Abstract

A two-week overwater experiment has been performed to verify the bulk aerodynamic method for calculating the index of refraction structure function parameter, CN2. Meteorological data were obtained on shipboard adjacent to a 13-km optical path over Monterey Bay. Model CN2 and measured CN2 values agree to within 33% on the average when there is spatial homogeneity. During periods of strong sea-surface temperature gradients, disagreements by a factor of 10 are common.

© 1981 Optical Society of America

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  1. K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
    [CrossRef]
  2. J. C. Wyngaard, Y. Izumi, S. A. Collins, J. Opt. Soc. Am. 61, 1646 (1971).
    [CrossRef]
  3. K. F. Schmitt, C. A. Friehe, C. H. Gibson, J. Phys. Oceangr. 8, 115 (1978).
    [CrossRef]
  4. M. L. Wesely, J. Geophys. Res. 84, 3696 (1979).
    [CrossRef]
  5. C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
    [CrossRef]
  6. C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).
  7. G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
    [CrossRef]
  8. S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).
  9. E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).
  10. G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).
  11. J. C. Wyngaard, S. F. Clifford, J. Atmos. Sci., 35, 1204 (1978).
    [CrossRef]
  12. C. A. Friehe, J. C. La Rue, F. H. Champagne, C. H. Gibson, G. F. Dreyer, J. Opt. Soc. Am. 65, 1502 (1975).
    [CrossRef]
  13. C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
    [CrossRef]
  14. J. C. Wyngaard, Workshop on Micrometeorology, AMS Publication (Science, Ephrata, Pa.1973), p. 127.
  15. C. A. Friehe, Appl. Opt. 16, 334 (1977).
    [CrossRef] [PubMed]
  16. J. C. Wyngaard, P. Lemone, J. Atmos. Sci. 37, 1573 (1980).
    [CrossRef]
  17. J. A. Businger, “Workshop on Micrometeorology,” AMS publication (Science Press, Ephrata, Pa., 1973), pp. 76–77.
  18. J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
    [CrossRef]
  19. J. R. Garratt, Mon. Weather Rev., 105, 915 (1975)
    [CrossRef]
  20. J. Kondo, Boundary Layer Meteorol. 9, 91 (1975).
    [CrossRef]

1981 (1)

G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
[CrossRef]

1980 (2)

C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
[CrossRef]

J. C. Wyngaard, P. Lemone, J. Atmos. Sci. 37, 1573 (1980).
[CrossRef]

1979 (2)

C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
[CrossRef]

M. L. Wesely, J. Geophys. Res. 84, 3696 (1979).
[CrossRef]

1978 (3)

K. F. Schmitt, C. A. Friehe, C. H. Gibson, J. Phys. Oceangr. 8, 115 (1978).
[CrossRef]

J. C. Wyngaard, S. F. Clifford, J. Atmos. Sci., 35, 1204 (1978).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

1977 (1)

1975 (3)

J. R. Garratt, Mon. Weather Rev., 105, 915 (1975)
[CrossRef]

J. Kondo, Boundary Layer Meteorol. 9, 91 (1975).
[CrossRef]

C. A. Friehe, J. C. La Rue, F. H. Champagne, C. H. Gibson, G. F. Dreyer, J. Opt. Soc. Am. 65, 1502 (1975).
[CrossRef]

1971 (2)

J. C. Wyngaard, Y. Izumi, S. A. Collins, J. Opt. Soc. Am. 61, 1646 (1971).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

Bradley, E. F.

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

Burk, S. D.

S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).

Businger, J. A.

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

J. A. Businger, “Workshop on Micrometeorology,” AMS publication (Science Press, Ephrata, Pa., 1973), pp. 76–77.

Champagne, F. H.

Clifford, S. F.

J. C. Wyngaard, S. F. Clifford, J. Atmos. Sci., 35, 1204 (1978).
[CrossRef]

Collins, S. A.

Cooper, A. W.

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

Crittenden, E. C.

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

Davidson, K. L.

G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
[CrossRef]

C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).

G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).

Dreyer, G. F.

Fairall, C. W.

G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
[CrossRef]

C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).

G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).

Friehe, C. A.

Garratt, J. R.

J. R. Garratt, Mon. Weather Rev., 105, 915 (1975)
[CrossRef]

Gibson, C. H.

Goroch, A.

S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).

Houlihan, T. M.

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).

Izumi, Y.

J. C. Wyngaard, Y. Izumi, S. A. Collins, J. Opt. Soc. Am. 61, 1646 (1971).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

Kalmbach, S. H.

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

Kondo, J.

J. Kondo, Boundary Layer Meteorol. 9, 91 (1975).
[CrossRef]

La Rue, J. C.

Lemone, P.

J. C. Wyngaard, P. Lemone, J. Atmos. Sci. 37, 1573 (1980).
[CrossRef]

Milne, E. A.

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

Panofsky, H.

S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).

Rodeback, G. W.

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

Schacher, G. E.

G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
[CrossRef]

C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
[CrossRef]

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).

G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).

Schmitt, K. F.

K. F. Schmitt, C. A. Friehe, C. H. Gibson, J. Phys. Oceangr. 8, 115 (1978).
[CrossRef]

Spiel, D. E.

G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).

Weinstein, A.

S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).

Wesely, M. L.

M. L. Wesely, J. Geophys. Res. 84, 3696 (1979).
[CrossRef]

Wyngaard, J. C.

J. C. Wyngaard, P. Lemone, J. Atmos. Sci. 37, 1573 (1980).
[CrossRef]

J. C. Wyngaard, S. F. Clifford, J. Atmos. Sci., 35, 1204 (1978).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

J. C. Wyngaard, Y. Izumi, S. A. Collins, J. Opt. Soc. Am. 61, 1646 (1971).
[CrossRef]

J. C. Wyngaard, Workshop on Micrometeorology, AMS Publication (Science, Ephrata, Pa.1973), p. 127.

Appl. Opt. (1)

Boundary Layer Meteorol. (4)

K. L. Davidson, T. M. Houlihan, C. W. Fairall, G. E. Schacher, Boundary Layer Meteorol. 15, 507 (1978).
[CrossRef]

C. W. Fairall, G. E. Schacher, K. L. Davidson, Boundary Layer Meteorol. 19, 81 (1980).
[CrossRef]

G. E. Schacher, K. L. Davidson, C. W. Fairall, Boundary Layer Meteorol. 20, 321 (1981).
[CrossRef]

J. Kondo, Boundary Layer Meteorol. 9, 91 (1975).
[CrossRef]

J. Appl. Meteorol. (1)

C. W. Fairall, K. L. Davidson, G. E. Schacher, J. Appl. Meteorol. 18, 1237 (1979).
[CrossRef]

J. Atmos. Sci. (2)

J. C. Wyngaard, P. Lemone, J. Atmos. Sci. 37, 1573 (1980).
[CrossRef]

J. A. Businger, J. C. Wyngaard, Y. Izumi, E. F. Bradley, J. Atmos. Sci. 28, 181 (1971).
[CrossRef]

J. Atmos. Sci., (1)

J. C. Wyngaard, S. F. Clifford, J. Atmos. Sci., 35, 1204 (1978).
[CrossRef]

J. Geophys. Res. (1)

M. L. Wesely, J. Geophys. Res. 84, 3696 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Oceangr. (1)

K. F. Schmitt, C. A. Friehe, C. H. Gibson, J. Phys. Oceangr. 8, 115 (1978).
[CrossRef]

Mon. Weather Rev. (1)

J. R. Garratt, Mon. Weather Rev., 105, 915 (1975)
[CrossRef]

Other (6)

J. A. Businger, “Workshop on Micrometeorology,” AMS publication (Science Press, Ephrata, Pa., 1973), pp. 76–77.

J. C. Wyngaard, Workshop on Micrometeorology, AMS Publication (Science, Ephrata, Pa.1973), p. 127.

C. W. Fairall, G. E. Schacher, K. L. Davidson, T. M. Houlihan, “Atmospheric Marine Boundary Layer Measurements in the Vicinity of San Nicholas Island,” NPS report NPS61-78-007 (Sept.1978).

S. D. Burk, A. Goroch, A. Weinstein, H. Panofsky, “Modeling the Refractive Index Structure in the Marine Planetary Boundary Layer,” NEPRF Technical Report TR78-03 (1979).

E. C. Crittenden, E. A. Milne, A. W. Cooper, G. W. Rodeback, S. H. Kalmbach, “Overwater Optical Scintillation Measurements during MAGAT-8,” NPS Report NPS-61-80-018 (1980).

G. E. Schacher, D. E. Spiel, C. W. Fairall, K. L. Davidson, “Details of NPS Shipboard and Aircraft Meteorological Measurements Systems,” NPS Report NPS-61-80-017 (1980).

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Figures (3)

Fig. 1
Fig. 1

Experimentation area.

Fig. 2
Fig. 2

C N 2 - optics vs C N 2 - bulk model. Open circles are nonequilibrium conditions, solid line is perfect agreement, and dashed lines are a factor of 2 disagreement.

Fig. 3
Fig. 3

Aircraft measured IR sea-surface temperature and C T 2 vs distance from shore. Optical path location is shown by vertical dark line.

Tables (1)

Tables Icon

Table I Wind Speed vs cDN at 10 m from Kondo20

Equations (24)

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

C N 2 = ( 79 × 10 - 6 P / T 2 ) 2 ( C T 2 + 0.113 C T Q + 3.1 × 10 - 3 C Q 2 ,
C y 2 = [ y ( x ) - y ( x + d ) ] 2 / d 2 / 3 ,
C T 2 = T * 2 Z - 2 / 3 f ( ζ ) ,
C Q 2 = Q * 2 Z - 2 / 3 A f ( ζ ) ,
C T Q = r T Q T * Q * Z - 2 / 3 A 1 / 2 f ( ζ ) ,
L = ( T / k g ) U * 2 ( T * + 6.1 × 10 - 4 T q * ) - 1 ,
U * = k U [ ln ( Z / Z 0 ) - ψ U ( ζ ) ] - 1 ,
T * = ( T - T S ) α T k [ ln ( Z / Z 0 T ) - Ψ T ( ζ ) ] - 1 ,
q * = ( q - q S ) α T k [ ln ( Z / Z 0 T ) - Ψ T ( ζ ) ] - 1 ,
U * = c D 1 / 2 U ,
T * = c T 1 / 2 ( T - T S ) .
q * = c T 1 / 2 ( q - q S ) .
c D 1 / 2 = ( k / ln Z / Z 0 ) [ 1 - ( ln Z / Z 0 ) - 1 Ψ U ( ζ ) ] - 1 .
c D 1 / 2 = k ( ln Z / Z 0 ) - 1 ,
c T N 1 / 2 = α T k ( ln Z / Z 0 T ) - 1 .
Z 0 = Z exp ( - k / c D N 1 / 2 ) ,
Z 0 T = Z exp ( - α T k / c T N 1 / 2 ) .
ζ = ζ 0 [ 1 - ( ln Z / Z 0 ) - 1 Ψ U ( ζ ) ] 2 1 - ( ln Z / Z 0 T ) - 1 Ψ T ( ζ ) ,
ζ 0 = ( k g Z / T ) ( c T N 1 / 2 / c D N ) ( Δ T + 6.1 × 10 - 4 T Δ q ) U - 2 .
Ψ U ( ζ < 0 ) = 2 ln [ ( 1 + x ) / 2 ] + ln [ ( 1 + x 2 ) / 2 ] - 2 tan - 1 ( x ) + π / 2 , x = ( 1 - 15 ζ ) 1 / 4 , Ψ U ( ζ > 0 ) = - 4.7 ζ .
Ψ T ( ζ < 0 ) = 2 ln [ ( 1 + x ) / 2 ] , x = ( 1 - 9 ζ ) 1 / 2 , Ψ T ( ζ > 0 ) = - 6.5 ζ .
T s = T s ( bulk ) - 0.025 T a - 0.1             ( U < 6 msec - 1 ) T s = T s ( bulk ) - 0.1 T a - 0.8 + U ( 0.117 + 0.0125 T a )             ( U > 6 msec - 1 ) .
Z L = g k Z T * ( T a + 273.16 ) U * 2 ( 1 + 0.07 B 0 ) .
B 0 = C p L H T * Q * ,

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