Estimating absorption coefficients of colored dissolved organic matter (CDOM) using a semi-analytical algorithm for southern Beaufort Sea waters: application to deriving concentrations of dissolved organic carbon from space

A series of papers have suggested that freshwater discharge, including a large amount of dissolved organic matter (DOM), has increased since the middle of the 20th century. In this study, a semi-analytical algorithm for estimating light absorption coefficients of the colored fraction of DOM (CDOM) was developed for southern Beaufort Sea waters using remote sensing reflectance at six wavelengths in the visible spectral domain corresponding to MODIS ocean color sensor. This algorithm allows the separation of colored detrital matter (CDM) into CDOM and non-algal particles (NAP) through the determination of NAP absorption using an empirical relationship between NAP absorption and particle backscattering coefficients. Evaluation using independent datasets, which were not used for developing the algorithm, showed that CDOM absorption can be estimated accurately to within an uncertainty of 35% and 50% for oceanic and coastal waters, respectively. A previous paper (Matsuoka et al., 2012) showed that dissolved organic carbon (DOC) concentrations were tightly correlated with CDOM absorption in our study area ( r 2 = 0.97). By combining the CDOM absorption algorithm together with the DOC versus CDOM relationship, it is now possible to estimate DOC concentrations in the near-surface layer of the southern Beaufort Sea using satellite ocean color data. DOC concentrations in the surface waters were estimated using MODIS ocean color data, and the estimates showed reasonable values compared to in situ measurements. We propose a routine and near real-time method for deriving DOC concentrations from space, which may open the way to an estimate of DOC budgets for Arctic coastal waters.


Introduction
The colored fraction of dissolved organic matter (CDOM) plays various roles in physical and biogeochemical processes (e.g., Carder et al., 1989;Miller and Moran, 1997;Nelson et al., 1998;Miller et al., 2002;Matsuoka et al., 2012). The contribution of CDOM light absorption to the total non-water absorption for Arctic waters is significantly higher than at lower latitudes (Bélanger et al., 2006;Matsuoka et al., 2007Matsuoka et al., , 2009Matsuoka et al., , 2011, playing a role as a heat absorption mechanism and thereby contributing to sea ice reduction (Hill, 2008;Matsuoka et al., 2011). Recent findings suggest that, on land, global warming likely induces thawing of the permafrost containing a significant amount of dissolved organic carbon (DOC) (Freeman et al., 2001;Camill, 2005;Frey and Smith, 2005). Because the freshwater discharge into Arctic rivers Published by Copernicus Publications on behalf of the European Geosciences Union.

A. Matsuoka et al.: A semi-analytical CDOM algorithm
has increased since the middle of the 20th century McClelland et al., 2006), a large amount of CDOM, whose absorption is often highly correlated with DOC concentrations at the mouth of a river (e.g., Mannino et al., 2008;Fichot and Benner, 2011;Matsuoka et al., 2012), is expected to be delivered into the Arctic Ocean by the river discharge relative to its autotrophic sources. During ice-free seasons, this material covers the surface ocean and significantly reduces penetration of ultraviolet irradiation that influences marine organisms such as phytoplankton and bacteria (Judd et al., 2007;Leu et al., 2007;Bonilla et al., 2009;Hessen et al., 2012). In the context of the expansion of the hole in ozone layer at high northern latitudes (e.g., Wirth and Renger, 1996;Andersen and Knudsen, 2002), variability in CDOM absorption can impact the physiological status or acclimation/adaptation of marine organisms. Quantitative estimation and monitoring of CDOM in Arctic coastal environments are therefore urgently needed to better understand the modification in biogeochemical processes resulting from ongoing global warming.
Because of the similarity in absorption spectra between CDOM and non-algal particles (NAP), the two are often combined together as a single geophysical value, CDM (= CDOM + NAP) absorption (e.g., Garver and Siegel, 1997;Lee et al., 2002;Maritorena et al., 2002). Although basinscale observations of CDM absorption using ocean color have provided insights into its linkages with phytoplankton biomass or the influence of photobleaching Bricaud et al., 2012), two important issues remain unsolved. First, these studies did not take into account variability in CDM absorption in coastal areas where large amounts of suspended sediments and dissolved organic matter are delivered by rivers. Because of the optical complexity of coastal waters, retrieved inherent optical properties (IOPs) tend to be more variable and thus uncertain in coastal areas compared to those in open ocean areas (e.g., IOCCG, 2006;Kostadinov et al., 2007). In contrast to open oceanic waters in which CDOM absorption and DOC concentration are generally not correlated Nelson and Siegel, 2002), the tight correlation between these two variables for coastal waters can be used for deriving DOC concentrations from space when CDOM absorption is estimated accurately using ocean color data.
The second issue related to the use of CDM absorption is that it is difficult to understand the different dynamics of CDOM and NAP separately. For example, particles sink rather quickly, at a vertical speed ranging from a few meters to several hundred meters per day (Fischer and Karakas, 2009), while CDOM can be transported by an ocean current over long distances (>1000 km) in a few months (Matsuoka et al., 2011. Consequently, partitioning CDM into CDOM and NAP using a semi-analytical algorithm is required, but it is difficult due to their similar spectral shapes (IOCCG, 2006). While recent studies developed local and empirical algorithms for estimating CDOM absorp-tion (D'Sa, 2008;Mannino et al., 2008), the products derived using those algorithms can be significantly affected by spatial and seasonal variations in the empirical relationships. A semi-analytical algorithm is thus required to account for these variations. Such an algorithm was recently developed for the Mississippi and Atchafalaya regions (Zhu et al., 2011).
The objective of this study is to develop a semi-analytical algorithm for estimating CDOM absorption for Arctic waters. The application for deriving DOC concentrations using ocean color data is proposed at the end of this paper.

Datasets for developing the CDOM absorption algorithm
The IOPs datasets used for developing our semi-analytical CDOM absorption algorithm are documented in Matsuoka et al. (2007Matsuoka et al. ( , 2011 . Discrete water samples were collected using Niskin bottles, except at the surface where a polyethylene container was used during the MR aut cruise. In total, 110, 119, and 179 water samples were collected at 30 (SBI spr), 29 (SBI sum), and 51 (MR aut) stations for pigment and absorption analyses within the euphotic zone (i.e., between the surface and the euphotic depth, z eu , where 1 % of the surface irradiance subsists). Absorption coefficients of particles (a p (λ), m −1 ) retained on GF/F filters were determined from 350 to 750 nm using a MPS-2400 spectrophotometer (Shimazu Corp.). Phytoplankton pigments retained on the filters were extracted using methanol (Kishino et al., 1985), absorption coefficients of NAP (a NAP (λ), m −1 ) were measured on the bleached filter, and phytoplankton absorption coefficients (a ϕ (λ), m −1 ) were obtained by subtracting a NAP (λ) from a p (λ). For the absorption measurements of CDOM, water samples were filtered using 0.22 µm Millipore membranes immediately after water sampling and then poured into a 0.1 m quartz cell. Absorption coefficients of CDOM were determined from 280 to 700 nm using a MPS2400 spectrophotometer (Shimazu Corp.). All absorption measurements were made following the NASA ocean color protocols (Mitchell et al., 2003). In this study, chl a concentrations were determined fluorometrically with 90 % acetone (Holm-Hansen et al., 1965) for SBI spr and SBI sum and with dimethylformamide (DMF) (Holm-Hansen et al., 1965;Suzuki and Ishimaru, 1990) for MR aut using a 10AU field fluorometer (Turner Designs). Suzuki and Ishimaru (1990) showed that chl a concentration obtained using DMF is not significantly different from that determined using 90 % acetone.

CDOM absorption and DOC determination
CDOM absorption datasets for evaluating our CDOM algorithm are documented in Matsuoka et al. (2012). Briefly, measurements were performed in the southern Beaufort Sea during the France-Canada-USA joint Arctic campaign, MA-LINA, in the area from approximately latitudes 69 • to 72 • N and longitudes 125 • to 145 • W ( Fig. 1). Sampling was conducted from 30 July to 26 August 2009 aboard the Icebreaker CCGS Amundsen, and 37 stations were visited. A barge and/or zodiac were also deployed (32 stations out of 37) during the same time periods of the CTD deployment to obtain surface water samples (see Fig. A1 of . The absorption of CDOM in the sample filtrate was measured over the spectral range 200-735 nm using an UltraPath liquid waveguide system (World Precision Instruments, Inc.). A 2 m optical pathlength was used for almost all waters, except for coastal waters in the Mackenzie River mouth where a 0.1 m optical pathlength was used. The detailed methodology is described in Matsuoka et al. (2012).
Dissolved organic carbon (DOC) was measured using the high-temperature combustion method and a TOC-V analyzer (Shimadzu) (Benner and Strom, 1993). Water samples using Whatman GF/F filters were stored frozen until analysis in laboratory. In total, 256 samples were collected for DOC analyses at 29 stations (DOC measurements were made by R. Benner).

Calculation of remote sensing reflectance
A detailed methodology for obtaining in-water upwelled radiance (L u ) and downward irradiance (E d ) is documented in Hooker et al. (2013). Briefly, a Compact-Optical Profiling System (C-OPS) (Morrow et al., 2010) was deployed at 36 stations during the MALINA cruise. We obtained above-and in-water light measurements at 18 channels (i.e., 320,340,380,395,412,443,465,490,510,532,555,560,625,665,670,683,710, and 780 nm). The above-water global solar irradiance (E s ) measurements were used to correct the E d and L u data for change in the incident light field. Additional corrections included dark currents, pressure tares, aperture offsets (distance to pressure transducer), tilt filtering (5 • or less), and self-shading (Hooker et al., 2013). Subsurface L u at null depth (i.e., L u (0 − , λ)) were obtained from the slope and intercept given by the least-squares linear regression of the log-transformed light parameter versus z. The top and the bottom of the extrapolation interval were, on average, 0.12 m and 1.96 m, respectively. The principal data product used here is the remote sensing reflectance, R rs (λ) = 0.54 L u (0 − , λ)/E s (λ), where λ indicates wavelength. In this study, R rs (λ) at six wavelengths (i.e., 412, 443, 490, 532, 555, and 670 nm corresponding approximately to MODIS bands) were used.

Semi-analytical algorithms for deriving CDOM absorption and DOC concentration
In this study, we developed a semi-analytical algorithm for estimating CDOM absorption at 443 nm for Arctic waters. The overview of this algorithm is schematically shown in www.biogeosciences.net/10/917/2013/ Biogeosciences, 10, 917-927, 2013

Fig. 2.
A flow-chart of our semi-analytical algorithm for estimating CDOM absorption. A "#" represents parameters which can be set either to be constant or as a function of R rs (λ), depending on water class. These classes are determined using cluster analysis (Sect. 3.2). The coefficients used in the relationship a * ϕ (λ) = A(λ)(chl) −B(λ) and the empirical relationship between a NAP (443) and b bp (555) used in our CDOM algorithm are summarized in Table A1.  also Table A1). Basically, we used a mathematical iteration method for minimizing the difference between measured R rs (λ) and R rs (λ) calculated using absorption and backscattering coefficients, as in the Garver-Siegel-Maritorena (GSM) model (Garver and Siegel, 1997;Maritorena et al., 2002), but with the following 5 modifications: (1) chl a-specific absorption coefficients of phytoplankton for Arctic waters (Matsuoka et al., 2011) were used; (2) spectral slopes of CDM absorption, S CDM (nm −1 ), and of b bp (λ) and η (unitless) were set either to be constants or as a function of R rs (λ) (those parameters were determined based on a sensitivity analysis conducted in this study; see section 3.2 for details); (3) b bp (555) was calculated using b bp (443) and η; (4) a NAP (443) was calculated using the empirical relationship between a NAP (443) and b bp (555) obtained for Arctic waters (i.e., a NAP (443) = b bp (555)/0.2393; Matsuoka et al., 2007); and (5) a CDOM (443) was obtained by subtracting a NAP (443) from a CDM (443). Finally, DOC concentrations were estimated using an empirical relationship between DOC concentrations and CDOM absorption obtained in the southern Beaufort Sea (i.e., DOC (µM) = 55 + 357 × a CDOM (443), Matsuoka et al., 2012).

Ocean color data
Three-weeks composite images of R rs (λ) at 412, 443, 488, 531, 551, and 670 nm in August 2009 were generated us-ing Aqua/MODIS ocean color data. After Level 1A data were downloaded from the ocean color website (http:// oceancolor.gsfc.nasa.gov/cgi/browse.pl?sen=am), geometric correction was made using the SeaWiFS Data Analysis System (SEADAS) software. Because the use of MODIS nearinfrared bands (748 and 869 nm) for atmospheric correction (i.e., NASA standard atmospheric correction: Gordon and Wang, 1994;Gordon, 1997) often yielded pixels having negative values, especially in R rs (412) in coastal areas of the southern Beaufort Sea (which were flagged), a new method that can be applied to turbid ocean waters, proposed by Wang and Shi (2007), was used to obtain R rs (λ) images in this study. This algorithm basically operates in the same way as that of Gordon and Wang (1994), but the two NIR bands (i.e., 748 and 869 nm) are replaced by two SWIR bands (i.e., 1240 and 2130 nm) for atmospheric correction.

Variability in R rs (λ)
Because we used R rs (λ) spectra to estimate CDOM absorption using our semi-analytical algorithm (section 3.2), those spectra are presented first. There were a variety of R rs (λ) spectral shapes observed in this study from coastal to open ocean waters (Fig. 3a): R rs (λ) spectra in coastal waters had a peak at 555 nm or longer wavelengths, while those in offshore waters showed a peak at wavelengths ranging from 412 to 490 nm. These spectral shapes look similar to those observed everywhere at lower latitudes (see Werdell and Bailey, 2005, and references therein), but the IOPs for Arctic waters are significantly different from those for lower latitudes (Matsuoka et al., 2007(Matsuoka et al., , 2011. A parameterization of IOPs specific to Arctic waters is therefore required to adequately derive geophysical values from R rs (λ) spectra (Matsuoka et al., 2011). In this study, Arctic-specific parameters are used for estimating CDOM absorption (Sect. 3.2). To generalize R rs (λ) spectral shapes, k-means cluster analysis was performed. The best number of classes (CN) was determined based on a minimum value of the Calinski-Harabasz index, which was found to be equal to 4 ( Fig. 3b and Table 1). This index is one of the best methods to objectively obtain an optimal number of classes and may be applied to a variety of datasets (Calinski and Harabasz, 1974). Turbidity of waters tended to increase from cluster 1 to 4, with the clusters roughly corresponding to those observed in the Chukchi Sea, except for cluster 4 (Matsuoka et al., 2007). Cluster 4 was observed especially in the Mackenzie River mouth. Similar clusters were also identified when a CN of 2 was set (gray solid and dashed lines for oceanic and coastal waters, respectively, in Fig. 3b). Therefore, although a CN of 4 was determined from the statistical point of view, it is noted that two clusters (oceanic and coastal) are enough for estimating CDOM absorption using the algorithm developed in this study. Waters can then be classified automatically and systematically before our CDOM absorption algorithm is applied (see Fig. 6 and Sect. 4).

Evaluating our algorithm for the retrieval of CDOM absorption
In situ a CDOM (443) values for southern Beaufort Sea waters varied widely from offshore to the coast (0.018 < a CDOM (443) < 1.08 m −1 ; see Fig. 4 of Matsuoka et al., 2012). In our observations, a CDOM (443) on average ac- counted for 72 ± 15 % of total non-water absorption, which is consistent with previous findings in the same study area (Bélanger et al.., 2006;Matsuoka et al., 2007Matsuoka et al., , 2009). The a CDOM (443) values estimated using our CDOM absorption algorithm (a mod CDOM (443), m −1 ) were evaluated against in situ measurements (Fig. 4). In this study, a sensitivity analysis of the algorithm was performed by varying η and S CDM values (i.e., the step 2 in the Fig. 2; see also Table 2), which are often set as constants (Lee et al., 2002;Maritorena et al., 2002); these can actually be parameterized as functions of R rs (λ) (see Appendix A). Since CDOM absorption values were significantly different between CTD/Niskin and Barge samples (see Fig. A1 of Matsuoka et al., 2012), the performance of the algorithm was evaluated separately for each category (i.e., CTD/Niskin or Barge; CTD/Niskin and Barge correspond to oceanic and coastal waters, respectively). Note that while three empirical algorithms for estimating a CDOM (443) using SBI spr and SBI sum datasets (MR dataset was not used because of lack of R rs (555) data) were evaluated, there were almost no correlations between a CDOM (443) and each R rs (λ) ratio (see Table A2). Thus, these relationships could not be used for estimating a CDOM (443) in this study.
For oceanic samples, the best performance was obtained when η and S CDM were set to be 1.0 and 0.0185, respectively (Fig. 4a). Excluding only one outlier (dotted circle), all data points fell within the ±35 % error. The root mean squared error (RMSE) and absolute percent difference (APD) were low, and the corresponding coefficient of determination was high (RMSE = 0.06, APD = 11.1 %, and r 2 = 0.98). It is important www.biogeosciences.net/10/917/2013/ Biogeosciences, 10, 917-927, 2013 1-1: η = 1.0 and S CDM = 0.0185. 1-2: η = 1.0 and S CDM = f (R rs (λ)). 2-1: η = f (R rs (λ)) and S CDM = 0.0185. 2-2: η = f (R rs (λ)) and S CDM = f (R rs (λ)). RMSE: root mean square error. APD : absolute percent difference. (443)) with in situ measurements (a obs CDOM (443)). Upper panels: a mod CDOM (443) using a fixed η = 1.0 and S CDM = 0.0185 (case 1-1 in Table 2) for (a) oceanic and (b) coastal waters. Lower panels: a mod CDOM (443) using η as a function of R rs (λ) and a constant S CDM = 0.0185 (case 2-1 in Table 2) for (c) oceanic and (d) coastal waters. to note that this evaluation was conducted using independent datasets (i.e., MALINA datasets) that were not used for developing the algorithm (i.e., SBI spr, SBI sum, and MR aut datasets were used for this development). While parameterization of IOPs was made for typical oceanic waters (not directly influenced by river discharge) of the Arctic Ocean (Matsuoka et al., 2011), the evaluation results suggest this parameterization can also be applied for Arctic coastal waters directly influenced by the discharge of the Mackenzie River. This idea is partly supported by the fact that phytoplankton absorption properties, which were used for tuning the algorithm (see step 1 in Fig. 2), are similar between oceanic and coastal waters for the same season in the Arctic Ocean (Matsuoka et al., 2009).

Fig. 4. A comparison of estimated CDOM absorption (a mod CDOM
A slope slightly lower than 1 was obtained using our algorithm (slope = 0.88; see Table 2 and Fig. 4a). This bias should be examined in a future study by collecting more samples over a wide range of CDOM content. Nonetheless, this semianalytical algorithm provides estimates of CDOM absorption within a ±35 % accuracy for oceanic waters. was high (i.e., 1.51). The best performance was obtained for coastal samples when using fixed S CDM and varying η as a function of R rs (λ) (Fig. 4d; see also Appendix A). Using this algorithm, we were able to estimate CDOM absorption for coastal waters within ±50 % accuracy except for a few data points. This suggests that unlike S CDM , the choice of the η value impacts the performance of the CDOM algorithm for coastal waters (Fig. 4c). This result is consistent with the fact that optical properties in a thin layer at the top of the surface waters were characterized by high backscattering of various types of particles, especially in the Mackenzie River mouth (Hooker et al., 2013;Doxaran et al., 2012), altering the η value. Due to scattering of particles as well as high CDOM absorption, the light penetration depth was very shallow in the Mackenzie River mouth (1.38 ± 1.82 m), but was deep in offshore areas (16.65 ± 9.84 m). Thus, η and S CDM parameters need to be set separately for oceanic and coastal waters. S CDM varies widely in global ocean basins , while this value tends to be constant in coastal areas (Babin et al., 2003;Magnuson et al., 2004). Our result may imply that waters in the southern Beaufort Sea are strongly influenced by one given end-member, the Mackenzie River discharge, making S CDM stable . The variability in this parameter needs to be examined further for Arctic waters.

Deriving DOC concentration using ocean color
In this section, we applied our CDOM absorption algorithm for Aqua/MODIS ocean color images. The three-week composite images in August 2009 were generated in order to correspond to the period of the MALINA cruise.
Overall, a sat CDOM (443) values were high in the western channel compared to those in the eastern channel of the Mackenzie delta. This result is consistent with our field observations ( Fig. 5a; see Fig. 6 in Matsuoka et al., 2012). Geometric mean and geometric standard deviation values of a sat CDOM (443) (0.034 and 2.776 m −1 , respectively) were of the same order of magnitude compared to our observations for the MALINA cruise (0.055 and 2.265 m −1 , respectively) ( Fig. 5b; Matsuoka et al., 2012).
In the Mackenzie River mouth,  observed that DOC concentrations (ranging 55 µM < DOC < 500 µM) in the surface layer were tightly correlated with a CDOM (443) (ranging 0.018 m −1 < a CDOM (443) < 1.08 m −1 ) (r 2 = 0.97; p < 0.0001).  (443) values, high DOC concentrations (>100 µM) were widely distributed in the Mackenzie shelf area (Fig. 5c-d). The geometric mean of DOC sat was 79 µM, which was similar to that observed for the MALINA cruise . This result suggests that our estimation of DOC concentrations performs reasonably well, highlighting the potential utility of the algorithm for deriving DOC concentrations in the surface layer and further estimating the DOC budget for Arctic coastal waters.

Conclusions
In this study, we developed a semi-analytical algorithm for estimating CDOM absorption for Arctic waters. Comparison with in situ measurements showed that a CDOM (443) can be estimated accurately to within an uncertainty of 35 % and 50 % for oceanic and coastal waters of the Arctic Ocean, respectively. While we acknowledge that the estimation of a CDOM (443) in highly turbid waters is still a challenging task (Zhu et al., 2011;this study), to our knowledge, this is the first semi-analytical algorithm for estimating CDOM absorption for Arctic waters. This approach allows a partitioning of CDM (i.e., CDOM plus NAP) into CDOM and NAP absorption contributions, thereby promoting an understanding of the dynamics for each component.
As a result of combining the CDOM absorption algorithm together with the DOC versus CDOM relationship, we propose a routine and near real-time method for deriving DOC concentrations for Arctic coastal waters using satellite ocean color data (Fig. 6). First, satellite R rs (λ) spectra are categorized into two classes according to their spectral shapes. This can be made using supervised classification referring to clusters 1 and 2 obtained in this study (Fig. 3b). Second, parameterization of η and S CDM is set to be either constant or as a function of R rs (λ) depending on a R rs (λ) spectral class. Third, our CDOM absorption algorithm is applied. Finally, DOC concentrations are estimated using a relationship between DOC and a CDOM (443) derived from in situ measurements. Although this kind of method is potentially useful for estimating and monitoring change in DOC budgets for Arctic coastal waters as a result of ongoing global warming, the DOC versus a CDOM (443) relationship was obtained empirically during summer in the southern Beaufort Sea and might vary seasonally; a peak DOC flux occurs during ice melt in the early spring, significantly contributing to the DOC budget (Holmes et al., 2008). Further field observations are thus required to address this issue.

Appendix A
In this study, we have a limited number of data for parameterizing η and S CDM as a function of R rs (λ). These parameterizations were made using a large dataset including coastal waters from all over the world (Lee et al., 2009 where r rs (λ) represents below-surface R rs (λ) as calculated by R rs (λ)/0.5238 (Gordon et al., 1988). Consequently, we decided to apply these equations to our CDOM algorithm for coastal waters. Detailed performance of the algorithm using these is shown in Fig. 4 and Table 2. The original code of the GSM algorithm (called GSM01) is now freely available on the ocean color website (http://oceancolor.gsfc.nasa.gov/DOCS/MSL12/master prodlist.html/#prod15). To run our CDOM algorithm, this code needs to be modified (minor modification) using the specific relationships used in our study. These values are summarized in Table A1.