# A tuned ocean color algorithm for the Arctic Ocean: a solution for waters with high CDM content

Juan Li, Atsushi Matsuoka, Stanford Hooker, Stéphane Maritorena, Xiaoping Pang, Marcel Babin

## ► To cite this version:

Juan Li, Atsushi Matsuoka, Stanford Hooker, Stéphane Maritorena, Xiaoping Pang, et al.. A tuned ocean color algorithm for the Arctic Ocean: a solution for waters with high CDM content. Optics Express, 2023, 31 (23), pp.38494. 10.1364/OE.500340. hal-04803367

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Submitted on 9 Jan 2025

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# A tuned ocean color algorithm for the Arctic Ocean: a solution for waters with high CDM content

JUAN LI,<fnref n="1" />,<fnref n="2" />,<fnref n="3" /> ID ATSUSHI MATSUOKA,<fnref n="4" /> STANFORD B. HOOKER,<fnref n="5" /> STÉPHANE MARITORENA,<fnref n="6" /> XIAOPING PANG,<fnref n="2" />,<fnref n="3" /> ID AND MARCEL BABIN<fnref n="2" />,\*

**Abstract:** The Arctic Ocean (AO) is the most river-influenced ocean. Located at the land-sea interface wherein phytoplankton blooms are common, Arctic coastal waterbodies are among the most affected regions by climate change. Given phytoplankton are critical for energy transfer supporting marine food webs, accurate estimation of chlorophyll a concentration (Chl), which is frequently used as a proxy of phytoplankton biomass, is critical for improving our knowledge of the Arctic marine ecosystem and its response to the ongoing climate change. Due to the unique and complex bio-optical properties of the AO, efforts are still needed to obtain more accurate Chl estimates, especially for coastal waters with high colored detrital material (CDM) content. In this study, we optimized the the Garver-Siegel-Maritorena (GSM) algorithm, using an Arctic bio-optical dataset comprised of seven wavelengths (the original GSM wavelengths plus 625 nm). Results suggested that our tuned algorithm, denoted GSMA, outperformed an alternative AO GSM algorithm denoted AO.GSM, but the accuracy of Chl estimates was only improved by 8%. In addition, GSMA showed appreciable robustness when assessed using a satellite image and two non-Arctic coastal datasets.

© 2023 Optica Publishing Group under the terms of the [Optica Open Access Publishing Agreement](#)

## 1. Introduction

The Arctic Ocean (AO) contains only 1% of the global volume of seawater but receives 11% of the world's river flow [1]. The AO drainage basin $19 \times 10^6$ km$^2$, which is larger than the AO surface area of $14.7 \times 10^6$ km$^2$ [2], thereby making it the most river-influenced ocean basin [1,3]. Because the AO is nearly enclosed by land, the corresponding coastal waterbodies are subjected to the combined influences of various physical and chemical processes associated with the land-sea interface, as follows (among others): a) large amounts of riverine nutrients [4,5]; b) coastal upwelling [6,7]; c) wind-driven mixing [8,9], and d) loss of sea ice [10,11]. These processes foster phytoplankton blooms, making these coastal waterbodies highly dynamic and productive. Given that coastal phytoplankton blooms are major ecological events that provide a substantial part of the annual primary production and energy transfer supporting the entire marine food web [12,13], the accurate estimation of phytoplankton biomass in coastal waters is

<footnote n="1">¹Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan 430079, China</footnote>

<footnote n="2">²Takuvik Joint International Laboratory, CNRS (France) & ULaval (Canada), Pavillon Alexandre-Vachon, Local 2064, 1045, avenue de la Médecine, Département de Biologie, Université Laval, Québec, QC G1V 0A6, Canada</footnote>

<footnote n="3">³Key Laboratory of Polar Surveying and Mapping, Ministry of Nature Resources of the People's Republic of China, Wuhan 430079, China</footnote>

<footnote n="4">⁴University of New Hampshire, Durham, Institute for the Study of Earth, Oceans, and Space, Durham, New Hampshire 03824, USA</footnote>

<footnote n="5">⁵NASA Goddard Space Flight Center, Ocean Ecology Laboratory, Greenbelt, Maryland 20771, USA</footnote>

<footnote n="6">⁶Earth Research Institute, University of California Santa Barbara, Santa Barbara, CA 93106, USA</footnote>

<footnote>\*marcel.babin@takuvik.ulaval.ca</footnote>
essential to improve our knowledge about marine ecosystem and its response to ongoing climate
change.

The International Ocean Colour Coordinating Group (IOCCG) Polar Seas Working Group has promoted the use of semi-analytical algorithms in the AO, because they have the ability to discriminate and quantify the contribution of non-phytoplankton constituents to the optical properties of seawater, especially coastal waters where there are large amounts of colored detrital material (CDM) resulting from river discharge [14]. Prior studies [15–17] have shown that models similar to the Garver-Siegel-Maritorena (GSM) algorithm [18] might be a good choice. [15] documented that a broadly used version of GSM, denoted GSM01, outperforms global Ocean Color (OC) chlorophyll *a* algorithms, as well as AO regional empirical algorithms for the southeast Beaufort Sea. The global OC algorithms are distinguished by the number of wavebands, the satellite involved, and the version number, e.g., OC4v6, OC3Mv6, and OC4Mev6 ( [19]; [20] or link to the appropriate GSFC Ocean Color page needed); the Arctic regional empirical algorithms are similarly named and include OC4L and OC4P ( [21] and [22], respectively).

[15] also optimized the parameters of the GSM algorithm for the southeast Beaufort Sea and obtained a regional model that showed large improvement over the original GSM01. Recently, [23] tuned the GSM model at a pan-Arctic scale using a large bio-optical database [16], and showed that their tuned algorithm, denoted AO.GSM, performs better than the other algorithms applied to the AO, e.g., OC3L [24], OC4L [25], and GSM01. However, the mean absolute error (MAE) of the chlorophyll *a* concentration (Chl) estimates derived using AO.GSM is still as high as 2.23, and this algorithms often tends not to return estimates because of inversion failures. Consequently, more efforts are needed to improve the accuracy of Chl estimates in the AO, especially for coastal waters with high CDM content (hereafter CDM-rich waters).

To circumvent the problems due to interference of CDM with phytoplankton signal, and thus to better detect phytoplankton using ocean color remote sensing (OCRS), in this study, we further tuned the GSM algorithm (denoted GSMA) for the AO by adding the 625 nm waveband using a high-quality bio-optical in *situ* dataset. This was motivated by two considerations: a) for CDM-rich waters, the signal observed at 625 nm is generally high and interferes less with CDM compared to blue-green wavelengths; and b) [26] and [27] showed that expanding the algorithmic spectral range to longer wavelengths improves robustness for above- and in-water remote sensing algorithms, respectively. Therefore, the tuned model with extra effective and important information at 625 nm should improve the ability of GSM variants to obtain more accurate results in CDM-rich waters.

**2. Data**

**2.1. Bio-optical in situ data sets**

Four in *situ* datasets were used in this study. The first one was collected in the AO and was used to tune the GSM algorithm (hereafter referred to as T-Arctic). The second dataset is also from the AO and was used in this study for validation purposes (hereafter referred to as V-Arctic). The other two datasets are non-Arctic coastal datasets from the Coastal Surveillance Through Observation of Ocean Color (COASTIOOC) project [28] and the CoastColour Round Robin (CCRR) activity [29], respectively. The latter two are used to expand the amount of validation data for this study.

The T-Arctic dataset is composed of five field campaigns, as follows: the France-Canada-USA joint Arctic campaign called MALINA [30]; the Impacts of Climate on Ecosystems and Chemistry of the Arctic Pacific Environment (ICESCAPE) in 2010 and 2011 [31]; the Tara Oceans Polar Circle expedition [32]; and the Green Edge project [33]. There are 148 data records containing contemporaneous observations of Chl and the spectral remote sensing reflectance, R<sub>rs</sub>(λ), where λ indicates wavelength. The number of coincident phytoplankton absorption spectra, a<sub>ph</sub>(λ),
absorption coefficient of CDM at 443 nm, ($a_{cdm}$(443)), and particulate backscattering coefficient at 443 nm, ($b_{bp}$(443)), are 101, 96, and 36, respectively.

The V-Arctic dataset includes in situ measurements from ArcticNet2011 [34], ArcticNet2013 [35], AREX2017 [36], plus a global dynamic range in bio-optical data collected for planning the Aerosol, Cloud, Ecosystems (ACE) satellite mission [26]. Unlike the Arctic bio-optical database (a collection of data acquired by multiple instruments) compiled by [16], the two Arctic datasets (i.e., T-Arctic and V-Arctic) used in this study only contain samples wherein $R_{rs}(\lambda)$ observations were obtained using a Compact-Optical Profiling System (C-OPS) and Chl was determined in the laboratory with a high performance liquid chromatography (HPLC) method (Sects. 2.1.1 and 2.1.2, respectively). This approach maximizes consistency and avoids discrepancies between different instruments. Details about the number of stations, sampling dates, sampling regions and data sources of the two Arctic datasets are summarized in Table 1 with station locations shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Map of the Arctic Ocean showing the locations of stations from various datasets.</figcaption></figure>

In regard to the two coastal datasets, the COASTIOOC dataset consists of measurements in various coastal waters around Europe during six campaigns in 1997 and 1998 [28], and the CCRR dataset was collected from a global range of coastal waters from 2002 to 2010. For the three validation datasets, only record with concurrent measurements of Chl and full $R_{rs}(\lambda)$ spectral (i.e., at 412, 443, 490, 510, 550, 625, 670 nm) were kept in this study. The total numbers of samples are 77, 168, and 309 for V-Arctic, COASTIOOC, and CCRR, respectively.

### 2.1.1. $R_{rs}(\lambda)$ measurements

Derivations of $R_{rs}(\lambda)$ for the two Arctic datasets were obtained using the same C-OPS instrument manufactured by Biospherical Instrument Inc. [37] having 19 wavebands spanning approximately from 300-900 nm, following the procedures described in [38] and [39]. Briefly, in-water upwelling radiance, $L_u(z, \lambda)$, in-water downward irradiance, $E_d(z, \lambda)$, and above-water solar
<table><caption>Table 1. Summary of in situ datasets</caption><thead><tr><th>Data</th><th>Station</th><th>Year</th><th>Month</th><th>Region</th><th>Source</th></tr></thead><tbody><tr><td>MALINA</td><td>37</td><td>2009</td><td>July-August</td><td>Southern Beaufort Sea</td><td>SeaBASS</td></tr><tr><td>ICESCAPE2010</td><td>34</td><td>2010</td><td>June-July</td><td>Chukchi and Beaufort Sea</td><td>SeaBASS</td></tr><tr><td>ICESCAPE2011</td><td>18</td><td>2011</td><td>June-July</td><td>Chukchi and Beaufort Sea</td><td>SeaBASS</td></tr><tr><td>ARCTICNET2011</td><td>9</td><td>2011</td><td>August</td><td>Baffin Bay</td><td>Individual</td></tr><tr><td>ARCTICNET2013</td><td>9</td><td>2013</td><td>August</td><td>Baffin Bay</td><td>Individual</td></tr><tr><td>TARA</td><td>27</td><td>2013</td><td>May-November</td><td>Polar circle</td><td>SeaBASS</td></tr><tr><td>GreenEdge</td><td>34</td><td>2016</td><td>June-July</td><td>Baffin Bay</td><td>Individual</td></tr><tr><td>AREX</td><td>11</td><td>2017</td><td>July</td><td>Greenland Sea</td><td>Individual</td></tr><tr><td>ACE Mission</td><td>48</td><td>2010, 2013-2017</td><td>March-December</td><td>Arctic Ocean</td><td>Individual</td></tr><tr><td>COASTIOOC</td><td>168</td><td>1997-1998</td><td>January-December</td><td>Europe coastal areas</td><td>Individual</td></tr><tr><td>CCRR</td><td>309</td><td>2002-2010</td><td>February-October</td><td>Global coastal areas</td><td>PANGAEA</td></tr></tbody></table>

irradiance, $E_s(\lambda)$, were measured simultaneously with in-water pressure (to derive depth, z) plus the two-axis vertical tilt. After solar correction with $E_s(\lambda)$ and 5° tilt filtering (plus a variety of other corrections), subsurface $L_u(\lambda)$ and $E_d(\lambda)$ at null depth ($z = 0^\circ$) were determined using the slope and intercept obtained by the least-squares linear regression of the log-transformed $L_u(z, \lambda)$ and $E_d(z, \lambda)$ versus z. Finally, $R_{rs}(\lambda)$ was calculated as: $R_{rs}(\lambda) = 0.54L_u(\lambda)/E_d(\lambda)$. Details of the data acquisition and processing protocols with applicable corrections are described in [40] and [41].

For the COASTIOOC dataset, in-water upwelling irradiance $E_u(z, \lambda)$ and downwelling irradiance just above the sea surface $E_d(\lambda)$ were measured with a Atlantic free-fall SPMR (SeaWiFS Profiling Multichannel Radiometer) and SMSR (SeaWiFS Multichannel Surface Reference) at 13 wavelengths (412, 443, 456, 490, 510, 532, 560, 620, 665, 683, 705, 779 and 866 nm). $E_u(\lambda)$ was obtained by extrapolating $E_u(z, \lambda)$ to subsurface by fitting an exponential function (see [28]). Then $L_u(\lambda)$ was calculated as $L_u(\lambda) = E_u(\lambda)/3.8$ [42]. Afterwards, $R_{rs}(\lambda)$ was obtained by the same process described above. For the CCRR dataset, water-leaving reflectance ($L_w$, unitless) at 9 wavelengths (412, 443, 490, 510, 560, 620, 665, 681, 709 nm) were measured through 3 Atlantic sensors mounted on a free falling HyperPRO optical profiler platform [43]. Then $R_{rs}(\lambda)$ was obtained by $L_w(\lambda)/\pi$. Note that, in the present study, only common wavebands (412, 443, 490, 510, 555, 625, 670 nm) of the Arctic datasets were used. For the coastal data sets, because 555, 625, and 670 nm were missing, 560, 620, and 665 nm were adopted instead.

### 2.1.2. Chl measurements

All Chl measurements were made by HPLC. Generally, 25-mm GF/F filters were used to collect phytoplankton from seawater samples. Filters were soaked in 100% methanol for pigment extraction, disrupted by sonication and clarified by filtration (GF/F Whatman) before being analyzed by HPLC later in the laboratory to obtain separated pigments [44,45]. Finally, total chlorophyll a pigment concentration was defined as the sum of mono and divinyl chlorophyll a concentrations, chlorophyllide a plus the allomeric and epimeric forms of chlorophyll a [46,47].

### 2.1.3. Absorption measurements

Only the absorption measurements of the T-Arctic dataset were used in this study. Absorption spectra of particulate, $a_p(\lambda)$, and non-algal particles, $a_{nap}(\lambda)$, were determined using a Perkin-Elmer Lambda-19 spectrophotometer equipped with a 15 cm integrating sphere following the methodology described in [48]. Phytoplankton absorption spectra, $a_{ph}(\lambda)$, were calculated by subtracting $a_{nap}(\lambda)$ from $a_p(\lambda)$. The chlorophyll-specific absorption spectra for phytoplankton,
$a_{ph}^*(\lambda)$, are defined as $a_{ph}(\lambda)$ normalized by Chl. The absorption spectra of colored dissolved organic matter (CDOM), $a_{cdom}(\lambda)$, was measured using a liquid core waveguide system, UltraPath, following [49]. The sum of $a_{cdom}(\lambda)$ and $a_{nap}(\lambda)$ yields $a_{cdm}(\lambda)$. The spectral slope of $a_{cdm}(\lambda)$, S, was calculated by fitting individual spectrum (350~500 nm) to

$$a_{cdm}(\lambda) = a_{cdm}(\lambda_0)e^{-S(\lambda-\lambda_0)}, \qquad (1)$$

where the scaling wavelength $\lambda_0$ is 443 nm in this study.

## 2.2. Satellite image

For application purposes, a Sentinel-3B OLCI (Ocean and Land Colour Instrument) image (file name: S3B OL 2 WFR 20200910T031808_20200910T032108_20200911T11 4327_0179_043_175_1620_MAR_O_NT_002.SEN3) at full spatial resolution (approximately 300 m) around the Lena River delta taken on 10 September 2020 was downloaded from https://catalogue.onda-dias.eu.

# 3. Methods

## 3.1. GSM model

$R_{rs}(\lambda)$ was converted to a below-surface value, $r_{rs}(\lambda)$, following [50]:

$$r_{rs}(\lambda) = \frac{R_{rs}(\lambda)}{0.52 + 1.7R_{rs}(\lambda)}. \qquad (2)$$

For the satellite image, the $R_{rs}(\lambda)$ values were derived from the radiometric products by dividing by $\pi$, then converted to $r_{rs}(\lambda)$ using (2), and finally applied in the model to retrieve Chl and $a_{cdm}(443)$ using self-written Python codes.

$r_{rs}(\lambda)$ is approximated using inherent optical properties (IOPs) following [50]:

$$r_{rs}(\lambda) = g_0 \frac{b_b(\lambda)}{a(\lambda) + b_b(\lambda)} + g_1 \left( \frac{b_b(\lambda)}{a(\lambda) + b_b(\lambda)} \right)^2, \qquad (3)$$

where $g_0 \approx 0.0949$ and $g_1 \approx 0.0794$ for oceanic case 1 waters. Backscattering ($b_b(\lambda)$) and absorption ($a(\lambda)$) spectral coefficients can be expanded as:

$$b_b(\lambda) = b_{bw}(\lambda) + b_{bp}(\lambda) \text{ and} \qquad (4)$$

$$a(\lambda) = a_w(\lambda) + a_{ph}(\lambda) + a_{cdm}(\lambda). \qquad (5)$$

Absorption and backscattering spectra of seawater ($a_w(\lambda)$ and $b_{bw}(\lambda)$, respectively) are assumed to be known constants [51,52]. The non-aquatic IOP spectra are then parameterized in terms of a known shape but an unknown magnitude, as follows:

$$b_{bp}(\lambda) = b_{bp}(\lambda_0) \left( \frac{\lambda}{\lambda_0} \right)^{-\eta} \text{ and} \qquad (6)$$

$$a_{ph}(\lambda) = \text{Chl} a_{ph}^*(\lambda), \qquad (7)$$

where $a_{ph}^*(\lambda)$ is the phytoplankton chlorophyll a-specific absorption coefficient; $\eta$ is the power-law exponent for the particulate backscattering spectra; $a_{cdm}(\lambda)$ has been expressed by Eq. (1). $a_{ph}^*(\lambda)$, $\eta$, and S from Eqs. (6), (7), and (1) respectively, collectively denote as $\Psi$ hereafter, were first determined by optimization (see below) and then used as model parameters in the GSM formulation. Afterwards, an inversion method (e.g., Ameoba, Quasi-Newton, Gauss-Newton, etc. [53]) was applied to retrieve the three unknowns, denoted $\Theta = \{\text{Chl}, a_{cdm}(443), b_{bp}(443)\}$, by minimizing the mean squared difference between $r_{rs}(\lambda)$ modeled and as derived from in situ data.
## 3.2. Simulated annealing Θ optimization

To optimize the GSM parameters, a simplistic approach is to list all potential interacting sets of Ψ within the assumed limits for each input parameter to be optimized, and identify the one that yields the smallest mean difference between retrieved and measured. For $a_{ph}^*(\lambda)$, S, and η, the associated limits are [0.001, 0.3 m² mg⁻¹], [0.01, 0.035 nm⁻¹], and [0, 4.3], respectively. But because the number of possible sets of Ψ is large and the GSM algorithm is highly nonlinear, this method would be extremely time-consuming and labor intensive. To circumvent this problem, an iterative heuristic method called simulated annealing was used [54]. This alternative has proved useful when seeking a global optimum for a complex nonlinear objective function containing large numbers of optima [18,55].

Simulated annealing is a downhill method, but it allows searching for solutions in the uphill direction to reduce the probability of falling into a local minimum, thereby facilitating the determination of a global minimum. This feature also reduces the importance of the first guess used to initiate the process, which is often a critical aspect of minimization techniques based on steepest descent methods. Simulated annealing includes three basic elements: a) a cost function (CF) to evaluate the performance for a given set of Ψ; b) a candidate generator that stochastically selects new values for Ψ; and c) a decreasing temperature parameter that introduces the randomness in the process and controls the overall progress.

In this study, a modified version of the CF described in [56] was adopted, as follows:

$$CF = 0.2N_{INV} + \sum_{k=1}^{N_{\Theta}} (a_k|1 - r_k^2| + b_k|1 - Slope_k| + c_k RMSE_k), \quad (8)$$

where $N_{INV}$ is the number of invalid retrievals; $N_θ$ is the number of retrievals for the subject parameter; $r_k^2$ and $Slope_k$ are the determination coefficient and slope generated through a type II regression between the kth observed and estimated variables in log scale, respectively; $RMSE_k$ is the root mean square error of the kth variable; and $a_k, b_k$, and $c_k$ are subjective weights associated with $R_k^2, Slope_k$, and $RMSE_k$, respectively. For the first retrieval Chl, $a_1, b_1$, and $c_1$ were assigned 1, 1.5, and 1, respectively. For the second retrieval $a_{cdm}(443)$, since concurrent $a_{cdm}(443)$ measurements account for 65% (96 to 148) of the total samples, $a_2, b_2$, and $c_2$ were set as 0.65, 0.98, and 0.65, respectively, to ascribe less weight than for Chl. Because only 24.3% of the total samples has coincident $b_{bp}(443)$ measurements, the performance of $b_{bp}(443)$ estimates were not assessed in this study, therefore, $N_θ = 2$ in this study.

The GenSA package (written in the R programming language) was adopted to provide the candidate generator and temperature control process. GenSA has proved to be more robust and efficient in searching for a global optimal solution than other packages, e.g., the differential evolution algorithm “DEoptim” [57] and genetic algorithm “rgenoud” [58]), as shown in [54]. The GenSA candidate generator is highly dependent on the temperature in the optimization process, wherein the next candidate is generated according to a Cauchy-Lorentz distribution with a scale proportional to the actual temperature [54]. The latter needs to be initialized and will decrease according to the logarithmic cooling schedule described in [59]. The starting temperature is of significant importance because it directly influences the likelihood of accepting worse responses and, thus, the stochastic part of the optimization. When temperature is high, a solution that is worse than the current solution is kept more often. This property allows for a more extensive search for the global optimum, making it the fundamental part of simulated annealing optimization.

Apart from the aforementioned three basic elements, GenSA also provides other controlling parameters, such as the upper and lower bounds of Ψ to be optimized, the maximum number of iterations, and the maximum running time (to name a few). In this study, the upper and lower bounds of Ψ were set according to their constraints mentioned above. The other controlling
parameters were set to the default values assigned within GenSA, because they have proved to work well for general optimization cases [54]. A flowchart of the tuning process is illustrated in Fig. 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2. The strategy used to find the best set of input parameters for the GSM algorithm illustrated as a flow chart (variable definitions in accompanying text).</figcaption></figure>

### 3.3. Performance metrics

Algorithm performance is assessed following the metrics described in [60]. The parameters of interest are the mean bias (MBIAS), the mean absolute difference (MAD), percent wins (Wins) through pair-wise comparison, slope and coefficient of determination ($r^2$) for log-transformed variable via type II reduced major axis (RMA) regression [61]. The formulations for the first two are as follows:

$$ MBIAS = 10^{\text{mean}(\log10(X^M) - \log10(X^E))} \quad \text{and} \quad (9) $$

$$ MAD = 10^{\text{mean}|\log10(X^M) - \log10(X^E)|}, \quad (10) $$

where X denotes Chl or $a_{cdm}(443)$ and the M and E superscripts indicate a measured and estimated value, respectively.

### 3.4. Classification

The variability in Chl and $a_{cdm}(443)$ of the T-Arctic data set is illustrated in Fig. 3, wherein the median values were 0.35 mg m⁻³ and 0.067 m⁻¹ for Chl and $a_{cdm}(443)$, respectively. Using the latter, the dataset was arbitrarily classified into four types. Briefly, first the dataset was split by half according to the median value of Chl. For the part with $Chl \le 0.35 mg m^{-3}$, samples with $a_{cdm}(443) \le 0.067 m^{-1}$ were labelled as chl.acdm, and the others with $a_{cdm}(443) > 0.067 m^{-1}$ were labelled as chl.ACDM. The same approach was applied to the other part of the dataset with $Chl > 0.35 mg m^{-3}$, which resulted in CHL.acdm and CHL.ACDM labelling. The thresholds for the classification approach are summarized in Table 2.
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** The frequency distribution of *in situ* (a) Chl and (b) $a_{cdm}$(443). The Gaussian curve is shown the normal distribution that corresponds to the median values and standard deviations.</figcaption></figure>

<table><caption>**Table 2.** Classification criteria</caption><thead><tr><td>Water type</td><td>Threshold</td><td>Number</td></tr></thead><tbody><tr><td>chl.acdm</td><td>Chl ≤ 0.35 mg m<sup>-3</sup>, a<sub>cdm</sub>(443) ≤ 0.067 m<sup>-1</sup></td><td>48</td></tr><tr><td>CHL.acdm</td><td>Chl > 0.35 mg m<sup>-3</sup>, a<sub>cdm</sub>(443) ≤ 0.067 m<sup>-1</sup></td><td>26</td></tr><tr><td>chl.ACDM</td><td>Chl ≤ 0.35 mg m<sup>-3</sup>, a<sub>cdm</sub>(443) > 0.067 m<sup>-1</sup></td><td>26</td></tr><tr><td>CHL.ACDM</td><td>Chl > 0.35 mg m<sup>-3</sup>, a<sub>cdm</sub>(443) > 0.067 m<sup>-1</sup></td><td>48</td></tr></tbody></table>

# 4. Results

## 4.1. Optimized algorithm GSMA

The innovation of the tuned GSMA algorithm compared to GSM01 and AO.GSM is the use of simulated annealing for optimization and the addition of the 625 nm waveband. For optimization, 148 coincident in *situ* measurements of $R_{rs}$ (at 412, 443, 490, 510, 555, 625, and 670 nm) plus Chl, accompanied by 96 concurrent $a_{cdm}$(443) were used in the simulated annealing optimization strategy to find the optimal $\Psi = \{a_{ph}^*(\lambda), S, \eta\}$ (Sect. 3.2). Table 3 lists the $\Psi$ for GSM01, AO.GSM, and GSMA along with the measured (in *situ*) median (MM) values of $a_{ph}^*(\lambda)$ and $S$; $\eta$ is missing due to the lack of concurrent measurements.

Table 3 shows $a_{ph}^*(\lambda)$ for GSMA are generally closer to GSM01 than MM. The primary difference between MM and both GSMA and GSM01 for $a_{ph}^*(\lambda)$ is at 412 nm, wherein the MM $a_{ph}$(412) value is much higher. Secondly, the AO.GSM $a_{ph}^*(\lambda)$ values are quite different from those of GSMA, GSM01, and MM, especially at 412 and 443 nm, wherein the AO.GSM $a_{ph}^*$ values are as high as 0.285 m$^2$ mg$^{-1}$, which is rarely observed. Although the optimized $\Psi$ for GSMA is not ideal spectrally, it still provides improved estimates, which is the main objective for this study (Sect. 1).

## 4.2. Performance of Chl estimates

Given the AO.GSM algorithm has been proven to have better performance in the AO than the original GSM01 [23], Chl retrievals generated from AO.GSM using the T-Arctic dataset were compared with those derived from the GSMA algorithm (Fig. 4 and Table 4). Hereafter, retrievals
<table><caption>Table 3. The parameters for the GSM01, AO.GSM, and GSMA algorithms</caption><thead><tr><th>Parameters</th><th>GSM01</th><th>AO.GSM</th><th>GSMA</th><th>MM<sup>a</sup></th></tr></thead><tbody><tr><td>a<sup>*</sup><sub>ph</sub> (412)</td><td>0.00665</td><td>0.28503</td><td>0.00646</td><td>0.05120</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (443)</td><td>0.05582</td><td>0.21099</td><td>0.06243</td><td>0.05923</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (490)</td><td>0.02055</td><td>0.089298</td><td>0.02471</td><td>0.04157</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (510)</td><td>0.01910</td><td>0.066926</td><td>0.03181</td><td>0.02626</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (555)</td><td>0.01015</td><td>0.029377</td><td>0.01407</td><td>0.00884</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (625)</td><td>-</td><td>-</td><td>0.00677</td><td>0.00770</td></tr><tr><td>a<sup>*</sup><sub>ph</sub> (670)</td><td>0.01424</td><td>0.15073</td><td>0.01670</td><td>0.02431</td></tr><tr><td>S</td><td>0.0206</td><td>0.018996</td><td>0.0196</td><td>0.0142</td></tr><tr><td>η</td><td>1.0337</td><td>1.3309</td><td>1.0316</td><td>-</td></tr></tbody></table>

derived from algorithm was denoted algorithm-derived (e.g., GSMA-derived) estimates. Figure 4 shows that, for chl.acdm, the GSMA retrievals are generally closer to the 1:1 line than the estimates from AO.GSM, indicating better performance, while the opposite was found for CHL.acdm. For CDM-rich waters (in this study, referred to waters wherein $a_{cdm}(443) > 0.067 m^{-1}$, i.e., water types chl.ACDM and CHL.ACDM), GSMA produced 17 (11.5% of the total samples) more retrievals belonging to either chl.ACDM or CHL.ACDM compared with AO.GSM (see the “star” symbols showed in Fig. 4(b) and 4(d)).

As for the performance metrics showed in Table 4, overall, both GSMA and AO.GSM had positive values of MBIAS (1.09 and 1.24, respectively), indicating these algorithms over-predict the in situ variables. Compared with AO.GSM, GSMA-derived Chl retrievals were less biased by 15%, and the regression slope was much closer to 1. Owing to the omission of 24 failures (16.2% of the total samples) in the statistical analysis, AO.GSM obtained a smaller MAD and a larger value of $r^2$. According to the decision metric, Wins, which directly account for the failures, GSMA outperformed AO.GSM with 59.5% Wins.

Looking closer to each water type, except CHL.acdm, GSMA performed better than AO.GSM as the Wins (89.6%, 69.2%, and 52.1% for chl.acdm, chl.ACDM, and CHL.ACDM, respectively) suggested. For waters with low CDM content, both AO.GSM and GSMA succeeded to generate effective retrievals for all samples. AO.GSM performed better for CHL.acdm samples and GSMA obtained better results for chl.acdm ones, but their MAD differed only slightly between 1.41 and 1.78. For CDM-rich waters, the two GSM algorithms obtained larger MADs (from 1.81 to 2.31), and they both produced failures but to different extent. AO.GSM obtained 8 and 9 more failures than GSMA for chl.ACDM and CHL.ACDM samples, respectively, indicating that GSMA is more robust for CDM-rich waters.

### 4.3. Performance of $a_{cdm}(443)$ estimates

Comparisons between measured and estimated $a_{cdm}(443)$ derived from AO.GSM and GSMA are shown in Table 4 and Fig. 5. AO.GSM-derived $a_{cdm}(443)$ estimates exhibited a trend of underestimation for all water types. GSMA-derived retrievals generally distributed along the 1:1 regression line, indicating better performance than AO.GSM. Besides, AO.GSM obtained 32 (accounts for 33.7% of $a_{cdm}(443)$ measurements) optimization failures, while GSMA succeeded for all samples, and improved the accuracy by 168% when compared with AO.GSM. Consequently, the Wins of GSMA reached up to 91.6%.

<footnote>aMM refers to measured median values.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** T-Arctic dataset comparisons between Chl estimates derived using AO.GSM and GSMA for the following four classifications: (a) chl.acdm, (b) chl.ACDM, (c) CHL.acdm and (d) CHL.ACDM. The plus symbols indicate the same data pairs derived using AO.GSM and GSMA, while the star symbols denote a data pair wherein derivation failed using AO.GSM but succeeded using GSMA.</figcaption></figure>

4.4. *Validations*

In this study, algorithm tuning and validation were based on different and independent datasets. The V-Arctic dataset was used to assess the performance of the GSMA algorithm for Chl retrievals (see Fig. 6 and Table 4). For comparison purpose, Chl estimates derived from AO.GSM are shown as well. As seen from Fig. 6, GSMA-derived Chl estimates generally distributed closer to the 1:1 line than those derived from AO.GSM. Any one of the metrics (listed in Table 4) suggests that GSMA performed better than AO.GSM, indicating that our tuned algorithm, GSMA, indeed improved the performance of Chl estimates in the AO. However, the overall improvement of the accuracy is merely 8%.
<table><caption>Table 4. Performance metrics for Chl and $a_{cdm}$ (443) derived using the AO.GSM and GSMA algorithms and the T-Arctic, V-Arctic, COASTIOOC, and CCRR datasets</caption><thead><tr><th>Data</th><th>Algorithm</th><th>N</th><th>MBIAS</th><th>MAD</th><th>Wins (%)</th><th>Failure</th><th>r<sup>2</sup></th><th>slope</th></tr></thead><tbody><tr><td rowspan="10">T-Arctic</td><td>chl.acdm, n = 48</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AO.GSM</td><td>48</td><td>1.74</td><td>1.78</td><td>10.4</td><td></td><td>0.75</td><td>0.92</td></tr><tr><td>GSMA</td><td>48</td><td>1.48</td><td>1.56</td><td>89.6</td><td></td><td>0.74</td><td>0.88</td></tr><tr><td>CHL.acdm, n = 26</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AO.GSM</td><td>26</td><td>0.74</td><td>1.41</td><td>92.3</td><td></td><td>0.50</td><td>1.11</td></tr><tr><td>GSMA</td><td>26</td><td>0.59</td><td>1.71</td><td>7.7</td><td></td><td>0.47</td><td>1.26</td></tr><tr><td>chl.ACDM, n = 26</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AO.GSM</td><td>15</td><td>2.02</td><td>2.02</td><td>19.2</td><td>11 (7.4%)</td><td>0.65</td><td>1.25</td></tr><tr><td>GSMA</td><td>23</td><td>1.98</td><td>2.31</td><td>69.2</td><td>3 (2.0%)</td><td>0.08</td><td>1.26</td></tr><tr><td>CHL.ACDM, n = 48</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">n = 148</td><td>AO.GSM</td><td>35</td><td>0.92</td><td>1.81</td><td>39.6</td><td>13 (8.8%)</td><td>0.47</td><td>0.79</td></tr><tr><td>GSMA</td><td>44</td><td>0.82</td><td>2.25</td><td>52.1</td><td>4 (2.7%)</td><td>0.27</td><td>1.26</td></tr><tr><td>Across all, n = 148</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AO.GSM</td><td>124</td><td>1.24</td><td>1.73</td><td>35.8</td><td>24 (16.2%)</td><td>0.79</td><td>0.77</td></tr><tr><td></td><td>GSMA</td><td>141</td><td>1.09</td><td>1.90</td><td>59.5</td><td>7 (4.7%)</td><td>0.55</td><td>0.94</td></tr><tr><td rowspan="3">V-Arctic</td><td>a<sub>cdm</sub> (443), n = 95</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>AO.GSM</td><td>63</td><td>0.36</td><td>2.99</td><td>8.4</td><td>32 (33.7%)</td><td>0.74</td><td>1.46</td></tr><tr><td>GSMA</td><td>95</td><td>0.89</td><td>1.31</td><td>91.6</td><td></td><td>0.92</td><td>1.15</td></tr><tr><td rowspan="2">n = 77</td><td>AO.GSM</td><td>74</td><td>1.38</td><td>1.92</td><td>35.1</td><td>3 (3.9%)</td><td>0.70</td><td>0.78</td></tr><tr><td>GSMA</td><td>76</td><td>1.28</td><td>1.84</td><td>63.6</td><td>1 (1.3%)</td><td>0.71</td><td>0.84</td></tr><tr><td rowspan="2">COASTIOOC</td><td>AO.GSM</td><td>65</td><td>0.46</td><td>3.19</td><td>17.3</td><td>103 (61.3%)</td><td>0.00</td><td>0.05</td></tr><tr><td>GSMA</td><td>161</td><td>0.65</td><td>2.26</td><td>81.5</td><td>7 (4.2%)</td><td>0.36</td><td>0.77</td></tr><tr><td rowspan="2">CCRR</td><td>AO.GSM</td><td>154</td><td>0.67</td><td>2.00</td><td>27.5</td><td>155 (50.2%)</td><td>0.50</td><td>0.88</td></tr><tr><td>GSMA</td><td>262</td><td>0.63</td><td>2.28</td><td>57.3</td><td>47 (15.2%)</td><td>0.28</td><td>0.77</td></tr></tbody></table>

## 4.5. Satellite application

A general insight of the applicability of AO.GSM and GSMA for Arctic coastal waters was obtained by applying both algorithms to the OLCI image taken by Sentinel 3B around the Lena River Delta on 10 September 2020 (see Fig. 7). It appears that most Chl estimates derived from the two GSM models away from the coast agreed well with each other. In the coastal area, however, GSMA generated more and higher Chl estimates than AO.GSM. As for $a_{cdm}$ (443) estimates, GSMA generated much more retrievals (i.e., fewer optimization failures) than AO.GSM, especially for waters away from the coast.

Figure 8 shows the kernel density plot of AO.GSM- and GSMA-derived Chl estimates for further comparisons. Failures of AO.GSM and GSMA account for 11.2% and 1.3%, respectively, of the total effective pixels (7,207,409). GSMA-derived Chl values could reach up to ~40.0 mg m⁻³, and the median value is 2.09 mg m⁻³. The maximum and median of AO.GSM-derived Chl were much lower (~10.0 and 1.39 mg m⁻³, respectively). As for $a_{cdm}$ (443) estimates, GSMA produced 7,204,683 retrievals (optimization failures of less than 0.1%), while the number of effective retrievals generated using AO.GSM was merely 834,325 (optimization failures of 88.4%).
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** T-Arctic dataset comparisons between *a*<sub>cdm</sub>(443) estimates using AO.GSM and GSMA for the following four classifications: (a) chl.acdm, (b) chl.ACDM, (c) CHL.acdm and (d) CHL.ACDM. The plus symbols indicate the same data pairs derived using AO.GSM and GSMA, while the star symbols denote a data pair wherein derivation failed using using AO.GSM but succeeded using GSMA.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** V-Arctic dataset comparisons between Chl estimates derived using AO.GSM and GSMA. The plus symbols indicate the same data pairs derived using AO.GSM and GSMA, while the star symbols denote a data pair wherein derivation failed using AO.GSM but succeeded using GSMA.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** V-Arctic dataset comparisons between Chl estimates derived using AO.GSM and GSMA. The plus symbols indicate the same data pairs derived using AO.GSM and GSMA, while the star symbols denote a data pair wherein derivation failed using AO.GSM but succeeded using GSMA.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** AO.GSM-derived (a) Chl, (b) $a_{cdm}(443)$, and GSMA-derived (c) Chl, (d) $a_{cdm}(443)$ using the OLCI reflectance image taken by Sentinel 3B around the Lena River plume on 10 September 2020.</figcaption></figure>
# 5. Discussions

## 5.1. Model limitations

The basic principle of the GSM model is to minimize the difference between observed and modeled $R_{rs}(\lambda)$ using non-linear inversion until a predefined convergence threshold is met. In essence, it is a spectral-fitting approach. For coastal waters, CDM content can be very high thus interfere significantly with the phytoplankton reflectance signal. The addition of the 625 nm channel where CDM and phytoplankton absorption is relative small, and scattering by particles is relatively significant (particle scattering to absorption ratio at maximum, see Fig. 3(c) in [62]), provides additional and less ambiguous information for the GSM inversion model to disentangle the three major non-water optical coefficients (i.e., $a_{ph}$, $a_{cdm}$, and $b_{bp}$), which will in return lead to better estimates of all three unknowns. We think this is the main reason why GSMA showed better performance for waters with high CDM content, compared with AO.GSM. The inclusion of a longer waveband thus helps improving the robustness of above- and in-water remote sensing algorithms [27,63]. This is why GSMA has less inversion failures than the other two GSM algorithms without 625 nm as the validations using both in *situ* datasets and satellite images suggested, especially for coastal waterbodies.

While for oceanic waters whose optical properties are determined primarily by phytoplankton and related CDM, to obtain accurate Chl estimates, it is important to understand phytoplankton physiology and phenology. The disentanglement of $a_{ph}$, $a_{cdm}$, and $b_{bp}$ is less of a problem. This might be the reason why GSMA did not outperform AO.GSM for such type of waters.

However, we must recognize that the improvement brought by GSMA was limited to some extent. The overall improvement of the accuracy of GSMA-derived Chl estimates was merely 8% compared to AO.GSM when validated using the V-Arctic dataset. This is because the GSM model itself has some limitations as it adopts several simplified assumptions to limit the number of unknowns. For instance, $g_0$ and $g_1$ were used to described oceanic case 1 waters [64]. [65] has found that $g_0 = 0.084$ and $g_1 = 0.17$ work better for higher-scattering coastal waters. In particular, $\Psi$ is held constant to describe the spectral shapes of IOP (Inherent Optical Properties), which actually varies in nature. $a_{ph}^*(\lambda)$ is assumed proportional to Chl, while true phytoplankton absorption spectra vary dramatically due to photoadaptation and/or composition of phytoplankton assemblage [66]. S actually depends on a complex system involving land/sea interactions, the

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Kernel density plot of Chl estimates through AO.GSM and GSMA using the OLCI reflectance product taken by Sentinel 3B around the Lena River plume on 10 September 2020.</figcaption></figure>
productivity and state of the phytoplankton communities, the microbial loop and photochemistry [18]. Similarly, $b_{bp}$ is modeled using a simple function with a fixed spectral dependence ($\eta$), while $\eta$ varies in the world ocean and such wavelength dependence tends to disappear in turbid waters [50,67,68].

Moreover, GSM is a blue-light-dependent algorithm. That is, for extremely eutrophic waters where Chl is high, the blue reflectance might drop below the limits of detection due to the high absorption of phytoplankton. Then GSM becomes less efficient and even useless. Therefore, semi-analytical algorithms that are less dependent or even independent on the signal observed at blue range, such as fluorescence-based algorithms, are needed. Nevertheless, GSM has been extensively and widely used by oceanographers as it can outperform standard empirical algorithms (e.g., in the AO, [15]; [23]) and generate multiple retrievals, not only Chl estimates.

## 5.2. Assessment for non-Arctic coastal waters

Our major objective is to tune the GSM model for CDM-rich AO waters, especially for the coastal regions. However, due to the scarcity of in situ measurements in the Arctic coastal areas, two non-Arctic coastal datasets (CCRR and COASTIOOC) were included to assess the applicability of the GSMA model for coastal waters at large. Results are shown in Fig. 9 and Table 4. As seen from Fig. 9, GSMA showed obvious underestimation in the Chl > 10.0 mg m⁻³ range for both datasets, and produced 96 (accounts for 57.1%) and 108 (accounts for 35%) more effective Chl retrievals than AO.GSM using COASTIOOC and CCRR datasets, respectively. In addition, the MADs of GSMA obtained from the two coastal datasets are larger than those assessed with the two Arctic datasets, indicating that the uncertainties in Chl retrievals is larger for coastal waters.

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Comparison between AO.GSM- and GSMA-derived Chl estimates using the (a) CCRR and (b) COASTIOOC datasets. The plus symbols indicate the same data pairs derived using AO.GSM and GSMA, while red star symbols denote a data pair wherein derivation failed using AO.GSMA but succeeded using GSMA, the orange star symbols refer to the opposite.</figcaption></figure>

As for AO.GSM, it significantly underestimated Chl in the Chl > 2.0 mg m⁻³ range for the COASTIOOC dataset, but did not show a similar trend for the CCRR dataset. Besides, it is not surprising that AO.GSM obtain more than half of the failures. The poor performance of the two GSM algorithms results from the fact that they were not tuned only for coastal waters wherein Chl is generally larger than 0.2 mg m⁻³ (many can go up to 10 mg m⁻³), but for the Arctic waters wherein Chl spans from 0.02 to ~10 mg m⁻³.
Nevertheless, the assessments on coastal waters confirm that GSMA is robust for coastal waters as the < 15.2% failures suggested. However, efforts are still needed to improve the accuracy of Chl estimates for coastal waters.

### 5.3. Conclusions

For CDM-rich Arctic waters, the addition of signal at 625 nm where particulate scattering is relatively significant is very useful to provide less ambiguous information to disentangle $a_{ph}$, $a_{cdm}$, and $b_b$, thus leads to better estimates of all the three retrievals for GSM models. In the present study, we tuned GSM for the AO by adding 625 nm and obtained a new version—GSMA. Results indicated that GSMA outperformed AO.GSM, and improved the accuracy of Chl estimates by 8%. In addition, another pronounced advantage is that when AO.GSM failed, GSMA was still able to generate reasonable retrievals most of the time for CDM-rich waters. Assessments on a satellite image and two non-Arctic coastal datasets further confirmed that GSMA exhibited significant robustness when applied to coastal waters.

However, we should keep in mind that the success of GSMA depends on the reliable detection of the blue signal. When the observed blue signal drops below the limits of detection due to the high absorption of phytoplankton and CDM, semi-analytical algorithm that do not rely on blue signal (such as fluorescence-based algorithms) may be a viable alternative in the future, especially for eutrophic coastal waters.

**Funding.** Canada First Research Excellence Fund; ArcticNet; Stratégie de Mesure Autonome, Agile, Robuste et Transdisciplinaire (SMAART); Natural Sciences and Engineering Research Council of Canada; NASA ROSES project (1658689); Japan Aerospace Exploration Agency (22RT000298).

**Disclosures.** The authors have declared that no competing interests exist.

**Data availability.** The datasets used in this study can be found at MALINA (Ref. [30]), ICESCAPEs (Ref. [31]), TARA (Ref. [32]), GREEN EDGE (Ref. [33]), ArcticNet2011 (Ref. [34]), ArcticNet2013 (Ref. [35]), AREX2017 (Ref. [36]), ACE (Ref. [26]), COASTIOOC (Ref. [28]), and CCRR (Ref. [29]).

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