## Influence of Raman scattering on the light field in natural waters: a simple assessment

Optics Express, Vol. 22, Issue 3, pp. 3675-3683 (2014)

http://dx.doi.org/10.1364/OE.22.003675

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### Abstract

A simple, surprisingly accurate, method for estimating the influence of Raman scattering on the upwelling light field in natural waters is developed. The method is based on the single (or quasi-single) scattering solution of the radiative transfer equation with the Raman source function. Given the light field at the excitation wavelength, accurate estimates (~1-10%) of the contribution of Raman scattering to the light field at the emission wavelength are obtained. The accuracy is only slightly degraded when typically measured aspects of the light field at the excitation are available.

© 2014 Optical Society of America

## 1. Introduction

2. S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn **40**(6), 397–404 (1984). [CrossRef]

14. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. **38**(15), 3166–3174 (1999). [CrossRef] [PubMed]

*single*Raman scattering – is sufficiently accurate to be useful in both of the above assessments.

16. H. R. Gordon, D. K. Clark, J. L. Mueller, and W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science **210**, 63–66 (1980). [CrossRef] [PubMed]

17. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. **22**, 20–36 (1983). [CrossRef] [PubMed]

18. H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. **33**(3), 443–452 (1994). [CrossRef] [PubMed]

*quasi*-single scattering [19

19. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. **12**(12), 2803–2804 (1973). [CrossRef] [PubMed]

20. H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. **14**(2), 417–427 (1975). [CrossRef] [PubMed]

## 2. Characteristics and governing equations of the light field

*z*direction, which is into the water. Let

*L*(z,

*u*,

*ϕ*,

*λ*) be the radiance at a wavelength

*λ*propagating in a direction specified by the polar and azimuth angles

*θ*and

*ϕ*, respectively, with

*u*= cos

*θ*, and

*θ*measured from the +

*z*axis. The downward (

*E*), upward (

_{d}*E*), and scalar (

_{u}*E*

_{0}) irradiances are defined according to [15]

*x*=

*d*,

*u*, or 0.

*c*(

*z*,

*λ*) is the beam attenuation coefficient profile in the water body,

*λ*to the unprimed direction at

_{Ε}*λ*, and

*L*(

*z*,

*u*′,

*ϕ*′,

*λ*) is the radiance in the primed direction at

_{E}*λ*. We write the last term aswhereNow make the transition to dimensionless variables

_{Ε}*dτ*=

*c*(

*z*,

*λ*)

*dz*,

*P =*4π

*β*/

*b*and

*ω*

_{0}(

*z*,

*λ*) =

*b*(

*z*,

*λ*)/

*c*(

*z*,

*λ*), where

*b*is the scattering coefficient at

*λ*. Then, the RTE (Eq. (2)) can be writtenWe assume that the radiance at

*λ*is known, so

_{Ε}*z*= 0 of

*L*(0,

_{Inc}*u*,

*ϕ*,

*λ*) for

*u*positive. Actually, since we are interested only in the inelastic contribution to the radiance at

*λ*, we will take the surface boundary condition to be

*L*(0,

_{Inc}*u*,

*ϕ*,

*λ*) = 0 for

*u*positive. Were we interested in the elastic component as well, the surface boundary condition would be the radiance incident at

*λ*from the sun and sky.

## 3. The solution of the RTE for the inelastic component

*z*= 0 for

*u*positive, and forming the sum

*f*

^{(}

^{n}^{)}(

*τ*) is a known function of

*τ,*derived either from

*Q*or

*L*

^{(}

^{n}^{-1)}(

*τ*). The solution to each differential equation in the set Eq. (6) can be developed by introducing an integrating factor (exp[

*τ*/

*u*]) and performing integration from

*τ*to

_{a}*τ*:For the downward radiance at

_{b}*τ*(

*u*> 0) we take

*τ*= 0 and

_{a}*τ*=

_{b}*τ*, while for upward radiance, we take

*τ*= infinity and

_{a}*τ*=

_{b}*τ*, with

*n*= 0) yieldswhich provides the lowest order solution for the inelastic component at

*λ*. Use of this lowest order solution represents the single scattering approximation to the inelastically-generated radiance.

*β*=

_{I}*β*, the dependence of the scattering on direction is similar to that for Rayleigh scattering but with a different depolarization factor [4

_{R}4. B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. **29**(1), 71–84 (1990). [CrossRef] [PubMed]

*β*over all solid angles is

_{R}*b*, the Raman scattering coefficient. Raman scattering at

_{R}*λ*is excited by a narrow band of wavelengths (Δ

*λ*) near

_{E}*λ*, where

_{E}4. B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. **29**(1), 71–84 (1990). [CrossRef] [PubMed]

12. J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. **37**(15), 3324–3332 (1998). [CrossRef] [PubMed]

^{−1}.

*E*

_{0}(

*z, λ*). These could be available through detailed radiative transfer computations at

_{E}*λ*, experimental measurements at

_{E}*λ*, or some combination of the two.

_{E}*λ*= 464 nm. Monte Carlo simulations of the light field at 464 nm show that in this case

_{E}*E*

_{0}(

*z, λ*) decays exponentially with depth:

_{E}*c*is constant) the integration can be carried out yieldingThis shows that the upwelling radiance decays exponentially with a decay coefficient being

*K*

_{0}at the excitation wavelength. Comparison between the predictions of the above relationship (at

*z*= 0) and results of solving the full RTE (Eq. (2)) using Monte Carlo (MC) methods are provided in Table 1. Note that the difference between the Monte Carlo simulation of the radiance and that computed via Eq. (17) is less than 1%. This shows the accuracy that can be obtained by computing

*L*

_{up}^{(0)}(0,

*λ*) using Eq. (16) or (17) when the light field at the excitation wavelength is known. If we want the estimate

*L*

_{up}^{(0)}(0,

*λ*) in an experimental situation, usually the only properties of the excitation light field that would be measured are

*E*(

_{d}*z, λ*) and

_{E}*L*

_{u}^{(0)}(0,

*λ*) or

_{E}*E*(

_{u}*z, λ*). Thus, we need to estimate

_{E}*K*

_{0}(

*z, λ*),

_{E}*E*

_{0}(0,

*λ*) and

_{E}21. K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. **34**(8), 1614–1622 (1989). [CrossRef]

22. J. Wei, R. Van Dommelen, M. R. Lewis, S. McLean, and K. J. Voss, “A new instrument for measuring the high dynamic range radiance distribution in near-surface sea water,” Opt. Express **20**(24), 27024–27038 (2012). [CrossRef] [PubMed]

23. D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. **30**(1), 74–95 (2013). [CrossRef]

*K*

_{0}(

*z, λ*) can be effected by approximating it with

_{E}*K*(

_{d}*z, λ*). The scalar irradiance is given bywhere

_{E}*μ*is the average cosine of the upwelling light field, i.e,

_{u}*E*(

_{u}*z, λ*) /

_{E}*E*

_{0}

*(*

_{u}*z, λ*). Given that the radiance at

_{E}*λ*is strongly peaked in the direction of the refracted incident solar beam, we expect

_{E}*u*

_{0}

*= cos(*

_{w}*θ*

_{0}

*) with*

_{w}*θ*

_{0}

*the polar angle of the refracted solar beam. Further, since*

_{w}*E*(0) >>

_{d}*E*(0), a precise approximation to

_{u}*μ*is not particularly important, and an asymptotic value of 0.4 is used [15]. If

_{u}*L*(0,

_{up}*λ*) is measured rather than

_{E}*E*(0,

_{u}*λ*), Eq. (18) with these approximations to

_{E}*μ*and

_{d}*μ*, can still be used with

_{u}*E*(0,

_{u}*λ*) replaced by π

_{E}*L*(0,

_{up}*λ*). This assumes that

_{E}*L*is independent of

_{u}*u*. The final quantity required can be approximated through

*L*

_{up}^{(0)}(0,

*λ*) computed using these approximations and shows that again the agreement with the Monte Carlo simulations is excellent.

*μ,ϕ*) is

^{2}α yields terms constant in

*z*, and

*z*integral in Eq. (7) can be carried out analytically yielding

*K*

_{0}at the excitation wavelength serving as the decay coefficient. Table 1 compares the value of

*λ*, to which must be added the upwelling Raman irradiance at

_{E}*λ*reflected from the surface into the downwelling stream. The reflected Raman radiance just beneath the surface can be computed with reasonable accuracy; however, since this radiance is nearly diffuse its attenuation coefficient, which is critical in estimating its contribution at depth, is difficult to estimate. Considering these complications and the fact that the elastic component of

*E*is much larger near the surface than the Raman component (by a factor of 100 or more) [3

_{d}3. R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. **27**(19), 4002–4011 (1988). [CrossRef] [PubMed]

9. Y. Ge, K. J. Voss, and H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. **100**(C7), 13,227–13,236 (1995). [CrossRef]

*E*.

_{d}*K*

_{0}depends strongly on depth, especially when the solar zenith angle is large. Using a bio-optical model similar to that in Ref [14

14. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. **38**(15), 3166–3174 (1999). [CrossRef] [PubMed]

^{3}and a solar zenith angle of 60 deg. Then using Eq. (16), along with the required quantities at the excitation wavelength, we computed

*L*

^{(0)}just beneaththe surface (

*z*= 0). Table 2 provides the results for 450 and 550 nm (excitation at 391 and 464 nm, respectively) computed using Eq. (16) directly (the single scattering approximation) and by replacing

*c*by

*a*+

*b*in Eq. (16) (the quasi-single scattering approximation [19

_{b}19. H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. **12**(12), 2803–2804 (1973). [CrossRef] [PubMed]

20. H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. **14**(2), 417–427 (1975). [CrossRef] [PubMed]

*L*

_{up}^{(0)}(Approx.) refers to the same computation when

*E*

_{0}is replaced by its estimate from

*E*and

_{d}*L*, and the average squared cosine is replaced by (

_{up}*u*

_{0}

*)*

_{w}^{2}. Such replacements would be required in a typical experimental scenario. The error using quasi-single scattering is reduced by a large factor compared to single scattering, with an error of 9% at 450 nm and 1.6% at 550 nm. The larger error at 450 nm is to be expected because the single scattering albedo is significantly larger there (0.71) than at 550 nm (0.44), so the quasi-single scattering approximation is less effective. The error in

*L*

_{up}^{(0)}(Approx.) is larger than it is when the correct excitation quantities are used, but still not excessive (13.4% at 450 nm and 5.2% at 550 nm). The relative error (using Eq. (16) with the correct

*E*

_{0}and

*μ*) increases as a function depth: reaching 16% at 20 m and 30% at 100 m for 450 nm; and 3.2% at 20 m and <5% at 100 m for 550 nm. This increase is mainly due to the ineffectiveness of the QSSA as the depth increases.

_{d}## 4. Concluding remarks

*E*(

_{d}*z*,

*λ*) and

*E*(

_{u}*z*,

*λ*) or

*E*(

_{d}*z*,

*λ*) and

*L*are measured throughout the spectrum, then the Raman contribution can be estimated in a manner similar to

_{up}*L*

_{up}^{(0)}(Approx.) and

*E*

_{u}^{(0)}(Approx.) in Table 1 and

*L*

_{up}^{(0)}(Approx.) in Table 2. Of course, the attenuation coefficient

*c*(

*z*,

*λ*) must be known or estimated at the wavelength of interest. The solution provided is equivalent to single scattering with the appropriate source function. Should more accuracy be needed,

*L*

^{(0)}(

*z,u,ϕ,λ*) can be inserted into Eq. (6) and

*L*

^{(1)}(

*z,u,ϕ,λ*) computed. This is an arduous task; however, as in Table 2, one can employ the quasi-single scattering approximation for this purpose which involves the simple replacement of

*c*(

*z*,

*λ*) in Eqs. (15)–(21) by

*a*(

*z*,

*λ*) +

*b*(

_{b}*z*,

*λ*) or

*u*

_{0}

*(*

_{w}K_{d}*z*,

*λ*).

14. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. **38**(15), 3166–3174 (1999). [CrossRef] [PubMed]

^{3}, the Raman contribution to

*L*varies from ~10 to 12% at 440 nm and 25 to 11% at 550 nm. Thus, even with an error of 10% in Eq. (16), the error in retrieval of the elastic component of

_{up}*L*from the total would not exceed 2%, over and above any error in the measurement of

_{up}*L*.

_{up}16. H. R. Gordon, D. K. Clark, J. L. Mueller, and W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science **210**, 63–66 (1980). [CrossRef] [PubMed]

17. H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. **22**, 20–36 (1983). [CrossRef] [PubMed]

24. M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles **19**(1), GB1006 (2005). [CrossRef]

25. T. K. Westberry, E. Boss, and Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. **52**(22), 5552–5561 (2013). [CrossRef] [PubMed]

*a*contained in phytoplankton. For fluorescence, the emission is isotropic, i.e.,

*β*=

_{I}*β*is independent of the direction of the incident and scattered photons, so

_{F}26. H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll *a* fluorescence at 685 nm,” Appl. Opt. **18**(8), 1161–1166 (1979). [CrossRef] [PubMed]

*a*fluorescence near 683 nm. Raman scattering by water is typically a more important inelastic process than fluorescence, as it is almost always much larger than fluorescence except in specific regions of the spectrum (e.g., near 683 nm at high chlorophyll concentrations).

**38**(15), 3166–3174 (1999). [CrossRef] [PubMed]

27. C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. **32**(36), 7484–7504 (1993). [CrossRef] [PubMed]

## References and links

1. | H. R. Gordon and A. Y. Morel, |

2. | S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn |

3. | R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. |

4. | B. R. Marshall and R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. |

5. | G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. |

6. | V. I. Haltrin and G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. model,” Appl. Opt. |

7. | Y. Ge, H. R. Gordon, and K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. |

8. | R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. |

9. | Y. Ge, K. J. Voss, and H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. |

10. | K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. |

11. | J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean color,” 1996, M.S. Thesis, Dalhousie University, Halifax, Nova Scotia. |

12. | J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. |

13. | S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. |

14. | H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. |

15. | C. D. Mobley, |

16. | H. R. Gordon, D. K. Clark, J. L. Mueller, and W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science |

17. | H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, and W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. |

18. | H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. |

19. | H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. |

20. | H. R. Gordon, O. B. Brown, and M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. |

21. | K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. |

22. | J. Wei, R. Van Dommelen, M. R. Lewis, S. McLean, and K. J. Voss, “A new instrument for measuring the high dynamic range radiance distribution in near-surface sea water,” Opt. Express |

23. | D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, and P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. |

24. | M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles |

25. | T. K. Westberry, E. Boss, and Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. |

26. | H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll |

27. | C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. |

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(010.5620) Atmospheric and oceanic optics : Radiative transfer

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: November 12, 2013

Revised Manuscript: January 16, 2014

Manuscript Accepted: January 17, 2014

Published: February 7, 2014

**Citation**

Howard R. Gordon, "Influence of Raman scattering on the light field in natural waters: a simple assessment," Opt. Express **22**, 3675-3683 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-3675

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### References

- H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .
- S. Sugihara, M. Kishino, N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn 40(6), 397–404 (1984). [CrossRef]
- R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27(19), 4002–4011 (1988). [CrossRef] [PubMed]
- B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29(1), 71–84 (1990). [CrossRef] [PubMed]
- G. W. Kattawar, X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31(30), 6491–6500 (1992). [CrossRef] [PubMed]
- V. I. Haltrin, G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic scattering in oceanic optics: I. model,” Appl. Opt. 32(27), 5356–5367 (1993). [CrossRef] [PubMed]
- Y. Ge, H. R. Gordon, K. J. Voss, “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32(21), 4028–4036 (1993). [PubMed]
- R. H. Stavn, “Effects of Raman scattering across the visible spectrum in clear ocean water: a Monte Carlo study,” Appl. Opt. 32(33), 6853–6863 (1993). [CrossRef] [PubMed]
- Y. Ge, K. J. Voss, H. R. Gordon, “In situ measurements of inelastic light scattering in Monterey Bay using solar Fraunhofer lines,” J. Geophys. Res. 100(C7), 13,227–13,236 (1995). [CrossRef]
- K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995). [CrossRef]
- J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean color,” 1996, M.S. Thesis, Dalhousie University, Halifax, Nova Scotia.
- J. S. Bartlett, K. J. Voss, S. Sathyendranath, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37(15), 3324–3332 (1998). [CrossRef] [PubMed]
- S. Sathyendranath, T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998). [CrossRef] [PubMed]
- H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999). [CrossRef] [PubMed]
- C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).
- H. R. Gordon, D. K. Clark, J. L. Mueller, W. A. Hovis, “Phytoplankton pigments from the Nimbus-7 Coastal Zone Color Scanner: Comparisons with surface measurements,” Science 210, 63–66 (1980). [CrossRef] [PubMed]
- H. R. Gordon, D. K. Clark, J. W. Brown, O. B. Brown, R. H. Evans, W. W. Broenkow, “Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates,” Appl. Opt. 22, 20–36 (1983). [CrossRef] [PubMed]
- H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994). [CrossRef] [PubMed]
- H. R. Gordon, “Simple calculation of the diffuse reflectance of the ocean,” Appl. Opt. 12(12), 2803–2804 (1973). [CrossRef] [PubMed]
- H. R. Gordon, O. B. Brown, M. M. Jacobs, “Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14(2), 417–427 (1975). [CrossRef] [PubMed]
- K. J. Voss, “Use of the radiance distribution to measure the optical absorption coefficient in the ocean,” Limnol. Oceanogr. 34(8), 1614–1622 (1989). [CrossRef]
- J. Wei, R. Van Dommelen, M. R. Lewis, S. McLean, K. J. Voss, “A new instrument for measuring the high dynamic range radiance distribution in near-surface sea water,” Opt. Express 20(24), 27024–27038 (2012). [CrossRef] [PubMed]
- D. Antoine, A. Morel, E. Leymarie, A. Houyou, B. Gentili, S. Victori, J.-P. Buis, N. Buis, S. Meunier, M. Canini, D. Crozel, B. Fougnie, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013). [CrossRef]
- M. J. Behrenfeld, E. Boss, D. A. Siegel, D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005). [CrossRef]
- T. K. Westberry, E. Boss, Z. Lee, “Influence of Raman scattering on ocean color inversion models,” Appl. Opt. 52(22), 5552–5561 (2013). [CrossRef] [PubMed]
- H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18(8), 1161–1166 (1979). [CrossRef] [PubMed]
- C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, R. H. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt. 32(36), 7484–7504 (1993). [CrossRef] [PubMed]

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