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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 9 — Oct. 2, 2013
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Influence of Raman scattering on ocean color inversion models

Toby K. Westberry, Emmanuel Boss, and Zhongping Lee  »View Author Affiliations


Applied Optics, Vol. 52, Issue 22, pp. 5552-5561 (2013)
http://dx.doi.org/10.1364/AO.52.005552


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Abstract

Raman scattering can be a significant contributor to the emergent radiance spectrum from the surface ocean. Here, we present an analytical approach to directly estimate the Raman contribution to remote sensing reflectance, and evaluate its effects on optical properties estimated from two common semianalytical inversion models. For application of the method to ocean color remote sensing, spectral irradiance products in the ultraviolet from the OMI instrument are merged with MODerate-resolution Imaging Spectroradiometer (MODIS) data in the visible. The resulting global fields of Raman-corrected optical properties show significant differences from standard retrievals, particularly for the particulate backscattering coefficient, bbp, where average errors in clear ocean waters are 50%. Given the interest in transforming bbp into biogeochemical quantities, Raman scattering must be accounted for in semianalytical inversion schemes.

© 2013 Optical Society of America

1. Introduction

Ocean color inversion models provide a means of relating the emergent radiance spectrum to various absorbing and scattering components in the surface ocean [1

1. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988). [CrossRef]

]. In turn, these absorption and scattering indices convey rich information on suspended and dissolved materials that can now be estimated from satellite at global, synoptic scales. Some of the better characterized bio-optical signals (e.g., chlorophyll or water transparency) have been used to examine long-term changes in ocean properties associated with climate variability [2

2. C. R. McClain, S. R. Signorini, and J. R. Christian, “Subtropical gyre variability observed by ocean-color satellites,” Deep-Sea Research, Part II 51, 281–301 (2004). [CrossRef]

4

4. M. J. Behrenfeld, R. T. O’Malley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature 444, 752–755 (2006). [CrossRef]

]. However, the accuracy of retrieved quantities depends upon a number of factors ranging from satellite sensor calibration to the formulation of the inversion algorithm itself. The latter depends upon the ability to account for all significant processes affecting light transmission and propagation in the ocean and atmosphere. Some of these processes and relationships can be expressed analytically in an inversion algorithm, while others rely on empirically derived information.

Despite the presumed importance of Raman scattering, few studies have included it in semianalytical algorithms designed to invert in situ or satellite ocean color reflectance data. In particular, three such algorithms have been put forward [21

21. Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994). [CrossRef]

23

23. H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]

], but their implementation of Raman scatter has not been carried forward in subsequent studies or in the comprehensive report by the IOCCG [24

24. IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications” (International Ocean Colour Coordination Group, 2006), Report Number 5.

]. This may be due, in part, to the fact that ocean color remote sensing satellites do not currently have ultraviolet (UV) bands, which are needed to compute Raman excitation in the blue part of the visible spectrum. Indeed, these efforts have relied on empirical relationships or lookup tables derived from radiative transfer simulations. Here, we present a simulated dataset to examine the effects of Raman scattering on IOP inversion products from semianalytical models. We then develop an approach to directly estimate the inelastic Raman contribution to remote sensing reflectance and the resulting effects of its removal on inversion of simulated and satellite ocean color data.

2. Methods

A. Radiative Transfer Simulations

A series of radiative transfer simulations (HydroLight, Sequoia Scientific, Inc.) were generated to (1) demonstrate the magnitude of the Raman effect on Rrs(λ) (remote-sensing reflectance, the ratio of water-leaving radiance to downwelling irradiance just above the surface), and (2) provide a validation dataset for an approach to remove the Raman contribution to Rrs(λ). Paired runs with and without Raman scatter were simulated for Chl ranging from 0.01 to 5.0mgm3 (Chl=0.01,0.02,0.03,0.04,0.07,0.1,0.2,0.3,0.5,0.7,1.0,2.0,5.0mgm3). In order to efficiently incorporate Raman scattering into the radiative transfer equation, HydroLight uses an azimuthally averaged formulation of Raman scatter, which gives the correct Raman contribution to irradiances and nadir radiances (see Appendix A in [25

25. C. D. Mobley, B. Gentili, H. R. Gordon, Z. H. 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, 7484–7504 (1993). [CrossRef]

]). The standard “Case 1” model embedded in HydroLight was used to relate Chl to other IOPs, details of which can be found in Gordon and Morel [26

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

], Morel and Maritorena [27

27. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]

]. A fixed particle phase function (Fournier–Forand) was used with a particulate backscattering ratio (bbp/bp) equal to 0.01. In this model, pure seawater properties are specified by Pope and Fry [19

19. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. 2. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997). [CrossRef]

] and Smith and Baker [28

28. R. C. Smith and K. S. Baker, “Optical-properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981). [CrossRef]

] for absorption and scattering, respectively. For all simulations, a clear sky with solar zenith angle of 30° and a wind speed of 5ms1 was assumed.

B. Satellite Remote Sensing Data

Satellite products from two independent sensors were used in this work, the ozone mapping instrument (OMI) on Aura and the MODerate-resolution Imaging Spectroradiometer (MODIS) on Aqua. Both Aura and Aqua are part of the A-train constellation of Earth observing satellites, with Aura having an Equatorial crossing time just a few minutes later than Aqua (130pm). OMI data were obtained as daily, Level 3 products from Goddard Earth Sciences Data and Information Sciences Center (GES DISC), and were temporally binned to create monthly composites. These data consist of noon-time UV irradiances at four fixed wavelengths (305, 310, 324 and 380 nm). From MODIS, monthly Level 3 products of instantaneous PAR (iPAR) and spectral satellite remote sensing reflectances, Rrs(λ), were downloaded directly from the NASA Ocean Color Web portal (http://oceancolor.gsfc.nasa.gov/). iPAR was decomposed to estimate spectral downwelling irradiance (Ed(λ)) using fixed fractions estimated from an atmospheric radiative transfer model [29

29. P. Ricchiazzi, S. R. Yang, C. Gautier, and D. Sowle, “SBDART: a research and teaching software tool for plane-parallell radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteorol. Soc. 79, 2101–2114 (1998). [CrossRef]

]. The fractional constants are stable within 1%–6% depending on wavelength and illumination conditions. Together, resultant Ed(λ) in the visible and OMI UV flux data allow pixel-wise reconstruction of incident irradiance spectra. Ed(λ) at Raman excitation wavelengths corresponding to MODIS visible bands (365, 387.5, 421, 452.5, 467.5 nm for MODIS bands 8–12) were linearly interpolated and band-averaged (bandwidths 10nm). Global fields of MODIS Rrs(λ) were used to estimate IOPs using two semianalytical inversion models; the Garver–Siegel–Maritorena (GSM) model [30

30. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41, 2705–2714 (2002). [CrossRef]

] and the quasi-analytical algorithm (QAA) [31

31. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef]

]. Retrieved IOPs include the phytoplankton absorption (aph(λ), QAA only) or chlorophyll concentration (Chl, GSM only), particulate backscattering coefficients (bbp(λ)), and dissolved and detrital organic matter absorption coefficient (aCDM(λ)).

C. Calculation of Raman Contribution to Remote Sensing Reflectance

We build on the approaches of Bartlett [18

18. J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean colour,” M.S. thesis (Dalhousie University, 1996).

], Sathyendranath and Platt [22

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

], and Loisel and Stramski [23

23. H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]

] and express the remote sensing reflectance (Rrs) as
Rrs(λ,0)=Rrs,E(λ,0)+Rrs,IE(λ,0),
(1)
where the first term on the right-hand side accounts for the contribution to Rrs from elastic scattering (subscript E), and the second term accounts for inelastic scattering (subscript IE). For this exercise, we are functionally considering three distinct processes as sources of “inelastic scattering” that affect remotely sensed ocean color; fluorescence from colored dissolved material (CDOM) and chlorophyll, and Raman scatter from seawater itself. However, CDOM fluorescence can be considered negligible [32

32. D. Pozdiakov and H. Grassl, Color of Inland and Coastal Waters: A Methodology for its Interpretation (Springer-Praxis, 2003), p. 192.

], and chlorophyll fluorescence only impacts Rrs near 685 nm [33

33. H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18, 1161–1166 (1979). [CrossRef]

]. Hence, we assume that at all wavelengths except near 685 nm:
Rrs(λ,0)=Rrs,E(λ,0)+Rrs,Raman(λ,0).
(2)

Transmitting the radiance across the air–sea interface and normalizing to incident downwelling irradiance, Ed(0+,λem), yields an equivalent remote sensing reflectance:
Rrs,Raman(0+,λem)=t2n2β˜r(θsπ)br(λem)Ed(0+,λex)(Kd(λex)+κL(λem))Ed(0+,λem)[1+bb(λex)μu(Kd(λex)+κ(λex))+bb(λem)2μuκ(λem)].
(7)
The additional terms in brackets on the right-hand side of Eq. (7) account for higher orders of scattering (e.g., Raman scattered light in the downward direction, then elastically backscattered into the upwelling stream) and are derived in detail elsewhere [18

18. J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean colour,” M.S. thesis (Dalhousie University, 1996).

,22

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

].

In practice, the approach presented in Eq. (7) for estimating the Raman component of Rrs(λ) requires estimates of IOPs (a and bb) and diffuse attenuation (K-functions). Therefore, an initial semianalytical inversion must be made to provide an estimate of the total absorption and backscattering coefficients. Attenuation coefficients are then calculated as
Kd(λ)=a(λ)+bb(λ)μdandκ(λ)=a(λ)+bb(λ)μu,
(8)
μd and μu are the mean cosine of downwelling and upwelling light, respectively, and the latter is set as 0.5 as the light field is assumed similar to that of isotropic light [22

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

], and the mean cosine for downwelling irradiance is calculated following Gordon [37

37. H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?,” Limnol. Oceanogr. 34, 1389–1409 (1989). [CrossRef]

] and Lee et al. [38

38. Z. P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: an evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005). [CrossRef]

].

The semianalytical inversion models used here require specification of eigenfunctions describing the spectral shape of IOPs. Therefore, another consideration that arises is extension of the eigenfunctions to the UV region where UV irradiance excites Raman emission in the visible. CDOM absorption and particulate backscattering can be extrapolated to the UV with simple exponential or power laws that adequately capture their spectral behavior (e.g., [27

27. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]

]). Absorption by phytoplankton in the UV is more complicated and variable, as UV absorbing substances of phytoplankton (e.g., mycosporine-like amino acids) can vary independently of other pigments (e.g., [39

39. J. R. Morrison and N. B. Nelson, “Seasonal cycle of phytoplankton UV absorption at the Bermuda Atlantic Time-series Study (BATS) site,” Limnol. Oceanogr. 49, 215–224 (2004). [CrossRef]

,40

40. A. Bricaud, M. Babin, H. Claustre, J. Ras, and F. Tieche, “Light absorption properties and absorption budget of Southeast Pacific waters,” J. Geophys. Res. 115, C08009 (2010). [CrossRef]

]). Here, we assume that aph for λ<412nm is spectrally flat, which may reflect a “mean” spectrum (see [40

40. A. Bricaud, M. Babin, H. Claustre, J. Ras, and F. Tieche, “Light absorption properties and absorption budget of Southeast Pacific waters,” J. Geophys. Res. 115, C08009 (2010). [CrossRef]

]).

3. Results

A. Results from Forward Simulations

Fig. 1. Spectral remote sensing reflectance from HydroLight simulations. (a) Rrs(λ) for varying Chl for cases which include Raman scatter (dotted red lines) and which do not include Raman scatter (solid black lines). (b) Percent contribution of Raman scatter to Rrs(λ) expressed as the ratio of Rrs,R(λ):Rrs(λ) times 100. Details of simulations are described in Section 2.

B. Inversion Using Semianalytical Models

The simulated Rrs(λ) can be used as input to semianalytical inversion models for estimation of IOPs in the presence or absence of Raman scatter. In this work, we have chosen to use the GSM [30

30. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41, 2705–2714 (2002). [CrossRef]

] and QAA [31

31. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef]

] models, two approaches currently used by NASA to produce satellite evaluation products.

These models return various component absorption and backscattering properties. QAA provides estimates of phytoplankton absorption at 443 nm, aph(443), while GSM provides an estimate of Chl. Both models return absorption by colored dissolved and detrital matter at 443 nm, aCDM(443), and the particulate backscattering coefficient at 443 nm, bbp(443). Inversion results using the simulated reflectances are shown in Fig. 2. Biases exist in all retrieved parameters due to differing bio-optical relationships specified in the forward simulations (HydroLight) versus those assumed in the GSM and QAA inversion models. These differences could be easily reconciled by using the same expressions for phytoplankton, dissolved and detrital absorption, and particulate backscattering in the forward and inverse models (not shown). However, it is the relative difference in retrieved IOPs due to Raman scatter that we focus on in this work. The relative error (or bias) is defined as (IOPuncorrIOPcorr)/IOPcorr*100, where IOP is any retrieved IOP and the subscripts uncorr and corr refer to IOPs estimated from reflectance spectra that are uncorrected or corrected for Raman, respectively. As a control, simulated spectra with and without Raman scattering explicitly included are substituted in place of uncorrected and corrected reflectances, respectively. Results from these control runs (black lines in each panel of Fig. 3 shows that (1) the relative error in each IOP due to Raman scattering differs greatly between each IOP, (2) errors differ between inversion models (GSM versus QAA), (3) errors are greatest at low Chl and decrease with increasing Chl, and (4) errors are greatest in the retrieval of bbp(443) [Figs. 3(a)3(f)]. Chl and aph(443) are overestimated by 15%25% under the most oligotrophic conditions (Chl<0.02mgm3), and decrease to 5% when Chl>0.3mgm3 [Figs. 3(a) and 3(d)]. Errors in aCDM(443) are negligible across all trophic conditions [Figs. 3(b) and 3(e)]. Errors in bbp(443), however, can be >100% under ultraoligotrophic conditions and are still 20% when Chl>0.3mgm3 [Fig. 3(c)].

Fig. 2. IOPs from inversion of HydroLight Rrs(λ) with and without Raman scatter included. Values plotted on the abscissae in each panel are taken from HydroLight and considered the “true” IOP value. (a) Chl from GSM (bottom and left axes) and aph(443) from QAA (top and right axes); (b) aCDM(443); (c) bbp(443). In each panel, “x” and “o” represent GSM and QAA retrievals, respectively. Red and blue symbols represent inversions of Rrs(λ) with and without Raman scatter included, respectively.
Fig. 3. Relative error in inverted IOPs due to Raman scatter as a function of chlorophyll concentration. Bias is calculated as normalized difference (%) between each retrieved IOP from Rrs(λ) with and without Raman scatter included. In each panel three curves are shown that represent: error in retrievals using uncorrected Rrs (black line), error in retrievals after correction of Rrs with exact IOPs (blue line), and error in retrievals after correction of Rrs with estimated IOPs from either GSM or QAA (red lines) IOPs in the top and bottom row, respectively. (a) GSM Chl; (b) GSM aCDM(443); (c) GSM bbp(443); (d) QAA aph(443); e, QAA aCDM(443); and (f) QAA bbp(443).

C. Evaluation of Raman Contribution Removal Scheme

The steps outlined in Section 2.C [Eq. (7)] result in an estimate of Rrs,R(λ). We can provide a measure of validation for the approach using the simulated dataset by comparing estimates of Rrs,R(λ) with the absolute difference in Rrs(λ) taken from consecutive runs with and without Raman scattering included (ΔRrs) (Fig. 4). In the best case scenario, exact IOP inputs from HydroLight can be used to estimate Rrs,R(λ) and the resultant agreement with ΔRrs is very good across the whole range of anticipated Rrs and over all visible satellite wave bands r2=0.95, slope=1.08, mean bias=19%). When Rrs,R(λ) is estimated using inverted IOPs rather than those taken directly from HydroLight, predictability is slightly degraded with differences depending upon which inversion model is used (red versus blue dots in Fig. 4). For example, application of GSM IOPs results in good linear correlation (r2=0.93), but with a tendency to underpredict ΔRrs (slope=0.82, mean bias=43%). If QAA IOPs are used to estimate Rrs,R(λ) the pattern is similar, but with slightly greater tendency to underestimate ΔRrs (r2=0.94, slope=0.69, mean bias=50%).

Fig. 4. Estimation of Raman component of Rrs(λ). Rrs,R is directly estimated from Eq. (7). ΔRrs is the arithmetic difference between radiative transfer simulations with and without Raman scattering included. Results for all visible satellite wave bands are shown together. Diagonal line is 1:1 line.

Correction of Rrs for Raman scattering based upon IOPs from an initial inversion does not remove as much of the bias in each retrieved IOP as when exact HydroLight IOP input is used (compare red and blue lines in each panel of Fig. 3). For example, at low Chl(<0.3mgm3) biases in aph(443) (QAA) and Chl(GSM) of approximately 12% and 7% remain, respectively. Biases in aCDM(443) for both inversion models change by only a few percent upon correction for Raman, but are only a few percent even without correction. The largest changes between IOPs before and after correction for Raman are found in bbp(443) retrievals [Figs. 3(c) and 3(f)]. Large reductions in bias are achieved for QAA and GSM bbp(443), but significant errors are still present, particularly at lower Chl concentrations. In the most oligotrophic examples (Chl<0.03mgm3) Raman bias >40% is still unaccounted for by the existing correction (see Discussion).

D. Application to Remote Sensing Data

Figure 5 shows the Raman contribution to Rrs(λ) for a single monthly composite of MODIS data from October 2004. Results are shown for all MODIS ocean visible wave bands, except in the red (667 and 678 nm), where the contribution from Chl fluorescence can be significant. Three general observations are evident and are consistent with results from the simulated data: (1) values range from <1% to 10%, (2) contributions from Raman increase at longer wavelengths, and (3) contributions from Raman tend to be a decreasing function of biomass. The latter point can be seen as higher relative contribution to Rrs(λ) from Raman scatter in the oligotrophic gyres and lower values in productive high latitude waters and areas of strong upwelling (Fig. 5). Further, if the global data are binned into three broad Chl ranges, which can loosely be categorized as oligotrophic, mesotrophic, and eutrophic (Chl<0.05mgm3, 0.1<Chl<0.5mgm3, and Chl>1.0mgm3, respectively), we can collapse the spatial information and look at results across all wave bands (Fig. 6). The spectral variability is similar to that seen in the simulated data presented in Fig. 1, where the Raman component contributes very little (2%) to Rrs at 412 nm, but then increases more rapidly for clearer water. Maximal Rrs,R/Rrs is observed at 547 nm (formerly referred to as 551 nm) among the bands analyzed here and is approximately 11%, 7%, and 2% for oligotrophic, mesotrophic, and eutrophic waters.

Fig. 5. Fractional contribution of Raman component to total Rrs(λ) calculated for a single L3 monthly MODIS composite image (October 2004). Values are expressed as a percentage (%) and each panel shows different MODIS wave bands in the visible.
Fig. 6. Fractional contribution of Raman scattered radiance to total Rrs(λ) for various ranges of observed satellite Chl (October 2004). Chl bins are for values <0.05mgm3 (top curve), 0.1<Chl<0.5mgm3 (middle curve), and Chl>1.0mgm3 (bottom curve). Error bars represent ranges of variability within each Chl bin. Results for MODIS wave bands >551nm not shown, due to contamination by Chl fluorescence.

Last, we remove the estimated Rrs,R(λ) from satellite Rrs(λ) and re-invert the global fields to provide Raman-corrected IOP estimates (Fig. 7). The global distribution of IOPs before and after correction show varied responses. For the GSM model, median Chl decreases only slightly (8%) from 0.12mgm3 to 0.11mgm3 after correction for Raman [Fig. 7(a)]. Median phytoplankton absorption (aph(443)) estimated from the QAA decreases similarly (8%) following correction [Fig. 7(d)]. Retrievals of CDOM and detrital absorption, aCDM(443), are particularly insensitive to the presence of Raman scattering and only change by <3% for either inversion model [Figs. 7(b) and 7(e)]. The largest differences resulting from the Raman correction are observed in bbp(443), similar to that seen in the simulated dataset. Global distributions of bbp(443) from GSM and QAA, precorrection and postcorrection are shown in Figs. 7(c) and 7(f). The distributions for each model are shifted downward after Raman correction, and the overall distributions become flatter. The changes in bbp(443) are further examined in Fig. 8, which shows the overall distribution of the difference due to Raman correction (expressed as a relative bias, %), as well as the spatial distribution of this bias. Differences are consistently higher for GSM bbp(443) retrievals [Fig. 8(a)] than for the QAA. Raman correction results in values that are much lower across most of the mid-latitudes, and to a lesser extent at high latitudes. The median bias is 30% and 20% for the GSM and QAA, respectively, and suggests that bbp(443) is significantly overestimated over much of the ocean when using either model. While these “average” biases may not seem too large on their own, it is important to note that up to 30% of the ocean has errors due to Raman in excess of 50% [see CDF in Fig. 8(c)].

Fig. 7. Histograms of global IOP retrievals for a single L3 monthly composite (October 2004). Top panels show GSM retrievals of (a) Chl; (b) aCDM(443); (c) bbp(443). Bottom panels show QAA retrievals for (d) aph(443); (e) aCDM(443); (f) bbp(443). In each panel, the black histogram is from monthly values estimated without any correction for Raman scattering (the default), and the red line is from inversion after removing the Raman contribution to Rrs(λ).

4. Discussion and Conclusions

The approach presented here is not without its limitations, and significant biases due to Raman remain in inverted quantities even after correction. However, nearly all of the error due to Raman scatter can be corrected for, and removed if all inherent and apparent optical property input data is known accurately, such as the example shown with simulated data (blue lines in Fig. 3). This suggests that inability to completely correct for the Raman scattering is not due to the method presented in Eq. (7), but rather to the inversion schemes themselves. Conceptually, this procedure should be run iteratively, with each iteration removing slightly more Raman-associated bias. What we found in doing so, however, is that the exercise converged after a single iteration. Inspection of Eqs. (7) and (8) show that the IOPs required to estimate Rrs,R(λ) are total absorption, a(λ), and backscattering, bb(λ). Since a(λ)bb(λ) in the oligotrophic ocean, Rrs,R(λ) is primarily dependent upon total absorption, which is retrieved relatively well, particularly when including pure seawater absorption. So, while errors in bbp(λ) may remain relatively large, the correction cannot improve them with subsequent iterations. Similar findings were reported by Loisel and Stramski [23

23. H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]

]. Interestingly, inversion estimates of aCDM(443) are relatively insensitive to the presence of Raman and its correction. This is most likely because aCDM(λ) is weighted toward short wavelengths (UV and blue/violet) and there is very little inelastic contribution to Rrs(λ) in this region (Fig. 1). This, in turn, results from the strongly attenuated excitation irradiances for these emission bands at the sea surface (peak excitation wavelengths for the 412 and 443 nm MODIS bands are at 365 and 387 nm, respectively).

There are other confounding factors for unraveling the effect of Raman scattering on ocean color inversion models. For example, field data that is used to parameterize models (e.g., NASA’s NOMAD, [42

42. P. J. Werdell and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

]) already contain inelastic scattering contributions from Raman. The process of optimizing the inversion models [27

27. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]

,31

31. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef]

] should mitigate some of the Raman effect, such that errors estimated here may be viewed as upper bounds. Further, if inversion model coefficients have been optimized to match Rrs containing Raman with coincident IOPs, then subsequent removal of the Raman component will necessarily degrade the model’s ability to correctly retrieve the IOPs. In this context, a more appropriate test for Raman effects on inversion models would be to evaluate the retrieval of IOPs from corrected Rrs with a model that has been “re”-optimized with a dataset that has had Raman contributions to Rrs removed.

The global patterns and conclusions drawn here result from the analysis of an illustrative example of a single monthly satellite composite. This approach must be applied to a longer time period in order to better characterize the extent of bias attributed to Raman scatter in the global ocean. The steep dependence of the Raman bias on Chl dictates how important it may be for a particular application. For example, regional studies in highly productive areas might ignore Raman effects with only modest errors in retrieved IOPs. In contrast, targeted studies of the oligotrophic gyres would be well-served to consider Raman contributions to Rrs(λ) and inverted IOPs. The results conveyed in Figs. 7 and 8 provide an illustrative example of global patterns. Last, the biases calculated must be propagated through to the biogeochemical quantities of interest to evaluate the significance of this process. For example, relationships that estimate particle stocks from bbp (e.g., [47

47. D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5, 171–201 (2008). [CrossRef]

,48

48. T. Westberry, M. J. Behrenfeld, D. A. Siegel, and E. Boss, “Carbon-based primary productivity modeling with vertically resolved photoacclimation,” Global Biogeochem Cycles 22, GB2024 (2008). [CrossRef]

]) will be affected in direct proportion to the Raman bias. However, some applications [e.g., calculation of net primary production (NPP)] will require more detailed sensitivity analyses to understand the impact of the Raman bias.

Fig. 8. Comparison of satellite bbp(443) inversions before and after removal of Raman component of remote sensing reflectance, Rrs,R(λ). (a) and (b) show the spatial distribution of error in bbp(443) due to Raman for the GSM and QAA inversions, respectively. (c) and (d) are histograms of each respective image. Black lines are cumulative distribution functions of each field. Bias is calculated as normalized difference between bbp(443) estimated from satellite Rrs(λ) with and without Raman scatter included (×100 to express as a percentage).

References

1.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988). [CrossRef]

2.

C. R. McClain, S. R. Signorini, and J. R. Christian, “Subtropical gyre variability observed by ocean-color satellites,” Deep-Sea Research, Part II 51, 281–301 (2004). [CrossRef]

3.

D. G. Boyce, M. R. Lewis, and B. Worm, “Global phytoplankton decline over the past century,” Nature 466, 591–596 (2010). [CrossRef]

4.

M. J. Behrenfeld, R. T. O’Malley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature 444, 752–755 (2006). [CrossRef]

5.

C. V. Raman, “On the molecular scattering of light in water and the colour of the sea,” Proc. R. Soc. London Ser. A 101, 64–80 (1922). [CrossRef]

6.

C. V. Raman and K. S. Krishnan, “A new type of secondary radiation,” Nature 121, 501–502 (1928). [CrossRef]

7.

G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967). [CrossRef]

8.

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

9.

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

10.

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

11.

R. A. Desiderio, “Application of the Raman scattering coefficient of water to calculations in marine optics,” Appl. Opt. 39, 1893–1894 (2000). [CrossRef]

12.

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

13.

R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields—Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988). [CrossRef]

14.

Y. T. 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, 4028–4036 (1993).

15.

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

16.

Y. T. 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, 13227–13236 (1995). [CrossRef]

17.

C. M. Hu and K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997). [CrossRef]

18.

J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean colour,” M.S. thesis (Dalhousie University, 1996).

19.

R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. 2. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997). [CrossRef]

20.

H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009). [CrossRef]

21.

Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994). [CrossRef]

22.

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

23.

H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]

24.

IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications” (International Ocean Colour Coordination Group, 2006), Report Number 5.

25.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. H. 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, 7484–7504 (1993). [CrossRef]

26.

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

27.

A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]

28.

R. C. Smith and K. S. Baker, “Optical-properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981). [CrossRef]

29.

P. Ricchiazzi, S. R. Yang, C. Gautier, and D. Sowle, “SBDART: a research and teaching software tool for plane-parallell radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteorol. Soc. 79, 2101–2114 (1998). [CrossRef]

30.

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41, 2705–2714 (2002). [CrossRef]

31.

Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef]

32.

D. Pozdiakov and H. Grassl, Color of Inland and Coastal Waters: A Methodology for its Interpretation (Springer-Praxis, 2003), p. 192.

33.

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

34.

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

35.

V. I. Haltrin and G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic-scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5356–5367 (1993). [CrossRef]

36.

C. Mobley, “Interpretation of Raman scattering computations,” HydroLight Technical Note, 10 (2012).

37.

H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?,” Limnol. Oceanogr. 34, 1389–1409 (1989). [CrossRef]

38.

Z. P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: an evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005). [CrossRef]

39.

J. R. Morrison and N. B. Nelson, “Seasonal cycle of phytoplankton UV absorption at the Bermuda Atlantic Time-series Study (BATS) site,” Limnol. Oceanogr. 49, 215–224 (2004). [CrossRef]

40.

A. Bricaud, M. Babin, H. Claustre, J. Ras, and F. Tieche, “Light absorption properties and absorption budget of Southeast Pacific waters,” J. Geophys. Res. 115, C08009 (2010). [CrossRef]

41.

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990). [CrossRef]

42.

P. J. Werdell and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]

43.

Z. P. Lee, S. L. Shang, C. M. Hu, M. Lewis, R. Arnone, Y. H. Li, and B. Lubac, “Time series of bio-optical properties in a subtropical gyre: Implications for the evaluation of interannual trends of biogeochemical properties,” J. Geophys. Res. 115, C09012 (2010). [CrossRef]

44.

Z. P. Lee, C. M. Hu, S. L. Shang, K. Du, M. Lewis, and R. Arnone, “Penetration of UV-visible solar light in the global oceans: insights from ocean color remote sensing,” J. Geophys. Res.-Oceans, in review.

45.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998). [CrossRef]

46.

A. Morel, Y. Huot, B. Gentili, P. J. Werdell, S. B. Hooker, and B. A. Franz, “Examining the consistency of products derived from various ocean color sensors in open ocean (Case 1) waters in the perspective of a multi-sensor approach,” Remote Sens. Environ. 111, 69–88 (2007). [CrossRef]

47.

D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5, 171–201 (2008). [CrossRef]

48.

T. Westberry, M. J. Behrenfeld, D. A. Siegel, and E. Boss, “Carbon-based primary productivity modeling with vertically resolved photoacclimation,” Global Biogeochem Cycles 22, GB2024 (2008). [CrossRef]

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.1690) Atmospheric and oceanic optics : Color
(010.5630) Atmospheric and oceanic optics : Radiometry
(010.0280) Atmospheric and oceanic optics : Remote sensing and sensors

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: March 18, 2013
Revised Manuscript: June 12, 2013
Manuscript Accepted: July 6, 2013
Published: August 1, 2013

Virtual Issues
Vol. 8, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Toby K. Westberry, Emmanuel Boss, and Zhongping Lee, "Influence of Raman scattering on ocean color inversion models," Appl. Opt. 52, 5552-5561 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-52-22-5552


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References

  1. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988). [CrossRef]
  2. C. R. McClain, S. R. Signorini, and J. R. Christian, “Subtropical gyre variability observed by ocean-color satellites,” Deep-Sea Research, Part II 51, 281–301 (2004). [CrossRef]
  3. D. G. Boyce, M. R. Lewis, and B. Worm, “Global phytoplankton decline over the past century,” Nature 466, 591–596 (2010). [CrossRef]
  4. M. J. Behrenfeld, R. T. O’Malley, D. A. Siegel, C. R. McClain, J. L. Sarmiento, G. C. Feldman, A. J. Milligan, P. G. Falkowski, R. M. Letelier, and E. S. Boss, “Climate-driven trends in contemporary ocean productivity,” Nature 444, 752–755 (2006). [CrossRef]
  5. C. V. Raman, “On the molecular scattering of light in water and the colour of the sea,” Proc. R. Soc. London Ser. A 101, 64–80 (1922). [CrossRef]
  6. C. V. Raman and K. S. Krishnan, “A new type of secondary radiation,” Nature 121, 501–502 (1928). [CrossRef]
  7. G. E. Walrafen, “Raman spectral studies of effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967). [CrossRef]
  8. S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984). [CrossRef]
  9. B. R. Marshall and R. C. Smith, “Raman-scattering and in-water ocean optical-properties,” Appl. Opt. 29, 71–84 (1990). [CrossRef]
  10. J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998). [CrossRef]
  11. R. A. Desiderio, “Application of the Raman scattering coefficient of water to calculations in marine optics,” Appl. Opt. 39, 1893–1894 (2000). [CrossRef]
  12. H. R. Gordon, “Contribution of Raman scattering to water-leaving radiance: a reexamination,” Appl. Opt. 38, 3166–3174 (1999). [CrossRef]
  13. R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields—Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988). [CrossRef]
  14. Y. T. 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, 4028–4036 (1993).
  15. K. J. Waters, “Effects of Raman-scattering on the water-leaving radiance,” J. Geophys. Res. 100, 13151–13161 (1995). [CrossRef]
  16. Y. T. 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, 13227–13236 (1995). [CrossRef]
  17. C. M. Hu and K. J. Voss, “In situ measurements of Raman scattering in clear ocean water,” Appl. Opt. 36, 6962–6967 (1997). [CrossRef]
  18. J. S. Bartlett, “The influence of Raman scattering by seawater and fluorescence by phytoplankton on ocean colour,” M.S. thesis (Dalhousie University, 1996).
  19. R. M. Pope and E. S. Fry, “Absorption spectrum (380–700 nm) of pure water. 2. Integrating cavity measurements,” Appl. Opt. 36, 8710–8723 (1997). [CrossRef]
  20. H. R. Gordon, M. R. Lewis, S. D. McLean, M. S. Twardowski, S. A. Freeman, K. J. Voss, and G. C. Boynton, “Spectra of particulate backscattering in natural waters,” Opt. Express 17, 16192–16208 (2009). [CrossRef]
  21. Z. P. Lee, K. L. Carder, S. K. Hawes, R. G. Steward, T. G. Peacock, and C. O. Davis, “Model for the interpretation of hyperspectral remote-sensing reflectance,” Appl. Opt. 33, 5721–5732 (1994). [CrossRef]
  22. S. Sathyendranath and T. Platt, “Ocean-color model incorporating transspectral processes,” Appl. Opt. 37, 2216–2227 (1998). [CrossRef]
  23. H. Loisel and D. Stramski, “Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering,” Appl. Opt. 39, 3001–3011 (2000). [CrossRef]
  24. IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications” (International Ocean Colour Coordination Group, 2006), .
  25. C. D. Mobley, B. Gentili, H. R. Gordon, Z. H. 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, 7484–7504 (1993). [CrossRef]
  26. H. R. Gordon and A. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery. A Review (Springer-Verlag, 1983).
  27. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: a reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001). [CrossRef]
  28. R. C. Smith and K. S. Baker, “Optical-properties of the clearest natural waters (200–800 nm),” Appl. Opt. 20, 177–184 (1981). [CrossRef]
  29. P. Ricchiazzi, S. R. Yang, C. Gautier, and D. Sowle, “SBDART: a research and teaching software tool for plane-parallell radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteorol. Soc. 79, 2101–2114 (1998). [CrossRef]
  30. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41, 2705–2714 (2002). [CrossRef]
  31. Z. P. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41, 5755–5772 (2002). [CrossRef]
  32. D. Pozdiakov and H. Grassl, Color of Inland and Coastal Waters: A Methodology for its Interpretation (Springer-Praxis, 2003), p. 192.
  33. H. R. Gordon, “Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm,” Appl. Opt. 18, 1161–1166 (1979). [CrossRef]
  34. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  35. V. I. Haltrin and G. W. Kattawar, “Self-consistent solutions to the equation of transfer with elastic and inelastic-scattering in ocean optics: 1. Model,” Appl. Opt. 32, 5356–5367 (1993). [CrossRef]
  36. C. Mobley, “Interpretation of Raman scattering computations,” HydroLight Technical Note, 10 (2012).
  37. H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?,” Limnol. Oceanogr. 34, 1389–1409 (1989). [CrossRef]
  38. Z. P. Lee, M. Darecki, K. L. Carder, C. O. Davis, D. Stramski, and W. J. Rhea, “Diffuse attenuation coefficient of downwelling irradiance: an evaluation of remote sensing methods,” J. Geophys. Res. 110, C02017 (2005). [CrossRef]
  39. J. R. Morrison and N. B. Nelson, “Seasonal cycle of phytoplankton UV absorption at the Bermuda Atlantic Time-series Study (BATS) site,” Limnol. Oceanogr. 49, 215–224 (2004). [CrossRef]
  40. A. Bricaud, M. Babin, H. Claustre, J. Ras, and F. Tieche, “Light absorption properties and absorption budget of Southeast Pacific waters,” J. Geophys. Res. 115, C08009 (2010). [CrossRef]
  41. W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990). [CrossRef]
  42. P. J. Werdell and S. W. Bailey, “An improved in-situ bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005). [CrossRef]
  43. Z. P. Lee, S. L. Shang, C. M. Hu, M. Lewis, R. Arnone, Y. H. Li, and B. Lubac, “Time series of bio-optical properties in a subtropical gyre: Implications for the evaluation of interannual trends of biogeochemical properties,” J. Geophys. Res. 115, C09012 (2010). [CrossRef]
  44. Z. P. Lee, C. M. Hu, S. L. Shang, K. Du, M. Lewis, and R. Arnone, “Penetration of UV-visible solar light in the global oceans: insights from ocean color remote sensing,” J. Geophys. Res.-Oceans, in review.
  45. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998). [CrossRef]
  46. A. Morel, Y. Huot, B. Gentili, P. J. Werdell, S. B. Hooker, and B. A. Franz, “Examining the consistency of products derived from various ocean color sensors in open ocean (Case 1) waters in the perspective of a multi-sensor approach,” Remote Sens. Environ. 111, 69–88 (2007). [CrossRef]
  47. D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5, 171–201 (2008). [CrossRef]
  48. T. Westberry, M. J. Behrenfeld, D. A. Siegel, and E. Boss, “Carbon-based primary productivity modeling with vertically resolved photoacclimation,” Global Biogeochem Cycles 22, GB2024 (2008). [CrossRef]

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