Knowledge on absorption by colored dissolved organic matter, acdom, spatio-temporal variability in coastal areas is of fundamental importance in many field of researches related to biogeochemical cycles studies, coastal areas management, as well as land and water interactions in the coastal domain. A new method, based on the theoretical link between the vertical attenuation coefficient, Kd, and the absorption coefficient, has been developed to assess acdom. This method, confirmed from radiative transfer simulations and in situ measurements, and tested on an independent in situ data set (N = 126), allows acdom to be assessed with a Mean Relative Absolute Difference, MRAD, of 33% over two order of magnitude (from 0.01 to 1.16 m−1). In the frame of ocean color observation, Kd is not directly measured but estimated from the remote sensing reflectance, Rrs. Based on 109 satellite (SeaWiFS) and in situ coincident (i.e. match-up) data points acdom is retrieved with a MRAD value of 37%. This simple model generally presents slightly better performances than recently developed empirical or semi-analytical algorithms.
© 2014 Optical Society of America
Colored dissolved organic matter (CDOM) (referred as yellow substances, Gelbstoff, or gilvin) refers to a complex mixture of water-soluble organic substances including mainly humic and fulvic acids. CDOM in coastal waters mainly originates from rivers and land washing, but can also be locally produced by phytoplankton as well as through the degradation processes of this marine organic matter [1–3]. CDOM plays a significant role for a variety of marine biogeochemical processes in coastal waters for instance through its controlling action of the marine light field available for phytoplankton primary production. CDOM is usually expressed as the absorption coefficient of a water sample filtered through a 0.2 μm filter, acdom(λ) (in m−1). The increasing exponential shape of CDOM absorption from long to short wavelengths induces that CDOM can prevent, when present in sufficient concentration, against photochemical damage induced by ultra violet radiations on aquatic organisms [see references in 2]. Previous works have also stressed that CDOM, especially in coastal water masses influenced by terrestrial inputs, can be used to assess the concentration of dissolved organic carbon, DOC, which represents the main reservoir of organic carbon in the ocean, still poorly quantified at global scale [4–6]. At last but not least, the presence of CDOM in waters has been shown to bias the estimation of the chlorophyll-a concentration, Chla, from ocean color remote sensing [7–11]. Loisel et al.  for instance illustrated that Chla is over-estimated in waters presenting higher CDOM concentrations than averaged values, and vice versa.
For the different reasons stated above, knowledge on the temporal and spatial distribution of CDOM is of great interest for marine sciences. Remote sensing of ocean color from space sensors is the dedicated tool for that purpose. However, due to their similar spectral shapes, the non-algal particulate matter absorption, anap, and colored dissolved organic matter absorption, acdom, coefficients are difficult to distinguish from ocean color radiometric measurements. These two absorption coefficients are therefore usually gathered into one coefficient, the colored detrital matter absorption coefficient, acdm. Numerous efforts have been undertaken this last decade to assess acdm from remote sensing over open ocean and coastal waters, e.g, [9,12–14]. While, acdm can be assimilate to acdom over open ocean waters, in good approximation , this is not the case for coastal waters. In these optically complex aquatic environments, the contribution of acdom and anap to the total absorption (minus water) can drastically change at both regional and temporal scales [3,16]. This is due to the strong decoupling between source and sink processes controlling the variability of these two absorption coefficients. Considering the importance of CDOM in our understanding of biogeochemical processes occurring in coastal regions, recent algorithms have been developed to assess acdom from ocean color remote sensing over these optically complex waters. For instance, some empirical relationships have been established between acdom at different wavelengths and remote sensing reflectance, Rrs, ratios from data collected in various coastal environments [4,17–19]. Two steps algorithms, requiring the assessment of other inherent optical properties (IOPs) as intermediate products, have been also proposed. For instance, the acdom(412) to the total absorption coefficient ratio, which has been parameterized as a function of Rrs at different wavelengths , could be used once the total absorption is assessed using another algorithm [12,21]. Others methods, aim at removing the contribution of particulate matter from acdm(λ) based on estimates of the backscattering coefficient derived from dedicated algorithms [22,23].
The present paper aims at developing a new algorithm for assessing the absorption coefficient of colored dissolved organic matter at 412 nm, acdom(412), from the diffuse attenuation coefficient, Kd, in coastal surface waters. The latter parameter can be estimated from in situ measurements of vertical profiles of downwelling irradiance, as well as from the inversion of ocean color remote sensing measurements. A synthetic data set, based on numerical radiative transfer simulations, as well as an in situ data set gathering measurements performed in contrasted coastal waters, are used for the theoretical development of the model. The performances of this new algorithm are evaluated using an independent in situ data set, and comparisons with other empirical and semi-analytical algorithms are provided.
2. Synthetic and in situ data set
Three different data sets are used for the present study. The first one (thereafter referred as DS1) is only used to develop the theoretical background of the algorithm. This synthetic data set has been generated from numerical simulations of the radiative transfer performed for various inherent optical properties (IOPs) and three different sun zenith angles (0°, 30°, and 60°). More details on this data set are provided in the IOCCG report 5 . The second data set (DS2) only gathers in situ data collected in various and mainly coastal environments. For DS2 we use the NOMAD data set  together with data collected during other oceanographic cruises occurring in European and French Guiana coastal waters [16,26–28]. DS2 is divided into two sub-data sets, one for the algorithm development (DS2-D), the other for validation exercises (DS2-V). DS2-D and DS2-V encompass 80% (N = 505) and 20% (N = 126) of the data points and presents the same distribution in terms of acdom(410) values. The last data set (DS3) used in the present study is the NOMAD SeaWiFS match-up data set (N = 109) which is composed by in situ acdom(410) measurements and nearly simultaneous SeaWiFS derived remote sensing reflectance, Rrs, after atmospheric correction of the top of atmosphere signal.
The mean, standard deviation, and range values of Kd(λ), acdom(410), and acdom/atot(410), where atot is the sum of the particulate (ap) and colored dissolved organic matter absorption (acdom) coefficients, for the different data sets are provided in Table 1. The acdom(410) values cover a great range of variability, about three order of magnitude, for both the synthetic and in situ data sets (Table 1). The mean and standard deviations values of acdom(410) for DS1, DS2-D, DS2-V, and DS3 are 0.51 ± 0.74, 0.23 ± 0.26, 0.24 ± 0.27, and 0.13 ± 0.20 m−1, respectively. The acdom(410) values are equally distributed in DS2-D and DS2-V (with however some slight differences in the maximum values). The contribution of acdom(410) to the total absorption process, represented by the acdom/atot ratio, are very similar among the three data sets and range between about 16 to 93% (Table 1). Besides the acdom(410), atot(410), Kd(410), and Kd(670) parameters gathered in the three considered data sets, DS2-V and DS3 also include the remote sensing reflectance, Rrs(λ), values at the standard ocean color visible wavelengths (412, 443, 490, 510, 550, and 670 nm). Rrs(λ) is considered for DS2-V and DS3 for validation purposes in the context of remote sensing applications, where Rrs is the input parameter used for calculating Kd(λ) which represent the input parameter for deriving acdom(410) from the present algorithm.
3. Theoretical background
The diffuse attenuation coefficient Kd(λ) at a given wavelength, λ, is a function of inherent optical properties (IOPs) and illumination conditions at the sea surface [29–33]. Different parameterizations, based on extensive radiative transfer calculations, have been developed between Kd, IOPs, and the sun zenith angle, θ0, at some specific depths, and for the first attenuation layer, which corresponds to the ocean surface layer that can be detected from an ocean color satellite sensor . For example, simple parameterizations were proposed between Kd/a and b/a accounting for the sun zenith angles, where a and b are the total (including pure water coefficients) absorption and scattering coefficients, respectively [29,30]. Further parameterizations, were then aimed at including the effect of the variation of the total phase function (through the respective proportion between molecular and total scattering) as well as that of the aerosol optical thickness [31,33]. Based on the fact that the absorption and backscattering, bb, coefficients can be estimated from space , Kd has also been parameterized as a function of a, bb, and θ0 [32,35,36]. Empirical parameterizations between Kd(λ) and the surface chlorophyll-a concentration, Chla, were also proposed [37,38] for Case 1 waters for which IOPs only depend on phytoplankton organisms and their associated material . In this latter parameterization Kd(λ) is decomposed as follows:
Two main considerations drive the development of the present model to assess acdom(412) from ocean color remote sensing observations. The first one relies on the fact that the diffuse attenuation coefficient, Kd(λ), can now be estimated with a relatively good accuracy from the remote sensing reflectance, Rrs(λ) [36,40–42]. For instance, based on an extensive in situ and synthetic data set, the average absolute relative error (i.e. uncertainty) value on the Kd assessment at 490 nm using 5 different approaches ranges between 14 and 32% . The second motivation of the current approach is to take advantage of the fact that, for a given sun angle, Kd(λ) can roughly be considered as a inherent optical properties in the surface layer, and then can be decomposed into different subcomponents [32,37,38,43]. Based on radiative transfer simulations Gordon  confirmed that by removing the dependence of Kd(λ) on the structure of the incident light field at the sea surface, Kd(λ) verifies the Lambert-Beer law near the sea surface.
4. Algorithm development
4.1 General formulation of the model
The different works referred previously emphasize that Kd(λ) is mainly driven by the absorption coefficient, at first order. However, as soon as the b/a(λ) (or bb/a(λ)) ratio increases significantly, the attenuation of light through scattering processes cannot be neglected. Due to the exponential increase of acdom(λ) from longer to shorter wavelengths, the present model will estimate acdom(λ) at 412 nm. Based on these different considerations Kd(412) can be expressed as follows:16,44]. However, the signal-to-noise ratio at 670 nm is generally lower than that at 555 nm for current ocean color sensors [45,46]. Besides, the retrieval of the remote sensing reflectance is more challenging in the red than in the green, most likely due to the small level of signal in this part of the spectrum . Formulations considering these two wavelengths will be tested and compared. In practice, for a peculiar wavelength, λp, we assume that:
4.2 Development of the model from the synthetic data set DS1
The theoretical background and general formulation of the model presented in the previous section is now analyzed from radiative transfer simulations data gathered in DS1. While acdom will be estimated at 412 nm from the in situ database (section 4.2), the development based on DS1 is performed at 410 nm, the available wavelength in the blue. The pure sea water values of the vertical attenuation coefficient are set from radiative transfer simulations using the Hydrolight radiative transfer code  for a pure sea water body, different sun zenith angles, and in presence of Raman scattering. The resulting Kw(λ) values at 410, 555, and 670 nm for a sun angle at 30° are 0.0097, 0.0645, and 0.4878 m−1, respectively. These values are only slightly higher from those generally adopted in the literature (Kw(410) = 0.00812 m−1, Kw(555) = 0.06053 m−1, and Kw(670) = 0.43946 m−1) and calculated through the simple addition of pure sea water absorption and backscattering coefficients . In Eq. (3) we assume that colored dissolved organic matter does not absorb (or insignificantly) at the considered wavelength, λp. Therefore, by simply removing Kd(λp) to Kd(410), part of the particulate impact on the variability of Kd(410) should be removed (with however a strong wavelength dependence still remaining). From Eqs. (2) and (3) acdom(410) can be expressed as follows:Fig. 1).While other parameterizations were also tested to assess (Δp(410)-Δp(λp)), the latter ones has been found to be the more appropriated for remote sensing application (see discussion below). The sun angle dependence in the (Δp(410)-Δp(λp)) vs. f(Kd(410)) relationship is relatively smaller for λp = 555 (Fig. 1c) than for λp = 670 nm (Fig. 1(a)).
The impact of each term of Eq. (4) on the accuracy of acdom(410) retrieval is analytically examined from the synthetic data set DS1, which by nature is not affected by uncertainties measurements (Fig. 2). This cannot be considered as a validation exercise (as the same data set is used for the development and the evaluation), but rather to an evaluation of the actual impact of each step on the formulation proposed by Eq. (4). This will not be the case in the next section where the final algorithm will be develop and validated using two independents in situ data sets. The following statistical estimators are used for that purpose:
The impact of the successive steps on the retrieval accuracy of acdom(410) clearly appears in Fig. 2(a) and 2(c). Indeed, the whole data points get closer to the 1:1 line when the algorithm successively accounts for the different terms. The simple relationship between acdom(410) and the first term of Eq. (4), (Kd(410) – Kw(410)), already allows acdom(410) to be retrieved with a reasonable accuracy over the whole range of variability. The relative root mean square difference, RMSD, and Mean Relative Absolute Difference, MRAD, values for a sun angle at 30° are 0.12 m−1 and 23.47%, respectively. By accounting for the second term and third term of Eq. (4), (Kd(λp) – Kw(λp)) and (Δp(410)-Δp(λp)), the RMSD, and MRAD values are respectively 0.08 m−1 and 16.99%, using 670 nm (Fig. 2(b)), and 0.1 m−1 and 19.16%, using 555 nm (Fig. 2(d)).
The performance of the model does therefore not significantly change according to the choice of the examined λp wavelength. While Kd(555) is still affected by absorption by colored dissolved organic matter (acdom/atot(555) = 0.17 ± 0.17), the third term allows this residual effect to be taken into account. Among the three different terms appearing in the right side of Eq. (4), (Kd(410) - Kw(410)) represents the highest contribution to the whole term between bracket (thereafter referred as X). The median values calculated from the DS1 (at 30°) data set of (Kd(410) - Kw(410))/X, (Kd(670) - Kw(670))/X, and (Δp(410)-Δp(670))/X are 1.78, 0.28, and 0.53, respectively. The median values calculated from the DS1 data set of (Kd(555) - Kw(555))/X, and (Δp(410)-Δp(555))/X are 0.49, and 0.59, respectively. The final empirical equation used to assess acdom(410) from Kd measurements performed at 410 and 555 nm, and a sun angle at 30° using the DS-1 data set is:
4.3 Development of the model from the in situ data set
The evaluation of the impact of each term of Eq. (4) is now performed using the in situ data set DS2-D. Considering that the performance of the method established from DS1 is relatively similar for red and green channels and the greater complexity to assess Kd from space in the red part of the spectrum, this part will only focus on the green channel. The advantage of each step on the proposed approach is summarized in Fig. 3. As for the synthetic data set, a tight relationship is observed between acdom(410) and (Kd(410) - Kw(410)) over the whole range of variability of DS2-D (Fig. 3(a)). Note that this relationship slightly differs from the one established using the synthetic data set. The inherent uncertainties associated with in situ measurements, but also the relationship between acdom and absorption by phytoplankton cells used in the synthetic data set , are at the origin of the observed discrepancies.
The RMSD, MRAD, and bias decrease from the first step to the last one by a factor of 1.22 (RMSD = 0.09 m−1), 1.13 (MRAD = 34.01%), and 1.32 (bias = 9%). To quantitatively assess the impact of turbidity on the performance of the model, the whole data set is split into four equal parts computed according to Hyndman and Fan recommendation . The RMSD, MRAD, and bias values for the sub-data sets characterized by the highest (and lowest) ap(410)/acdom(410) values are 0.1(0.06) m−1, 40(37)% and 36 (−24)%. These values globally agree with the ones calculated for the whole data set. The small impact (at least on the present data sets) of turbidity on the acdom(410) vs. (Kd(412) - Kw(412)) relationship is explained by the fact that turbid waters in coastal areas are generally associated with a high concentration of CDOM (and vice versa) . The bias values for the first and last quartile significantly differ from the one established from the whole data set. This latter pattern emphasizes that a residual effect of the particulate matter still remains. Such effect, inherent to all empirical approaches , could however be corrected through classification approaches [28,50].
Based on these different findings the following relationship, developed from the in situ data set DS2-D, is adopted:Eqs. (5) and 6 are mainly explained by the assumptions used to generate acdom from aphy in the synthetic data set (DS1), which may not be totally adapted to cover the whole type of waters in DS2 .
5. Validation and comparison with previous algorithms
5.1 Using Kd as input parameters
The model presented in Eq. (6) is now tested against an independent data set, DS2-V, previously presented in Table 1. The RMSD, MRAD, and bias values are 0.09 m−1, 33.6%, and 17.7%, respectively for the final acdom(412) estimated values. Consistently with the synthetic data set, the performance of the acdom(412) retrieval is improved with the successive steps of the algorithms (Fig. 4). The use of the parameterization considering Kd(555)-Kw(555) and (Δp(412)- Δp(555)) rather than the expression only based on Kd(412) decreases the RMSD, MRAD and bias by a factor 1.33, 1.21, and 1.37, respectively.
5.2 Using Rrs as input parameters
The model is now tested in the context of ocean color remote sensing observations, where Kd is not directly measured, but instead estimated from Rrs. Different approaches presented in section 3 have been developed to assess Kd at different wavelengths from ocean color observations. Because of the structure of the present model (Eq. (6), the errors on the estimation of Kd at each wavelength are additive. To limit this impact, the Kd differences appearing in Eq. (6) are directly assessed from Rrs using a new parameterization developed from the IOCCG (2006) data set:Table 2 and Fig. 5. Comparison with two empirical [4,17] and one semi-analytical existing algorithms  is also provided.
While the acdom retrieval values are slightly better when Kd is measured (Fig. 4(c)) than when it is inversed (Fig. 5(a)), they are still in good agreement with field measurements. All the data points are well distributed along the 1:1 line. The RMSD, MRAD, and bias values are 0.21 m−1, 42.82%, and 7.12%, respectively considering the whole model description. The two previously published algorithms developed for the U.S. Middle Atlantic Bight waters , andcoastal waters under the influence of the Mississippi river , that is for two specific coastal areas, performed also relatively well, in spite of relatively higher MRAD and bias values (Fig. 5 (b), (c), and Table 2). However, by fitting the empirical formulations used in these acdom vs. Rrs empirical models to the DS2-D data set, their performances evaluated on DS2-V improve. For instance, the RMSD values decrease by a factor of 1.58, and 1.06 for the models of Mannino et al. , and D'Sa et al. , respectively. The formulation between Rrs and acdom used in these models are therefore relatively dependent on the data set used for their development. Note that the number of validation data points is reduced for Mannino et al., ’s algorithm which, by construction, cannot be applied when the Rrs(490)/Rrs(555) ratio becomes lower than 0.4443 (resulting to a logarithmic calculation of a negative expression). The recent semi-analytical approach developed by Dong et al. , also shows relatively good performance over the present data set, with a Mean Relative Absolute Difference of 51% (against 70 and 60% for the approaches of Mannino et al. , and D'Sa et al. , respectively, when their coefficients are adapted to the present data set).
Similar results are also obtained using the NOMAD matchup data set which includes uncertainties related to atmospheric corrections (Fig. 6, Table 3). Note that the use of a reflectance ratio in Eq. (8) reduces the impact of Rrs uncertainties on the acdom retrieval accuracy. Due to the fact that Rrs(412) is generally more affected by atmospheric correction errors than Rrs(443) , the Rrs(443)/Rrs(555) ratio can also be used instead of Rrs(412)/Rrs(555) in Eq. (8). In this case, the (A, B, C, D) coefficients values are (−0.2925, 0.4015, −1.365, −0.863) for a sun at zenith. However, while acdom(412) retrieval is improved (see Table 3), the dynamics toward high acdom(412) values is reduced. Considering the present approach, the tight link between Kd and acdom is theoretically expected, and confirmed from synthetic and in situ data sets. The accuracy of our model is tightly linked to the retrieval accuracy of Kd, and depends on the quality of the empirical relationships adopted (Eqs. (6) and (7)). The dispersion observed around these relationships is mainly explained by the residual impact of the absorption and scattering properties of particulate matter, even though this effect is greatly reduced from step 1 to step 3 (see Fig. 2).
As atmospheric correction is one of the main challenges for the exploitation of ocean color remote sensing over coastal areas, the impact of potential atmospheric correction errors on the acdom(412) retrieval should be assessed. According to the ESA (2012)  validation report, the relative percentage differences calculated between the estimated and measured reflectance values in coastal waters at 412 and 560 nm are + 1.6% and −6.3%, respectively. The impact of these errors on the acdom(412) retrieval accuracy is assessed using the validation data set DS2-V, by comparing the acdom(412) values calculated using the true Rrs values, acdom(412)-error-free, with the acdom(412) values calculated using these Rrs values modified by the relative differences provided above, acdom(412)-error. These atmospheric correction errors only slightly impact the acdom(412) retrieval accuracy, as the mean relative absolute difference and bias values calculated between these two acdom(412) values in linear scale are 8.68% and 8.68%, respectively. The median value of the (acdom(412)-error- acdom(412)free)/acdom(412)-error is −8.67% ± 2.95% on the validation data set.
6. Concluding remarks
A new model has been developed to assess the colored dissolved organic matter in natural waters from the vertical attenuation coefficient of the downwelling irradiance, Kd. A theoretical background has been defined to relate acdom to a combination of Kd at 412 and 555 nm. The development of the acdom vs. Kd relationships is based on a large in situ data set (N = 505) gathering measurements performed in various costal environments. In the frame of ocean color remote sensing applications, only Rrs is available, and then Kd has first to be estimated. This model can only be applied for the range of acdom(412) considered here, that is about [0.02; 5.0 m−1]. The performance of this model has been successfully tested using a relatively large in situ data set (N = 126) and the Nomad match-up data set (N = 109) covering very contrasted coastal environments.
The authors would like to thank all participants and voluntary contributors for collecting data that have been assembled in the NOMAD data set. This study has been performed in the frame of the GlobCoast (www.foresea.fr/globcoast) which is funded by the Agence Nationale de la Recherche (ANR-11-BLAN-BS56-018-01). The GlobCoast project is affiliated to LOICZ and AQUIMER. This work has also been supported by the French Spatial Agency (CNES) through the TOSCA program in the frame of the MODOC project. S. Shang is deeply thanked for providing us the results of the Dong et al. (2013)’s model. We thank the two anonymous reviewers for their comments and suggestions.
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