Abstract

A new model for seawater scattering was developed, in which Gibbs function was used exclusively to derive the thermodynamic parameters that are associated with density fluctuation. Because Gibbs function was determined empirically from highly accurate measurements of a group of thermodynamic variables and is valid for SA up to 120 g kg−1 (Deep-Sea Research I, 55, 1639, 2008), we expect the model is also valid over the extended range of salinity. The model agrees with the measurements by Morel (Cahiers Oceanographiques, 20, 157, 1968) with an average difference of −0.6% for S = 0 and 2.7% for S = 38.4. The scattering by seawater as predicted increases with salinity in a non-linear fashion, and linear extrapolation of scattering based on Morel’s measurements would overestimate by up to 30%. The extrapolation of ZHH09 model (Optics Express, 17, 5698, 2009), which is valid for SA up to 40 g kg−1, however, agrees with the prediction within ± 2.5% over the entire range of salinity. Even though there are no measurements available for validation, the results suggested that the uncertainty is limited in using the newly developed model in estimating the scattering by seawater of high salinity.

© 2009 OSA

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References

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  1. A. Morel, “Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures,” J. Chim. Phys. 10, 1359–1366 (1966).
  2. A. Morel, “Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures,” Cah. Oceanogr. 20, 157–162 (1968).
  3. C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, 1994).
  4. E. Boss and W. S. Pegau, “Relationship of light scattering at an angle in the backward direction to the backscattering coefficient,” Appl. Opt. 40(30), 5503–5507 (2001).
    [CrossRef]
  5. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17(7), 5698–5710 (2009).
    [CrossRef] [PubMed]
  6. A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” Ann. Phys. 338(16), 1275–1298 (1910).
    [CrossRef]
  7. X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17(3), 1671–1678 (2009).
    [CrossRef] [PubMed]
  8. B. W. Logan and D. E. Cebulski, “Semimentary Environments of Shark Bay, Western Australian,” in Carbon Sedimentation and Environments, Shark Bay, Western Australia, B. W. Logan, G. R. Davies, J. F. Read, and D. E. Cebulski, eds. (The American Association of Petroleum Geologists, Tulsa, 1970), p. 205.
  9. F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
    [CrossRef]
  10. R. Feistel, “A Gibbs function for seawater thermodynamics for −6 to 80 °C and salinity up to 120 g kg−1,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(12), 1639–1671 (2008).
    [CrossRef]
  11. R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
    [CrossRef]
  12. R. Feistel and G. M. Marion, “A Gibbs-Pitzer function for high-salinity seawater thermodynamics,” Prog. Oceanogr. 74(4), 515–539 (2007).
    [CrossRef]
  13. F. J. Millero and W. H. Leung, “The thermodynamics of seawater at one atmosphere,” Am. J. Sci. 276, 1035–1077 (1976).
    [CrossRef]
  14. R. W. Austin, and G. Halikas, “The index of refraction of seawater,” (Scripps Institute of Oceanography, La Jolla, 1974), p. 121.
  15. Y. Miyake, “Chemical studies of the Western Pacific Ocean. IV. The refractive index of sea water,” Bull. Chem. Soc. Jpn. 14(6), 239–242 (1939).
    [CrossRef]
  16. X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34(18), 3477–3480 (1995).
    [CrossRef] [PubMed]
  17. R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
    [CrossRef]
  18. W. Wagner and A. Pruß, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2), 387–535 (2002).
    [CrossRef]

2009 (2)

2008 (2)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

R. Feistel, “A Gibbs function for seawater thermodynamics for −6 to 80 °C and salinity up to 120 g kg−1,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(12), 1639–1671 (2008).
[CrossRef]

2007 (1)

R. Feistel and G. M. Marion, “A Gibbs-Pitzer function for high-salinity seawater thermodynamics,” Prog. Oceanogr. 74(4), 515–539 (2007).
[CrossRef]

2003 (1)

R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
[CrossRef]

2002 (1)

W. Wagner and A. Pruß, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2), 387–535 (2002).
[CrossRef]

2001 (1)

1995 (1)

1976 (2)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[CrossRef]

F. J. Millero and W. H. Leung, “The thermodynamics of seawater at one atmosphere,” Am. J. Sci. 276, 1035–1077 (1976).
[CrossRef]

1968 (1)

A. Morel, “Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures,” Cah. Oceanogr. 20, 157–162 (1968).

1966 (1)

A. Morel, “Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures,” J. Chim. Phys. 10, 1359–1366 (1966).

1939 (1)

Y. Miyake, “Chemical studies of the Western Pacific Ocean. IV. The refractive index of sea water,” Bull. Chem. Soc. Jpn. 14(6), 239–242 (1939).
[CrossRef]

1910 (1)

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” Ann. Phys. 338(16), 1275–1298 (1910).
[CrossRef]

Boss, E.

Einstein, A.

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” Ann. Phys. 338(16), 1275–1298 (1910).
[CrossRef]

Farinato, R. S.

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[CrossRef]

Feistel, R.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

R. Feistel, “A Gibbs function for seawater thermodynamics for −6 to 80 °C and salinity up to 120 g kg−1,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(12), 1639–1671 (2008).
[CrossRef]

R. Feistel and G. M. Marion, “A Gibbs-Pitzer function for high-salinity seawater thermodynamics,” Prog. Oceanogr. 74(4), 515–539 (2007).
[CrossRef]

R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
[CrossRef]

Fry, E. S.

He, M.-X.

Hu, L.

Leung, W. H.

F. J. Millero and W. H. Leung, “The thermodynamics of seawater at one atmosphere,” Am. J. Sci. 276, 1035–1077 (1976).
[CrossRef]

Marion, G. M.

R. Feistel and G. M. Marion, “A Gibbs-Pitzer function for high-salinity seawater thermodynamics,” Prog. Oceanogr. 74(4), 515–539 (2007).
[CrossRef]

McDougall, T. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

Millero, F. J.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

F. J. Millero and W. H. Leung, “The thermodynamics of seawater at one atmosphere,” Am. J. Sci. 276, 1035–1077 (1976).
[CrossRef]

Miyake, Y.

Y. Miyake, “Chemical studies of the Western Pacific Ocean. IV. The refractive index of sea water,” Bull. Chem. Soc. Jpn. 14(6), 239–242 (1939).
[CrossRef]

Morel, A.

A. Morel, “Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures,” Cah. Oceanogr. 20, 157–162 (1968).

A. Morel, “Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures,” J. Chim. Phys. 10, 1359–1366 (1966).

Pegau, W. S.

Pruß, A.

W. Wagner and A. Pruß, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2), 387–535 (2002).
[CrossRef]

Quan, X.

Rowell, R. L.

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[CrossRef]

Wagner, W.

W. Wagner and A. Pruß, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2), 387–535 (2002).
[CrossRef]

Wright, D. G.

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

Zhang, X.

Am. J. Sci. (1)

F. J. Millero and W. H. Leung, “The thermodynamics of seawater at one atmosphere,” Am. J. Sci. 276, 1035–1077 (1976).
[CrossRef]

Ann. Phys. (1)

A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” Ann. Phys. 338(16), 1275–1298 (1910).
[CrossRef]

Appl. Opt. (2)

Bull. Chem. Soc. Jpn. (1)

Y. Miyake, “Chemical studies of the Western Pacific Ocean. IV. The refractive index of sea water,” Bull. Chem. Soc. Jpn. 14(6), 239–242 (1939).
[CrossRef]

Cah. Oceanogr. (1)

A. Morel, “Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures,” Cah. Oceanogr. 20, 157–162 (1968).

Deep Sea Res. Part I Oceanogr. Res. Pap. (2)

F. J. Millero, R. Feistel, D. G. Wright, and T. J. McDougall, “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(1), 50–72 (2008).
[CrossRef]

R. Feistel, “A Gibbs function for seawater thermodynamics for −6 to 80 °C and salinity up to 120 g kg−1,” Deep Sea Res. Part I Oceanogr. Res. Pap. 55(12), 1639–1671 (2008).
[CrossRef]

J. Chem. Phys. (1)

R. S. Farinato and R. L. Rowell, “New values of the light scattering depolarization and anisotropy of water,” J. Chem. Phys. 65(2), 593–595 (1976).
[CrossRef]

J. Chim. Phys. (1)

A. Morel, “Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures,” J. Chim. Phys. 10, 1359–1366 (1966).

J. Phys. Chem. Ref. Data (1)

W. Wagner and A. Pruß, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2), 387–535 (2002).
[CrossRef]

Opt. Express (2)

Prog. Oceanogr. (2)

R. Feistel, “A new extended Gibbs thermodynamic potential of seawater,” Prog. Oceanogr. 58(1), 43–114 (2003).
[CrossRef]

R. Feistel and G. M. Marion, “A Gibbs-Pitzer function for high-salinity seawater thermodynamics,” Prog. Oceanogr. 74(4), 515–539 (2007).
[CrossRef]

Other (3)

R. W. Austin, and G. Halikas, “The index of refraction of seawater,” (Scripps Institute of Oceanography, La Jolla, 1974), p. 121.

C. D. Mobley, Light and water: radiative transfer in natural waters (Academic Press, San Diego, 1994).

B. W. Logan and D. E. Cebulski, “Semimentary Environments of Shark Bay, Western Australian,” in Carbon Sedimentation and Environments, Shark Bay, Western Australia, B. W. Logan, G. R. Davies, J. F. Read, and D. E. Cebulski, eds. (The American Association of Petroleum Geologists, Tulsa, 1970), p. 205.

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Figures (2)

Fig. 1
Fig. 1

Spectral scattering of seawater estimated using Eq. (12) and ZHH09 for S = 0 and 38.4 and Tc = 20°C are compared with Morel’s measurements.

Fig. 2
Fig. 2

Scattering of seawater are estimated for λ = 546 nm and Tc = 20°C as a function of absolute salinity using Eq. (12), ZHH09 model, and linear extrapolation (Eq. (3) of Ref. 5).

Equations (14)

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

β(90)=βd(90)+βc(90) ,
βd(90)=π22λ4(ρn2ρ)T2kTβTf(δ)
βc(90)=π22λ4NA(n2S)2MwρSlnaw/Sf(δ) .
g(SA,Tc,p)=μW+SA(μSμW)
g(SA,Tc,p)=gW(Tc,p)+gS(SA,Tc,p)
mRTϕ=gS(SA,Tc,p)SASAg(SA,Tc,p)
lnaw=mMwϕ
lnawSA=MwRTSA(gSSAgSSA)=MwRTSA2gSSA2=MwSARTgss .
βT=gppgp,
ρ=1gp .
βc(90)=π22λ4(ρn2ρ)2βTkT(gps2gppgss)f(δ) .
β(90)=π2kT2λ4(ρn2ρ)2(gppgp+gps2gpgss)f(δ) .
β(θ)=β(90)(1+1δ1+δcos2(θ))
b=8π3β(90)2+δ1+δ .

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