Abstract

The variance and power spectrum of atmospheric optical refractive-index fluctuations are shown to be composed of three terms: the variance and power spectra of the temperature and humidity fluctuations and the correlation and cospectrum of the temperature and humidity fluctuations, respectively. Humidity fluctuations are found to be significant because of the correlation term. The signs of the temperature-humidity correlation and cospectrum can be positive or negative, and therefore can add to or subtract from refractive-index fluctuations caused by only temperature fluctuations. The results of two atmospheric boundary-layer experiments are reported, which show the large effect of the temperature-humidity correlation term. For cold air blowing over warm ocean water, the correlation term was positive and accounted for 17% of the total refractive-index variance. For dry hot desert air blowing over the cold Salton Sea, the correlation was -268% of the total, effectively cancelling the contribution due to temperature variance.

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  1. V. I. Tatarskii, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (Dover, New York, 1961).
  2. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Technical Information Services, Springfield, Va, 1971), p. 102.
  3. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
  4. J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).
  5. E. K. Webb, Appl. Optics 3, 1329 (1964).
  6. C. A. Friehe, C. H. Gibson, and G. F. Dreyer, J. Opt. Soc. Am. 62, 1341A (1972).
  7. M. L. Wesley and E. C. Alcaraz, J. Geophys. Res. 78, 6224 (1973).
  8. E. E. Gossard, IRE Trans. AP-8, 186 (1960).
  9. D. T. Gjessing, A. G. Kjelaas, and E. Golton, Boundary-Layer Meteorol. 4, 475 (1973).
  10. G. T. Phelps and S. Pond, J. Atmos. Sci. 28, 918 (1971).
  11. G. F. Dreyer, Ph.D. thesis (University of California, 1974).
  12. N. E. J. Boston and R. W. Burling, J. Fluid Mech. 55, 473 (1972).
  13. C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).
  14. R. M. Williams, Jr., Ph.D. thesis (Oregon State University, 1974).
  15. J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).
  16. H. Barrell and J. E. Sears, Philos. Trans. R. Soc. London, Ser. A 238, 1 (1939).
  17. Note that changes of refractive index of air are, in general, not proportional to changes of mass density, as is often assumed, but to number density and the type of gas molecule. The proportionality is corrected for a gas of only one component. A comment by E. K. Webb brought this to our attention.
  18. J. A. Elliott, J. Fluid Mech. 54, 427 (1972).
  19. S. Corrsin, J. Appl. Phys. 22, 469 (1951).
  20. H. Roll, Physics of Marine Atmosphere (Academic, New York, 1965).

Alcaraz, E. C.

M. L. Wesley and E. C. Alcaraz, J. Geophys. Res. 78, 6224 (1973).

Barrell, H.

H. Barrell and J. E. Sears, Philos. Trans. R. Soc. London, Ser. A 238, 1 (1939).

Boston, N. E. J.

N. E. J. Boston and R. W. Burling, J. Fluid Mech. 55, 473 (1972).

Burling, R. W.

N. E. J. Boston and R. W. Burling, J. Fluid Mech. 55, 473 (1972).

Clifford, S. F.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).

Collins, S. A.

J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).

Corrsin, S.

S. Corrsin, J. Appl. Phys. 22, 469 (1951).

Coté, O. R.

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).

Dreyer, G. F.

G. F. Dreyer, Ph.D. thesis (University of California, 1974).

C. A. Friehe, C. H. Gibson, and G. F. Dreyer, J. Opt. Soc. Am. 62, 1341A (1972).

Elliott, J. A.

J. A. Elliott, J. Fluid Mech. 54, 427 (1972).

Friehe, C. A.

C. A. Friehe, C. H. Gibson, and G. F. Dreyer, J. Opt. Soc. Am. 62, 1341A (1972).

Gibson, C. H.

C. A. Friehe, C. H. Gibson, and G. F. Dreyer, J. Opt. Soc. Am. 62, 1341A (1972).

C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).

Gjessing, D. T.

D. T. Gjessing, A. G. Kjelaas, and E. Golton, Boundary-Layer Meteorol. 4, 475 (1973).

Golton, E.

D. T. Gjessing, A. G. Kjelaas, and E. Golton, Boundary-Layer Meteorol. 4, 475 (1973).

Gossard, E. E.

E. E. Gossard, IRE Trans. AP-8, 186 (1960).

Izumi, Y.

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).

J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).

Kaimal, J. C.

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).

Kjelaas, A. G.

D. T. Gjessing, A. G. Kjelaas, and E. Golton, Boundary-Layer Meteorol. 4, 475 (1973).

Lawrence, R. S.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).

Ochs, G. R.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).

Phelps, G. T.

G. T. Phelps and S. Pond, J. Atmos. Sci. 28, 918 (1971).

Pond, S.

G. T. Phelps and S. Pond, J. Atmos. Sci. 28, 918 (1971).

Roll, H.

H. Roll, Physics of Marine Atmosphere (Academic, New York, 1965).

Sears, J. E.

H. Barrell and J. E. Sears, Philos. Trans. R. Soc. London, Ser. A 238, 1 (1939).

Stegen, G. R.

C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (Dover, New York, 1961).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Technical Information Services, Springfield, Va, 1971), p. 102.

Webb, E. K.

E. K. Webb, Appl. Optics 3, 1329 (1964).

Wesley, M. L.

M. L. Wesley and E. C. Alcaraz, J. Geophys. Res. 78, 6224 (1973).

Williams, R. B.

C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).

Williams, Jr., R. M.

R. M. Williams, Jr., Ph.D. thesis (Oregon State University, 1974).

Wyngaard, J. C.

J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).

Other (20)

V. I. Tatarskii, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (Dover, New York, 1961).

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation, TT-68-50464 (National Technical Information Services, Springfield, Va, 1971), p. 102.

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).

J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).

E. K. Webb, Appl. Optics 3, 1329 (1964).

C. A. Friehe, C. H. Gibson, and G. F. Dreyer, J. Opt. Soc. Am. 62, 1341A (1972).

M. L. Wesley and E. C. Alcaraz, J. Geophys. Res. 78, 6224 (1973).

E. E. Gossard, IRE Trans. AP-8, 186 (1960).

D. T. Gjessing, A. G. Kjelaas, and E. Golton, Boundary-Layer Meteorol. 4, 475 (1973).

G. T. Phelps and S. Pond, J. Atmos. Sci. 28, 918 (1971).

G. F. Dreyer, Ph.D. thesis (University of California, 1974).

N. E. J. Boston and R. W. Burling, J. Fluid Mech. 55, 473 (1972).

C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).

R. M. Williams, Jr., Ph.D. thesis (Oregon State University, 1974).

J. C. Kaimal, J. C. Wyngaard, Y. Izumi, and O. R. Coté, Quart. J. R. Meterol. Soc. 98, 563 (1972).

H. Barrell and J. E. Sears, Philos. Trans. R. Soc. London, Ser. A 238, 1 (1939).

Note that changes of refractive index of air are, in general, not proportional to changes of mass density, as is often assumed, but to number density and the type of gas molecule. The proportionality is corrected for a gas of only one component. A comment by E. K. Webb brought this to our attention.

J. A. Elliott, J. Fluid Mech. 54, 427 (1972).

S. Corrsin, J. Appl. Phys. 22, 469 (1951).

H. Roll, Physics of Marine Atmosphere (Academic, New York, 1965).

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