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.

© 1975 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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).
    [Crossref]
  4. J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1246 (1971).
    [Crossref]
  5. E. K. Webb, Appl. Optics 3, 1329 (1964).
    [Crossref]
  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).
    [Crossref]
  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).
    [Crossref]
  10. G. T. Phelps and S. Pond, J. Atmos. Sci. 28, 918 (1971).
    [Crossref]
  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).
    [Crossref]
  13. C. H. Gibson, G. R. Stegen, and R. B. Williams, J. Fluid Mech. 41, 153 (1970).
    [Crossref]
  14. R. M. Williams, 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).
    [Crossref]
  16. H. Barrell and J. E. Sears, Philos. Trans. R. Soc. London, Ser. A 238, 1 (1939).
    [Crossref]
  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).
    [Crossref]
  19. S. Corrsin, J. Appl. Phys. 22, 469 (1951).
    [Crossref]
  20. H. Roll, Physics of Marine Atmosphere (Academic, New York, 1965).

1973 (2)

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

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

1972 (4)

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

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

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

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

1971 (2)

1970 (2)

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

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

1964 (1)

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

1960 (1)

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

1951 (1)

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

1939 (1)

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

Alcaraz, E. C.

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

Barrell, H.

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

Boston, N. E. J.

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

Burling, R. W.

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

Clifford, S. F.

Collins, S. A.

Corrsin, S.

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

Coté, O. R.

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

Dreyer, G. F.

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

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

Elliott, J. A.

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

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).
[Crossref]

Gjessing, D. T.

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

Golton, E.

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

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).
[Crossref]

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

Kaimal, J. C.

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

Kjelaas, A. G.

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

Lawrence, R. S.

Ochs, G. R.

Phelps, G. T.

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

Pond, S.

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

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).
[Crossref]

Stegen, G. R.

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

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).
[Crossref]

Wesley, M. L.

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

Williams, R. B.

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

Williams, R. M.

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

Wyngaard, J. C.

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

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

Appl. Optics (1)

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

Boundary-Layer Meteorol. (1)

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

IRE Trans. (1)

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

J. Appl. Phys. (1)

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

J. Atmos. Sci. (1)

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

J. Fluid Mech. (3)

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

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

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

J. Geophys. Res. (1)

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

J. Opt. Soc. Am. (3)

Philos. Trans. R. Soc. London (1)

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

Quart. J. R. Meterol. Soc. (1)

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

Other (6)

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.

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

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

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.

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

FIG. 1
FIG. 1

Variation of fluctuating temperature coefficient of refractivity of dry air with mean temperature. Pressure is 760 torr. –, optical frequencies from Barrell and Sears (Ref. 16); – · –, optical frequencies from Tatarskii (Ref. 2); — —, radio frequencies from Tatarskii (Ref. 2).

FIG. 2
FIG. 2

Variation of fluctuating temperature coefficient of refractivity of dry air with mean pressure. Temperature = 15 °C. —, optical frequencies from Barrell and Sears (Ref. 16); – · –, optical frequencies from Tatarskii (Ref. 2); — —, radio frequencies from Tatarskii (Ref. 2).

FIG. 3
FIG. 3

Spar buoy FLIP used for open-ocean experiments. Atmospheric sensors are located on end of 20 m boom. Wind direction is out of page toward reader.

FIG. 4
FIG. 4

Calibration of Lyman-alpha humidiometer. (Obtained at Naval Undersea Center Hygrometer Facility.)

FIG. 5
FIG. 5

Typical time series of humidity (upper curve) and temperature (lower curve) at the Salton Sea.

FIG. 6
FIG. 6

Typical time series of humidity (upper curve) and temperature (lower curve) over the open ocean.

FIG. 7
FIG. 7

Typical time series of squared refractive-index fluctuations and the corresponding time series for temperature times humidity, humidity squared, and temperature squared from the Salton Sea data shown in Fig. 5.

FIG. 8
FIG. 8

Typical time series for the same variables as shown in Fig. 7 but from the open ocean data shown in Fig. 6.

FIG. 9
FIG. 9

Power spectra of humidity (upper curve) and temperature (lower curve) from the open ocean (FLIP) data. The straight line (middle curve) has a - 5 3 slope.

FIG. 10
FIG. 10

Power spectra of humidity (upper curve) and temperature (lower curve) from the Salton Sea data. The straight line (middle curve) has a - 5 3 slope.

FIG. 11
FIG. 11

Negative of cospectrum of temperature and humidity for the Salton Sea. The straight line has a slope of - 5 3.

FIG. 12
FIG. 12

Cospectrum of temperature and humidity for the open ocean (FLIP). The straight line has a slope of - 5 3.

FIG. 13
FIG. 13

Refractive index power spectrum and contributions from the Salton Sea data. —, refractive index; – – –, temperature contribution, – · –, negative of temperature–humidity contribution; and ⋯, humidity contribution.

FIG. 14
FIG. 14

Refractive index power spectrum and contributions for the open ocean, (FLIP) data. —, refractive index; ⋯, temperature contribution, - - - - -, temperature–humidity contribution; and – · –, humidity contribution.

Tables (2)

Tables Icon

TABLE I Average experimental conditions.

Tables Icon

TABLE II Variance of n′ × 103 from Eq. (18).

Equations (32)

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

[ n ( x ) - n ( x + r ) ] 2 ¯ = C n 2 r 2 / 3 ,
Φ n ( k 1 ) = 0.25 C n 2 k 1 - 5 / 3 ,
N = N ( T , P , Q ) ,
d N = ( N T ) P , Q d T + ( N P ) T , Q d P + ( N Q ) T , P d Q .
n ( N T ) T ¯ , P 0 , Q ¯ θ + ( N P ) T ¯ , P 0 , Q ¯ p + ( N Q ) T ¯ , P 0 , Q ¯ q ,
N = A ( λ ) P { 1 + ( 1.049 - 0.157 T ) P × 10 - 6 } 1 + T / 273.16 - B ( λ ) f 1 + T / 273.16 = ( N d . a . + N w ) ,
A ( λ ) = 0.378125 + 0.0021414 λ 2 + 0.00001794 λ 4 , B ( λ ) = 0.0624 - 0.000680 λ 2 ,
( N d . a . ) T | T ¯ , P 0 = - A ( λ ) 1 + T ¯ / 273.16 [ [ 1 + ( 1.049 - 0.157 T ¯ ) P 0 × 10 - 6 ] P 0 273.16 ( 1 + T ¯ / 273.16 ) + 1.57 × 10 - 7 P 0 2 ] ,
( N d . a . ) P | T ¯ , P 0 = A ( λ ) 1 + T ¯ / 273.16 [ 1 + 2 ( 1.049 - 0.157 T ¯ ) P 0 × 10 - 6 ] .
n d . a . = ( N d . a . ) T | T ¯ , P 0 θ + ( N d . a . ) P | T ¯ , P 0 p .
n r = - 79 P m T ¯ a 2 θ + 79 T ¯ a p m             ( radio frequencies ) , n d . a . = - 80 P m T ¯ a 2 θ             ( optical ) ,
n d . a . = - 1.00 θ + 0.366 p .
f P = r 0.622 + r ,
ρ v 0.622 ρ d . a . f P ,             or ρ v 0.622 29 82.06 T a ( P 760 ) f P ,             or ρ v 2.892 × 10 - 4 f T a ,             g / cm 3 ,
Q = 10 6 ρ v ,             μ g / cm 3 .
Q = 2.892 × 10 2 f T a .
n w = N w Q | T ¯ , P 0 , Q ¯ q = - B ( λ ) 1 + T ¯ / 273.16 T ¯ a 2.892 × 10 2 q , n w = - 0.05667 q .
N w T | P 0 , Q ¯ , T ¯ = B ( λ ) f ( 1 + T ¯ / 273.16 ) 2 273.16 2 × 10 - 4 Q ¯ ,
n = - 1.00 θ + 0.366 p - 0.05667 q ,
p s 2.6 τ ¯ s ,
C D = ( τ ¯ s / ρ ) / U 2 1.0 × 10 - 3 ,
n = - 1.00 θ - 0.05667 q .
n 2 ¯ = 1.00 θ 2 ¯ + 0.113 θ q ¯ + 3.215 × 10 - 3 q 2 ¯ ,
Φ n ( f ) = 1.00 Φ θ ( f ) + 0.113 Co θ q ( f ) + 3.215 × 10 - 3 Φ q ( f ) ,
n 2 ¯ = 0 Φ n ( f ) d f , θ 2 ¯ = 0 Φ θ ( f ) d f , θ q ¯ = 0 Co θ q ( f ) d f ,
Φ θ ( k 1 ) = β θ χ θ - 1 / 3 k 1 - 5 / 3 ,
Φ q ( k 1 ) = β q χ q - 1 / 3 k 1 - 5 / 3 ,
Φ θ ( k 1 ) = 0.25 C T 2 k 1 - 5 / 3 .
Φ q ( k 1 ) = 0.25 C Q 2 k 1 - 5 / 3 .
Φ θ ( f ) ~ C T 2 f - 5 / 3 ,
Φ q ( f ) ~ C Q 2 f - 5 / 3 .
Co θ q ( k 1 ) = 0.25 C T Q k 1 - 5 / 3 .