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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 3675–3683
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Influence of Raman scattering on the light field in natural waters: a simple assessment

Howard R. Gordon  »View Author Affiliations


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

The backscattered solar radiance exiting natural waters contains information regarding the water’s constituents such as phytoplankton, other suspended material, dissolved organic material, etc [1

1. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .

]. The goal of water color remote sensing is to use this radiance to estimate the concentration of such constituents. Raman scattering by water molecules is also an important contributor to the light field in natural waters [2

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]

15

15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

]. In particular, as much as 25% of the solar reflected radiance in clear ocean water at wavelengths greater than 500 nm can be attributed to Raman scattering [14

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

]. The constituents influence the Raman contribution both through their effect on the excitation radiance as well as the emission radiance. It is important to be able to assess (1) the contribution of Raman scattering in predicting the influence of constituents on the light field through simulations, and (2) account for its contribution in experimental measurements of various aspects of the light field. In this paper we provide a simple procedure for such assessments. In particular, we show that determining the lowest order of Raman scattering – basically single Raman scattering – is sufficiently accurate to be useful in both of the above assessments.

Because it yields simple analytical expressions to complex radiative transfer problems, the single scattering approximation has played an important role, over and above pedagogy, in water color remote sensing. It was central to the original atmospheric correction algorithm for the Coastal Zone Color Scanner [16

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

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]

], and formed the basis for more accurate and complex approaches [18

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]

]. The simple replacement of the beam attenuation coefficient by the sum of the absorption and backscattering coefficients – 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]

] – in the single scattering solution for the diffuse reflectance of natural waters enabled estimation of said reflectance with considerable accuracy for even highly multiple scattering media [20

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]

]. Here, we apply it to the estimation of Raman-induced light fields.

We begin by providing basic definitions of important properties of the light field and the governing equation – the radiative transfer equation (RTE). Next, we solve the RTE for the contribution from Raman scattering in the lowest order. Finally, the resulting Raman contribution to various light field characteristics is compared with “exact” Monte Carlo simulations.

2. Characteristics and governing equations of the light field

Consider a horizontally homogeneous water body that is stratified in the 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 = cosθ, and θ measured from the + z axis. The downward (Ed), upward (Eu), and scalar (E0) irradiances are defined according to [15

15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

]
Ed(z,λ)=02πdϕ01uL(z,u,ϕ,λ)du,Eu(z,λ)=02πdϕ01|u|L(z,u,ϕ,λ)du,E0(z,λ)=02πdϕ11L(z,u,ϕ,λ)du,
(1)
and their associated decay coefficients are defined by Kx(z,λ)=dn[Ex(z,λ)]/dz,where x = d, u, or 0.

The radiance is governed by the radiative transfer equation [15

15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

]
udL(z,u,ϕ,λ)dz+c(z,λ)L(z,u,ϕ,λ)=02πdϕ'11du'β(z,u'u,ϕ'ϕ,λ)L(z,u',ϕ',λ)+AllλEdλE02πdϕ'11du'βI(z,u'u,ϕ'ϕ,λEλ)L(z,u',ϕ',λE),
(2)
where c(z, λ) is the beam attenuation coefficient profile in the water body, β(z,u'u,ϕ'ϕ',λ) is the volume scattering function for scattering from the primed direction to the unprimed direction, βI(z,u'u,ϕ'ϕ,λEλ) is the inelastic (e.g., Raman) volume scattering function for scattering from the primed directions at λΕ to the unprimed direction at λ, and L(z, u ′, ϕ ′, λE) is the radiance in the primed direction at λΕ . We write the last term as
Q(z,u,ϕ,λ)=AllλEdλEJ(z,u,ϕ,λE,λ),
(3)
where
J(z,u,ϕ,λE,λ)=02πdϕ'11du'βI(z,u'u,ϕ'ϕ,λEλ)L(z,u',ϕ',λE).
(4)
Now make the transition to dimensionless variables = c(z, λ) dz, P =β/b and ω0(z, λ) = b(z, λ)/c(z, λ), where b is the scattering coefficient at λ. Then, the RTE (Eq. (2)) can be written
[uddτ+1]L=ω04π02πdϕ'11PLdu'+Qc.
(5)
We assume that the radiance at λΕ is known, so Q=Q(z,u,ϕ,λ) is a known function of its arguments. This equation must be solved subject to the boundary condition of incident radiance at z = 0 of LInc(0,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 LInc(0,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

The solution to Eq. (5) can be developed by considering the set of differential equations;
[uddτ+1]L(0)=Qc[uddτ+1]L(1)=ω04π02πdϕ'11PL(0)du'[uddτ+1]L(2)=ω04π02πdϕ'11PL(1)du'etc.,
(6)
subject to L(0)=L(1)=L(2)etc.=0at z = 0 for u positive, and forming the sum L=L(0)+L(1)+L(2)etc. Each of these equations is of the form
[uddτ+1]L(n)=f(n)(τ),
(7)
where 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 τa to τb:
L(n)(τb)exp(τb/u)L(n)(τa)exp(τa/u)=1uτaτbf(n)(τ')exp[τ'/u]dτ'.
(8)
For the downward radiance at τ (u > 0) we take τa = 0 and τb = τ, while for upward radiance, we take τa = infinity and τb = τ, with L(n)()=0. The first of these equations (n = 0) yields
L(0)(τ,u,ϕ,λ)=exp(τ/u)uτaτQ(τ',u,ϕ,λ)c(τ',λ)exp[τ'/u]dτ',
(9)
which 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.

For Raman scattering, βI = βR, the dependence of the scattering on direction is similar to that for Rayleigh scattering but with a different depolarization factor [4

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]

]:
βR(z,u'u,ϕ'ϕ,λEλ)=bR(z,λEλ)4π(1.1833)(1+0.55cos2α),
(10)
where cosα=uu'+[(1u2)(1u'2)]1/2cos(ϕ'ϕ), and the factor 1.1833 is required so that the integral of βR over all solid angles is bR, the Raman scattering coefficient. Raman scattering at λ is excited by a narrow band of wavelengths (ΔλE) near λE, where λE=λ/(1+3.357×104λ) with the wavelengths given in nm. The Raman scattering coefficient for the entire Raman band is [4

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]

,11

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

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]

]
bR(λEλ)ΔλE=2.61×104(589λ)4.8,
(11)
where the wavelength is in nm and bR(λEλ)ΔλE is in m−1.

The quantities related to the light field that are most often measured experimentally are vertical profiles of zenith propagating radiance (Lup) and upward (Eu) and downward (Ed) propagating irradiance. Let us examine the Raman contribution to Lup first. In this case, u = −1, ϕ is irrelevant, and the expression for Q is easily found by replacing the integral over λE by simple multiplication by ΔλE:
Q(z,u=1,ϕ,λ)=0.0673  bR(λEλ)ΔλE02πdϕ'11du'(1+0.55u'2)L(z,u',ϕ',λE).
(12)
We define the average cosine squared of the light field according to
u2E02πdϕ'11u'2L(z,u',ϕ',λE)du'02πdϕ'11L(z,u',ϕ',λE)du',
(13)
where the denominator is just the scalar irradiance E0(z, λE) at the excitation wavelength (the last entry in Eq. (1)). Then
Q(z,u=1,ϕ,λ)=0.0637bR(λλE)ΔλE(1+0.55u'2E)E0(z,λE).
(14)
Detailed radiative transfer calculations show that the average cosine squared of the light field is only weakly dependent on depth, and very nearly equal to the square of the downward average cosine of the light field: μd, the downward irradiance Ed(z, λE), divided by E0d(z, λE), the downward scalar irradiance given by
E0d(z,λE)=02πdϕ01L(z,u,ϕ,λE)du.
(15)
The upwelling scalar irradiance (used later), E0u(z, λE), is defined through a similar equation but with the integration limits on u going from −1 to 0 rather than 0 to 1 in Eq. (15).

The lowest order approximation (Eq. (3)) to the desired upward radiance is then
Lup(0)(τ,λ)=0.0673bR(λEλ)ΔλE×τdτ'(1+0.55u2E)exp[(τ'τ)]c(τ',λ)E0(τ',λE).
(16)
To use this equation one must have u2E and E0(z, λE). These could be available through detailed radiative transfer computations at λE, experimental measurements at λE, or some combination of the two.

To test its applicability in natural waters, we consider the contribution of Raman scattering in a particle-free water body beneath an aerosol-free atmosphere at 550 nm for solar zenith angles of 0 and 60 deg. In this case λE = 464 nm. Monte Carlo simulations of the light field at 464 nm show that in this case u2E is essentially independent of depth and that E0(z, λE) decays exponentially with depth: E0(z,λE)=E0(0,λE)exp[K0(λE)z]. When this is the case (and c is constant) the integration can be carried out yielding
Lup(0)(z,λ)=0.0673bR(λEλ)ΔλEc(λ)+K0(λE)×(1+0.55u2E)E0(0,λE)exp[K0(λE)z].
(17)
This shows that the upwelling radiance decays exponentially with a decay coefficient being K0 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

Table 1. Exact values of the Raman scattering contribution to Lup(0, λ) in mW/cm2µm Sr and Eu(0) at 550 nm for a pure sea water water body, compared with values of Lup(0)(0, λ) and Eu(0, λ) computed using Eqs. (17) and (22), respectively, with u2E = µd2 . The values labeled “Approx.” are computed by replacing K0 with Kd, estimating E0 from Ed(0) and Eu(0) and the approximation u2E=u0w2.

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. 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 Lup(0)(0, λ) using Eq. (16) or (17) when the light field at the excitation wavelength is known. If we want the estimate Lup(0)(0, λ) in an experimental situation, usually the only properties of the excitation light field that would be measured are Ed(z, λE) and Lu(0)(0, λE) or Eu(z, λE). Thus, we need to estimate K0(z, λE), E0(0, λE) and u2E. (Note however, that instrumentation capable of measuringthe entire radiance distribution exists [21

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

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]

], and has recently been miniaturized [23

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]

], so increasingly in the future these needed quantities at the excitation wavelength will be directly available.) The estimate of K0(z, λE) can be effected by approximating it with Kd(z, λE). The scalar irradiance is given by
E0(0,λE)=Ed(0,λE)/μd+Eu(0,λE)/μu,
(18)
where μu is the average cosine of the upwelling light field, i.e, Eu(z, λE) / E0u(z, λE). Given that the radiance at λE is strongly peaked in the direction of the refracted incident solar beam, we expectμdu0w, where u0w = cos(θ0w) with θ0w the polar angle of the refracted solar beam. Further, since Ed(0) >> Eu(0), a precise approximation to μu is not particularly important, and an asymptotic value of 0.4 is used [15

15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

]. If Lup(0, λE) is measured rather than Eu(0, λE), Eq. (18) with these approximations to μd and μu, can still be used with Eu(0, λE) replaced by πLup(0, λE). This assumes that Lu is independent of u. The final quantity required can be approximated through u2Eu0w2, which is similar to the approximation μdu0w. The 4th column in Table 1 provides Lup(0) (0,λ) computed using these approximations and shows that again the agreement with the Monte Carlo simulations is excellent.

The upwelling irradiance in the lowest order is also easy to find in this approximation. Letting μ=u the upward radiance in the direction (μ,ϕ) is
L(0)(τ,μ,ϕ,λ)=0.0673bR(λEλ)ΔλEμ×02πdϕ'11du'τdτ'(1+0.55cos2α)exp[(τ'τ)/μ]c(τ',λ)L(τ',u',ϕ',λE),
(19)
and the upwelling irradiance is
Eu(0)(τ,λ)=0.0673bR(λEλ)ΔλE02πdϕ01dμ×02πdϕ'11du'τdτ'(1+0.55cos2α)exp[(τ'τ)/μ]c(τ',λ)L(τ',u',ϕ',λE).
(20)
Expanding cos2α yields terms constant in ϕ, proportional to cos(ϕ'ϕ) and to cos2(ϕ'ϕ) allowing the ϕand the integrations to be carried out easily. The result is
Eu(0)(τ,λ)=0.0673bR(λEλ)ΔλE01dμτdτ'exp[(τ'τ)/μ]c(τ',λ)×(1+0.55[u2Eμ2+0.5(1u2E)(1μ2)])E0(τ',λE).
(21)
If the water body is homogeneous (τ=cz), u2E is assumed to be independent of z, and E0(z,λE)=E0(0,λE)exp[K0(λE)z], the z integral in Eq. (7) can be carried out analytically yielding
Eu(0)(z,λ)=0.0673bR(λEλ)ΔλEE0(z,λE)exp[K0(λE)z]×01μdμ(1+0.55[u2Eμ2+0.5(1u2E)(1μ2)])c(λ)+μK0(λE).
(22)
This shows that the upwelling irradiance also decays exponentially with depth with K0 at the excitation wavelength serving as the decay coefficient. Table 1 compares the value of Eu(0)(0,λ) computed using Eq. (22) with the Monte Carlo simulations. Again, the results are excellent when the actual light field at the excitation wavelength is provided, and reasonably accurate when approximate values of the required quantities are used. In a like manner, the downwelling irradiance can be computed with similar accuracy; however, with the boundary conditions we used, the computation yields only the component directly generated from λE, to which must be added the upwelling Raman irradiance at 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 Ed is much larger near the surface than the Raman component (by a factor of 100 or more) [3

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

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]

], computation of the Raman component is usually of little interest. In the light of these complications and facts, we omit the solution to Ed.

We now consider a more realistic example, e.g., a water body with particles, below an atmosphere with aerosols, Eq. (17) cannot be used because K0 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]

], but tuned to better match experimental measurements in clear waters off Hawaii, we computed the Raman contribution to the radiance for a phytoplankton pigment concentration of 0.3 mg/m3 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

Table 2. Exact values of the Raman scattering contribution to Lup(0, λ) in mW/cm2µm Sr and at 450 and 550 nm for a modeled water body with a pigment concentration of 0.3 mg/m3, compared with values of Lup(0)(0, λ) computed using Eq. (16) with u2E = µd2 . The solar zenith angle was 60 deg. The values labeled “Approx.” are computed by replacing E0 by its estimate from Ed and Lup (Eq. (18)), and the approximation u2E=u0w2. “Model” refers to using Eq. (15) directly with c, or replacing c by a + bb, its quasi-single scattering value.

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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 + bb in Eq. (16) (the quasi-single scattering approximation [19

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

,20

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]

]), which approximately accounts for the multiple scattering of Raman-generated radiance. Note that, in the quasi-single scattering approximation, a(λ)+bb(λ)=u0wKd(λ), which would be available from Ed(z,λ), i.e., measurements of the downwelling irradiance at the emission wavelength (near the surface, it is only weakly influenced by Raman scattering). The fraction of the Raman contribution to the total radiance at the surface was 7.7% and 14.5%, respectively, at 450 and 550 nm (note, however, that the elastic contribution is strongly dependent on the bio-optical model). The quantity Lup(0)(Approx.) refers to the same computation when E0 is replaced by its estimate from Ed and Lup, and the average squared cosine is replaced by (u0w)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 Lup(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 E0 and μd) 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.

4. Concluding remarks

We have provided a simple, surprisingly accurate, estimate of the contribution of Raman scattering of water molecules to several commonly measured properties of the in-water light field. It can be used both to compute the Raman component based on simulations of the light field at the excitation wavelength and to estimate the Raman contribution to field measurements of light field properties given similar measurements at the excitation wavelength. In particular, if Ed(z, λ) and Eu(z, λ) or Ed(z, λ) and Lup are measured throughout the spectrum, then the Raman contribution can be estimated in a manner similar to Lup(0)(Approx.) and Eu(0)(Approx.) in Table 1 and Lup(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) + bb(z, λ) or u0wKd(z,λ).

Although, in the cases provided here, the solutions are in error by ~1-10%, the accuracy is still sufficient to assess the contribution of Raman scattering in most situations. Full radiative transfer simulations [14

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

] using a bio-optical model relating the phytoplankton pigment concentration to the inherent optical properties suggest, that for pigment concentrations varying from 0 to 0.3 mg/m3, the Raman contribution to Lup 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 Lup from the total would not exceed 2%, over and above any error in the measurement of Lup.

To understand the impact of Raman scattering effects to ocean color remote sensing, one must consider the actual application. The traditional empirical algorithms relating water-leaving radiance to pigment concentrations were all based on measurements that included Raman effects [1

1. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .

,16

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

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]

] (even though it was not recognized at the time). Thus, to a certain extent the Raman correction is already “built in” to such algorithms and their more modern counterparts. However, recent algorithms, particularly those that relate the water’s backscattering coefficient to phytoplankton biomass [24

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]

], rely on being able to estimate the backscattering coefficient from remote measurements. If the Raman augmentation of the radiance is not removed, then the retrieved backscattering coefficient will be too large roughly by the ratio of the Raman water-leaving radiance to the total water-leaving radiance which in can be as high as 25% at wavelengths > 500 nm in low-chlorophyll waters. The biomass will then be overestimated roughly by the same ratio, i.e., there would be a positive bias in biomass estimates, which would vary with the pigment concentration [25

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 second inelastic process of interest in oceanic optics is fluorescence of dissolved organic material or of chlorophyll a contained in phytoplankton. For fluorescence, the emission is isotropic, i.e., βI = βF is independent of the direction of the incident and scattered photons, so βF=bF(z,λEλ)/4π. The equations developed here can be adapted to handle fluorescence as well, by replacing 0.55 by 0 and 1.1833 by 1 in Eq. (4) and all subsequent equations. When these changes are made the resulting equations agree with those developed earlier [26

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]

] for the chlorophyll 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).

It is understood that the Raman contribution can be accurately assessed using available radiative transfer codes and the vertical profiles of the absorption coefficients, the scattering coefficients, and the particulate scattering phase function at both the excitation and emission wavelength [14

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

,15

15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

,27

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]

]. The principal values of the simple expressions developed here is in allowing rapid estimates of the Raman contribution in experimental measurements which allows separation of the elastic and inelastic components of the light field. Pedagogically the derived expressions also isolate the important parameters of the problem and provide a simple way to explore the influence of various optical properties of the medium on the Raman contribution.

References and links

1.

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .

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]

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]

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]

5.

G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31(30), 6491–6500 (1992). [CrossRef] [PubMed]

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. 32(27), 5356–5367 (1993). [CrossRef] [PubMed]

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. 32(21), 4028–4036 (1993). [PubMed]

8.

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]

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]

10.

K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995). [CrossRef]

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. 37(15), 3324–3332 (1998). [CrossRef] [PubMed]

13.

S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998). [CrossRef] [PubMed]

14.

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

15.

C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).

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]

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]

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]

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]

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]

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]

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

  1. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer, 1983) .
  2. 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]
  3. 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]
  4. B. R. Marshall, R. C. Smith, “Raman scattering and in-water ocean optical properties,” Appl. Opt. 29(1), 71–84 (1990). [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. K. J. Waters, “Effects of Raman scattering on water-leaving radiance,” J. Geophys. Res. 100(C7), 13151–13161 (1995). [CrossRef]
  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, A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37(15), 3324–3332 (1998). [CrossRef] [PubMed]
  13. S. Sathyendranath, T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37(12), 2216–2227 (1998). [CrossRef] [PubMed]
  14. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38(15), 3166–3174 (1999). [CrossRef] [PubMed]
  15. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic, 1994).
  16. 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]
  17. 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]
  18. 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]
  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, 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]
  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, 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, P. Henry, “Underwater radiance distributions measured with miniaturized multispectral radiance cameras,” J. Atmos. Oceanic Technol. 30(1), 74–95 (2013). [CrossRef]
  24. 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]
  25. 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]
  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]
  27. 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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