# Deriving Particulate Organic Carbon in Coastal Waters from Remote Sensing: Inter-Comparison Exercise and Development of a Maximum Band-Ratio Approach

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## Abstract

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_{rs,}with POC concentrations covering three orders of magnitude. Twelve existing algorithms have then been tested on this data set, and a new one was proposed. The results show that the performance of historical algorithms depends on the type of water, with an overall low performance observed for mineral-dominated waters. Furthermore, none of the tested algorithms provided satisfactory results over the whole POC range. A novel approach was thus developed based on a maximum band ratio of R

_{rs}(red/blue, red/yellow or red/green ratio). Based on the standard statistical metric for the evaluation of inverse models, the new algorithm presents the best performance. The root-mean square deviation for log-transformed data (RMSD

_{log}) is 0.25. The mean absolute percentage difference (MAPD) is 37.48%. The mean bias (MB) and median ratio (MR) values are 0.54 μg L

^{−1}and 1.02, respectively. This algorithm replicates quite well the distribution of in situ data. The new algorithm was also tested on a matchup dataset gathering 154 coincident MERIS (MEdium Resolution Imaging Spectrometer) R

_{rs}and in situ POC concentration sampled along the French coast. The matchup analysis showed that the performance of the new algorithm is satisfactory (RMSD

_{log}= 0.24, MAPD = 34.16%, MR = 0.92). A regional illustration of the model performance for the Louisiana continental shelf shows that monthly mean POC concentrations derived from MERIS with the new algorithm are consistent with those derived from the 2016 algorithm of Le et al. which was specifically developed for this region.

## 1. Introduction

_{bp}) and chlorophyll-a concentration (Chla) [8] performed the best. While the application of these algorithms to OCR observations allowed the pool of POC over the open ocean to be estimated (about 0.4 and 1.2 Pg. C in the first attenuation and euphotic layers, respectively), [15], such information is still not available for global coastal waters, which are more complex bio-optical environments [18]. To overcome this limitation on our understanding of the POC dynamics, some purely empirical approaches were recently developed from in situ measurements performed in offshore and coastal waters [19,20,21,22] or exclusively from measurements collected in coastal waters (mainly in river-dominated systems) [23] to estimate the surface POC concentration from OCR. However, these algorithms were almost all developed from limited datasets gathered in specific regions. This dictates that the results and performance of these approaches at a global scale may be strongly conditioned by the representativeness of the dataset used for their development. In other words, these algorithms may be not suitable to catch the large POC variability encountered in optically contrasted coastal areas.

## 2. Data and Methods

#### 2.1. In Situ Data

_{rs}(λ) where λ is the wavelength. Measurements were collected by different contributors and instruments undoubtedly introducing uncertainties, which are not necessarily well characterized (Table 1). The field measurement protocols and data processing are described in detail in related papers listed in Table 1. Measurements were sampled between 1997 and 2015 in various coastal regions (Figure 1): European coastal waters [24,25,26,27,28,29], French Guiana [30], Eastern Viet Nam Sea [31,32], coastal waters of South East Pacific [33] and North Canada [34]. The particulate organic carbon is here considered as particulate carbon from organic origin retained by a Whatman GF/F filter according to the JGOFS (Joint Global Ocean Flux Study) protocol [5]. The POC is then composed of particles with a diameter between 0.4 and 200 μm, with pre-filtration usually performed.

^{−1}and Mekong River 4623 μg L

^{−1}. The lowest POC concentrations (< 100 μg L

^{−1}) are associated with the Chilean upwelling system sampled during the Biosope campaign [35]. The Chilean upwelling system was identified as coastal waters on criteria based on bathymetry (4000 m), distance to the coast (200 km), and Chla concentration (> 0.8 μg L

^{−1}) [32]. Biosope upwelling data were included in our dataset in order to consider the transition zone between coastal and open waters.

_{rs}(λ) spectra considered, about 69% were obtained from hyperspectral measurements performed from 310 to 950 nm with a 3 nm spectral resolution, while the remaining 31% were obtained from multispectral measurements at the standard spectral bands of ocean color sensors. Hyperspectral data were interpolated to obtain R

_{rs}(λ) at every nanometer, to be able to test the different published algorithms considering their specific input spectral bands. Quality controls were applied on R

_{rs}(λ) spectra based on criteria developed in [36] (unusual spectral shape, negative values in the near-infrared, strong deviation in the Rrs vs. SPM relationship in the red). The whole dataset (named DSW) consists of 606 measurements of POC concentrations (N

_{POC}) associated with hyperspectral (73%) and multispectral (27%) R

_{rs}(λ) spectra. Note that, for some of the 606 POC measurements, coincident Chla and SPM concentrations are missing so N

_{POC}> N

_{Chla}> N

_{SPM}. The POC, Chla, and SPM concentrations vary from 45.37 to 5744 μg L

^{−1}, 0.034 to 48.66 μg L

^{−1}, and 207.4 to 2626 x 10

^{3}μg L

^{−1}, respectively (Table 1 and Figure 2).

_{POC}= N = 606) was randomly split (Monte Carlo method) into a development dataset (DSD) and a validation dataset (DSV), which represent 67.8% (N = 411) and 32.2% (N = 195) of DSW, respectively. The ranges of R

_{rs}(490), R

_{rs}(555), and R

_{rs}(665) and proportion of mineral-dominated, organic-dominated, and mixed waters are quite similar for DSW, DSD, and DSV (Figure 3). DSD and DSV cover about three orders of magnitude in terms of POC concentration (Figure 4) being representative of the large natural variability of coastal environments.

#### 2.2. Satellite-In Situ Matchup Data Base

_{rs}(λ), ratio of the standard deviation to the mean computed over the pixel window, lower than 30%), and (4) number of valid pixels per pixel window greater than 6. After the application of all these criteria, the final matchup dataset is then composed of 154 matched points (Table 2). For the matchup dataset, POC concentrations are between 26.58 and 658.2 μg L

^{−1}, Chla ranges from 0.04 to 10.04 μg L

^{−1}, and SPM from 80 to 20,270 μg L

^{−1}, respectively (Figure 6). According to the value of the in situ POC/SPM ratio, 38.31%, 15.58%, and 46.1% of matchups concern mineral-dominated, organic-dominated, and mixed waters, respectively.

#### 2.3. Candidate Algorithms

_{rs}(λ) [23], R

_{rs}band ratios [11,19,20,21], or color index [22] as input parameters.

#### 2.3.1. Band Ratio-based Algorithms

_{rs}(λ) ratios at two different wavelengths to derive POC concentration in open ocean waters. This algorithm was developed from in situ data (N = 53) collected within oligotrophic and upwelling waters of the eastern South Pacific Ocean (10 ≤ POC ≤ 270 μg L

^{−1}) during the Biosope campaign. This algorithm is based on an empirical power-law between near-surface POC and blue-to-green ratio of R

_{rs}(λ). Stramski et al. (2008) showed that the following two algorithms have the best performance for their dataset:

^{−1}. The authors tested correlations of POC concentrations with reflectance ratios at various spectral bands leading to the selection of the R

_{rs}(555)/R

_{rs}(589) ratio:

_{rs}(490)/R

_{rs}(625) ratio, which has benefits to consider the input R

_{rs}close to bands potentially available from satellite observations:

^{−3}. Their algorithm is quite similar to the 2008 algorithm from Stramski et al. as it is based on a blue-to-green reflectance ratio. The authors examined the following band ratios:

_{equi}(λ) is the equivalent reflectance for a band with a central wavelength λ, f(λ) is the spectral response function, available from the Ocean Color website (http://oceancolor.gsfc.nasa.gov/), r(λ) is the in situ remote-sensing reflectance, L(λ) is the solar irradiance at mean Earth-Sun distance, λ

_{min}is equal to 350 nm, and λ

_{max}is 800 nm. The authors selected an approach based on two different band ratios, and used an optimization approach to determine the best band combination:

_{1}= 678 nm, λ

_{2}= 488 nm, λ

_{3}= 748 nm, and λ

_{4}= 412 nm. The regression coefficients are b

_{0}= 0.0078, b

_{1}= 1.3973, and b

_{2}= −1.2397. Equation (9) is named Liu15. It was shown that the R

_{rs}(λ) values at the central bands are very similar to the equivalent reflectance values calculated using the band spectral response at all visible bands of the different OCR [36]. For this reason, the central remote-sensing reflectance at 678, 488, 748, and 412 nm are used instead of the equivalent reflectance in this inter-comparison exercise.

#### 2.3.2. Absolute R_{rs}-based Algorithms

_{rs}(λ), Le et al., 2016 [23] developed multiple regression algorithms for two river-dominated estuaries in the northern Gulf of Mexico (the Louisiana Continental Shelf and Mobile Bay). The multiple linear regression models which showed the lowest prediction error between log(POC) (log-transformed base 10) and R

_{rs}(λ) are given in Equation (10) (named Le16-1) and in Equation (11) (L16-2). L16-1 and L16-2 were developed using MODIS and SeaWiFS (Sea Viewing Wide Field of View Sensor) spectral bands, respectively.

_{rs}(488) − 120.74 × R

_{rs}(531) + 245.42 × R

_{rs}(547) − 493.54 × R

_{rs}(667) + 489.3 × R

_{rs}(678) − 0.59

_{rs}(490) − 53.64 × R

_{rs}(510) + 172.13 × R

_{rs}(555) − 40.06 × R

_{rs}(670) − 0.54

#### 2.3.3. Color Index Algorithm

_{rs}(λ) data obtained from matchups. This approach uses three spectral bands centered at 490 nm, 550 nm, and 670 nm to determine a color index (CI

_{POC}, Equation (12)), from which the POC concentration is estimated (Equations (13) and (14)). This approach is named Le18-1.

_{POC}= R

_{rs}(555) − (R

_{rs}(490) + (555 − 490)/(670 − 490) × (R

_{rs}(670) − R

_{rs}(490)))

_{POC}≤ −0.0005: log(POC) = 185.72 × CI

_{POC}+ 1.97

_{POC}≥ −0.0005: log(POC) = 485.19 × CI

_{POC}+ 2.1

_{POC}is less than –0.0005 is more suitable for open waters, whereas Equation (16) used when CI

_{POC}is greater than –0.0005 is suitable for coastal waters, respectively.

_{POC}≤ −0.0005: log(POC) = −0.66 × log[R

_{rs}(443)/R

_{rs}(555)] + 2.06

_{POC}≥ −0.0005: log(POC) = −1.38 × log[R

_{rs}(443)/R

_{rs}(555)] + 2.31

#### 2.4. Statistical Indicators Used for Model Development and Validation

_{log}) (Equation (17)), the root mean square Deviation for un-transformed data (RMSD) (Equation (18)), and the median absolute percent difference (MAPD) (Equation (19)):

_{i}

^{obs}and POC

_{i}

^{mod}are the in situ and model—derived POC concentration. The mean bias (MB) (Equation (20)) and the median ratio (MR) (Equation (21)) are also calculated:

^{2}) calculated between POC and R

_{rs}(λi)/R

_{rs}(λj) as it does not matter which R

_{rs}(λ) is taken as a numerator or denominator.

## 3. Results and Discussion

#### 3.1. Development of a New Algorithm for POC

_{rs}(λ) measurements in DSD (N=298, representing 72.5% of DSD). For each spectrum, R

_{rs}(λ) in the visible part (400–700 nm) is measured at 300 different wavelengths (R

_{rs}(λ

_{i})). Mathematically, the different R

_{rs}(λ) ratios, defined as R

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}) where i ≠ j, correspond to k-combinations (R

_{rs}(λ

_{i}), R

_{rs}(λ

_{j})) of the set composed of DSD hyperspectral R

_{rs}(λ). The number of k-combinations is equal to 44,850. It corresponds to the binomial coefficient calculated using the factorials according to:

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}) ratios. Both POC concentration and R

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}) were log-transformed to base 10. Figure 7 summarizes through a half matrix representation the value of the coefficient of determination (R

^{2}) for the 44,850 regressions. The highest R

^{2}values (about 0.68) are obtained for band ratios R

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}) with λ

_{i}ranging from 675 to 695 nm and λ

_{j}ranging from 490 and 590 nm. It corresponds to red-to-blue, red-to-green, or red-to-yellow ratios. However, as the spectral region around 680 nm corresponds to the maximum of chlorophyll fluorescence [44,45], the R

_{rs}(λ) signal may be contaminated by light emission, which may bias the POC retrieval. Figure 7 shows that R

_{rs}(λ) between 660–670 nm and R

_{rs}(λ) between 490–560 are “statistically promising” spectral band combinations. The advantage is that many ocean color sensors have bands in the corresponding spectral region. These results are in agreement with those of Woźniak et al. in 2016, who obtained good performance for a blue-to-red ratio (R

_{rs}(490)/R

_{rs}(625) (Equation (4)). As MERIS data will be used in the matchup exercise, a focus is performed on bands for that sensor, selecting the following red-to-green and red-to-blue band ratios: R

_{rs}(665)/R

_{rs}(555), R

_{rs}(665)/R

_{rs}(510), R

_{rs}(665)/R

_{rs}(490) (Table 4 and Figure 8). Note that these bands are also available on OLCI, SeaWiFS, and VIIRS (Visible Infrared Imaging Radiometer Suite).

^{2}and RMSD) observed between POC and the different latter band ratios (see Table 4), a linear (and polynomial) type II regression (log-transformed data) based on the maximum band ratio (MBR) are also examined (Figure 9). Considering both statistical and graphical criteria, the linear type II regression based on MBR presents rather better performance with linear type II regression based on a single band ratio. The coefficient of determination is a bit higher (R

^{2}= 0.67 instead of R

^{2}between 0.59 and 0.66) and the RMSD

_{log}is a bit lower (RMSD

_{log}= 0.242 instead of RMSD

_{log}between 0.246 and 0.267) (Table 4). As already discussed by [46] for Chla estimates from OC4 algorithm, the MBR allows to switch from a given band ratio to another, thereby avoiding, in some cases, a low and potentially noisy band ratio. Thus, in the context of satellite applications, it is expected that using MBR instead of a single band ratio allow maximization of the model precision over the entire range of POC. Among the three band ratios, R

_{rs}(665)/R

_{rs}(490) and R

_{rs}(665)/R

_{rs}(555) are maximal for POC above 500 μg L

^{−1}and POC below 500 μg L

^{−1}, respectively (Figure 10). The latter pattern can be explained by the fact that, over their broad range of variability, SPM and POC tend, at first order, to co-vary in coastal waters (R

^{2}= 0.63 on DSW). For instance, high SPM values increase R

_{rs}in the red, while associated high POC values will increase absorption in the blue-green part of the spectrum, hence decreasing R

_{rs}(490). Although the R

_{rs}(665)/R

_{rs}(510) ratio is maximum for only 4 data points over the present dataset, this ratio is more frequently selected as the MBR over the MERIS coastal archive (not shown here). As observed for OC4 [46,47], there is an overlap, over the POC range, in the bands selected for the MBR definition, so there is a smooth transition for MBR around 0.2, which corresponds to POC concentrations between 100 and 500 μg L

^{−1}(Figure 10). Second and third order polynomial regressions, which theoretically allow for a better account of specific spectral features, were also tested. Statistical results obtained for the second-order polynomial are similar to those obtained for the type II linear regression (Figure 9, Table 4) while those for the third polynomial regression do not show any improvements (not shown). Therefore, only the linear (Equation (27)) and second-order polynomial (Equations (28)–(29)) fits based on the maximum band ratio, named CPOC-1st and CPOC-2nd (Coastal POC), will be evaluated in the following section.

#### 3.2. Inter-comparison Exercise of Existing Algorithms

_{rs}(λ) at wavelengths available from hyperspectral measurements only, multi-spectral measurements of DSV cannot be used for their evaluation. The W16-1, W16-2, Le16-2, and Liu15 algorithms are therefore tested using 150, 146, and 144 data points, respectively. The number of used hyperspectral data changes based on the availability of the bands required by each algorithm. DSV was however not restricted to hyperspectral data to allow a wide representativeness of this validation dataset in terms of geographical distribution as well as biogeochemical and optical variability. The inter-comparison exercise is realized in two steps. First, the performance of the algorithms was assessed using hyperspectral and multispectral data (when possible) to cover a wide range of variability. Second, the inter-comparison exercise was performed on a consistent number of hyperspectral data (N = 144) to observe if the number of data impacts the ranking of the algorithms’ performance.

_{log}and MR values, and a much wider POC distribution compared to the in-situ ones (Figure 11f and Figure 12f). For the organic-dominated waters, Le18-1 performs quite well as data points (green dots) are distributed along the 1:1 line. However, for mixed or organic-dominated waters, the variability in POC concentration is not reproduced and modeled POC values can be 100 times higher than in situ ones. In view of these results, this algorithm was excluded from further steps of the inter-comparison exercise. The statistical metrics (Table 5) provide a range of values among the 11 remaining algorithms for which the MAPD values vary between 38.83% and 64.40%, RMSD

_{log}between 0.27 and 0.44, MR between 1.04 and 1.59, and MB between −104.78 and 1237 μg L

^{−1}. Note that the Liu15 algorithm generates 10 negative POC values, which were not considered within the log-scale statistics may be leading to an artificial increase in the algorithm performance. The radar plot in Figure 13 gives an overview of the statistical indicators by displaying the normalized MAPD, RMSD

_{log}, MB and MR (Equations (20–23)). The best performance, related to the smallest area in the normalized radar diagram (Figure 13), is obtained for the Hu15-3 algorithm. The Hu15-3 presents the smallest MAPD (38.87%), the smallest RMSD

_{log}(0.27), and an MR close to one (1.11) (Table 5). The Hu15-3 algorithm provides relatively good performance for organic-dominated (green dots close to the 1:1 line in Figure 11c). Data points sampled in mixed waters are scattered but follow the 1:1 line. However, for mineral-dominated waters, the Hu15-3 algorithm tends to underestimate high concentrations (POC > 1000 μg L

^{−1}) (Figure 11c and 12c) and overestimates POC concentrations lower than 1000 μg L

^{−1}(blue dots in Figure 11c). This results in the the regression slope between in situ and derived POC being lower than 1 (= 0.5). Similar observations can be made for the Hu15-2 and Hu15-1 algorithms.

^{−1}), as it was developed mainly from data collected in open ocean waters. The performances of these algorithms are degraded at high concentrations, and for mineral dominated waters (blue dots in Figure 11h,i). Two Biosope data points in DSV were used previously by Stramski et al. (2008) to establish the S08-1 and S08-2 relationships and may artificially increase the performance of the S08-1 and S08-2. The performances of the S08 algorithms however do not change when removing these Biosope data points. The performance of the L18-2 algorithm is quite similar to the performance of the S08-1, 2 (Figure 11g, Table 5 and Table A1). This was expected as Le18-2, S08-1 and S08-2 are based on a blue-to-green ratio.

^{−3}. This results in MAPD and RMSD

_{log}being 61.32% and 0.337 for W16-2, respectively, against 64.08% and 0.427 for W16-1. The histograms in Figure 12k,l show that the shape of the frequency distribution of POC estimates and in situ data differ. The peak of frequency between 200 and 500 μg L

^{−1}observed for the in-situ data is absent for modeled data.

#### 3.3. Performance of the New Algorithms

^{st}and CPOC-2

^{nd}algorithms improve the overall performance as compared to Hu15-3 algorithm. The second-order polynomial relationship shows the best performance with a smaller MAPD and smaller MB than the Type II linear regression. The MAPD is 37.48%, the RMSD

_{log}is 0.25, MB is = 0.54, MR is equal to 1.02, and the regression slope is around 0.78. Most of the POC values in waters identified as mineral-dominated are overestimated, whereas the POC values in organic-dominated waters are underestimated (Figure 15). We tried to develop a specific second-order polynomial regression according to the type of waters to adjust the POC concentration from Equation (28) according to the POC/SPM ratio with SPM concentration from Han et al., 2016. Results are not shown as it does not improve the accuracy of the estimates. As no specific regional pattern has been noticed on the validation results (not shown), the performance of the algorithm is more related to the chemical nature of the bulk suspended particulate matter, as opposed to any regional aspects. The shape of the POC distribution of model-derived and in situ data are quite similar (Figure 15b and Figure 16b). Nevertheless, the maximum of occurrence is slightly shifted towards higher POC values. This results in the median calculated for modeled data being a bit higher (425 μg L

^{−1}instead of 391 μg L

^{−1}), whereas the mean values are equal (=569 μg L

^{−1}).

_{rs}(λ) measurements gathered in the match-up dataset described in Section 2.2. The matchup analysis shows that the CPOC-2nd algorithm, developed only on R

_{rs}(λ) and POC in situ data, is able to estimate satisfactorily the surface POC concentration from satellite observation over coastal waters. The histograms (Figure 17) show a good agreement between the in situ and estimated maximum values (around 100 μg L

^{−1}), as well as between the in situ and estimated median values (102.5 and 108.4 μg L

^{−1)}, respectively. The MAPD, RMSD

_{log}, MR, and MB values are 34.16%, 0.24, 0.92, and −25.93 μg L

^{−1}, respectively [43,48]. Note that overestimations and underestimations of POC values are only observed for two of the eight sampling stations (Banyuls-sur-Mer and Marseille). These differences can be due to uncertainties on in situ POC measurements as well as satellite remote-sensing reflectance (partly due to atmospheric corrections uncertainties). Concerning this latter aspect, we verified the retrieval accuracy of R

_{rs}based on an extensive matchup exercise of 760 coincident data points collected from the AERONET-OC sites (Ocean Color component of the Aerosol Robotic Network). A bias of 3.4 × 10

^{−3}, 1.5 × 10

^{−3}, −1.9 × 10

^{−4}between in situ AERONET and MERIS R

_{rs}(λ) at 490, 555 and 665 has been observed, respectively. Taking into account these bias values for the MERIS R

_{rs}(λ) values over the SOMLIT matchup dataset, we showed that this correction only slightly modifies the POC estimates. Inaccuracies can also be explained by the fact that the range of POC concentration used in this matchup exercise is lower than the range of POC concentration of DSD. For instance, the median POC value for the SOMLIT in situ dataset is 108.4 μg L

^{−1}, while it reaches 366.4 for DSD. The fact that the statistical values are better for the match-up data set than for DSV may be partly explained by the fact that the SOMLIT POC data set used for the match-up exercise gathers less mineral dominated waters (38 %) for which a slight over-estimation by CPOC-2nd has been observed, against 50% for DSV.

#### 3.4. Satellite POC Estimates for Coastal Regions

^{nd}compared to Le16-2 is observed when all pixels are taken into account (Figure 18c). However, by restricting only the comparison to coastal pixels (as defined by R

_{rs}(665) > 0.0012 [49]) for which the CPOC-2nd has been developed, an excellent agreement between the two POC products is observed (Figure 18d–f). The two histograms are more similar than previously, and the medians are closer: 700.25 μg L

^{−1}for Le16-2 and 627.50 μg L

^{−1}for CPOC-2nd estimates. This pattern shows that part of the discrepancies between the Le16-2 and CPOC-2nd are related to open water situations for which the CPOC-2nd and Le16-2 are not suitable.

## 4. Concluding Remarks

_{rs}(λ), which were sampled in highly contrasting bio-optical coastal environments. While these existing algorithms perform relatively well over POC ranges for which they were developed, they present some lack of accuracy over a broad range of POC concentrations. With the objective of improving POC estimates at the global scale for coastal waters, a new empirical relationship was proposed based on a second-order polynomial regression using the maximum band ratio. The new algorithm (CPOC) shows relevant capacity to estimate POC concentrations on the in-situ validation dataset (MAPD = 37.48%, RMSD

_{log}= 0.25, MB = 0.54 μg L

^{−1}, and MR = 1.02). Robust results were found when the algorithm was tested on the matchup dataset as illustrated by the consistency in the median values computed for the modeled POC (102.5 μg L

^{−1}) and the in situ POC datasets (108.4 μg L

^{−1}). While the use of a spectral band ratio to retrieve POC reduces the impact of atmospheric corrections, the latter continues to have an impact as the accuracy of R

_{rs}retrieval is spectrally dependent [50]. The new algorithm was applied to MERIS data in the Louisiana Continental Shelf in June 2006. The observed spatial and temporal (not shown) patterns were in good agreement with the patterns observed by Le et al. who developed an algorithm specifically for this region in 2006. The algorithm developed in this study performs consistently across the three types of water (mineral-dominated, mixed, and organic-dominated). However, the POC concentration in mineral-dominated waters tends to be overestimated, whereas POC concentration in organic-dominated waters tends to be underestimated. Second-order polynomial regressions specific to the type of waters to adjust the POC concentration according to the POC/SPM ratio were evaluated, but such formulations did not improve the estimates. From these results, several key points of development are highlighted as necessary to the development of greater knowledge pertaining to the composition of the particulate pool.

_{bp}/b

_{p}), measured by commercial optical backscattering sensors, such as WetLabs Eco-VSF and ECO-BB, could be a valuable parameter. Indeed, previous studies [37,51,52] have shown that b

_{bp}/b

_{p}could be an indicator of the amount of organic material relative to mineral particles. It would be interesting to re-conduct these studies on coincident POC, R

_{rs}(λ), SPM, and b

_{bp}/b

_{p}in situ measurements to define some criteria at the global scale and to better characterize which kind of particles dominate in a defined water mass.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Algorithms | N | MAPD | MB | RMSD_{log} | RMSD | MR | R^{2} | Slope | Intercept | Negative Value |
---|---|---|---|---|---|---|---|---|---|---|

Hu15-1 | 144 | 55.44 | −50.55 | 0.31 | 651.0 | 1.41 | 0.37 | 0.28 | 1.98 | 0 |

Hu15-2 | 144 | 41.01 | −142.6 | 0.29 | 666.9 | 1.14 | 0.41 | 0.31 | 1.82 | 0 |

Hu15-3 | 144 | 41.77 | −101.3 | 0.28 | 677.6 | 1.11 | 0.41 | 0.44 | 1.48 | 0 |

Le16-1 | 144 | 62.68 | 126.8 | 0.4 | 1084 | 1.51 | 0.14 | 0.33 | 1.87 | 0 |

Le16-2 | 144 | 60.89 | 1237 | 0.44 | 4715 | 1.59 | 0.42 | 0.9 | 0.46 | 0 |

Le18-1 | 144 | 2818 | 1,801,776 | 1.87 | 15,865,153 | 29.19 | 0.03 | 0.68 | 2.26 | 0 |

Le18-2 | 144 | 53.89 | 50.53 | 0.32 | 674.9 | 1.44 | 0.37 | 0.43 | 1.63 | 0 |

Liu15 | 134 | 62.71 | 202.8 | 0.38 | 749.4 | 1.4 | 0.28 | 0.62 | 1.1 | 10 |

CPOC-2nd | 144 | 44.62 | 22.60 | 0.27 | 561.7 | 1.18 | 0.55 | 0.77 | 0.64 | 0 |

S08-1 | 144 | 42.82 | −139.5 | 0.3 | 665.5 | 1.16 | 0.37 | 0.31 | 1.83 | 0 |

S08-2 | 144 | 49.59 | 17.34 | 0.3 | 675.4 | 1.4 | 0.41 | 0.42 | 1.64 | 0 |

W16-1 | 144 | 64.08 | 228.8 | 0.43 | 859.7 | 1.18 | 0.45 | 1.06 | −0.15 | 0 |

W16-2 | 144 | 61.32 | 252.4 | 0.34 | 719.9 | 1.51 | 0.53 | 0.9 | 0.39 | 0 |

**Figure A1.**Comparison of the statistical performance of the eleven algorithms. The algorithms were tested using hyperspectral data only. The number of data (N = 144) is the same for the 11 algorithms (Table 5).

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**Figure 1.**Geographical distribution of the 606 in situ coincident measurements of POC and R

_{rs}listed in Table 1; In situ data were collected (

**a**) in the Beaufort Sea—Arctic ocean, (

**b**) in the coastal water of French Guiana, (

**c**) in the South East Pacific ocean, (

**d**) in European coastal waters: the North Sea, the English Channel and Bay of Biscay, (

**e**) in the Baltic Sea and, (

**f**,

**g**) the Eastern Viet Nam Sea. The color scale corresponds to surface POC concentrations (in μg L

^{−1}).

**Figure 2.**Frequency distribution of (

**a**) POC, (

**b**) SPM, and (

**c**) Chla concentration. Dashed lines stand for the median values (M) of each parameter.

**Figure 3.**Frequency distribution of the POC to SPM ratio for (

**a**) DSW, (

**b**) DSD, and (

**c**) DSV. Dot-dashed lines represent the values, which delimit the POC/SPM ranges for the mineral-dominated, mixed, and organic-dominated waters according to [39]. The percentages between brackets indicate the percentage of in situ data for each type of water.

**Figure 4.**POC and R

_{rs}values at 665, 555 and, 490 nm for the whole (

**a**–

**d**), development (

**e**–

**h**), and validation dataset (

**i**–

**l**) named DSW, DSD and DSV, respectively. Dashed lines display the median values, M.

**Figure 5.**Map of SOMLIT stations location around France, presented for divers’ type of waters in coastal area.

**Figure 6.**Frequency distribution of the biogeochemical measurements for the matchup dataset (DSM). (

**a**) POC, (

**b**) Chla, (

**c**) SPM concentration (μg L

^{−1}), and (

**d**) POC/SPM. The dashed lines in (

**a**), (

**b**), and (

**c**) display the median values (M). The dot-dashed lines in (

**d**) delimit the POC/SPM range for the mineral-dominated, mixed and organic-dominated waters according to [39].

**Figure 7.**Coefficient of determination (R

^{2}) for linear type II regression (in log space) between POC and band ratio defined as R

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}). The dashed lines represent the central wavelength of MERIS spectral bands (units, nm).

**Figure 8.**The relationship between POC and the different band ratios developed from the DSD dataset (N = 411): (a) R

_{rs}(665)/R

_{rs}(555), (b) R

_{rs}(665)/R

_{rs}(510), and (c) R

_{rs}(665)/R

_{rs}(490). Green, red and blue dots correspond to organic-dominated, mixed, and mineral-dominated waters; gray dots indicate the in-situ data points without information of SPM that cannot be classified according to POC/SPM ratio. The black line stands for the linear type II regression to log-transformed data. The letter “X” represents the band ratio.

**Figure 9.**Relationships (in log-transformed) between POC and the maximum band ratio (MBR) developed from the DSD dataset (N = 411). Green, red and blue dots correspond to organic-dominated, mixed and mineral-dominated waters; gray dots indicate the in-situ data points without information of SPM that cannot be classified according to POC/SPM ratio. The black line stands for (

**a**) linear type II regression (

**b**) second-order polynomial regression to log-transformed data. The letter “X” represents the MBR.

**Figure 10.**Relationships (log-transformed) between POC and the maximum band ratio (MBR) developed from the DSD dataset (N = 411). Symbols indicate which ratio is maximal for each data point. For open circles, it is R

_{rs}(665)/R

_{rs}(555), which is maximum, whereas for crosses and filled triangles, it is R

_{rs}(665)/R

_{rs}(490) and R

_{rs}(665)/R

_{rs}(510), respectively.

**Figure 11.**Comparison of in situ and model-derived POC for the selected algorithms (log-transformed data). Each subplot was made using a different algorithm to retrieve POC: (

**a**) Hu15-1; (

**b**) Hu15-2; (

**c**) Hu15-3; (

**d**) Le16-1; (

**e**) Le16-2; (

**f**) Le18-1; (

**g**) Le18-2; (

**h**) S08-1; (

**i**) S08-2; (

**j**) Liu15; (

**k**) W16-1; (

**l**) W16-2. Green, red, and blue dots correspond to organic-dominated, mixed, and mineral-dominated waters, respectively. Gray dots indicate the in situ data points without information of SPM that cannot be classified according to the POC/SPM ratio. The black dashed line is the 1:1 line, and the solid red line is the type II linear regression.

**Figure 12.**Frequency distribution of in situ (grey) and model-derived (white) POC. Each subplot was made using a different algorithm to retrieve POC: (

**a**) Hu15-1; (

**b**) Hu15-2; (

**c**) Hu15-3; (

**d**) Le16-1; (

**e**) Le16-2; (

**f**) Le18-1; (

**g**) Le18-2; (

**h**) S08-1; (

**i**) S08-2; (

**j**) Liu15; (

**k**) W16-1; (

**l**) W16-2. The dashed lines represent the median of in situ POC measurements for DSV (=391 μg L

^{−1}), and the solid line the median values of POC estimates. The median values of POC estimates (M) are indicated in each panel.

**Figure 13.**Comparison of the statistical performance of the eleven algorithms. The algorithms were tested using hyperspectral and multispectral data. The number of data changes according the considered algorithm (Table 5).

**Figure 14.**Statistical performance of the new developed algorithms named CPOC (Coastal POC) as compared to the Hu15-3 algorithm. The normalized MAPD, MR, MB, and RMSD

_{log}were calculated on DSV. The black line and red line present statistics obtained with the CPOC-1st and CPOC-2nd algorithm, respectively.

**Figure 15.**(

**a**) Comparison of in situ and model-derived POC for the CPOC-1st algorithm. The dashed line is the 1:1 line, and the solid line is the type II linear regression. Green, red and blue dots correspond to organic-dominated, mixed and mineral-dominated waters; gray dots indicate the in-situ data points without information of SPM that cannot be classified according to the POC/SPM ratio. (

**b**) The frequency distribution of in situ (grey) and POC measurements derived from the CPOC-1st algorithm (black contour). The dashed lines represent the median of in situ POC measurement of DSV (=391 μg L

^{−1}), and the solid line the median value of model-derived POC value of DSV.

**Figure 16.**(

**a**) Comparison of in situ and model-derived POC for the CPOC-2nd algorithm. The dashed line is the 1:1 line, and the solid line is the type II linear regression. Green, red and blue dots correspond to organic-dominated, mixed and mineral-dominated waters; gray dots indicate the in-situ data points without information of SPM that cannot be classified according to the POC/SPM ratio. (

**b**) The frequency distribution of in situ (grey) and POC measurements derived from the CPOC-2nd algorithm (black contour). The dashed lines represent the median of in situ POC measurement of DSV (=391 μg L

^{−1}), and the solid line the median value of model-derived POC value of DSV.

**Figure 17.**(

**a**) Comparison of in situ and model-derived POC concentrations using the matchup dataset. The dashed line displays the 1:1 line and the solid one the linear type II regression. Green, red and blue dots correspond to organic-dominated, mixed and mineral-dominated waters, respectively. (

**b**) Frequency distribution of in situ (grey) and POC measurements derived from the CPOC-2nd algorithm (black contour). The dashed lines represent the median of in situ POC measurement (=108.4 μg L

^{−1}), and the solid line the median value of model-derived POC value.

**Figure 18.**Near-surface POC concentration model-derived from MERIS, Louisiana Continental Shelf, June 2006 (

**a**) using CPOC-2nd (

**b**) Le16-2 algorithms. The black line in the upper left panel delimits pixels, close to the coast, with R

_{rs}(665) > 0.0012 [49] and offshore pixels with R

_{rs}(665) < 0.0012 (

**c**,

**d**). Density plots of POC as derived with the CPOC-2nd and Le16-2 algorithms for (c) all the pixels of the scene (

**d**) only for pixels with R

_{rs}(665) > 0.0012. Distribution of POC estimates with CPOC-2nd and Le16-2 algorithm for (

**e**) all pixels of the scene (

**f**) only for pixels with R

_{rs}(665) > 0.0012. The black and red lines represent the median of POC estimates using the Le16-2 and CPOC-2nd algorithms, respectively.

**Table 1.**Information on the in-situ data used in this study: number of data (N), minimum (Min), maximum (Max), mean, and standard deviation (StdDev) values of POC concentrations (μg L

^{−1}). M and H stand for multispectral and hyperspectral data, respectively.

Region | Year | N_{POC} | N_{Rrs} | Min | Max | Mean | StdDev | Reference | Multispectral (M) or Hyperspectral Data (H) |
---|---|---|---|---|---|---|---|---|---|

Baltic Sea | 1998 | 33 | 33 | 330.0 | 1990 | 823.3 | 339.7 | [24,25] | M |

Bay of Biscay-France | 2012 | 38 | 38 | 157.0 | 3930 | 1225 | 1056 | [28] | H |

Beaufort Sea Arctic Ocean | 2004 | 20 | 20 | 49.80 | 319.7 | 120.8 | 64.15 | [34] | M |

East Sea-Viet Nam | 2010 | 14 | 14 | 188.0 | 1248 | 485.1 | 365.6 | [31,32] | H |

2011 | 125 | 125 | 68.90 | 1203 | 283.7 | 200.4 | H | ||

2013 | 37 | 37 | 221.0 | 1858 | 649.5 | 248.1 | H | ||

2014 | 72 | 72 | 65.41 | 4623 | 588.3 | 816.9 | H | ||

2015 | 17 | 17 | 45.37 | 144.5 | 99.98 | 36.92 | H | ||

English Channel | 1997 | 47 | 47 | 60.00 | 221.0 | 119.4 | 41.53 | [24,25] | M |

2004 | 84 | 84 | 214.7 | 2262 | 754.0 | 388.2 | [26,27] | H | |

2010 | 20 | 20 | 110.2 | 2159 | 331.6 | 276.9 | [29] | H | |

French Guiana | 2012 | 35 | 35 | 216.0 | 5744 | 1406 | 1309 | [30,40] | H |

North Sea | 1998 | 58 | 58 | 190.0 | 2470 | 505.8 | 390.5 | [24,25] | M |

South Pacific Ocean | 2004 | 6 | 6 | 112.9 | 277.8 | 192.6 | 62.79 | [33] | M |

Overall | 606 | 606 | 45.37 | 5744 | 575.6 | 662.5 |

**Table 2.**In situ data from the French SOMLIT network (DSM dataset) sampled simultaneously with MERIS overpass.

Station | Location | Distance to Coastline (km) | Number of In Situ POC Data | Number of Matchups |
---|---|---|---|---|

S 01 | Wimereux, North of France (Channel Sea) | 1.6 | 30 | 6 |

S 02 | Wimereux, North of France (Channel Sea) | 8.1 | 56 | 11 |

S 03 | Roscoff, Brittany (Channel Sea) | 3.5 | 42 | 30 |

S 10 | Banyuls-sur-Mer (Mediterranean Sea) | 0.8 | 92 | 78 |

S 11 | Marseille (Mediterranean Sea) | 4.8–6.4 | 69 | 28 |

S 12 | Villefranche-sur-Mer, French Riviera, (Mediterranean Sea) | 0.5 | 44 | |

S 17 | Luc-sur-Mer, Normandy, (Channel Sea) | 0.175 | 1 | |

S 18 | La Rochelle, Bay of Biscay (Atlantic Ocean) | 8.046 | 2 | 1 |

Total | 336 | 154 |

**Table 3.**Candidate algorithms used for the inter-comparison exercise. The four last columns provide relevant information on the algorithms: inputs of algorithm, region where the data were collected, the range of POC, and number of data used for the development of the algorithm.

Authors | Abbreviation | Inputs | Region | POC Range (μg L ^{−1}) | N |
---|---|---|---|---|---|

Band ratio-based algorithms | |||||

Stramski et al. 2008 | S08-1S08-2 | R_{rs}(443)/R_{rs}(555)R _{rs}(490)/R_{rs}(555) | Eastern South Pacific | 10–270 | 53 |

Woźniak et al. 2016 | W16-1 W16-2 | R_{rs}(555)/R_{rs}(589),R _{rs} (490)/R_{rs}(625) | Baltic Sea Gulf of Gdańsk (Poland) | 145–2370 | 73 |

Hu et al. 2015 | Hu15-1 Hu15-2 Hu15-3 | R_{rs}(443)/R_{rs}(555)R _{rs}(490)/R_{rs}(555)R _{rs}(510)/R_{rs}(555) | China Sea | 17.59–687.5 | 120 |

Liu et al. 2015 | Liu15 | R_{rs}(678)/R_{rs}(488) & R _{rs}(748)/R_{rs}(412) | Pearl River Estuary, (China) | 113–1402 | 103 |

R_{rs} based algorithm | |||||

Le et al. 2016 | Le16-1 Le16-2 | R_{rs}(488), R_{rs}(532), R_{rs}(547), R_{rs} (667), R_{rs}(678)R _{rs}(490), R_{rs}(510), R_{rs}(550), R_{rs} (670) | Louisiana & Mobile Bay (Gulf of Mexico) | 11.5–230 | 230 |

Color index algorithm | |||||

Le et al. 2018 | Le18-1 Le18-2 | R_{rs}(490) & R_{rs}(555) & R_{rs}(665),R _{rs}(443)/R_{rs}(555) | Global ocean * | 52.6–375.2 | 297 |

*****The algorithm was developed from satellite R

_{rs}and coincident in situ POC measurements through a matchup exercise.

**Table 4.**Statistical results for POC algorithms. The formulations are power function, $\mathrm{POC}={10}^{{\mathrm{a}}_{1}\mathrm{X}+{\mathrm{a}}_{0}}$ or second-order polynomial $\mathrm{POC}={10}^{{\mathrm{a}}_{2}{\mathrm{X}}^{2}+{\text{}\mathrm{a}}_{1}\mathrm{X}\text{}+{\text{}\mathrm{a}}_{0}}$ (log is for decimal logarithm).

X | Functional Form | a_{o} | a_{1} | a_{2} | R^{2} | RMSD_{log} |
---|---|---|---|---|---|---|

log(R_{rs}(665)/R_{rs}(555)) | Power | 3.097 | 1.122 | 0.59 | 0.267 | |

log(R_{rs}(665)/R_{rs}(510)) | Power | 2.926 | 0.906 | 0.65 | 0.249 | |

log(R_{rs}(665)/R_{rs}(490)) | Power | 2.861 | 0.833 | 0.66 | 0.246 | |

log(MRB) | Power | 2.875 | 0.928 | 0.67 | 0.242 | |

log(MRB) | Second-order polynomial | 2.873 | 0.945 | 0.025 | 0.67 | 0.242 |

**Table 5.**Statistics obtained on DSV for the tested algorithms. The best results for each statistic are shown in bold.

Algorithms | N | MAPD | MB | RMSD_{log} | RMSD | MR | R^{2} | Slope | Intercept | Negative Value |
---|---|---|---|---|---|---|---|---|---|---|

CPOC-1st | 195 | 38.37 | −2.77 | 0.25 | 488.02 | 1.03 | 0.60 | 0.78 | 0.58 | 0 |

CPOC-2nd | 195 | 37.48 | 0.54 | 0.25 | 489.88 | 1.02 | 0.60 | 0.78 | 0.58 | 0 |

Hu15-1 | 195 | 64.40 | 29.45 | 0.32 | 581.37 | 1.55 | 0.39 | 0.32 | 1.9 | 0 |

Hu15-2 | 195 | 38.83 | −104.8 | 0.28 | 582.1 | 1.14 | 0.48 | 0.35 | 1.72 | 0 |

Hu15-3 | 195 | 38.87 | −74.53 | 0.27 | 589.8 | 1.11 | 0.47 | 0.5 | 1.31 | 0 |

Le16-1 | 195 | 61.75 | 127.5 | 0.38 | 943.3 | 1.52 | 0.22 | 0.4 | 1.7 | 0 |

Le16-2 | 144 | 60.89 | 1237 | 0.44 | 4715 | 1.59 | 0.42 | 0.9 | 0.46 | 0 |

Le18-1 | 195 | 1781 | 1,340,760 | 1.76 | 13,608,584 | 18.81 | 0.08 | 0.94 | 1.48 | 0 |

Le18-2 | 195 | 68.94 | 157.7 | 0.35 | 651.5 | 1.63 | 0.39 | 0.48 | 1.52 | 0 |

Liu15 | 134 | 62.71 | 202.8 | 0.38 | 749.4 | 1.4 | 0.28 | 0.62 | 1.1 | 10 |

S08-1 | 195 | 45.09 | −60.53 | 0.3 | 584.0 | 1.26 | 0.39 | 0.36 | 1.73 | 0 |

S08-2 | 195 | 49.19 | 44.14 | 0.29 | 590.4 | 1.41 | 0.48 | 0.47 | 1.51 | 0 |

W16-1 | 150 | 64.29 | 214.9 | 0.44 | 842.5 | 1.04 | 0.48 | 1.13 | −0.33 | 0 |

W16-2 | 146 | 61.32 | 247.5 | 0.34 | 715.1 | 1.48 | 0.53 | 0.91 | 0.35 | 0 |

S08-1* | 193 | 45.46 | −61.03 | 0.30 | 587.0 | 1.26 | 0.38 | 0.35 | 1.75 | 0 |

S08-2 * | 193 | 49.19 | 44.47 | 0.30 | 593.5 | 1.41 | 0.48 | 0.46 | 1.52 | 0 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tran, T.K.; Duforêt-Gaurier, L.; Vantrepotte, V.; Jorge, D.S.F.; Mériaux, X.; Cauvin, A.; Fanton d’Andon, O.; Loisel, H.
Deriving Particulate Organic Carbon in Coastal Waters from Remote Sensing: Inter-Comparison Exercise and Development of a Maximum Band-Ratio Approach. *Remote Sens.* **2019**, *11*, 2849.
https://doi.org/10.3390/rs11232849

**AMA Style**

Tran TK, Duforêt-Gaurier L, Vantrepotte V, Jorge DSF, Mériaux X, Cauvin A, Fanton d’Andon O, Loisel H.
Deriving Particulate Organic Carbon in Coastal Waters from Remote Sensing: Inter-Comparison Exercise and Development of a Maximum Band-Ratio Approach. *Remote Sensing*. 2019; 11(23):2849.
https://doi.org/10.3390/rs11232849

**Chicago/Turabian Style**

Tran, Trung Kien, Lucile Duforêt-Gaurier, Vincent Vantrepotte, Daniel Schaffer Ferreira Jorge, Xavier Mériaux, Arnaud Cauvin, Odile Fanton d’Andon, and Hubert Loisel.
2019. "Deriving Particulate Organic Carbon in Coastal Waters from Remote Sensing: Inter-Comparison Exercise and Development of a Maximum Band-Ratio Approach" *Remote Sensing* 11, no. 23: 2849.
https://doi.org/10.3390/rs11232849