in a disturbed boundary layer over snow,” J. Atmos. Sci. 44, 1912–1939 (1987).
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    [CrossRef]
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  14. K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
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  15. J. C. Wyngaard, M. A. Lemone, “Behavior of the refractive index structure parameter in the entraining convective boundary layer,” J. Atmos. Sci. 37, 1573–1585 (1980).
    [CrossRef]
  16. W. Kohsiek, “Measuring Ct2, Cq2, and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
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  17. E. E. Gossard, “Power spectra of temperature, humidity and refractive index from aircraft and tethered balloon measurements,” IRE Trans. Antennas Propag. AP-8, 186–201 (1960).
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  19. R. J. Hill, S. F. Clifford, R.-S. Lawrence, “Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity, and pressure fluctuations,” J. Opt. Soc. Am. 70, 1192–1205 (1980).
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  20. G. A. McBean, J. A. Elliott, “Pressure and humidity effects on optical refractive-index fluctuations,” Boundary-Layer Meteorol. 20, 101–109 (1981).
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    [CrossRef]
  36. A. J. Dyer, “A review of flux-profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
    [CrossRef]
  37. A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
    [CrossRef]
  38. A. J. Dyer, E. F. Bradley, “An alternative analysis of fluxgradient relationships at the 1976 ITCE,” Boundary-Layer Meteorol. 22, 3–19 (1982).
    [CrossRef]
  39. W. G. Large, S. Pond, “Sensible and latent heat flux measurements over the ocean,” J. Phys. Oceanogr. 12, 464–482 (1982).
    [CrossRef]
  40. J. Wieringa, “A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding,” Boundary-Layer Meteorol. 18, 411–430 (1980).
    [CrossRef]
  41. C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
    [CrossRef]
  42. J. C. Wyngaard, Y. Izumi, S. A. Collins, “Behavior of the refractive-index-structure parameter near the ground,” J. Opt. Soc. Am. 61, 1646–1650 (1971).
    [CrossRef]
  43. C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
    [CrossRef]
  44. E. L. Andreas, “On the Kolmogorov constants for the temperature-humidity cospectrum and the refractive index spectrum,” J. Atmos. Sci. 44, 2399–2406 (1987).
    [CrossRef]
  45. J. C. Wyngaard, O. R. Coté, “The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,” J. Atmos. Sci. 28, 190–201 (1971).
    [CrossRef]
  46. J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
    [CrossRef]
  47. C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
    [CrossRef]
  48. G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
    [CrossRef]
  49. K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
    [CrossRef]
  50. K. E. Kunkel, D. L. Walters, G. A. Ely, “Behavior of the temperature structure parameter in a desert basin,” J. Appl. Meteorol. 20, 130–136 (1981).
    [CrossRef]
  51. J. C. Wyngaard, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
    [CrossRef]
  52. B. B. Hicks, H. C. Martin, “Atmospheric turbulent fluxes over snow,” Boundary-Layer Meteorol. 2, 496–502 (1972).
    [CrossRef]
  53. L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).
  54. D. C. McKay, G. W. Thurtell, “Measurements of the energy fluxes involved in the energy budget of a snow cover,” J. Appl. Meteorol. 17, 339–349 (1978).
    [CrossRef]
  55. M. R. Thorpe, E. G. Banke, S. D. Smith, “Eddy correlation measurements of evaporation and sensible heat flux over Arctic sea ice,” J. Geophys. Res. 78, 3573–3584 (1973).
    [CrossRef]
  56. E. L. Andreas, A. P. Makshtas, “Energy exchange over Antarctic sea ice in the spring,” J. Geophys. Res. 90, 7199–7212 (1985).
    [CrossRef]
  57. E. L. Andreas, “Atmospheric stability from scintillation measurements,” Appl. Opt. (to be published).
    [PubMed]
  58. C. W. Fairall, S. E. Larson, “Inertial-dissipation methods and turbulent fluxes at the air-ocean interface,” Boundary-Layer Meteorol. 34, 287–301 (1986).
    [CrossRef]
  59. E. G. Banke, S. D. Smith, R. J. Anderson, “Drag coefficients at AIDJEX from sonic anemometer measurements,” in Sea Ice Processes and Models, R. S. Pritchard, ed. (U. Washington Press, Seattle, Wash., 1980), pp. 430–442.
  60. K. Shirasawa, “Studies on wind stress on sea ice,” Low Temp. Sci. A 40, 101–118 (1981) (in Japanese; English summary).
  61. J. Kondo, H. Yamazawa, “Bulk transfer coefficient over a snow surface,” Boundary-Layer Meteorol. 34, 123–135 (1986).
    [CrossRef]
  62. E. L. Andreas, “A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice,” Boundary-Layer Meteorol. 38, 159–184 (1987).
    [CrossRef]
  63. E. L. Andreas, “A new method of measuring the snow-surface temperature,” Cold Regions Sci. Technol. 12, 139–156 (1986).
    [CrossRef]
  64. K. E. Kunkel, D. L. Walters, “Modeling the diurnal dependence of the optical refractive index structure parameter,” J. Geophys. Res. 88, 10999–11004 (1983).
    [CrossRef]
  65. W. T. Liu, K. B. Katsaros, J. A. Businger, “Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface,” J. Atmos. Sci. 36, 1722–1735 (1979).
    [CrossRef]
  66. J. Kondo, “Air-sea bulk transfer coefficients in diabatic conditions,” Boundary-Layer Meteorol. 9, 91–112 (1975).
    [CrossRef]
  67. W. Brutsaert, “The roughness length for water vapor, sensible heat, and other scalars,” J. Atmos. Sci. 32, 2028–2031 (1975).
    [CrossRef]
  68. J. R. Garratt, B. B. Hicks, “Momentum, heat and water vapour transfer to and from natural and artificial surfaces,” Q. J. R. Meteorol. Soc. 99, 680–687 (1973).
    [CrossRef]
  69. J. R. Garratt, “Review of drag coefficients over oceans and continents,” Mon. Weather Rev. 105, 915–929 (1977).
    [CrossRef]

1987 (3)

E. L. Andreas, “Spectral measurements in a disturbed boundary layer over snow,” J. Atmos. Sci. 44, 1912–1939 (1987).
[CrossRef]

E. L. Andreas, “On the Kolmogorov constants for the temperature-humidity cospectrum and the refractive index spectrum,” J. Atmos. Sci. 44, 2399–2406 (1987).
[CrossRef]

E. L. Andreas, “A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice,” Boundary-Layer Meteorol. 38, 159–184 (1987).
[CrossRef]

1986 (4)

E. L. Andreas, “A new method of measuring the snow-surface temperature,” Cold Regions Sci. Technol. 12, 139–156 (1986).
[CrossRef]

J. Kondo, H. Yamazawa, “Bulk transfer coefficient over a snow surface,” Boundary-Layer Meteorol. 34, 123–135 (1986).
[CrossRef]

C. W. Fairall, S. E. Larson, “Inertial-dissipation methods and turbulent fluxes at the air-ocean interface,” Boundary-Layer Meteorol. 34, 287–301 (1986).
[CrossRef]

R. J. Hill, R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

1985 (3)

R. A. Bohlander, R. W. McMillan, J. J. Gallagher, “Atmospheric effects on near-millimeter-wave propagation,” Proc. IEEE 73, 49–60 (1985).
[CrossRef]

J. T. Priestley, R. J. Hill, “Measuring high-frequency humidity, temperature and radio refractive index in the surface layer,” J. Atmos. Oceanic Technol. 2, 233–251 (1985).
[CrossRef]

E. L. Andreas, A. P. Makshtas, “Energy exchange over Antarctic sea ice in the spring,” J. Geophys. Res. 90, 7199–7212 (1985).
[CrossRef]

1983 (2)

K. E. Kunkel, D. L. Walters, “Modeling the diurnal dependence of the optical refractive index structure parameter,” J. Geophys. Res. 88, 10999–11004 (1983).
[CrossRef]

R. W. McMillan, R. A. Bohlander, G. R. Ochs, R. J. Hill, S. F. Clifford, “Millimeter wave atmospheric turbulence measurements: preliminary results and instrumentation for future measurements,” Opt. Eng. 22, 32–39 (1983).
[CrossRef]

1982 (5)

R. J. Hill, R. S. Lawrence, J. T. Priestley, “Theoretical and calculational aspects of the radio refractive index of water vapor,” Radio Sci. 17, 1251–1257 (1982).
[CrossRef]

A. J. Dyer, E. F. Bradley, “An alternative analysis of fluxgradient relationships at the 1976 ITCE,” Boundary-Layer Meteorol. 22, 3–19 (1982).
[CrossRef]

W. G. Large, S. Pond, “Sensible and latent heat flux measurements over the ocean,” J. Phys. Oceanogr. 12, 464–482 (1982).
[CrossRef]

W. Kohsiek, “Measuring Ct2, Cq2, and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

R. J. Hill, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
[CrossRef] [PubMed]

1981 (5)

K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
[CrossRef] [PubMed]

G. A. McBean, J. A. Elliott, “Pressure and humidity effects on optical refractive-index fluctuations,” Boundary-Layer Meteorol. 20, 101–109 (1981).
[CrossRef]

K. Shirasawa, “Studies on wind stress on sea ice,” Low Temp. Sci. A 40, 101–118 (1981) (in Japanese; English summary).

K. E. Kunkel, D. L. Walters, G. A. Ely, “Behavior of the temperature structure parameter in a desert basin,” J. Appl. Meteorol. 20, 130–136 (1981).
[CrossRef]

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

1980 (5)

C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

R. J. Hill, S. F. Clifford, R.-S. Lawrence, “Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity, and pressure fluctuations,” J. Opt. Soc. Am. 70, 1192–1205 (1980).
[CrossRef]

J. Wieringa, “A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding,” Boundary-Layer Meteorol. 18, 411–430 (1980).
[CrossRef]

J. C. Wyngaard, 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)

W. T. Liu, K. B. Katsaros, J. A. Businger, “Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface,” J. Atmos. Sci. 36, 1722–1735 (1979).
[CrossRef]

1978 (6)

J. C. Wyngaard, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).

D. C. McKay, G. W. Thurtell, “Measurements of the energy fluxes involved in the energy budget of a snow cover,” J. Appl. Meteorol. 17, 339–349 (1978).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
[CrossRef]

T.-I. Wang, G. R. Ochs, S. F. Clifford, “A saturation-resistant optical scintillometer to measure Cn2,” J. Opt. Soc. Am. 68, 334–338 (1978).
[CrossRef]

1977 (3)

C. A. Friehe, “Estimation of the refractive-index temperature structure parameter over the ocean,” Appl. Opt. 16, 334–340 (1977).
[CrossRef] [PubMed]

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

J. R. Garratt, “Review of drag coefficients over oceans and continents,” Mon. Weather Rev. 105, 915–929 (1977).
[CrossRef]

1976 (1)

M. L. Wesely, “The combined effect of temperature and humidity fluctuations on refractive index,” J. Appl. Meteorol. 15, 43–49 (1976).
[CrossRef]

1975 (3)

C. A. Friehe, J. C. LaRue, F. H. Champagne, C. H. Gibson, G. F. Dreyer, “Effects of temperature and humidity fluctuations on the optical refractive index in the marine boundary layer,” J. Opt. Soc. Am. 65, 1502–1511 (1975).
[CrossRef]

J. Kondo, “Air-sea bulk transfer coefficients in diabatic conditions,” Boundary-Layer Meteorol. 9, 91–112 (1975).
[CrossRef]

W. Brutsaert, “The roughness length for water vapor, sensible heat, and other scalars,” J. Atmos. Sci. 32, 2028–2031 (1975).
[CrossRef]

1974 (2)

1973 (3)

M. L. Wesely, E. C. Alcarez, “Diurnal cycles of the refractive index structure function coefficient,” J. Geophys. Res. 78, 6224–6232 (1973).
[CrossRef]

J. R. Garratt, B. B. Hicks, “Momentum, heat and water vapour transfer to and from natural and artificial surfaces,” Q. J. R. Meteorol. Soc. 99, 680–687 (1973).
[CrossRef]

M. R. Thorpe, E. G. Banke, S. D. Smith, “Eddy correlation measurements of evaporation and sensible heat flux over Arctic sea ice,” J. Geophys. Res. 78, 3573–3584 (1973).
[CrossRef]

1972 (2)

B. B. Hicks, H. C. Martin, “Atmospheric turbulent fluxes over snow,” Boundary-Layer Meteorol. 2, 496–502 (1972).
[CrossRef]

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
[CrossRef]

1971 (5)

J. C. Wyngaard, Y. Izumi, 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, O. R. Coté, “The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,” J. Atmos. Sci. 28, 190–201 (1971).
[CrossRef]

M. A. Kallistratova, D. F. Timanovskiy, “The distribution of the structure constant of refractive index fluctuations in the atmospheric surface layer,” Izv. Atmos. Oceanic Phys. 7, 46–48 (1971).

A. M. Obukhov, “Turbulence in an atmosphere with a nonuniform temperature,” Boundary-Layer Meteorol. 2, 7–29 (1971).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,”J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

1970 (3)

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
[CrossRef]

R. S. Lawrence, G. R. Ochs, S. F. Clifford, “Measurement of atmospheric turbulence relevant to optical propagation,” J. Opt. Soc. Am. 60, 826–830 (1970).
[CrossRef]

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

1967 (1)

1966 (1)

B. R. Bean, E. J. Dutton, Radio Meteorology, Natl. Bur. Stand. (U.S.) Monogr. 92 (1966).

1963 (1)

G. Boudouris, “On the index of refraction of air, the absorption and dispersion of centimeter waves by gases,” J. Res. Natl. Bur. Stand. Sect. D 67, 631–684 (1963).

1960 (1)

E. E. Gossard, “Power spectra of temperature, humidity and refractive index from aircraft and tethered balloon measurements,” IRE Trans. Antennas Propag. AP-8, 186–201 (1960).
[CrossRef]

Alcarez, E. C.

M. L. Wesely, E. C. Alcarez, “Diurnal cycles of the refractive index structure function coefficient,” J. Geophys. Res. 78, 6224–6232 (1973).
[CrossRef]

Anderson, R. J.

E. G. Banke, S. D. Smith, R. J. Anderson, “Drag coefficients at AIDJEX from sonic anemometer measurements,” in Sea Ice Processes and Models, R. S. Pritchard, ed. (U. Washington Press, Seattle, Wash., 1980), pp. 430–442.

Andreas, E. L.

E. L. Andreas, “A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice,” Boundary-Layer Meteorol. 38, 159–184 (1987).
[CrossRef]

E. L. Andreas, “Spectral measurements in a disturbed boundary layer over snow,” J. Atmos. Sci. 44, 1912–1939 (1987).
[CrossRef]

E. L. Andreas, “On the Kolmogorov constants for the temperature-humidity cospectrum and the refractive index spectrum,” J. Atmos. Sci. 44, 2399–2406 (1987).
[CrossRef]

E. L. Andreas, “A new method of measuring the snow-surface temperature,” Cold Regions Sci. Technol. 12, 139–156 (1986).
[CrossRef]

E. L. Andreas, A. P. Makshtas, “Energy exchange over Antarctic sea ice in the spring,” J. Geophys. Res. 90, 7199–7212 (1985).
[CrossRef]

E. L. Andreas, “Atmospheric stability from scintillation measurements,” Appl. Opt. (to be published).
[PubMed]

Banke, E. G.

M. R. Thorpe, E. G. Banke, S. D. Smith, “Eddy correlation measurements of evaporation and sensible heat flux over Arctic sea ice,” J. Geophys. Res. 78, 3573–3584 (1973).
[CrossRef]

E. G. Banke, S. D. Smith, R. J. Anderson, “Drag coefficients at AIDJEX from sonic anemometer measurements,” in Sea Ice Processes and Models, R. S. Pritchard, ed. (U. Washington Press, Seattle, Wash., 1980), pp. 430–442.

Bean, B. R.

B. R. Bean, E. J. Dutton, Radio Meteorology, Natl. Bur. Stand. (U.S.) Monogr. 92 (1966).

Bohlander, R. A.

R. A. Bohlander, R. W. McMillan, J. J. Gallagher, “Atmospheric effects on near-millimeter-wave propagation,” Proc. IEEE 73, 49–60 (1985).
[CrossRef]

R. W. McMillan, R. A. Bohlander, G. R. Ochs, R. J. Hill, S. F. Clifford, “Millimeter wave atmospheric turbulence measurements: preliminary results and instrumentation for future measurements,” Opt. Eng. 22, 32–39 (1983).
[CrossRef]

Boudouris, G.

G. Boudouris, “On the index of refraction of air, the absorption and dispersion of centimeter waves by gases,” J. Res. Natl. Bur. Stand. Sect. D 67, 631–684 (1963).

Bradley, E. F.

A. J. Dyer, E. F. Bradley, “An alternative analysis of fluxgradient relationships at the 1976 ITCE,” Boundary-Layer Meteorol. 22, 3–19 (1982).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,”J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

Brutsaert, W.

W. Brutsaert, “The roughness length for water vapor, sensible heat, and other scalars,” J. Atmos. Sci. 32, 2028–2031 (1975).
[CrossRef]

Busch, N. E.

N. E. Busch, “On the mechanics of atmospheric turbulence,” in Workshop on Micrometeorology, D. A. Haugen, ed. (American Meteorological Society, Boston, Mass., 1973), pp. 1–65.

Businger, J. A.

W. T. Liu, K. B. Katsaros, J. A. Businger, “Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface,” J. Atmos. Sci. 36, 1722–1735 (1979).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,”J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

J. A. Businger, “Turbulent transfer in the atmospheric surface layer,” in Workshop on Micrometeorology, D. A. Haugen, ed. (American Meteorological Society, Boston, Mass., 1973), pp. 67–100.

Champagne, F. H.

Clifford, S. F.

Collins, S. A.

Coté, O. R

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
[CrossRef]

Coté, O. R.

J. C. Wyngaard, O. R. Coté, “The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,” J. Atmos. Sci. 28, 190–201 (1971).
[CrossRef]

Davidson, K. L.

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
[CrossRef] [PubMed]

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

Dreyer, G. F.

Dutton, E. J.

B. R. Bean, E. J. Dutton, Radio Meteorology, Natl. Bur. Stand. (U.S.) Monogr. 92 (1966).

Dutton, J. A

H. A. Panofsky, J. A Dutton, Atmospheric Turbulence: Models and Methods for Engineering Applications (Wiley-Interscience, New York, 1984).

Dyer, A. J.

A. J. Dyer, E. F. Bradley, “An alternative analysis of fluxgradient relationships at the 1976 ITCE,” Boundary-Layer Meteorol. 22, 3–19 (1982).
[CrossRef]

A. J. Dyer, “A review of flux-profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
[CrossRef]

Elliott, J. A.

G. A. McBean, J. A. Elliott, “Pressure and humidity effects on optical refractive-index fluctuations,” Boundary-Layer Meteorol. 20, 101–109 (1981).
[CrossRef]

Ely, G. A.

K. E. Kunkel, D. L. Walters, G. A. Ely, “Behavior of the temperature structure parameter in a desert basin,” J. Appl. Meteorol. 20, 130–136 (1981).
[CrossRef]

Fairall, C. W.

C. W. Fairall, S. E. Larson, “Inertial-dissipation methods and turbulent fluxes at the air-ocean interface,” Boundary-Layer Meteorol. 34, 287–301 (1986).
[CrossRef]

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
[CrossRef] [PubMed]

C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

Friehe, C. A.

Gallagher, J. J.

R. A. Bohlander, R. W. McMillan, J. J. Gallagher, “Atmospheric effects on near-millimeter-wave propagation,” Proc. IEEE 73, 49–60 (1985).
[CrossRef]

Garratt, J. R.

J. R. Garratt, “Review of drag coefficients over oceans and continents,” Mon. Weather Rev. 105, 915–929 (1977).
[CrossRef]

J. R. Garratt, B. B. Hicks, “Momentum, heat and water vapour transfer to and from natural and artificial surfaces,” Q. J. R. Meteorol. Soc. 99, 680–687 (1973).
[CrossRef]

Gibson, C. H.

Goroch, A. K.

Gossard, E. E.

E. E. Gossard, “Power spectra of temperature, humidity and refractive index from aircraft and tethered balloon measurements,” IRE Trans. Antennas Propag. AP-8, 186–201 (1960).
[CrossRef]

Hicks, B. B.

J. R. Garratt, B. B. Hicks, “Momentum, heat and water vapour transfer to and from natural and artificial surfaces,” Q. J. R. Meteorol. Soc. 99, 680–687 (1973).
[CrossRef]

B. B. Hicks, H. C. Martin, “Atmospheric turbulent fluxes over snow,” Boundary-Layer Meteorol. 2, 496–502 (1972).
[CrossRef]

Hill, R. J.

R. J. Hill, R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

J. T. Priestley, R. J. Hill, “Measuring high-frequency humidity, temperature and radio refractive index in the surface layer,” J. Atmos. Oceanic Technol. 2, 233–251 (1985).
[CrossRef]

R. W. McMillan, R. A. Bohlander, G. R. Ochs, R. J. Hill, S. F. Clifford, “Millimeter wave atmospheric turbulence measurements: preliminary results and instrumentation for future measurements,” Opt. Eng. 22, 32–39 (1983).
[CrossRef]

R. J. Hill, R. S. Lawrence, J. T. Priestley, “Theoretical and calculational aspects of the radio refractive index of water vapor,” Radio Sci. 17, 1251–1257 (1982).
[CrossRef]

R. J. Hill, “Theory of measuring the path-averaged inner scale of turbulence by spatial filtering of optical scintillation,” Appl. Opt. 21, 1201–1211 (1982).
[CrossRef] [PubMed]

R. J. Hill, S. F. Clifford, R.-S. Lawrence, “Refractive-index and absorption fluctuations in the infrared caused by temperature, humidity, and pressure fluctuations,” J. Opt. Soc. Am. 70, 1192–1205 (1980).
[CrossRef]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
[CrossRef]

R. J. Hill, “Dispersion by atmospheric water vapor at frequencies less than 1 THz,” IEEE Trans. Antennas Propag. (to be published).

Houlihan, T.

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

Houlihan, T. M.

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

Izumi, Y.

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,”J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

J. C. Wyngaard, Y. Izumi, S. A. Collins, “Behavior of the refractive-index-structure parameter near the ground,” J. Opt. Soc. Am. 61, 1646–1650 (1971).
[CrossRef]

Kaimal, J. C.

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
[CrossRef]

Kallistratova, M. A.

M. A. Kallistratova, D. F. Timanovskiy, “The distribution of the structure constant of refractive index fluctuations in the atmospheric surface layer,” Izv. Atmos. Oceanic Phys. 7, 46–48 (1971).

Katsaros, K. B.

W. T. Liu, K. B. Katsaros, J. A. Businger, “Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface,” J. Atmos. Sci. 36, 1722–1735 (1979).
[CrossRef]

Kohsiek, W.

W. Kohsiek, “Measuring Ct2, Cq2, and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

W. Kohsiek, “Optical and in situ measuring of structure parameters relevant to temperature and humidity, and their application to the measuring of sensible and latent heat flux,” NOAA Tech. Memo. ERL WPL-96 (Wave Propagation Laboratory, Boulder, Colo., 1982).

Kondo, J.

J. Kondo, H. Yamazawa, “Bulk transfer coefficient over a snow surface,” Boundary-Layer Meteorol. 34, 123–135 (1986).
[CrossRef]

J. Kondo, “Air-sea bulk transfer coefficients in diabatic conditions,” Boundary-Layer Meteorol. 9, 91–112 (1975).
[CrossRef]

Korpov, B. M.

L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).

Kunkel, K. E.

K. E. Kunkel, D. L. Walters, “Modeling the diurnal dependence of the optical refractive index structure parameter,” J. Geophys. Res. 88, 10999–11004 (1983).
[CrossRef]

K. E. Kunkel, D. L. Walters, G. A. Ely, “Behavior of the temperature structure parameter in a desert basin,” J. Appl. Meteorol. 20, 130–136 (1981).
[CrossRef]

Large, W. G.

W. G. Large, S. Pond, “Sensible and latent heat flux measurements over the ocean,” J. Phys. Oceanogr. 12, 464–482 (1982).
[CrossRef]

Larson, S. E.

C. W. Fairall, S. E. Larson, “Inertial-dissipation methods and turbulent fluxes at the air-ocean interface,” Boundary-Layer Meteorol. 34, 287–301 (1986).
[CrossRef]

LaRue, J. C.

Lawrence, R. S.

R. J. Hill, R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

R. J. Hill, R. S. Lawrence, J. T. Priestley, “Theoretical and calculational aspects of the radio refractive index of water vapor,” Radio Sci. 17, 1251–1257 (1982).
[CrossRef]

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

R. S. Lawrence, G. R. Ochs, S. F. Clifford, “Measurement of atmospheric turbulence relevant to optical propagation,” J. Opt. Soc. Am. 60, 826–830 (1970).
[CrossRef]

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

Lawrence, R.-S.

Lemone, M. A.

J. C. Wyngaard, 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, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

Lenschow, D. H.

J. C. Wyngaard, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

Liu, W. T.

W. T. Liu, K. B. Katsaros, J. A. Businger, “Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface,” J. Atmos. Sci. 36, 1722–1735 (1979).
[CrossRef]

Makshtas, A. P.

E. L. Andreas, A. P. Makshtas, “Energy exchange over Antarctic sea ice in the spring,” J. Geophys. Res. 90, 7199–7212 (1985).
[CrossRef]

Markson, R.

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

Martin, H. C.

B. B. Hicks, H. C. Martin, “Atmospheric turbulent fluxes over snow,” Boundary-Layer Meteorol. 2, 496–502 (1972).
[CrossRef]

McBean, G. A.

G. A. McBean, J. A. Elliott, “Pressure and humidity effects on optical refractive-index fluctuations,” Boundary-Layer Meteorol. 20, 101–109 (1981).
[CrossRef]

McKay, D. C.

D. C. McKay, G. W. Thurtell, “Measurements of the energy fluxes involved in the energy budget of a snow cover,” J. Appl. Meteorol. 17, 339–349 (1978).
[CrossRef]

McMillan, R. W.

R. A. Bohlander, R. W. McMillan, J. J. Gallagher, “Atmospheric effects on near-millimeter-wave propagation,” Proc. IEEE 73, 49–60 (1985).
[CrossRef]

R. W. McMillan, R. A. Bohlander, G. R. Ochs, R. J. Hill, S. F. Clifford, “Millimeter wave atmospheric turbulence measurements: preliminary results and instrumentation for future measurements,” Opt. Eng. 22, 32–39 (1983).
[CrossRef]

Obukhov, A. M.

A. M. Obukhov, “Turbulence in an atmosphere with a nonuniform temperature,” Boundary-Layer Meteorol. 2, 7–29 (1971).
[CrossRef]

Ochs, G. R.

Owens, J. C.

Panofsky, H. A.

H. A. Panofsky, J. A Dutton, Atmospheric Turbulence: Models and Methods for Engineering Applications (Wiley-Interscience, New York, 1984).

Paulson, C. A.

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
[CrossRef]

Pennell, W. T.

J. C. Wyngaard, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

Pond, S.

W. G. Large, S. Pond, “Sensible and latent heat flux measurements over the ocean,” J. Phys. Oceanogr. 12, 464–482 (1982).
[CrossRef]

Priestley, J. T.

J. T. Priestley, R. J. Hill, “Measuring high-frequency humidity, temperature and radio refractive index in the surface layer,” J. Atmos. Oceanic Technol. 2, 233–251 (1985).
[CrossRef]

R. J. Hill, R. S. Lawrence, J. T. Priestley, “Theoretical and calculational aspects of the radio refractive index of water vapor,” Radio Sci. 17, 1251–1257 (1982).
[CrossRef]

Schacher, G. E.

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
[CrossRef] [PubMed]

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

Shirasawa, K.

K. Shirasawa, “Studies on wind stress on sea ice,” Low Temp. Sci. A 40, 101–118 (1981) (in Japanese; English summary).

Smith, S. D.

M. R. Thorpe, E. G. Banke, S. D. Smith, “Eddy correlation measurements of evaporation and sensible heat flux over Arctic sea ice,” J. Geophys. Res. 78, 3573–3584 (1973).
[CrossRef]

E. G. Banke, S. D. Smith, R. J. Anderson, “Drag coefficients at AIDJEX from sonic anemometer measurements,” in Sea Ice Processes and Models, R. S. Pritchard, ed. (U. Washington Press, Seattle, Wash., 1980), pp. 430–442.

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A survey of clear-air propagation effects relevant to optical communications,” Proc. IEEE 58, 1523–1545 (1970).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971);also publication TT 68-50464 (National Technical Information Service, Springfield, Va.).

Thorpe, M. R.

M. R. Thorpe, E. G. Banke, S. D. Smith, “Eddy correlation measurements of evaporation and sensible heat flux over Arctic sea ice,” J. Geophys. Res. 78, 3573–3584 (1973).
[CrossRef]

Thurtell, G. W.

D. C. McKay, G. W. Thurtell, “Measurements of the energy fluxes involved in the energy budget of a snow cover,” J. Appl. Meteorol. 17, 339–349 (1978).
[CrossRef]

Timanovskiy, D. F.

L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).

M. A. Kallistratova, D. F. Timanovskiy, “The distribution of the structure constant of refractive index fluctuations in the atmospheric surface layer,” Izv. Atmos. Oceanic Phys. 7, 46–48 (1971).

Walters, D. L.

K. E. Kunkel, D. L. Walters, “Modeling the diurnal dependence of the optical refractive index structure parameter,” J. Geophys. Res. 88, 10999–11004 (1983).
[CrossRef]

K. E. Kunkel, D. L. Walters, G. A. Ely, “Behavior of the temperature structure parameter in a desert basin,” J. Appl. Meteorol. 20, 130–136 (1981).
[CrossRef]

Wang, T.-I.

Wesely, M. L.

M. L. Wesely, “The combined effect of temperature and humidity fluctuations on refractive index,” J. Appl. Meteorol. 15, 43–49 (1976).
[CrossRef]

M. L. Wesely, E. C. Alcarez, “Diurnal cycles of the refractive index structure function coefficient,” J. Geophys. Res. 78, 6224–6232 (1973).
[CrossRef]

Wieringa, J.

J. Wieringa, “A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding,” Boundary-Layer Meteorol. 18, 411–430 (1980).
[CrossRef]

Wyngaard, J. C.

J. C. Wyngaard, 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, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, O. R Coté, “Spectral characteristics of surface-layer turbulence,” Q. J. R. Meteorol. Soc. 98, 563–589 (1972).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, “Flux-profile relationships in the atmospheric surface layer,”J. Atmos. Sci. 28, 181–189 (1971).
[CrossRef]

J. C. Wyngaard, O. R. Coté, “The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,” J. Atmos. Sci. 28, 190–201 (1971).
[CrossRef]

J. C. Wyngaard, Y. Izumi, 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, D. A. Haugen, ed. (American Meteorological Society, Boston, Mass., 1973), pp. 101–149.

Yaglom, A. M.

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

Yamazawa, H.

J. Kondo, H. Yamazawa, “Bulk transfer coefficient over a snow surface,” Boundary-Layer Meteorol. 34, 123–135 (1986).
[CrossRef]

Yelagina, L. G.

L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).

Appl. Opt. (4)

Boundary-Layer Meteorol. (16)

G. A. McBean, J. A. Elliott, “Pressure and humidity effects on optical refractive-index fluctuations,” Boundary-Layer Meteorol. 20, 101–109 (1981).
[CrossRef]

A. M. Obukhov, “Turbulence in an atmosphere with a nonuniform temperature,” Boundary-Layer Meteorol. 2, 7–29 (1971).
[CrossRef]

A. J. Dyer, “A review of flux-profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
[CrossRef]

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

A. J. Dyer, E. F. Bradley, “An alternative analysis of fluxgradient relationships at the 1976 ITCE,” Boundary-Layer Meteorol. 22, 3–19 (1982).
[CrossRef]

W. Kohsiek, “Measuring Ct2, Cq2, and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

J. Wieringa, “A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding,” Boundary-Layer Meteorol. 18, 411–430 (1980).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

C. W. Fairall, R. Markson, G. E. Schacher, K. L. Davidson, “An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer,” Boundary-Layer Meteorol. 19, 453–469 (1980).
[CrossRef]

G. E. Schacher, K. L. Davidson, T. Houlihan, C. W. Fairall, “Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean,” Boundary-Layer Meteorol. 20, 321–330 (1981).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, “Observation of the temperature structure function parameter, CT2, over the ocean,” Boundary-Layer Meteorol. 15, 507–523 (1978).
[CrossRef]

B. B. Hicks, H. C. Martin, “Atmospheric turbulent fluxes over snow,” Boundary-Layer Meteorol. 2, 496–502 (1972).
[CrossRef]

J. Kondo, H. Yamazawa, “Bulk transfer coefficient over a snow surface,” Boundary-Layer Meteorol. 34, 123–135 (1986).
[CrossRef]

E. L. Andreas, “A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice,” Boundary-Layer Meteorol. 38, 159–184 (1987).
[CrossRef]

C. W. Fairall, S. E. Larson, “Inertial-dissipation methods and turbulent fluxes at the air-ocean interface,” Boundary-Layer Meteorol. 34, 287–301 (1986).
[CrossRef]

J. Kondo, “Air-sea bulk transfer coefficients in diabatic conditions,” Boundary-Layer Meteorol. 9, 91–112 (1975).
[CrossRef]

Cold Regions Sci. Technol. (1)

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L. G. Yelagina, B. M. Korpov, D. F. Timanovskiy, “Certain characteristics of the atmospheric surface layer above snow,” Izv. Atmos. Oceanic Phys. 14, 652–655 (1978).

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J. T. Priestley, R. J. Hill, “Measuring high-frequency humidity, temperature and radio refractive index in the surface layer,” J. Atmos. Oceanic Technol. 2, 233–251 (1985).
[CrossRef]

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J. C. Wyngaard, M. A. Lemone, “Behavior of the refractive index structure parameter in the entraining convective boundary layer,” J. Atmos. Sci. 37, 1573–1585 (1980).
[CrossRef]

E. L. Andreas, “Spectral measurements in a disturbed boundary layer over snow,” J. Atmos. Sci. 44, 1912–1939 (1987).
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[CrossRef]

E. L. Andreas, “On the Kolmogorov constants for the temperature-humidity cospectrum and the refractive index spectrum,” J. Atmos. Sci. 44, 2399–2406 (1987).
[CrossRef]

J. C. Wyngaard, O. R. Coté, “The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer,” J. Atmos. Sci. 28, 190–201 (1971).
[CrossRef]

J. C. Wyngaard, W. T. Pennell, D. H. Lenschow, M. A. LeMone, “The temperature-humidity covariance budget in the convective boundary layer,” J. Atmos. Sci. 35, 47–58 (1978).
[CrossRef]

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K. Shirasawa, “Studies on wind stress on sea ice,” Low Temp. Sci. A 40, 101–118 (1981) (in Japanese; English summary).

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[CrossRef]

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Other (9)

R. J. Hill, “Dispersion by atmospheric water vapor at frequencies less than 1 THz,” IEEE Trans. Antennas Propag. (to be published).

W. Kohsiek, “Optical and in situ measuring of structure parameters relevant to temperature and humidity, and their application to the measuring of sensible and latent heat flux,” NOAA Tech. Memo. ERL WPL-96 (Wave Propagation Laboratory, Boulder, Colo., 1982).

N. E. Busch, “On the mechanics of atmospheric turbulence,” in Workshop on Micrometeorology, D. A. Haugen, ed. (American Meteorological Society, Boston, Mass., 1973), pp. 1–65.

J. A. Businger, “Turbulent transfer in the atmospheric surface layer,” in Workshop on Micrometeorology, D. A. Haugen, ed. (American Meteorological Society, Boston, Mass., 1973), pp. 67–100.

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E. L. Andreas, “Atmospheric stability from scintillation measurements,” Appl. Opt. (to be published).
[PubMed]

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Figures (12)

Fig. 1
Fig. 1

The nondimensional structure parameter g(ζ) according to Wyngaard33 [Eqs. (4.19)]; derived from the scalar variance budget, [Eq. (4.29) with Eqs. (4.9) and (4.10) for ϕh and with Eq. (4.30) for ϕ]; and as found experimentally by Kohsiek16 for Ct2 [Eq. (4.32)].

Fig. 2
Fig. 2

Dependence of the refractive-index scale on the temperature and humidity scales for four electromagnetic wavelengths. Atmospheric conditions are typical for a snow or sea ice surface: P = 1000 hPa, T = −10°C, Q = 1.93 × 10−3 kg m−3 (i.e., relative humidity of 90%). A wavelength of 337 μm corresponds to a frequency of 890 GHz. Notice that the n*/At* axis changes scale at ±10.

Fig. 3
Fig. 3

The sensitivity coefficients Sz and Su* computed from Eqs. (5.12) and (5.13), respectively.

Fig. 4
Fig. 4

The sensitivity coefficients (a) St* and (b) Sq* for an electromagnetic wavelength of 0.55 μm. The ambient conditions are P = 1000 hPa, T = −10°C, Q = 1.93 × 10−3 (i.e., a relative humidity of 90%). Notice that the ordinate changes scale at ±5.

Fig. 5
Fig. 5

As in Fig. 4 but for a wavelength of 10.6 μm.

Fig. 6
Fig. 6

As in Fig. 4 but for a wavelength of 337 μm (a frequency of 890 GHz).

Fig. 7
Fig. 7

As in Fig. 4 but for radio wavelengths.

Fig. 8
Fig. 8

The sensitivity coefficients Szz and SU computed from Eqs. (6.18) and (6.19). The reference height is 10 m, the wind speed there is 5 m sec−1, and the neutral-stability drag coefficient referenced to 10 m is 1.172 × 10−3 (i.e., ξ = 1 cm). Notice that the ordinate changes scale at ±2.

Fig. 9
Fig. 9

The sensitivity coefficients (a) SΔT and (b) SΔQ for an electromagnetic wavelength of 0.55 μm. The reference height is 10 m, and the 10-m neutral-stability drag coefficient is CDN10 = 1.172 × 10−3 (i.e., ξ = 1 cm). The ambient conditions are P = 1000 hPa, T = −10°C, Q = 1.93 × 10−3 kg m−3 (i.e., relative humidity of 90%), and U = 5 m sec−1. Notice that the ordinate changes scale at ±5.

Fig. 10
Fig. 10

As in Fig. 9 but for a wavelength of 10.6 μm.

Fig. 11
Fig. 11

As in Fig. 9 but for a wavelength of 337 μm (a frequency of 890 GHz).

Fig. 12
Fig. 12

As in Fig. 9 but for radio wavelengths.

Tables (2)

Tables Icon

Table 1 The Coefficients in Eq. (3.38)

Tables Icon

Table 2 Values of the Coefficients in the Polynomials [Eq. (6.4)] That Predict zs/z0 for Temperature (i.e., zT/z0) and Water Vapor (i.e., zq/z0)

Equations (144)

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[ n ( x ) n ( x + r ) ] 2 ¯ = C n 2 r 2 / 3 ,
Φ 3 n ( k ) = 0.033 C n 2 k 11 / 3 exp ( k 2 / k m 2 ) ,
Φ 1 n ( k 1 ) = 0.249 C n 2 k 1 5 / 3 ,
ñ = f ( λ , p , t , q ) .
ñ = N + n ,
p = P + p ,
t = T + t ,
q = Q + q .
ñ = N + n = f ( λ , P , T , Q ) + ( f p | P , T , Q ) p + ( f t | P , T , Q ) t + ( f t | P , T , Q ) q .
N = f ( λ , P , T , Q )
n = ( f p | P , T , Q ) p + ( f t | P , T , Q ) t + ( f q ¯ | P , T , Q ) q .
n = A ( λ , P , T , Q ) t + B ( λ , P , T , Q ) q ,
A = f t | P , T , Q ,
B = f q | P , T , Q .
10 6 ( ñ υ 1 ) = ñ υ d + ñ υ w ,
ñ υ d = m 1 ( λ ) [ ( p e ) / t ] ,
ñ υ w = m 2 ( λ ) ( e / t ) ,
m 1 ( λ ) = 23.7134 + 6839.397 130 σ 2 + 45.473 38.9 σ 2 ,
m 2 ( λ ) = 64.8731 + 0.58058 σ 2 0.0071150 σ 4 + 0.0008851 σ 6 ,
σ = λ 1
10 6 ( ñ υ 1 ) = m 1 ( λ ) ( p / t ) + [ m 2 ( λ ) m 1 ( λ ) ] ( e / t ) .
e = 10 2 q t R / M u ,
10 6 ( ñ υ 1 ) = m 1 ( λ ) ( p / t ) + 4.6150 [ m 2 ( λ ) m 1 ( λ ) ] q .
A υ = 10 6 m 1 ( λ ) ( P / T 2 ) ,
B υ = 4.6150 × 10 6 [ m 2 ( λ ) m 1 ( λ ) ] .
10 6 ( ñ i 1 ) = ñ υ d + ñ i w ,
10 6 ( ñ i 1 ) = m 1 ( λ ) ( p / t ) 4.6150 m 1 ( λ ) q + ñ i w .
ñ i w = q [ 957 928 θ 0.4 ( χ 1 ) 1.03 θ 0.17 19.8 χ 2 + 8.2 χ 4 1.7 χ 8 + 3.747 × 10 6 12499 χ 2 ] ,
θ = t / 273.16 K ,
χ = ( 10 μ m ) / λ .
A i = A υ d + A i w ,
B i = B υ d + B i w .
A υ d = 10 6 m 1 ( λ ) ( P / T 2 ) ,
B υ d = 4.6150 × 10 6 m 1 ( λ ) .
A i w = 10 6 Q { 1.359 θ 0.6 ( χ 1 ) H 1 [ 0.6135 θ 0.83 + 0.5949 θ 0.43 ( χ 1 ) ] H 2 } ,
B i w = 10 6 [ 957 928 θ 0.4 ( χ 1 ) ] H 1 + 3.747 / ( 12449 χ 2 ) ,
θ = T / 273.16 K ,
H = 1.03 θ 0.17 19.8 χ 2 + 8.2 χ 4 1.7 χ 8 .
10 6 ( ñ r 1 ) = ñ r d + ñ r w ,
ñ r d = 77.6 ( p e ) / t ,
ñ r w = 72.0 ( e / t ) + 0.375 × 10 6 ( e / t 2 ) .
ñ r d = 77.6 ( p / t ) 358 q ,
ñ r w = ( 332 + 1.73 × 10 6 / t ) q .
A r d = 77.6 × 10 6 ( P / T 2 ) ,
B r d = 358 × 10 6 ,
A r w = 1.73 ( Q / T 2 ) ,
B r w = 332 × 10 6 + 1.73 / T .
A r = ( 77.6 × 10 6 P + 1.73 Q ) / T 2 ,
B r = 26 × 10 6 + 1.73 / T ,
B r = 1.73 / T .
10 6 ( ñ m 1 ) = ñ r d + ñ r w + ñ m w 1 + ñ m w 2 .
ñ m w 1 = q j = 1 4 α j ( 296 / t ) a j [ 1 β j ( 296 / t ) ] ) ( 0.303 / λ ) 2 j .
A m = A r d + A r w + A m w 1 ,
B m = B r d + B r w + B m w 1 .
A m w 1 = 10 6 ( Q / T ) j = 1 4 α j ( 296 / T ) a j ( 0.303 / λ ) 2 j × [ a j + β j ( 296 / T ) ( 1 + a j ) ] ,
B m w 1 = 10 6 ( Q / T ) j = 1 4 α j ( 296 / T ) a j [ 1 β j ( 296 / T ) ] ( 0.303 / λ ) 2 j .
u * 2 = u w ¯ ,
u * t * = w t ¯ ,
u * q * = w q ¯ .
L 1 = γ κ u * 2 T ¯ ( t * + 0.61 T ¯ ρ + 0.61 Q ¯ q * ) .
U ( z ) z = u * κ z ϕ m ( ζ ) ,
T ( z ) z = t * κ z ϕ h ( ζ ) ,
Q ( z ) z = q * κ z ϕ w ( ζ ) .
ϕ m ( ζ ) = ( 1 16 ζ ) 1 / 4 ,
ϕ h ( ζ ) = ϕ w ( ζ ) = ( 1 16 ζ ) 1 / 2 ;
ϕ m ( ζ ) = ϕ h ( ζ ) = ϕ w ( ζ ) = 1 + 7 ζ .
U ( z ) = ( u * / κ ) [ ln ( z / z 0 ) ψ m ( ζ ) ] ,
T ( z ) = T s + ( t * / κ ) [ ln ( z / z T ) ψ h ( ζ ) ] ,
Q ( z ) = Q s + ( q * / κ ) [ ln ( z / z Q ) ψ h ( ζ ) ] .
ψ m ( ζ ) = 2 ln [ ( 1 + x ) / 2 ] + ln [ ( 1 + x 2 ) / 2 ] arctan ( x ) + π / 2 ,
ψ h ( ζ ) = 2 ln [ ( 1 + x 2 ) / 2 ] ,
x = ( 1 16 ζ ) 1 / 4 .
ψ m ( ζ ) = ψ h ( ζ ) = 7 ζ .
z 2 / 3 C t 2 t * 2 = g t ( ζ ) ,
g t ( ζ ) = 4.9 ( 1 6.1 ζ ) 2 / 3 for ζ 0
= 4.9 ( 1 + 2.2 ζ 2 / 3 ) for ζ 0 .
z 2 / 3 C q 2 q * 2 = g q ( ζ ) ,
z 2 / 3 C t q t * q * = g t q ( ζ ) .
C n 2 = A 2 C t 2 + 2 A B C t q + B 2 C q 2 .
w n ¯ = A w t ¯ + B w q ¯ ,
n * = A t * + B q * .
z 2 / 3 C n 2 n * 2 = g n ( ζ ) .
2 u * t * 2 ϕ h ( ζ ) κ z = N t ,
2 u * q * 2 ϕ h ( ζ ) κ z = N q ,
2 u * n * 2 ϕ h ( ζ ) κ z = N n ,
2 u * t * q * ϕ h ( ζ ) κ z = N t q ,
β t N t 1 / 3 = 0.249 C t 2 ,
β q N q 1 / 3 = 0.249 C q 2 ,
β n N n 1 / 3 = 0.249 C n 2 ,
β t q N t q 1 / 3 = 0.249 C t q 2 ,
= u * 3 κ z ϕ ( ζ ) ,
ϕ ( ζ ) = [ 1 + 0.46 ( ζ ) 2 / 3 ] 3 / 2 for 2 ζ 0
= [ 1 + 2.3 ζ 3 / 5 ] 3 / 2 for 0 ζ 2 .
z 2 / 3 C t 2 t * 2 = z 2 / 3 C q 2 q * 2 = z 2 / 3 C n 2 n * 2 = z 2 / 3 C t q t * q * = 2 β ϕ h ( ζ ) 0.249 κ 2 / 3 ϕ ( ζ ) 1 / 3 = 5.92 ϕ h ( ζ ) ϕ ( ζ ) 1 / 3 g b ( ζ ) ,
ϕ ( ζ ) = ( 1 3 ζ ) 1 / 2 for ζ 0
= 1 + 6 ζ for ζ 0 ,
z 2 / 3 C t 2 t * 2 = 1.21 ( ζ ) 2 / 3 for 0.02 .
g t ( ζ ) = g q ( ζ ) = g t q ( ζ ) = g n ( ζ ) g ( ζ ) ,
C n 2 = z 2 / 3 n * 2 g ( ζ ) ;
n * A t * = 1 + B q * A t * .
B o = ρ c p u * t * L s u * q * = ρ c p L s t * q * t * K q * ,
n * A t * = 1 + B K A Bo .
C n 2 = z 2 / 3 g ( ζ ) ( A 2 t * 2 + 2 A B t * q * + B 2 q * 2 ) .
d C n 2 = C n 2 z d z + C n 2 ζ d ζ + C n 2 t * d t * + C n 2 q * d q * .
d ζ = ζ z d z + ζ u * d u * + ζ t * d t * + ζ q * d q * .
d C n 2 C n 2 = z C n 2 [ C n 2 z + C n 2 ζ ζ z ] d z z + u * C n 2 [ C n 2 ζ ζ u * ] d u * u * + t * C n 2 [ C n 2 t * + C n 2 ζ ζ t * ] d t * t * + q * C n 2 [ C n 2 q * + C n 2 ζ ζ q * ] d q * q * .
d C n 2 C n 2 = S z ( d z / z ) + S u * ( d u * / u * ) + S t * ( d t * / t * ) + S q * ( d q * / q * ) .
ζ = ζ T + ζ Q = γ κ z t * u * 2 T ¯ ( 1 + 0.61 T ¯ ρ + 0.61 Q ¯ 1 K B o ) ,
= ζ T ( 1 + 0.61 T ¯ ρ + 0.61 Q ¯ 1 K Bo ) .
S z = z C n 2 ( C n 2 z + C n 2 ζ ζ z )
= 2 3 ( 1 + 6.1 ζ 1 6.1 ζ ) for ζ 0
= 2 3 ( 1 + 2.2 ζ 2 / 3 1 + 2.2 ζ 2 / 3 ) fo r ζ 0 ;
S u * u * C n 2 ( C n 2 ζ ζ u * ) ,
= ( 4 / 3 ) ( 6.1 ) ζ 1 6.1 ζ for ζ 0 ,
= ( 4 / 3 ) ( 2.2 ) ζ 2 / 3 1 + 2.2 ζ 2 / 3 for ζ 0 ;
S t * t * C n 2 ( C n 2 t * + C n 2 ζ ζ t * ) ,
= 2 1 + ( B / K A Bo ) + ( 2 / 3 ) ( 6.1 ) ζ T 1 6.1 ζ for ζ 0
= 2 1 + ( B / K A Bo ) + ( 2 / 3 ) ( 2.2 ) ζ T ζ 1 / 3 1 + 2.2 ζ 2 / 3 for ζ 0 ;
S q * q * C n 2 ( C n 2 q * + C n 2 ζ ζ q * )
= 2 B / K A Bo 1 + ( B / K A Bo ) + ( 2 / 3 ) ( 6.1 ) ζ Q 1 6.1 ζ for ζ 0
= 2 B / K A Bo 1 + ( B / K A Bo ) + ( 2 / 3 ) ( 2.2 ) ζ Q ζ 1 / 3 1 + 2.2 ζ 2 / 3 for ζ 0 .
C D N h = [ κ / ln ( h / z 0 ) ] 2 .
10 3 C D N 10 = 1.10 + 0.072 ξ ,
R * = u * z 0 / ν ,
ln ( z s / z 0 ) = b 0 + b 1 ln R * + b 2 ( ln R * ) 2 ,
u * = U h C D N h 1 / 2 κ 1 ψ m ( ζ ) ,
t * = Δ T C D N h 1 / 2 κ 1 [ ln ( z T / z 0 ) + ψ h ( ζ ) ] ,
q * = Δ Q C D N h 1 / 2 κ 1 [ ln ( z Q / z 0 ) + ψ h ( ζ ) ] .
d u * u * = d U h U h + ζ ( ψ m / ζ ) κ C D N h 1 / 2 ψ m d ζ ζ ,
d t * t * = d Δ T Δ T + ζ ( ψ h / ζ ) κ C D N h 1 / 2 ln ( z T / z 0 ) ψ h d ζ ζ ,
d q * q * = d Δ Q Δ Q + ζ ( ψ h / ζ ) κ C D N h 1 / 2 ln ( z Q / z 0 ) ψ h ζ ζ .
ζ ζ = D 1 ( d z z 2 d U h U h + ζ T ζ d Δ T Δ T + ζ Q ζ d Δ Q Δ Q ) ,
D = 1 + 2 ζ ( ψ m / ζ ) κ C D N h 1 / 2 ψ m ζ ( ψ h / ζ ) κ C D N h 1 / 2 ln ( z T / z 0 ) ψ h .
ψ ( ζ ) = 0 ζ 1 ϕ ( ζ ) ζ d ζ .
ψ ζ = 1 ϕ ( ζ ) ζ .
D = 1 + 2 [ 1 ϕ m ( ζ ) ] κ C D N h 1 / 2 ψ m ( ζ ) 1 ϕ h ( ζ ) κ C D N h 1 / 2 ln ( z T / z 0 ) ψ h ( ζ ) .
d C n 2 C n 2 = S z z d z z + S U d U h U h + S Δ T d Δ T Δ T + S Δ Q d Δ Q Δ Q .
F = D 1 { [ 1 ϕ m ( ζ ) ] S u * κ C D N h 1 / 2 ψ m ( ζ ) + [ 1 ϕ h ( ζ ) ] [ 2 ½ S u * ] κ C D N h 1 / 2 ln ( z T / z 0 ) ψ h ( ζ ) } ,
S z z = S z + F ,
S U = S u * 2 F ,
S Δ T = S t * + ( ζ T / ζ ) F ,
S Δ Q = S q * + ( ζ Q / ζ ) F .
B o = Δ T K Δ Q .
C n 2 = z 2 / 3 n * 2 g ( ζ ) ,

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