Abstract

The graphic presentation of relationships between a, b, R, and μ¯ in a previously published nomogram on calculation of inherent optical properties [Aust. J. Mar. Freshwater Res. 32, 533 (1981)] are replaced by explicit mathematical expressions.

© 1994 Optical Society of America

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References

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  1. V. A. Timofeeva, F. I. Gorobets, “On the relationship between the attenuation coefficients of collimated and diffuse light fluxes,” Izv. Atmos. Oceanic Phys. 3, 166–169 (1967).
  2. J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
    [CrossRef]
  3. D. M. Phillips, J. T. O. Kirk, “Study of the spectral variation of absorption and scattering in some Australian coastal waters,” Aust. J. Mar. Freshwater Res. 35, 635–644 (1984).
    [CrossRef]
  4. N. J. McCormick, G. E. Rinaldi, “Seawater optical property estimation from in situ irradiance measurements,” Appl. Opt. 28, 2605–2613 (1989).
    [CrossRef] [PubMed]
  5. J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
    [CrossRef]
  6. H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
    [CrossRef]
  7. J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
    [CrossRef]
  8. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).
  9. W. N. Vant, R. J. Davies-Colley, “Factors affecting clarity of New Zealand lakes,” N. Z. J. Mar. Freshwater Res. 18, 367–377(1984).
    [CrossRef]
  10. L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
    [CrossRef]
  11. A. D. Weidemann, T. T. Bannister, “Absorption and scattering coefficients in Irondequoit Bay,” Limnol. Oceanogr. 31, 567–583 (1986).
    [CrossRef]
  12. S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
    [CrossRef]
  13. R. L. Oliver, “Optical properties of waters in the Murray–Darling Basin, South-eastern Australia,” Aust. J. Mar. Freshwater Res. 41, 581–601 (1990).
    [CrossRef]
  14. J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
    [CrossRef]
  15. J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
    [CrossRef]
  16. J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467(1991).
    [CrossRef]
  17. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, San Diego, Calif., 1972).
  18. R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Inst. Monogr. 10, 11–30 (1961).
  19. J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411(1960).
  20. N. Hojerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
    [CrossRef]

1991

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467(1991).
[CrossRef]

1990

R. L. Oliver, “Optical properties of waters in the Murray–Darling Basin, South-eastern Australia,” Aust. J. Mar. Freshwater Res. 41, 581–601 (1990).
[CrossRef]

1989

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

N. J. McCormick, G. E. Rinaldi, “Seawater optical property estimation from in situ irradiance measurements,” Appl. Opt. 28, 2605–2613 (1989).
[CrossRef] [PubMed]

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

1987

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

1986

L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
[CrossRef]

A. D. Weidemann, T. T. Bannister, “Absorption and scattering coefficients in Irondequoit Bay,” Limnol. Oceanogr. 31, 567–583 (1986).
[CrossRef]

1984

W. N. Vant, R. J. Davies-Colley, “Factors affecting clarity of New Zealand lakes,” N. Z. J. Mar. Freshwater Res. 18, 367–377(1984).
[CrossRef]

D. M. Phillips, J. T. O. Kirk, “Study of the spectral variation of absorption and scattering in some Australian coastal waters,” Aust. J. Mar. Freshwater Res. 35, 635–644 (1984).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

1981

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

1975

N. Hojerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

1967

V. A. Timofeeva, F. I. Gorobets, “On the relationship between the attenuation coefficients of collimated and diffuse light fluxes,” Izv. Atmos. Oceanic Phys. 3, 166–169 (1967).

1961

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Inst. Monogr. 10, 11–30 (1961).

1960

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411(1960).

Bannister, T. T.

A. D. Weidemann, T. T. Bannister, “Absorption and scattering coefficients in Irondequoit Bay,” Limnol. Oceanogr. 31, 567–583 (1986).
[CrossRef]

Bowling, L. C.

L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
[CrossRef]

Brooks, C. M.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Davies-Colley, R. J.

W. N. Vant, R. J. Davies-Colley, “Factors affecting clarity of New Zealand lakes,” N. Z. J. Mar. Freshwater Res. 18, 367–377(1984).
[CrossRef]

Effler, S. W.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Field, S. D.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Gordon, H. R.

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

Gorobets, F. I.

V. A. Timofeeva, F. I. Gorobets, “On the relationship between the attenuation coefficients of collimated and diffuse light fluxes,” Izv. Atmos. Oceanic Phys. 3, 166–169 (1967).

Hojerslev, N.

N. Hojerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

Kirk, J. T. O.

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467(1991).
[CrossRef]

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

D. M. Phillips, J. T. O. Kirk, “Study of the spectral variation of absorption and scattering in some Australian coastal waters,” Aust. J. Mar. Freshwater Res. 35, 635–644 (1984).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

McCormick, N. J.

Meyer, M.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Oliver, R. L.

R. L. Oliver, “Optical properties of waters in the Murray–Darling Basin, South-eastern Australia,” Aust. J. Mar. Freshwater Res. 41, 581–601 (1990).
[CrossRef]

Perkins, M. G.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, San Diego, Calif., 1972).

Phillips, D. M.

D. M. Phillips, J. T. O. Kirk, “Study of the spectral variation of absorption and scattering in some Australian coastal waters,” Aust. J. Mar. Freshwater Res. 35, 635–644 (1984).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Inst. Monogr. 10, 11–30 (1961).

Rinaldi, G. E.

Steane, M. S.

L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
[CrossRef]

Timofeeva, V. A.

V. A. Timofeeva, F. I. Gorobets, “On the relationship between the attenuation coefficients of collimated and diffuse light fluxes,” Izv. Atmos. Oceanic Phys. 3, 166–169 (1967).

Tyler, J. E.

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411(1960).

Tyler, P. A.

L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
[CrossRef]

Vant, W. N.

W. N. Vant, R. J. Davies-Colley, “Factors affecting clarity of New Zealand lakes,” N. Z. J. Mar. Freshwater Res. 18, 367–377(1984).
[CrossRef]

Weidemann, A. D.

A. D. Weidemann, T. T. Bannister, “Absorption and scattering coefficients in Irondequoit Bay,” Limnol. Oceanogr. 31, 567–583 (1986).
[CrossRef]

Zaneveld, J. R. V.

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

Appl. Opt.

Aust. J. Mar. Freshwater Res.

J. T. O. Kirk, “Estimation of the scattering coefficient of natural waters using underwater irradiance measurements,” Aust. J. Mar. Freshwater Res. 32, 533–539 (1981).
[CrossRef]

D. M. Phillips, J. T. O. Kirk, “Study of the spectral variation of absorption and scattering in some Australian coastal waters,” Aust. J. Mar. Freshwater Res. 35, 635–644 (1984).
[CrossRef]

R. L. Oliver, “Optical properties of waters in the Murray–Darling Basin, South-eastern Australia,” Aust. J. Mar. Freshwater Res. 41, 581–601 (1990).
[CrossRef]

J. T. O. Kirk, “A Monte Carlo study of the nature of the underwater light field in, and the relationships between optical properties of, turbid yellow waters,” Aust. J. Mar. Freshwater Res. 32, 517–532 (1981).
[CrossRef]

Bull. Scripps Inst. Oceanogr.

J. E. Tyler, “Radiance distribution as a function of depth in an underwater environment,” Bull. Scripps Inst. Oceanogr. 7, 363–411(1960).

Freshwater Biol.

L. C. Bowling, M. S. Steane, P. A. Tyler, “The spectral distribution and attenuation of underwater irradiance in Tasmanian waters,” Freshwater Biol. 16, 313–335 (1986).
[CrossRef]

Izv. Atmos. Oceanic Phys.

V. A. Timofeeva, F. I. Gorobets, “On the relationship between the attenuation coefficients of collimated and diffuse light fluxes,” Izv. Atmos. Oceanic Phys. 3, 166–169 (1967).

Limnol. Oceanogr.

J. T. O. Kirk, “The upwelling light stream in natural waters,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

H. R. Gordon, “Absorption and scattering estimates from irradiance measurements: Monte Carlo simulations,” Limnol. Oceanogr. 36, 769–777 (1991).
[CrossRef]

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34, 1442–1452 (1989).
[CrossRef]

A. D. Weidemann, T. T. Bannister, “Absorption and scattering coefficients in Irondequoit Bay,” Limnol. Oceanogr. 31, 567–583 (1986).
[CrossRef]

N. Hojerslev, “A spectral light absorption meter for measurements in the sea,” Limnol. Oceanogr. 20, 1024–1034 (1975).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr. 36, 455–467(1991).
[CrossRef]

N. Z. J. Mar. Freshwater Res.

W. N. Vant, R. J. Davies-Colley, “Factors affecting clarity of New Zealand lakes,” N. Z. J. Mar. Freshwater Res. 18, 367–377(1984).
[CrossRef]

Union Geod. Geophys. Inst. Monogr.

R. W. Preisendorfer, “Application of radiative transfer theory to light measurements in the sea,” Union Geod. Geophys. Inst. Monogr. 10, 11–30 (1961).

Water Res. Bull.

S. W. Effler, C. M. Brooks, M. G. Perkins, M. Meyer, S. D. Field, “Aspects of the underwater light field of eight central New York lakes,” Water Res. Bull. 23, 1193–1201 (1987).
[CrossRef]

Other

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, San Diego, Calif., 1972).

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976).

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Tables (1)

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Table 1 Test of Algorithm for Calculating Absorption and Scattering Coefficients from Irradiance Dataa

Equations (10)

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

a = μ ¯ K E ,
K d ( z m ) = 1 μ 0 [ a 2 + G ( μ 0 ) a b ] 1 / 2 ,
G ( μ 0 ) = 0 . 473 μ 0 0 . 218 .
K E ( z m ) = 1 μ 0 [ a 2 + G E ( μ 0 ) a b ] 1 / 2 .
μ ¯ ( z m ) = μ 0 [ 1 + G E ( μ 0 ) b / a ] 1 / 2 ,
G E ( μ 0 ) = 0 . 473 μ 0 0 . 22 .
R ( z m ) = ( b / a ) 103 + ( b / a ) .
b a = 103 R ( z m ) 1 R ( z m ) ,
μ ¯ ( z m ) = μ 0 { 1 R ( z m ) 1 + R ( z m ) [ 103 G E ( μ 0 ) 1 ] } 1 / 2 ,
a = μ 0 K E ( z m ) { 1 R ( z m ) 1 + R ( z m ) [ 103 G E ( μ 0 ) 1 ] } 1 / 2

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