hyperspectral absorption coefficient of seawater in the...

Hyperspectral absorption coefficient of “pure”seawater in the range of 350–550 nm inverted

from remote sensing reflectance

Zhongping Lee,1,* Jianwei Wei,1 Ken Voss,2 Marlon Lewis,3

Annick Bricaud,4,5 and Yannick Huot6

1School for the Environment, University of Massachusetts Boston, Boston, Massachusetts 02125, USA2Department of Physics, University of Miami, Coral Gables, Florida 33124, USA

3Department of Oceanography, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada4Sorbonne Universités, UPMC Univ Paris 06, UMR 7093, LOV, Observatoire océanologique,

F-06230, Villefranche/mer, France5CNRS, UMR 7093, LOV, Observatoire océanologique, F-06230, Villefranche/mer, France

6Département de géomatique appliquée, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada

*Corresponding author: [email protected]

Received 20 October 2014; revised 5 December 2014; accepted 6 December 2014;posted 9 December 2014 (Doc. ID 225317); published 20 January 2015

Hyperspectral (every 5 nm) absorption coefficients of “pure” seawater in the range of 350–550 nm arederived from remote sensing reflectance measured in oligotrophic oceans. The absorption spectrum isreduced by ∼50–70% for the 350–400-nm range and ∼5–10% for the 510–530-nm range compared withthe commonly adopted standard for ocean color processing and shows different spectral curvatures. Theapplication of this new spectrum resulted in better retrievals of the phytoplankton absorption coefficientin oligotrophic oceans and will provide better closure of remote sensing reflectance for theUV–visible domain. © 2015 Optical Society of AmericaOCIS codes: (010.1030) Absorption; (010.4450) Oceanic optics; (010.0280) Remote sensing and

sensors; (010.7340) Water.http://dx.doi.org/10.1364/AO.54.000546

1. Introduction

The spectral absorption coefficient of pure seawater�aw�λ� �m−1�� is a basic inherent optical property(IOP) [1]. It is required for estimating and analyzingthe light field in the upper ocean and is critical foranalytically processing ocean color data. Becauseof its importance, many aw�λ� data have been ob-tained and reported in the literature (see reviewsin Morel and Prieur [2], Smith and Baker [3], Popeand Fry [4], and Fry [5]). Because of various limita-

tions, including the preparation of a “pure” watersample and the technical challenges associated withmeasuring very low absorption coefficients and sepa-rating them from scattering effects [6], these re-ported aw�λ� values differ by a factor of up to 5 inthe shorter wavelengths, particularly for wave-lengths in the range of ∼350–500 nm (see Fig. 1 inSmith and Baker [3] and Fig. 10 in Pope and Fry[4], for instance). For ocean optics studies and oceancolor data processing, the values in Pope and Fry [4][represented as aPF

w �λ� and aSPFw �λ� after merging the

values of Pope and Fry [4] for wavelengths equal to orgreater than 380 nm with those of Sogandares andFry [7] for wavelengths of less than 380 nm] have

1559-128X/15/030546-13$15.00/0© 2015 Optical Society of America

546 APPLIED OPTICS / Vol. 54, No. 3 / 20 January 2015

http://dx.doi.org/10.1364/AO.54.000546

been adopted as the “standard” by the ocean colorcommunity. However, an application of aSPF

w �λ�when modeling the remote sensing reflectance[Rrs�λ� �sr−1�, which is the ratio of the water-leavingradiance to the downwelling irradiance just abovethe surface] of oligotrophic oceans does not produceappropriate spectral curvature for wavelengths ofaround 400 nm [8]. In addition, for measurementsmade in the South Pacific Gyre, where the “clearest”natural water [9] has been measured, the applicationof aSPF

w �λ� will result in negative absorption coeffi-cients of yellow substance for wavelengths of around420 nm [9]. As further demonstrated in the followingsections, measurements in the oligotrophic oceansindicate that values of aSPF

w �λ� in the shorter wave-lengths (∼350–450 nm) do not provide a closure forRrs�λ� of such waters. As Fry [5] pointed out, “Theredoes not seem to be a best choice of data covering thegap 320 nm ≤ λ ≤ 380 nm.” Because NASA andthe international community are pushing ocean colorremote sensing to the UV region and the 350- to 400-nm spectral window could be significantly importantfor the retrieval of the absorption coefficient ofgelbstoff or yellow substance [10,11], it is thus ur-gently important to determine an appropriateaw�λ� spectrum for the UV–visible domain. Here,we address this problem through the use of the high-est-quality data from oligotrophic oceans, whereaw�λ� play a larger role compared with more produc-tive waters and derive an effective aw�λ� from theRrs�λ� spectrum. After demonstrating the nonclosureof Rrs�λ� in these waters when applying aSPF

w �λ�,details of the specific data and methodologies forthe derivation of aw�λ� are presented, followed bythe resultant aw�λ�. The impact of this aw�λ� on ana-lytical retrievals of the phytoplankton absorptioncoefficients in oligotrophic waters is then discussed.

2. Motivation

Because Rrs�λ� is a function of the IOPs [12,13], themeasured Rrs�λ� should match the Rrs�λ� calculatedwith the measured IOPs of the same water body ifall components are well determined experimentallyand if the assumptions of the models are fully met.For the South Pacific Gyre, comprehensive measure-ments of a wide range of water properties were madeduring the BIOSOPE cruise [14], which includedRrs�λ� [9,15] and various component IOPs [16–18].To check the closure of Rrs�λ�, a simplified but widelyused relationship between Rrs�λ� and the IOPs devel-oped based on numerical simulations of radiativetransfer [19] was used

rrs�λ� ��0.0979� 0.0794

bb�λ�a�λ� � bb�λ�

�bb�λ�

a�λ� � bb�λ�;

(1)

where rrs�sr−1� is the subsurface remote sensingreflectance, which is related to the above-surfaceremote sensing reflectance (Rrs) through [19,20]

Rrs�λ� �0.52rrs�λ�

1 − 1.7rrs�λ�: (2)

Here, a and bb are the total absorption and backscat-tering coefficients (units in m−1), respectively, andcan be expressed as [21,22]

a�λ� � aw�λ� � aph�λ� � ad�λ� � ay�λ�;bb�λ� � bbw�λ� � bbp�λ�: (3)

aph;d;y are the absorption coefficients of the phyto-plankton pigments, detritus, and yellow substance,respectively; and bbw and bbp are the backscatteringcoefficient of pure seawater and the suspended par-ticles, respectively. Generally, the spectra of both awand bbw are assumed to be well known and are takenas constants for the global oceans, although they varyslightly with temperature and salinity [23–25].Therefore, when the values of spectral aph;d;y andbbp—i.e., the IOPs of the active constituents—areknown, it is straightforward to calculate Rrs�λ� basedon Eqs. (1)–(3). In addition, if both the active IOPsand Rrs are accurately determined in the field andEqs. (1) and (2) are accurate, the modeled Rrs withthe measured IOPs should match the measuredRrs—i.e., a closure in Rrs will be achieved.

For measurements made in the South Pacific Gyreduring the BIOSOPE cruise, instead of comparingthe measured-versus-modeled Rrs�λ� station by sta-tion, we compared the averaged Rrs�λ� of the “clear-est” waters (Stations GYR2-5 and STB6-8) with themodeled Rrs�λ� using the averaged IOPs as inputs toshow a generalized pattern between the measuredand modeled Rrs�λ�. For an easier description ofthe component IOPs (e.g., aph;d;y and bbp), their spec-tral dependences are described following commonpractice [26,27] as

aph�λ� � aph�440�a�ph�λ�; (4a)

ad�λ� � ad�440�e−Sd�λ−440�;

ay�λ� � ay�440�e−Sy�λ−440�; (4b)

bbp�λ� � bbp�550��550λ

�Y: (4c)

Here, a�ph�λ� is the dimensionless spectral shape of

aph�λ� and was obtained from sample measurements[16]. For these super-blue waters, aph�440�was foundto be ∼0.0015 m−1, with an ad�440� of ∼0.0005 m−1

and an ay�440� of ∼0.0016 m−1 [16]. Sd;y �nm−1�and Y are the spectral shape parameters for ad;y andbbp, respectively; Sd was found to be ∼0.0094 nm−1

and Sy was found to be ∼0.0145 nm−1 [16]. Theaveraged bbp�550� for the South Pacific Gyre wasmeasured as ∼0.0003 m−1 [17,28], but a value of0.0003 m−1 was added to this measurement to reflecta likely uncertainty in the measured bbp [18] and to

20 January 2015 / Vol. 54, No. 3 / APPLIED OPTICS 547

ensure an Rrs closure at 550 nm—i.e., aw�550� fromPope and Fry [4] was considered correct. The dimen-sionless exponent Y was taken as 1.9 based on themeasured bbp values at 470 and 550 nm [28]. Forthe modeling of Rrs�λ� of such super-blue waters,the magnitudes of the component IOPs [e.g.,aph;d;y�440� and bbp�550�] were further disturbed by�50% to show the range of Rrs�λ� that would be ex-pected with these IOPs. On the other hand, for aw�λ�,both aSPF

w �λ� and that recommended inMorel et al. [9](aw1) were used, respectively.

Figure 1(a) shows the range of modeledRrs�λ� spec-tra (green lines) with aSPF

w �λ� and the active IOPs de-scribed previously, along with the averaged Rrs�λ�spectrum from 12 measurements of super-bluewaters (Stations GYR2-5 and STB6-8), whereRrs�440�∕Rrs�550� is larger than 12.0. Clearly thereare large differences between the modeled and themeasured Rrs�λ� in the 350–500-nm range, even witha�50% range of the measured component IOPs. Notonly are the values quite different but also the cur-vatures do not match each other. In particular, themodeled Rrs�λ� in the 350–400-nm range are ∼40%smaller than the measured Rrs�λ�. In other words,there is no closure in Rrs�λ� for the 350–500-nmrange. It is unlikely that the measured Rrs�λ� havesuch large overestimations, as the coefficient ofvariation at each wavelength of the 12 Rrs�λ� spectra(measured at seven stations) is less than4%. Further, the uncertainty of the Rrs–IOP modelitself [Eq. (1)] is just about 10% [19] (also refer toSection 4.A), which cannot explain the large devia-tions, specifically in the 350–400-nm window. Thisnonclosure actually echoes the finding of Morel et al.[9] that the aSPF

w �λ� values in the ∼350–400-nm rangeare too high for such waters.

Buiteveld et al. [29] and Morel et al. [9] proposedusing spectrally interpolated aw�λ� from the discretemeasurements in the UV in Boivin et al. [30] for val-ues in the shorter wavelengths, and Morel et al. [9]

suggested linking Boivin et al. [30] aw�λ� data afterinterpolation with that measured by Pope and Fry[4] at 420 nm [represented as aMPF

w �λ� in the follow-ing]. Thus, with the same IOPs but replacing theaSPFw �λ� values with those of aMPF

w �λ�, the modeledRrs�λ� are compared with the Rrs�λ� of the super-bluewaters again [refer to Fig. 1(b)]. For the same rangeof the component IOPs, the closure of Rrs�λ� for wave-lengths in the range of ∼350–410 nm improved sig-nificantly, but there was no improvement forwavelengths of around 450 nm [the modeled Rrs�λ�was still ∼20% less than the measuredRrs�λ�]—a spectral window important for analyticalderivation of the absorption coefficients of phyto-plankton and yellow substance. These observationssupport the findings of earlier studies regardingthe nonsuitability of the current “standard” purewater absorption coefficients in the shorter wave-lengths. In short, because (1) the results of Boivinet al. [30] are associated with large uncertainties[4]; (2) the combination of the values of Biovin et al.[30] and those of Pope and Fry [4] is subjective; and(3) the merger provides only “an upper limit of purewater absorption coefficient” [9], it is thus importantand necessary to obtain an aw�λ� spectrum that isconsistent with field observations.

3. Data

Data used for the derivation of aw�λ� spectral valueswere collected in the South Pacific Gyre and at theMarine Optical Buoy (MOBY). During the BIOSOPEcruise (November 2004), a free-fall hyperspectral(350–800 nm, 10-nm bandwidth, 3-nm interval) radi-ometer (Satlantic, Inc.) was used to measure the ver-tical profiles of upwelling radiance and downwellingirradiance for a series of stations located in theSoutheast Pacific Ocean [14]. Remote sensing reflec-tance (Rrs) was calculated from these profiles. Detailsof the data processing can be found in Lee et al. [15].Figure 2(a) presents examples of Rrs�λ� from these

0.000

0.005

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0.025

mea. Rrsmod. Rrs

(b)

350 400 450 500 550 600 650 700350 400 450 500 550 600 650 7000.000

0.005

0.010

0.015

0.020

0.025

mea. Rrsmod. Rrs

(a)

Fig. 1. Comparison between measured (blue) and modeled (green) Rrs spectra for measurements made in the South Pacific Gyre(November 2004). Measured Rrs represents the average of 12 casts of the “clearest” oceanic waters, and contribution from Raman scatter-ing is removed empirically (refer to Section 4.B). ModeledRrs (Mod_Rrs) is generated [Eqs. (1)–(4)] using the component IOPs measured atthe same “clearest” stations by adding �50% uncertainty to each optically active component. (a) Mod_Rrs used pure water absorptioncoefficients from Pope and Fry [4] (for wavelengths from 380 to 700 nm) and that from Sogandares and Fry [7] (for wavelengths from 350 to370 nm). (b) Mod_Rrs used pure water absorption coefficients from Pope and Fry [4] for wavelengths from 420 to 700 nm and those fromBoivin [30] for wavelengths from 350 to 420 nm, as proposed by Morel et al. [9].


measurements, with Rrs�λ� of pure seawater [simu-lated with HydroLight [31] and aSPF

w �λ� for absorptioncoefficients of pure seawater] also included, whichshows that the Rrs�λ� values of pure seawater arelower than those of the “clearest” natural water forthe range of ∼350–400 nm.

During the BIOSOPE cruise, there were also ex-tensive measurements of the absorption coefficientsof phytoplankton pigments, yellow substance, andthe scattering and backscattering coefficients of par-ticles (see Bricaud et al. [16], Twardowski et al. [17],and Stramski et al. [18]). Data of these measure-ments can be accessed at http://www.obs‑vlfr.fr/proof/vt/op/ec/biosope/bio.htm.

MOBY [32] is located approximately 20 km west ofLanai, Hawaii, where hyperspectral (∼1.0 nm reso-lution) measurements of upwelling radiance aremade at 1, 5, and 9 m below the surface, andwater-leaving radiance was estimated from thesemeasurements [32]. An irradiance sensor is placedabove the surface to measure downwelling irradiancejust above the surface for the calculation ofRrs�λ�. Forthis study, to have an adequate representation, threedays of high-quality Rrs�λ� for each season in 2013were randomly acquired from the MOBY websitehttp://coastwatch.noaa.gov/data/moby/filtered_spec/.For each day, two Rrs�λ� spectra (calculated from theupwelling measurements of the 1- and 5-m arms)were used, resulting in a total of 24 Rrs�λ� fromthe MOBY measurements utilized for this study.Figure 2(b) presents examples of MOBY Rrs�λ�(binned to 5-nm bandwidth and interpolated to 5-nmresolution), where the highest values are approxi-mately 0.016 sr−1, whereas the highest values for theSouth Pacific Gyre are approximately 0.025 sr−1.This is expected because the South Pacific Gyre isconsidered the most oligotrophic area of the world’soceans; thus, the absorption coefficients of MOBYwaters (not measured) are expected to be higher.The bumps in the MOBY Rrs�λ� around 400 nm—

not highly visible in the BIOSOPE data because ofthe lower spectral resolution—are the results ofthe filling of the Fraunhofer line [33] in the upwell-ing radiance from Raman scattering.

4. Method

A. Model for Remote Sensing Reflectance

The analytical derivation of bulk IOPs—and sub-sequently, aw�λ�—uses the dependence of Rrs�λ� asa function of the IOPs, along with the measuredRrs�λ� as inputs. Decades of numerical simulationsof radiative transfer have resulted in many analyti-cal forms to describe the relationship between Rrs�λ�and the bulk IOPs, specifically a�λ� and bb�λ�[19,34,35]. Using the most “accurate”model to obtaina�λ� from Rrs�λ� is important, as a modeling error inRrs�λ� will be propagated to the inverted a�λ� andthen aw�λ�. The relationship widely used by the com-munity was developed by Gordon et al. [19]—i.e.,Eq. (1). In this relationship, the spectral change ofthe scattering phase function of the bulk water isignored [36,37]. As a result, independent of wave-length, the estimated rrs�λ� will be the same as longas the ratio bb�λ�∕�a�λ� � bb�λ�� is the same. The sameapproach was followed for a fourth-order polynomialfunction developed by Albert and Mobley [38], lead-ing to the same wavelength-independent behavior,where rrs�λ� is described as

rrs�λ� � ωX4i�1

�gi

bb�λ�a�λ� � bb�λ�

�i; (5)

with parameter ω describing the effects due to windspeed and sun sensor viewing geometry and g1 �sr−1�for modeling coefficients to fit numerically simu-lated rrs�λ�.

However, water molecular scattering (Rayleighscattering) is much stronger at shorter wavelengthsthan at longer wavelengths [39], and its scatteringphase function is markedly different from that of par-ticle scattering. Therefore, it is necessary to separatethe effects of molecular and particle scatterings inthe resulting solution [40,41]. One attempt is themodel developed by Lee et al. [36], where the twoscattering processes are separated explicitly in anrrs�λ� model:

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0.015

(b)

350 400 450 500 550 600 650 7000.000

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0.015

0.020

0.025

(a)

Fig. 2. Remote sensing reflectance measured at (a) South Pacific Gyre and (b) the MOBY. Rrs(λ) of pure seawater, simulated by Hydro-Light with aSPF

w �λ� for pure water absorption coefficients, is included in (a) (green line) for a visual comparison.


http://www.obs-vlfr.fr/proof/vt/op/ec/biosope/bio.htm





http://coastwatch.noaa.gov/data/moby/filtered_spec/



rrs�λ� � 0.113bbw�λ�

a�λ� � bb�λ�� gp

bbp�λ�a�λ� � bb�λ�

; (6)

with model parameter gp�sr−1� described as

gp � 0.197�1 − 0.636 exp

�−2.552


��:

(7)

Because the gp function is complex, bbp cannot besolved analytically from the known rrs and a as proc-essed in the quasi-analytical algorithm (QAA) [20],and thus data processing efficiency is reduced. Toremedy this efficiency limitation, Eq. (6) and thetransmission function [Eq. (2)] were bundled to-gether as in Park and Ruddick [37] and modeledas [42]

Rrs�λ� ��Gw

0 �Gw1

bbw�λ�a�λ� � bb�λ�

�bbw�λ�

a�λ� � bb�λ�

��Gp

0 �Gp1


�bbp�λ�

a�λ� � bb�λ�; (8)

with the model parameters �Gw0 ; G

w1 ; G

p0; G

p1� for vari-

ous sun sensor viewing geometries determinedthrough HydroLight simulations [42].

To account for the change of the scattering phasefunction for different particle loading, Park and Rud-dick [37] also employed a fourth-order polynomialfunction of bb�λ�∕�a�λ� � bb�λ�� to model Rrs�λ� but in-troduced bbp∕bb-dependent gi �sr−1� coefficients, withvalues of gi tabulated for eight bbp∕bb ratios. Becauseit is not straightforward to describe the wavelengthdependence of these model parameters, a comparisonwith this model is omitted herein. Also omitted forcomparison is the model developed by Morel andGentili [43] and Morel et al. [44], where rrs is de-scribed as a function of g bb∕a, with g (which istermed f∕Q [44]) values tabulated for six chlorophyllconcentrations, seven wavelengths, and a series ofsun sensor angles under the assumption of “Case1” bio-optical dependences [45]. Because the dataunder study are hyperspectral, this rrs model is thusnot straightforwardly applicable.

To evaluate how the aforementioned analyticalmodels perform for oligotrophic waters, five Rrs�λ�spectra for the wavelength range of 350–700 nm(5-nm resolution) and chlorophyll concentrations([Chl]) of 0.02, 0.05, 0.1, 0.2, and 0.5 mg∕m3 weresimulated with HydroLight (V. 5.1.2) [31]. In thesesimulations, the sun angle was set as 30° fromzenith, with default bio-optical models embeddedin HydroLight for the component IOPs, except thatthe factor (F) for the yellow substance absorption co-efficient at 440 nm was set as 1.0 [i.e., ay�440� �aph�440�� for all five [Chl] values to better representoceanic waters [45]. The same IOP spectra used inthe HydroLight simulations were also used to calcu-late the Rrs�λ� spectrum with the analytical models

[Eqs. (1), (2), (5), (6), and (8), respectively] for each[Chl] value. Then, the ratio of the analyticallymodeled Rrs�λ� spectrum (Rrs_mod) to the Hydro-Light-simulated Rrs�λ� spectrum (Rrs_HL) wascalculated for each [Chl], along with the averageand standard deviation of the ratios, respectively,of the five [Chl] for each analytical model. Figure 3shows the results for the aforementioned four mod-els. Generally, these ratios are within �20%, consis-tent with the ranges presented in the articles formodel development, but the four models do exhibitdifferent behaviors. The ratio with the Gordon et al.[19] model (G88) shows a range of ∼1.03–1.15 andgenerally increases with wavelength; and the ratiohas a larger standard deviation for the longer wave-lengths. The ratio of the Albert and Mobley [38]model (A03) spans a range of ∼1.1 (shorter wave-length) to ∼0.9 (longer wavelength), with a widerange of deviations for each wavelength, indicatinga nonuniform performance for the [Chl] and wave-length. The ratio with the Lee et al. [36] model(L04) shows a range of ∼1.0–1.02 for the entire350–700-nm range and very small deviation acrossthe spectral range. The ratio with the Lee et al.[42] model (L11) shows a range of ∼1.03–1.07 and de-creases with increasing wavelength. Models A03,L04, and L11 were developed based on numericalsimulations by HydroLight, where a consistencybetween the model and HydroLight simulations isexpected. Model G88 was developed based on MonteCarlo simulations, so there is a slight difference dueto numerical handling of the radiative transfer [46]and the particle scattering phase functions used.Nevertheless, because models such as Eq. (6) providea uniform performance for different chlorophyll con-centrations and wavelengths, Model L04 is used inthe following for the inversion of the IOPs.

B. Correction of Contribution due to Raman Scattering

The aforementioned analytical models [Eqs. (1), (5),(6), and (8)] reflect the processes resulting from elas-tic scattering—i.e., where there is no change of wave-length between the incident and output photons.In the oceans, inelastic scattering processes also

350 400 450 500 550 600 650 700

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1.0

1.1

1.2

G88A03L04L11

Fig. 3. Performance of analytical Rrs expressions in modelinghyperspectral Rrs(λ). G88: Gordon et al. [19]; A03: Albert andMobley [38]; L04: Lee et al. [36]; L11: Lee et al. [42].


contribute photons to Rrs�λ�, and Raman scatteringis one of the inelastic scattering processes that canaccount for ∼20% of the signal for oligotrophic watersin the long wavelengths [47–50]. Therefore, it is nec-essary to correct this effect in the measured Rrs�λ�spectrum for accurate derivation of the IOPs.

From the radiative transfer equation, it is foundthat the contribution to Rrs�λ� from Raman scatter-ing can be written as [51,52]

RRars �λ�

� �1−ρL��1−ρE�n2

bRabw�λex�Kd�λex��kL�λ�

Ed�0�;λex�Ed�0�;λ� �1�δ�:

(9)

Here, ρL and ρE are the air–sea surface reflectance forupwelling radiance and downwelling irradiance,respectively; n is the refractive index of seawaterand is considered to be spectrally independent,bRabw�λex� is the Raman backscattering coefficient ofpure seawater; Kd and kL are the diffuse attenuationcoefficients (m−1) of downwelling irradiance andupwelling radiance, respectively; and Ed�0�� is thedownwelling irradiance just above the surface, whereλex is the excitation wavelength corresponding to λ.Parameter δ represents the secondary effects dueto multiple scattering.

The wavelength gap between λex and λ is∼40–140 nm for λ in the range of 350–700 nm(λ > λex). Therefore, it is necessary to have Kd andEd�0�� information in the domain of ∼310 −

350 nm to estimate RRars �λ� for λ in the 350–400-nm

range based on Eq. (9). The shortest wavelength ofthe radiance and irradiance measurements was ap-proximately 350 nm (see Section 3), which preventedus from using Eq. (9) to analytically estimate RRa

rs �λ�.To overcome this limitation in our data sets, we fol-lowed the empirical scheme as shown in Lee et al.[15,53] for the correction of Raman scattering.Basically, the no-Raman Rrs�λ� is expressed as

Rrs�λ� �RT

rs�λ�1� RF�λ� : (10)

Here, RTrs�λ� is the measured remote sensing reflec-

tance that includes the contribution from Ramanscattering, and RF is the Raman factor. Based on aseries of numerical simulations with HydroLightfor hyperspectral remote sensing reflectance, theempirical formula for RF�λ� is updated as

RF�λ� � α�λ��RT

rs�440�RT

rs�550�

�β�λ�� γ�λ�e−RT

rs�550�; (11)

with values for α, β, and γ for wavelengths in therange of 350–700 nm derived by fitting Eq. (11) tothe RF values obtained from HydroLight simula-tions. RF�λ� is sensitive to the bandwidth of radiom-eters, as there are stronger relative effects caused by

the filling of the Fraunhofer lines [33]. Thus, twosets of α, β, and γ values were determined via thisscheme—one for a bandwidth of 5 nm used forprocessing Rrs data measured at MOBYand anotherfor a bandwidth of 10 nm used for the processing ofRrs measured in the South Pacific Gyre.

Other inelastic scattering processes, such as thegelbstoff fluorescence [54] and the chlorophyll-a fluo-rescence [55], also contribute to the measuredupwelling radiance. Because the wavelength rangein this study is outside the chlorophyll fluorescenceband (∼680 nm with a ∼20 nm bandwidth) [55] andthe contribution from gelbstoff fluorescence is negli-gible for such waters [56], it is appropriate to omitthe contributions from these two sources for thestudies herein.

C. Derivation of Total Absorption Coefficient

As discussed in detail in Lee et al. [20] regarding theQAA scheme, there are just two unknowns for anygiven Rrs�λ�:a �λ� and bb�λ�. Therefore, bb�λ� can beanalytically calculated if a�λ� is known and viceversa. QAA starts the derivation process at a refer-ence wavelength (λ0), which is selected as 550 nm,and a�550� is estimated following QAA (version 5;http://www.ioccg.org/groups/software.html). At thisstep, it is assumed that the values of aSPF

w �λ� forλ ≥ 550 nm are reliable, and aSPF

w �550� was usedfor the estimation of a�550�. Further, instead ofthe “standard” QAA procedure for the calculationof bbp�550�, where Eq. (1) is used to link rrs withthe IOPs, here bbp�550� is derived numerically basedon Eq. (6) (i.e., Model L04) with rrs�550� and a�550�as inputs. bbp�550� is then extrapolated to the shorterwavelengths following Eq. (4) with Y � 1.9, anumber based on the bbp measurements presentedin Huot et al. [28]. With rrs�λ� and bbp�λ� knownfor the 350–550-nm range, the a�λ� of each wave-length in this range is then derived by solvingEq. (6) again. In this process, the bbw�λ� values based

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-0.0004

0.0000

0.0004aw

Rrs->adiff.

Fig. 4. Comparison between aSPFw �λ� (blue line) and inverted a�λ�

(green line) from HydroLight-simulated Rrs�λ� of pure seawater byQAA. Because there were no other components used in the Hydro-Light simulations, aSPF

w �λ� is also the total absorption coefficient.HydroLight simulation included Raman scattering; this wascorrected according to Eqs. (10) and (11). Red line (right axis) rep-resents the difference [a�λ� − aSPF

w �λ�].


http://www.ioccg.org/groups/software.html




on Zhang et al. [25] with salinity as 38.4% for pureseawater were used.

To test the performance of this retrieval process,we first applied the scheme to the HydroLight-simulated Rrs�λ� of pure seawater [the green linein Fig. 2(a) with Raman scattering included; thevalues of aSPF

w �λ�were used as the pure water absorp-tion coefficient]. Figure 4 compares the QAA-retrieved a�λ� with aSPF

w �λ� (which is the totalabsorption coefficient of this case). The deriveda�λ� closely match aSPF

w �λ� with a difference generallysmaller than ∼0.0004 m−1 (the red line in Fig. 4), in-dicating reliable retrievals of a�λ� via the QAAscheme for such extreme waters. The slight differ-ence between the two absorption spectra is dueto simplifications of the radiative transfer [e.g.,Eq. (6)] and the empirical handling of Ramancontributions.

Further, the derived a�420� from Rrs�λ� measure-ments made during BIOSOPE was compared withthat derived from the combination of Kd�420� andR�420� (irradiance reflectance, which is the ratio ofupwelling irradiance to downwelling irradiance justbelow the surface)—values derived from measure-ments of the vertical profiles of downwelling andupwelling irradiance [9]. Although the two ap-proaches are completely different, along with differ-ent quantities used as inputs, the derived a�420�values are very consistent (refer to a similar compari-son in Lee et al. [15]), with a�420� from Rrs�λ� slightlylower (∼0.001 m−1) than that from Kd�420�. Becausethere is no full spectral a�λ� in Morel et al. [9] toevaluate the performance at other wavelengths, weinstead compared the spectrum of Kd�λ� of these“clearest”waters with the results presented in Fig. 5.This is because, generally, a�λ� contributes 80% ormore to Kd�λ� [57,58]. Here, one Kd�λ� representsthe diffuse attenuation coefficient derived from ver-tical profiles of downwelling irradiance, while theother Kd�λ� represents that estimated from a�λ�and bb�λ� following the semi-analytical model devel-oped in Lee et al. [53,58], with both a�λ� and bb�λ�derived from Rrs�λ�.

The comparison between the averaged Kd�λ�(along with standard deviation) from vertical profilesand the averaged Kd�λ� (and standard deviation)from Rrs�λ� for the “clearest” waters (Stations GYR2-5 and STB6-8) is presented in Fig. 5. The coefficientof determination (R2) between the two averagedKd�λ� spectra is 0.996 (N � 30). The relative differ-ence between the two values of Kd�λ�—calculatedas 2 × jKd1 − Kd2j∕�Kd1 �Kd2�—spans a range of∼1–7% for the 355–500-nm range, and the averageover the wavelength range is ∼3.4%. These resultsindicate very consistent determinations of Kd�λ�from two independent methods for these “clearest”waters, although it is difficult to know which oneis closer to the “truth,” as each scheme has itsown uncertainties. For instance, the slightly larger(∼7%) difference for wavelengths around 420 nm[also the wavelengths with the lowest Kd�λ�] mightbe partially due to not correcting for Raman scatter-ing in deriving Kd�λ� from the vertical profiles ofdownwelling irradiance, which can lower the appar-ent attenuation of downwelling irradiance from thisextra light “source” [44]. Because a�λ� makes a largecontribution to Kd�λ�, these results—along with thecomparison of a�420� and retrievals of a�λ� from si-mulated pure water Rrs�λ�—provide a confidencemeasure on the a�λ� derived from the Rrs�λ� viaQAA for such oligotrophic waters.

Figure 6 shows the 12 derived a�λ� from the 12 Rrsspectra in super-blue waters [where Rrs�440�∕Rrs�550� > 12.0] measured at the South Pacific Gyre;values for the 500–550-nm range are omitted in thisfigure to highlight the low absorption coefficients inthe 350–500-nm range. The values generally vary ina range ∼0.007−0.019 m−1 for wavelengths of 350–500 nm and are very consistent among each other(less than a �5% variation). In addition, followingthe error propagation scheme [59], the uncertainty

350 400 450 5000.010

0.015

0.020

0.025

0.030

0

2

4

6

8Ed->KdRrs->KdRela. Diff.

Fig. 5. Comparison between Kd�λ� derived from Rrs�λ� and Kd�λ�derived from the vertical profiles of Ed�λ� for the “clearest”stations. Also shown (red line) is the spectrum of the relativedifference between the two Kd�λ�.

350 400 450 5000.000

0.005

0.010

0.015

0.020

0.025

0

2

4

6

Fig. 6. Results of a�λ� (black–blue lines) analytically derived fromRrs�λ� measured at the South Pacific Gyre, along with its relativeuncertainty (red line, right axis) from algorithm error and Rrs�λ�measurement error. Also shown is aSPF

w �λ� (green line) from Popeand Fry [4] (380–500 nm) and Sogandares and Fry [7] (350–375 nm, linearly interpolated to every 5 nm) and the baselineaBw�λ� (the cyan line) derived from the a�λ�.


in the derived a�λ� due to potential errors of theQAA scheme is just ∼2–5% for the 350–500-nm range(the red line in Fig. 6), which suggests high confi-dence in the derived a�λ�. Such high precision inthe derived a�λ� is due to (1) very consistent (<2%uncertainty) measurements of Rrs�λ� for suchwaters; and (2) the relatively large role played bymolecular scattering. For instance, at 440 nm,bbw�440� makes ∼67% of the total backscattering co-efficient. Thus, even a 20% error in the estimation ofbbp�440� will only result in a ∼6% error in theestimated a�440�. However, because a�550�, wherethe value of aSPF

w �550� is considered as the true value,can be nearly precisely estimated for such waters,the error in the estimated bbp�440� is less than 5%[mainly due to uncertainty in Rrs�550� and Eqs. (6)and (7)] based on the error propagation theory.Further, only two assumptions—a�550� and thebbp�λ� spectral dependence—are used in the deriva-tion of a�λ� from Rrs�λ� via QAA, which ensures highaccuracy and reliability of the analytically deriveda�λ� spectrum.

Also shown in Fig. 6 is aSPFw �λ�. The aSPF

w �λ� valuesare larger than the derived a�λ� for the ∼350- to400-nm range and are smaller (∼0.003 m−1) thana�λ� for wavelengths around 420 nm; there is almostno difference between aSPF

w �λ� and a�λ� for wave-lengths longer than 450 nm. Measurements fromwater samples �aph; ay� indicate that the contributionfrom the optically active components is ∼0.003 m−1

for 440 nm. This comparison explains the lack of clo-sure of Rrs in Fig. 1 and the conclusion in Morel et al.[9] that the aSPF

w �λ� values are likely still too high forthe 350–450-nm range for “pure” seawater. Thisfurther demonstrates the necessity to update thisbasic IOP for ocean optics and ocean color remotesensing.

To achieve this, we first derived an aw�λ� baseline[aB

w�λ�] from the analytically inverted a�λ� as

aBw�λ� � a�λ� − aph�λ� − ad�λ� − ay�λ�; (12)

where a�λ� is the average of the 12 a�λ� spectra.Values of aph;d;y�λ� were taken as the average ofthe lowest values of the gyre waters, as discussedin Section 2. This aB

w�λ� (the cyan line in Fig. 6) isnot proposed as the “pure” seawater absorptioncoefficient, however, because the Rrs�λ� duringBIOSOPE was measured with a spectroradiometer(Satlantic, Inc.) with a 10-nm bandwidth. Thus, somedetails of the spectral curvature of pure seawateraw�λ� could not be revealed. This aB

w�λ� is, rather,applied further to the hyperspectral data collectedat the MOBY site for the derivation of pureseawater aw�λ�.

D. Derivation of Pure Seawater Absorption Coefficient

Using the Rrs�λ� obtained at the MOBY site as input,a�λ� was derived in the same way as presented inSection 4.C, except the Y value in Eq. 4(c) was set

as 1.0, following the results presented in Gordonet al. [60].

Unfortunately, there were no concurrent measure-ments of the component absorption coefficients(i.e., aph;d;y) that could be used; thus, the contribu-tions of the optically active components had to be de-rived from a�λ�. Following widely adopted practices[27,61–63], the total absorption coefficient isexpressed as

a�λ� � aBw�λ� � aph�λ� � ady�λ�: (13)

Here, ady�λ� represents the sum of ad and ay and isalso expressed as an exponential function as Eq. 4(b)

ady�λ� � ady�440�e−Sdy�λ−440�: (14)

aph�λ� was modeled following Eq. 4(a), but two a�ph�λ�

shapes (shown in Fig. 7) were used separately to en-sure general representation. One a�

ph�λ� was mea-sured at the South Pacific Gyre, while the other isfrom measurements made during various field ex-periments; these were limited to an aph�440� of lessthan 0.02 m−1 (equivalent to [Chl] < 0.3 mg∕m3).Therefore, there are three unknowns for Eq. (13):aph�440�, ady�440�, and Sdy, and these unknowns

400 500 600 7000.0

0.2

0.4

0.6

0.8

1.0 Gulf of MexicoS. Pacific Gyre

+

aph

(λ)

Fig. 7. Spectral shapes of phytoplankton absorption coefficientused for the derivation process.

a

360 380 400 420 440 460 480 5000.000

0.005

0.010

0.015

0.020

0.025

0.030

inverted a from Rrsmodeled a with aw

SPF

modeled a with awB

Fig. 8. Examples of a�λ� when optimization is reached: one (redline) used the aSPF

w �λ� spectrum to model a�λ�, another (green line)used aB

w�λ�; the blue line is the aT�λ� that was analytically invertedfrom Rrs�λ�.


were derived by minimizing the following errorfunction:

Erra �P

λjaT�λ� − aM�λ�jPλa

T�λ� ; (15)

i.e., through a spectral optimization between thetarget aT�λ� and the modeled aM�λ�. Here, aT�λ� isthe spectrum analytically derived from Rrs�λ�, whileaM�λ� is that modeled via Eq. (13), and thewavelength range is 350–500 nm, a range in whichthe optically active components still make relativelylarge contributions. Figure 8 shows an example ofthe a�λ� spectra when optimization is achieved.Generally, Erra was approximately 2% when aB

w�λ�was used to model a�λ�, but it was approximately5% when aSPF

w �λ� was used. Using the aSPFw �λ�, it

was not possible to fit the 400–440-nm region well.This difference in Erra provides additional supportto the conclusion that values of aSPF

w �λ� in the 350-to 500-nm range need to be revised.

After the component IOPs were derived, the ab-sorption spectrum of “pure” seawater for λ in therange of 350–550 nm was derived [termed aD

w�λ� inthe following] from each a�λ� as

aDw�λ� � a�λ� − aph�λ� − ady�λ�: (16)

The final absorption spectrum of “pure” seawateris an average of the independently obtained aD

w�λ�.The derived seasonal aph�440�, ady�440�, and Sdy

are presented in Fig. 9, with aph�440� in the rangeof ∼0.006–0.009 m−1. This aph�440� range is equiva-lent to a [Chl] range of ∼0.05–0.10 mg∕m3, followingthe bio-optical relationship developed by Bricaudet al. [64], which is generally consistent with the[Chl] value of those waters [60] and the range derivedfrom the MODIS sensor. The derived ady�440� is inthe range of ∼0.003–0.005 m−1, with Sdy in the rangeof ∼0.014–0.017 nm−1

—both generally consistentwith sample observations in oligotrophic oceans[65,66]. In addition, from the vertical profiles ofupwelling and downwelling irradiance measured atthe MOBY site in February–March 2007, Gordonet al. [60] found that a�443� was ∼0.015 m−1, a valueconsistent with that derived from Rrs�λ� (refer toFig. 8). Further, without correcting the contributionof Raman scattering, Gordon et al. [60] obtainedbb�462� as 0.0028 m−1, which is consistent with avalue of 0.0027 m−1 for bb�460� derived from Rrs�λ�via QAA if the Raman correction is omitted (notshown). These results regarding the total and compo-nent IOPs thus provide a validation of the analyticalinversion of the total absorption and backscatteringcoefficients via QAA and the derivation of aph�λ� andady�λ� through spectral optimization, which thenfurther validate the estimation of aw�λ�.

5. Results and Discussion

Figure 10 shows the average (green diamond symbol)of aD

w�λ�, along with a few aw�λ� spectra found in theliterature and utilized in various eras. Also includedin Fig. 10(b) (and Table 1) is the estimated uncer-tainty of aD

w�λ�, which is derived from the absorptionproperties of the gyre waters following the errorpropagation scheme [67,68], which can be expressedas

0.000

0.002

0.004

0.006

0.008

0.010

0.010

0.012

0.014

0.016

0.018

0.020

aph(440)

ady(440)

Sdy

Fig. 9. Time series of aph�440�, ady�440�, and Sdy of the MOBYwater derived from a�λ� through spectral optimization.

350 400 450 500 5500.00

0.01

0.02

0.03

0.04

0.05

0.06T&P_79S&B_81B_94P&F_97S&F_97M_07C_11This study

a w

360 380 400 420 440 460 480 5000.000

0.005

0.010

0.015

0.020P&F_97S&F_97M_07C_11This studysmoothed

a w

(a) (b)

Fig. 10. aDw�λ� and uncertainty (dark green) spectrum, along with a few aw�λ� spectra found in the literature (a) for wavelengths in the

range of 350–550 nm and (b) zooming in on the range of 350–500 nm. T&P_79: Tam and Patel [6]; S&B_81: Smith and Baker [3]; B_94:Buiteveld [29]; P&F_97: Pope and Fry [4]; S&F_97: Sogandares and Fry [7]; M_07: Morel et al. [9]; C_11: Cruz et al. [69]. Spectra T&P_79,S&B_81, and B_94 were omitted in (b) for clarity.


Δaw�λ�

��Δa�λ��2 � �Δaph�λ��2 � �Δad�λ��2 � �Δay�λ��2

q;

(17)

where Δa�λ�, Δaph�λ�, Δad�λ�, and Δay�λ� are theuncertainties of each individual component, respec-tively.Δa�λ�was obtained following the QAA scheme,as discussed in Section 4.C, while the uncertainty ofthe component IOPs was estimated by assuming a15% uncertainty [16] for each component. ThisΔaw�λ� is generally found to be approximately0.0007 m−1 (∼1–20%) for the 350–550-nm range, sug-gesting high precision in the derived absorption co-efficient of “pure” seawater.

Because the difference between aDw�λ� and aSPF

w �λ�for the 500–550-nm range is small (∼1–10%), the fol-lowing discussions will focus on the 350–500-nmrange. However, from 510 to 550 nm, the aD

w�λ� followvery closely (the difference is <0.001 m−1 or <4%) tothe measurements of Tam and Patel [6], which arealso lower than aSPF

w �λ� in this spectral region. Forthe 420–500-nm range, the values of aD

w�λ� have al-most exactly the same spectral shape (R2 � 0.996,N � 17) as that of aSPF

w �λ�, including a shoulderaround 450 nm, but the aD

w�λ� values are slightlylower (∼0.002 m−1) than the values of aSPF

w �λ�. Forthe 350–415-nm range, however, aD

w�λ� do not havethe same spectral shape as that of aSPF

w �λ�(R2 � 0.871, N � 14), and the aD

w�λ� values aresmaller than aSPF

w �λ� by approximately a factor of2. Most importantly, as opposed to that shown inPope and Fry [4] and Sogandares and Fry [7], thevalues of aD

w�λ� do not increase significantly as the

wavelength decreases. However, for this spectralrange, aD

w�λ� show a very similar spectral shape(R2 � 0.974, N � 14) to aMPF

w �λ�, although the aDw�λ�

values are lower by approximately 0.002 m−1.Recently, Cruz et al. [69], with a thermal lens spec-trometry technique, measured the pure water ab-sorption coefficient at discrete wavelengths; theseare also presented in Fig. 10. Interestingly, for the410–510-nm range, the values of aD

w�λ� and aw�λ� ofCruz et al. [69] are nearly identical (<5% difference),although the aw�λ� values of Cruz et al. [69] areslightly lower than the values of aD

w�λ� for wave-lengths shorter than ∼405 nm.

There are four tiny dips in aDw�λ� for the 350- to

400-nm range, which are likely a result of an imper-fect removal of the Raman contributions in themeasured Rrs�λ� [refer to Fig. 2(b)]. We smoothedthese dips by a simple average between the should-ers, with the results shown as the green dottedline in Fig. 10(b). These results are also includedin Table 1.

The ∼0.002 m−1 lower value of aDw�λ� compared to

that of aSPFw �λ� for the 420–500 nm range is within the

uncertainty between Pope and Fry [4] and Sogan-dares and Fry [7]; they are also, generally, withintwo standard deviations of the measurements as re-ported by Pope and Fry [4]. Such differences and un-certainties indicate the difficulties in accuratelymeasuring such small values in the laboratory. Thisis particularly true for the wavelength range of 350–415 nm, where aw�λ� values are approximately or lessthan 0.005 m−1, which indicates a loss of just 0.5% ofthe optical signal due to absorption for a 1-m cuvette.For measured Rrs�λ� in the field, however, 90% of themeasured signal comes from the first attenuation

Table 1. Derived Absorption Coefficient of “Pure” Seawater along with Uncertainties (Δaw )a

Wavelength (nm) aw (m−1) Smoothed aw (m−1) Δaw (m−1) Wavelength (nm) aw (m−1) Δaw (m−1)

350 0.0071 — 0.0011 455 0.0073 0.0005355 0.0062 — 0.0011 460 0.0076 0.0005360 0.0052 0.0056 0.0010 465 0.0081 0.0005365 0.0050 — 0.0009 470 0.0089 0.0005370 0.0042 0.0046 0.0009 475 0.0099 0.0005375 0.0041 — 0.0008 480 0.0109 0.0005380 0.0037 — 0.0008 485 0.0118 0.0005385 0.0030 0.0035 0.0007 490 0.0132 0.0005390 0.0032 — 0.0007 495 0.0154 0.0005395 0.0028 0.0032 0.0006 500 0.0187 0.0005400 0.0034 0.0032 0.0006 505 0.0230 0.0006405 0.0032 — 0.0006 510 0.0302 0.0006410 0.0031 — 0.0005 515 0.0368 0.0007415 0.0031 — 0.0005 520 0.0387 0.0007420 0.0032 — 0.0005 525 0.0400 0.0008425 0.0033 — 0.0005 530 0.0418 0.0008430 0.0036 — 0.0005 535 0.0443 0.0008435 0.0038 — 0.0005 540 0.0470 0.0007440 0.0044 — 0.0005 545 0.0507 0.0006445 0.0054 — 0.0005 550 0.0562 0.0006450 0.0068 — 0.0005 — — —


depth [70]. Because the attenuation coefficients ofsuch waters are ∼0.015–0.025 m−1 for this spectralrange (refer to Fig. 5), this indicates that the mea-sured radiance originates from a layer deeper than∼40 m. Measurements of optical interactions oversuch long path lengths provide orders of magnitudestronger signal than many laboratory settings forsuch waters (the path length of the integratingsphere approach taken by Pope and Fry [4] can bea few meters for pure waters). Thus, more accurateresults can be expected. On the downside of suchdeterminations is the need for sophisticated modelsto interpret them and sufficient knowledge of the“contaminating” IOPs. The lower aD

w�λ� comparedto aMPF

w �λ� [9] for the 350–415-nm range, however,is consistent with the conclusion in Morel et al. [9]that the combination of Boivin et al. [30] and Popeand Fry [4] values works as an upper limit of theabsorption coefficient of pure seawater.

There is no “standard” to validate the aDw�λ� values,

apart from the fact that they must not be negativeand should be consistent in general with values inthe literature for wavelengths in the range of 350–550 nm (refer to Fig. 10). An indirect validation ofthis new aw�λ� is its application to the MODIS clima-tological times series over the South Pacific Gyre(140–130° W, 23–28° N), where MODIS Rrs�λ� wasused to retrieve aph�λ� using QAA (with the defaultscheme for the estimation of Sdy) for bands withcenter wavelengths at 443 and 488 nm. Further,the ratio aph�488�∕aph�443� was calculated, wherethere is no assumption about the value of this ratioin the QAA derivation process. For oligotrophicwaters with low [Chl], sample measurements indi-cate that this ratio is approximately 0.5 and very sta-ble [64,71]. However, when aSPF

w �λ� values were used,a wide and strange range of aph�488�∕aph�443� valuesresulted (Fig. 11, blue line), and many times theindependently derived aph�488� became negative.Although the inversion algorithm is not perfect, itis difficult to explain the negative aph�488� derivedfrom theMODISRrs�λ�, which went throughmultiplelayers of quality control (averaged over a large areaand from multi-year observations, along with screen-ing for observations with a large sensor viewing an-gle and sun angle, high sun glint, and heavy aerosol

load). In addition, the uncertainty in the deriveda�488� due to QAA is just about 2% for such waters(refer to Fig. 6). When the aSPF

w �λ� values were re-placed by aD

w�λ�with the same QAA process, however,the aph�488�∕aph�443� ratio changed to ∼0.4–0.6(refer to the green line in Fig. 11)—values generallyconsistent with sample measurements of phyto-plankton pigments. This significant change in theaph�488�∕aph�443� ratio that was independently de-rived from MODIS observations, at least partially,provides support for the fidelity of aD

w�λ� for “pure”seawater. At the very least, it shows internal consis-tency. The slight temporal variation of aph�488�∕aph�443� could be a result of an imperfect Ramancorrection for such climatological data and/or animperfect estimation of Sdy used in QAA, which isbeyond the scope of this research.

6. Conclusions

Based on hyperspectral measurements of remotesensing reflectance in the oligotrophic oceans andan accurate relationship between Rrs�λ� and theIOPs, and assuming that aSPF

w �550� is correct, thespectra of the total absorption coefficient and the ab-sorption coefficient of “pure” seawater were derivedanalytically (for the range of 350–550 nm). Thederived aw�λ� shows values that are consistent (verysimilar shape) with those from Pope and Fry [4]for the range of 420–550 nm. They are reduced by∼0.002 m−1 but nearly the same (differing by<0.001 m−1 or <4%) as those measured by Tamand Patel [6] for the 510–550-nm range and thoseof Cruz et al. [69] for the 410–510-nm range. Forthe 350–400-nm range, however, the derived aw�λ�values are considerably lower (by approximately afactor of 2) and do not have the same spectral shapeas those reported in Pope and Fry [4] and Sogandaresand Fry [7]; they are slightly higher (∼0.002 m−1)than those of Cruz et al. [69]. Initial tests with thenew aw�λ� values resulted in retrievals of more real-istic phytoplankton absorption spectral shapes fromobservations of Rrs�λ�. Based on multiple consistentlines of evidence, these newly derived aw�λ� valuesappear to be closer to the true absorption coefficientof “pure” seawater than previous estimates.

We are grateful for the financial support providedby the National Aeronautic and Space Administra-tion (NASA) Ocean Biology and Biogeochemistryand Water and Energy Cycle Programs and theNational Oceanic and Atmospheric Administration(NOAA) JPSS VIIRS Ocean Color Cal/Val Project.The BIOSOPE project was managed by H. Claustreand funded by the Centre National de la RechercheScientifique (CNRS), the Institut des Sciences del’Univers (INSU), the Centre National d’Etudes Spa-tiales (CNES), the European Space Agency (ESA),NASA, and the Natural Sciences and EngineeringResearch Council of Canada (NSERC). The authorsthank Marcel Babin for particulate absorptionmeasurements during this cruise. MOBY is sup-ported by NOAA/STAR. The comments and

-0.4

-0.2

0.0

0.2

0.4

0.6

w/ Pope_Fry aw

w/ new aw

Fig. 11. Ratio of aph�488� to aph�443� derived from climatologicalRrs�λ� collected at the South Pacific Gyre for a region (140–130°W,23–28°S) by MODIS Aqua.


suggestions from the two anonymous reviewers aregreatly appreciated.

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