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Edited by: Hervé Claustre, Centre National de la Recherche Scientifique (CNRS), France

Reviewed by: Emmanuel Boss, University of Maine, United States; David Antoine, Curtin University, Australia

*Correspondence: Hayley Evers-King

This article was submitted to Ocean Observation, a section of the journal Frontiers in Marine Science

†Present Address: Tihomir S. Kostadinov, Division of Hydrologic Sciences, Desert Research Institute, Reno, NV, United States

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Particulate Organic Carbon (POC) plays a vital role in the ocean carbon cycle. Though relatively small compared with other carbon pools, the POC pool is responsible for large fluxes and is linked to many important ocean biogeochemical processes. The satellite ocean-color signal is influenced by particle composition, size, and concentration and provides a way to observe variability in the POC pool at a range of temporal and spatial scales. To provide accurate estimates of POC concentration from satellite ocean color data requires algorithms that are well validated, with uncertainties characterized. Here, a number of algorithms to derive POC using different optical variables are applied to merged satellite ocean color data provided by the Ocean Color Climate Change Initiative (OC-CCI) and validated against the largest database of

Total particulate organic carbon (POC or _{o}) in the ocean is a key currency used in studies of both the biological export of carbon from the surface to the deep ocean, and the availability of food for marine organisms. The pool of POC in the ocean is relatively small (estimates include: 0.43 Pg C in the first light-attenuation depth—Gardner et al.,

The theoretical work of Stramski and Kiefer (

POC is readily quantifiable by filtering seawater samples, and forms a key component of many biological ocean models. However, _{rs} at SeaWiFS wavelengths and [Chl], as well as some additional inherent optical properties (IOPs) such as absorption and backscattering coefficients of phytoplankton and other particulate matter, and diffuse attenuation coefficient for downward plane irradiance, _{d} at 490 nm. There is a recognized need in the user community for additional products from ocean color that deal directly with POC, including separation of the contribution of phytoplankton, and the size distribution of particles. Further, these products need to be regionally optimized and their uncertainties well characterized. Both of these requirements may be addressed via optical classification (e.g., Moore et al.,

Remote sensing of POC through ocean color radiometry requires the exploitation of some optical signal that is associated with the material. In fact, optically, the beam attenuation coefficient of particles (_{p}), particle scattering coefficient (_{p}), backscattering coefficient (_{bp}) and the attenuation coefficient of downward irradiance _{d} are all sensitive to particle abundance (to a first order), and to particle composition (through refractive index), size, shape and internal structure. It has been demonstrated that POC is correlated with _{p} measured using transmissometers (Gardner et al., _{p} and _{p} are not among the data products that are routinely retrieved from remote sensing, satellite-based algorithms exist for retrieving POC from all the optical properties listed above, as well as from remote-sensing reflectance values.

This paper compares five different algorithms for estimating POC concentrations, selected as being representative of varied approaches that are prevalent for POC retrieval from ocean-color data. Each algorithm is applied to different optical properties derived from satellite ocean color data, and each uses different formulations for linking the parameters to the POC concentration. Matchups between

For this study, POC concentration data were collected from a number of existing databases and from individual contributors. Databases collated included PANGAEA (_{2}. The liberated CO_{2} is finally detected by thermal conductivity (Sharp,

Matchup extraction was based on the procedure developed for the OC-CCI. The daily, 4 km, sinusoidally projected OC-CCI version 2 data (Sathyendranath et al.,

Five different algorithms for determination of POC concentration were considered. For consistency of comparison, all algorithms were implemented using the appropriate variables from the OC-CCI product suite. Another reason for using the OC-CCI products is that a rigorous algorithm selection procedure for atmospheric correction (Müller et al.,

We also note that there are differences in how the five algorithms compared here were developed and implemented in the original work. For example, two of the algorithms (algorithms A and B presented below) were derived solely from coincidentally collected

This algorithm (designated _{o}(

The model parameters were determined using some 53 pairs of co-located _{rs} from oligotrophic and upwelling waters of the East Atlantic and the South Pacific. The authors have provided various fits to the models for different pairs of wavebands for _{rs} and for different selections of data. The one we have used here is based on all data, and for the 443–555 waveband pair, as recommended by the authors. This algorithm is currently used by the NASA Ocean Biology Processing Group to generate the global POC data product from ocean color data. The _{rs} values in the OC-CCI product suite were used as input to this algorithm for the validation exercise presented here. We note that a similar POC algorithm based on the blue-to-green reflectance ratio has been developed and validated with the data from the Southern Ocean (Allison et al.,

This algorithm (_{o}(_{bp}(555), the particulate backscattering coefficient at 555 nm (2), as input. The equation has the form:

Stramski et al. (_{bp} for the eventual determination of POC: firstly, the method of Maffione and Dana (^{o}. Next, using a two-step empirical approach, Stramski et al. (_{bp} by removing the backscattering coefficient for pure water [they used pure-water backscattering coefficients proposed by Buiteveld et al. (_{bw} was likely within the range of errors associated with the measurements themselves, and therefore did not substantially impact the performance of the algorithm for deriving POC]. Then, _{bp} was empirically related to POC concentrations (Equation 2). Stramski et al. (_{b}) and _{rs} or the Quasi Analytical Algorithm (QAA) approach of Lee et al. (_{bp} from _{rs}. They found that the comparison with measured _{bp} was improved considerably when an empirical correction based on their measurements of _{bp} was applied to the QAA algorithm. Thus, this algorithm uses a two-step approach: first, _{bp} is derived from _{rs}, and then that _{bp} is used in Equation (2) to calculate POC.

In the computation of OC-CCI _{bp} products, the QAA model was used, along with Zhang et al. (_{rs} at 440 nm and at 555 nm. A power law is then used to calculate the particle backscattering coefficients at other wavelengths given the value of the spectral backscattering coefficient and _{bp}(555), estimated from an analytical relationship using _{rs}(555) and the absorption coefficient (_{bp} were used to compute POC in the calculations presented here, without any empirical correction. For this algorithm a linear fit provided the best error statistics in the original study of Stramski et al. (

This algorithm (_{o}(_{bp}(490) and [Chl], and was proposed by Loisel et al. (_{bp} and [Chl] from SeaWIFS data using the method of Loisel and Stramski (_{bp}) and [Chl] (designated ^{−2} to go from total scattering coefficient to POC concentration. Combining these steps yields the following algorithm:

Algorithm C is implemented here using the Lee et al. (_{bp}), and a more recent OC4 (v6) for [Chl].

This algorithm (_{o}(_{d}(490) to beam attenuation coefficient for particles (_{p}), and then the beam attenuation coefficient to POC:

and

In Gardner et al. (_{d}(490) is obtained from SeaWIFS data where the algorithm of Mueller (

The _{d}(490) values used in the comparison presented here are obtained from the OC-CCI version 2 data, which uses the method of Lee et al. (

This algorithm (_{o}(_{bp} values at 490, 510, and 555 nm extracted from the OC-CCI matchup data (for which OC-CCI uses Lee et al. (_{bp} is instead retrieved using the formulation of Loisel and Stramski (_{o}), given η and _{bp} at 443 nm. The LUTs are constructed using theoretical forward simulations using Mie code (Bohren and Huffman, _{o}, the PSD is integrated to calculate particle volume in the 0.5 to 50 μm diameter range, and then volume is converted to carbon using existing allometric relationships derived from phytoplankton cultures (Menden-Deuer and Lessard, _{o} (based on PSD validation statistics) to achieve more realistic absolute carbon concentration values (Kostadinov et al.,

The OC-CCI product suite includes memberships of each pixel in 14 optical classes, following the fuzzy logic classification methodology of Moore et al. (

Statistical analysis used in the assessment of each algorithm was based on that used by OC-CCI (see Brewin et al., _{10} transformed and un-transformed data (_{10} transformed using parametric tests and for un-transformed data using non-parametric, rank-based, statistics. Statistical metrics computed were:

Pearsons correlation coefficient for log_{10} transformed data, and Spearman's correlation for un-transformed data (_{p} and _{s} respectively),

Root mean square differences for log_{10} transformed and un-transformed data (RMSD - Ψ, in log_{10} for the transformed data and mg m^{−3} of POC for the untransformed data),

Bias for log_{10} transformed data and untransformed data ((δ), in log_{10} for the transformed data and mg m^{−3} of POC for the untransformed data),

Median absolute percentage deviation between predictions and observations (MAPD in %), an estimate of bias and precision was estimated as the interquartile range (IQR) of the absolute percentage deviation for the untransformed data,

Center pattern root mean square deviation (Δ), in mg m^{−3}), which is the error of the predicted values with respect to the observations, irrespective of the average bias between the two distributions. It is related to the RMSD and bias as follows: Δ^{2} = Ψ - δ^{2}, and was calculated for both the log_{10} transformed and un-transformed data,

Slope and intercept (S, I) from a Type-II linear regression (Reduced Major Axis) for log_{10} transformed and un-transformed data.

To provide an indication of the stability of the statistics and to compute confidence intervals on them, bootstrapping (Efron,

Geographic distribution of the data in the ^{−3}) over measurements made in the top 10 m (total ^{−3}) measured. A number of expected patterns can be observed. Firstly, the number of valid matchups is much reduced relative to the total number of data points in the

Geographic distribution of Particulate Organic Carbon (POC) measurements within the ^{−3}) over the top 10 m.

Locations of OC-CCI satellite data matchups and associated ^{−3}).

Histograms summarizing distribution of _{rs} based), _{bp} based),

The histogram of the

As could be expected from the histograms (Figure ^{−3}, the original formulations of the algorithms were not, in general, implemented with such high POC data.

Scatter plots and statistics detailing performance of _{rs}), _{bp}),

The scatter plots and uncertainty statistics for Algorithm A shown in Figure

Summary of statistics of the algorithm performances for _{10} and untransformed data.

_{10} TRANSFORMED DATA |
|||||

_{s} |
0.73 | 0.79 | 0.80 | 0.78 | |

Ψ | 0.33 ± 0.01 | 0.34± 0.01 | 0.32± 0.01 | 0.53 ± 0.01 | |

Δ | 0.32± 0.01 | 0.31± 0.01 | 0.29± 0.01 | 0.30± 0.01 | |

δ | -0.04± 0.01 | -0.13± 0.01 | -0.13± 0.01 | -0.43± 0.01 | |

S | 0.92± 0.01 | 0.63± 0.01 | 0.63± 0.01 | 0.66± 0.01 | |

I | 0.14± 0.02 | 0.76± 0.02 | 0.63± 0.02 | 0.27± 0.02 | |

_{p} |
0.84 | 0.80 | 0.84 | 0.83 | |

Ψ | 420± 12.7 | 443± 13.3 | 463± 13.9 | 444± 13.1 | |

Δ | 417± 12.4 | 442 ± 13.1 | 460± 13.8 | 417± 12.1 | |

δ | -51.9± 13.1 | -48.5± 14.5 | -98.8 ± 12.6 | -154± 13.1 | |

S | 0.15 | 0.27 | 0.13 | 0.05 | |

I | 126 | 112 | 58.8 | 83.3 | |

MAPD±IQR | 42.5± 58.0 | 31.4± 36.5 | 31.7± 34.6 | 60.9 ± |

_{10}: r_{s} is Spearman's correlation; slope and intercept for were calculated with a Type-II linear regression model (Major Axis) and the statistics provided have uncertainty estimates (95% confidence interval), derived from 1,000 bootstrap realizations. For untransformed data: r_{p} is Pearson's correlation; Ψ, δ and Δ are provided with uncertainty estimates (95% confidence interval), derived from 1000 bootstrap realizations; slope and intercept for were calculated with a Reduced Major Axis regression model; MAPD is the median absolute percent deviation between predictions and observations and is a measure of bias, and IQR is the interquartile range of the absolute percent error, and is a measure of precision. Bold italic numbers are the best results for each statistic, for some is the highest value (e.g., r_{s} or r_{p}), for some is the lowest (e.g., Ψ, δ, Δ, Intercept and MAPD) and for some is the closest to one (e.g., Slope)

To further understand algorithm performance, the matchups were separated by their optical water class. The total number of matchups per water class, and their distribution spatially, is shown in Figures

Locations and associated water class for each satellite-

Histogram showing number of matchups associated with each OC-CCI water class.

Calculated RMSD

Performing the statistical analysis across the different water classes reveals some similarities in performance across all algorithms, and some consistency with the overall performance (Figure

In addition to application to the matchups points, the POC algorithms can also be applied to global satellite data to compare algorithm performance at synoptic scales. POC concentrations were estimated by applying algorithms A-E to a sample set of OC-CCI monthly products from May 2005 (Figure ^{o} west, shows the regional differences in algorithm estimates for POC, and the associated OC-CCI [Chl] for reference (Figure ^{−3} are scarce in the satellite products (though higher values are more frequent with Algorithm C than with Algorithm A). Also, the pronounced bimodal frequency distribution of the

POC estimated using the five candidate algorithms applied to a monthly composite of OC-CCI data from May 2005 _{rs}), _{bp}), ^{o} W for each algorithm, and the associated [Chl] from the OC-CCI data.

Each algorithm has uncertainties associated with its performance for each water class, calculated from the validation exercise. These values can be used to estimate uncertainties for pixels outside of direct matchup locations, using a weighted average based on the percent membership to each of the classes. This procedure was applied to the data in Figure _{rs} based algorithm of Stramski et al.,

Root Mean Squared Difference calculated for POC as estimated using water-class specific performance of the the five candidate algorithms applied to monthly composite OC-CCI data from May 2005 _{rs}), _{bp}),

Bias as estimated using per water class performance of the five candidate algorithms applied to monthly composite OC-CCI data from May 2005 _{rs}), _{bp}),

The strength of the relationships between bio-optical properties and POC concentration has been quantified in the original studies where the algorithms examined above were formulated, and in some cases, validated against satellite data. To the extent that some of the satellite data used in the original studies are included in the match-up dataset used here, the impact on the results is likely to be small because the size of the match-up data used here is much larger than that used in any of the previous studies. Furthermore, the comparisons presented here are based on a common satellite product suite (OC-CCI). However, further insights are gained from the bigger

Results from the OC-CCI based validation are generally consistent with the observations made by Stramski et al. (^{−3}, whilst the range for the data used here cover a broader range (2.7–8,097 mg m^{−3}). The waters sampled by Stramski et al. (_{rs} and POC performed better than two-step approaches where an inherent optical property (IOP) is derived from the _{rs} and then related to the POC. They also indicated relatively better performance of the _{rs} relationship over that derived from _{bp}, highlighting the uncertainties in the derivation of _{bp} as one source of error in estimation of POC from IOPs. Additionally, the relationships between POC and IOPs would be expected to vary as a result of the particle size distribution (PSD), the refractive index of particles, and the fractional POC concentrations within different particle types in the assemblage. For example, significant variations in the POC-specific backscattering coefficient has been reported for different water bodies of the Southern Ocean (see Figure 1 in Stramski et al.,

The algorithm of Loisel et al. (_{p} and POC, via a relationship between _{bp} and [Chl]. Though Loisel et al. (_{bp} and that measured _{bp}:[Chl] relationship, linked to changes in the particulate pool; they highlighted the variable influence of small particles consisting of dead cells, grazers, and minerals. Gardner et al. (_{p}) and POC. This relationship was shown to be strong, when _{p} from satellite ocean color measurements, Gardner et al. (_{p} was strongly correlated with [Chl] (_{d}(490)) (

Algorithm E, by Kostadinov et al. (_{bp} to derive a PSD, which is then converted to POC (and phytoplankton carbon) using allometric relationships. The focus of the Kostadinov et al. (

General sources of error associated with any ocean-color product include differences introduced by choice of sensor, sensor calibration, and the atmospheric correction procedure used to retrieve _{rs}. In addition to these, a further consideration, particularly in the cases where algorithms use IOPs, is the methods used to derive the IOP product from the _{rs} data. The OC-CCI processing uses the Quasi-Analytical Algorithm (QAA) of Lee et al. (_{bp} values used in this study. The original study by Kostadinov et al. (_{bp}. Stramski et al. (_{bp} from _{rs}, finding a corrected version of QAA produced a better estimate of _{bp}, and a strong relationship with POC (_{bp} on the POC estimates requires further consideration, which goes beyond the scope of this study, as this IOP is particularly poorly understood and validated (Lee et al.,

Despite the difficulties highlighted above, the overall performance of the algorithms studied here is encouraging. Percentage error estimates based on the OC-CCI methodology show how well these algorithms can generate products suitable for the needs of the scientific community. For example, the percentage errors associated with the Stramski et al. (_{rs} algorithm applied to OC-CCI data in May 2005 (Figure

Percentage error for POC as estimated using per water class performance of the Stramski et al. (_{rs}) applied to monthly composite OC-CCI data from May 2005.

Further perspective on the performance of the different algorithms can be gained by considering the covariance between POC and [Chl]. The relationship between the

Covariance between POC and [Chl] extracted from the OC-CCI matchups with the _{rs}), _{bp}),

The ratio of POC to [Chl] is important in the context of the discussion here for two reasons. Firstly, this ratio is important in the context of biogeochemical modeling, and the ecological and physiological processes that influence this ratio. Secondly, empirical relationships between POC and chlorophyll have been developed, which can be applied to satellite derived estimates of [Chl]. As mentioned above, these algorithms are typically similar to those employing blue:green reflectance ratios (e.g., Algorithm A from Stramski et al., _{rs} reflectance ratio. The same reflectance ratio is employed by Stramski et al. (^{2} value of 0.70. Using the various relationships shown in Figure ^{2} values between 0.63 and 0.69, lower than those returned for all the other algorithms assessed. The [Chl] based approaches show in Figure

Summary of _{rs} (443) to _{rs}(555) to show relationship to this ratio commonly used in algorithms to derive [Chl].

Even though to first order Chl and POC are positively correlated in the global ocean, a residual scatter in the relationship remains (e.g., in satellite observations—Figure

The OC-CCI archive can be used to estimate total pools of POC in the mixed layer, taking into account interannual and regional variability, which is well captured by this merged dataset. Algorithms A-D were applied to the monthly OC-CCI version 2 data, and the values integrated over the mixed-layer depth (derived from MIMOC, Schmidtko et al., _{bp} based algorithm, combined again with a 1/3 assumption and the method of Behrenfeld et al. (

A variety of POC algorithms were applied to matchup pixels extracted from the satellite OC-CCI ocean color data, and validated against _{rs}—Stramski et al.,

HE: All the calculations, preparation of figures, lead on writing the manuscript. VM: Project manager for Pools of Carbon project; development of matchup processing and statistical analysis. RB: Provision of code for statistical analysis based on OC-CCI methodology. GD: Provision of _{bp} uncertainties and impact of particle sizing. AH: Perspectives on community requirements, particularly for ecosystem modeling. TJ: Provision of code for calculation of per optical water class uncertainties, based on the OC-CCI methodology. HK: Collation of the

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank Peter Regner for his support and management of the POCO project. We would like to thank Oliver Fisher for his contributions to the project during his student internship. The authors would like to thank the participants of the Color and Light in the ocean from Earth Observation (CLEO) workshop, for their valuable discussions on POC, which contributed substantially to refining the approaches presented in this work. The authors would also like to thank the two reviewers who provided detailed and constructive comments which substantially improved this manuscript.

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