# Influence of the Accuracy of Chlorophyll-Retrieval Algorithms on the Estimation of Solar Radiation Absorbed in the Barents Sea

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}and using the OC3M algorithm for more productive waters with Chl > 0.2 mg m

^{−3}. The latter is a member of the OCx regression family of algorithms developed by NASA for various ocean color scanners, starting with SeaWiFS [9]. In between these values, the CI and OC3M algorithms are blended using a weighted approach. In addition to regression algorithms, quasi-analytical algorithms can be used, such as GIOP [5] and QAA [10], with the help of which spectral characteristics of light absorption by phytoplankton are determined, making it possible to estimate Chl and its contribution to the absorption of light energy by seawater.

_{b}) [28] to restore the volume-scattering function from the backscattering ratio b

_{b}/b. The latter does not depend much on the wavelength, which is true for spherical scattering particles and partly true for non-spherical, inhomogeneous particles. Although apparent optical properties can be calculated based on inherent properties [29,30], for additional validation, it is desirable to measure the underwater downwelling (E

_{d}(λ)) and upwelling (E

_{u}(λ)) plane irradiance and the remotely sensed reflectance (R

_{rs}(λ)), which makes it possible to solve direct and inverse problems of radiative transfer, which is important both to validate measurements and hydro-optical models.

## 2. Materials and Methods

#### 2.1. Study Area

^{−3}, which corresponds to mesotrophic waters. The presence of phytoplankton blooms and the influence of river runoff were not recorded. The studied waters are close to the case 1 type: phytoplankton cells and the associated OACs make the main contribution to the absorption and scattering of light in seawater relative to other OACs [7]. The quasi-homogeneous spatial distribution of bio-optical parameters in the areas of the stations makes it possible to extend the measurement results to regions with similar bio-optical characteristics and to calculate the solar energy absorbed in the seawater column.

#### 2.2. Field Measurements

_{d}(λ, z) and E

_{u}(λ, z), respectively), vertical profiles of photosynthetic active radiation (PAR), vertical profiles of the beam attenuation coefficient of seawater at a wavelength of 530 nm (c(530, z)), and spectra of the light absorption coefficient of optically active constituents of samples of the seawater surface layer (a

_{i}(λ)). The fluorescence intensities of chlorophyll-a (Fl

_{Chl}) obtained using a flow-through measuring complex were also used in the present study.

- An instrument complex to measure surface and underwater photosynthetically active radiation [31]. The complex was developed and built at the Ocean Optics Laboratory of the Shirshov Institute of Oceanology of the Russian Academy of Sciences (SIO) based on LI-192 LI-COR photodiode sensors (measuring total irradiance in the range of 400–700 nm), supplemented by devices to collect and transmit information.
- A set of two Ramses submersible hyperspectral radiometers. The radiometers are designed to measure underwater irradiance spectra in the wavelength range of 320–950 nm with a spectral resolution of 3.3 nm. The simultaneous use of two sensors, making it possible to carry out synchronous measurements of E
_{d}(λ, z) and E_{u}(λ, z). Thus, it is possible to directly calculate the spectral diffuse attenuation coefficients (K_{d}(λ, z)) from the obtained Ramses data. - A portable spectrophotometer with an integrating sphere ICAM (integrating cavity absorption meter) [32]. The device was used to determine the spectra of the total light absorption coefficient of seawater (a(λ)), as well as the spectra of the light absorption coefficient of particles (a
_{p}(λ)) and CDOM (a_{g}(λ)). The measurement data were processed according to the method described in [33]. - A PUM-200 submersible transmissometer. The device was designed and assembled at the Laboratory of Ocean Optics, SIO RAS [34]. Its goal is to measure vertical profiles (c(530, z)), as well as seawater temperature and chlorophyll-a fluorescence intensity.
- A flow-through measuring complex [35], which includes a PFD-2M two-channel flow-through fluorimeter, a laser hyperspectral fluorimeter [36], a PUM-A transmissometer, and a thermosalinograph. In the present study, we used only spatial distributions of the Chl fluorescence intensity (Fl
_{Chl}) excited by radiation at wavelength of 532 nm and registered near 685 nm. The measurements were taken in the seawater surface layer at a depth of 2–3 m, with a spatial resolution of about 50 m. Calibration of the flow-through fluorimeter according to the data of direct determinations of the Chl concentration made it possible to obtain the distributions of this quantity (Chl_{fl}) along the ship’s route. When calibrating the flow-through fluorimeter data, there were no significant deviations associated with non-photochemical quenching (NPQ) [37]. In our recent work [36], based on the results of the analysis of 648 samples, we demonstrated that the effect of NPQ on the relationship between the Chl fluorescence intensity and its concentration in the studied polar region is small. It is important to note that most of the samplings were carried out under conditions of a polar day in cloudy weather, which reduces the variations in the PAR flux and, accordingly, minimizes the influence of NPQ.

_{d}(λ)) were additionally calculated based on the obtained measurement data. Solving the inverse hydro-optical problem enabled determination of the backscattering index (b

_{b}(530)). The volume-scattering function and the seawater reflectance spectra (ρ

_{model}(λ)) were also modeled.

#### 2.3. Hydro-Optical Models and Algorithms

_{a}(869)) are taken from satellite ocean color scanner data.

_{cl}). In our case, it was assumed to equal 30, corresponding to the value providing an acceptable agreement with the results of measurements of irradiance by the Ramses instrument. The C1 water cloud model [43] was adopted as the cloud-scattering phase function.

^{−1}, corresponding to the conditions of shipboard measurements) showed that the instantaneous PAR values in the upper 10-m layer differ from the calculation results for a smooth surface by no more than 1%. Thus, all calculations were performed for the windless case.

_{s}and v

_{l}are concentrations of small and large particles, respectively, ${\nu}_{w}=4.3,{\nu}_{s}=1.7,\mathrm{and}\text{}{\nu}_{l}=0.3$; functions ${\beta}_{s}\left(\gamma \right)$ and ${\beta}_{l}\left(\gamma \right)$ are tabulated in [46].

_{f}and v

_{c}), we first integrated (1) over the whole sphere, then over the backward hemisphere. As a result, for each wavelength, we obtained a pair of linear equations with two variables [47]:

_{w}+ v

_{s}b

_{s}+ v

_{l}b

_{l};

b

_{b}= ½ b

_{w}+ v

_{f}b

_{bs}+ v

_{c}b

_{bl},

_{f}, v

_{c}) and (b, b

_{b})). In other words, within the framework of this model, the parameters b(λ) and b

_{b}(λ) for a fixed value of wavelength completely determine the scattering properties of seawater. If the solutions of Equation (2) are substituted into (1) and the normalization factor is taken into account, then we obtain the scattering phase function and, consequently, all the parameters necessary for the numerical solution of the radiative transfer equations.

_{b}) for a given wavelength (λ

_{0}) (530 nm in our case).

_{b}according to the subsurface radiance reflectance, ρ = π·L

_{u}/E

_{d}, where L

_{u}is the subsurface upwelling radiance, and E

_{d}is the subsurface downwelling irradiance. This algorithm is based on the well-known formulae [48,49,50,51] that enable calculation of the backscattering coefficient according to parameters ρ and a. This approximate formula can be used to express the subsurface reflectance (ρ(λ)) through the parameter u = b

_{b}/(a + b

_{b}). Solving the equation ρ = F(u) with respect to u yields parameter b

_{b}. The spectra (ρ(λ)) were calculated based on remote sensing reflectance (R

_{rs}(λ)) using the following formula [49]: $\rho \left(\lambda \right)=\pi {R}_{rs}\left(\lambda \right)/\left(0.52+1.7{R}_{rs}\left(\lambda \right)\right)$, where R

_{rs}(λ) was measured by MODIS/Aqua and OLCI/Sentinel-3A. To determine the absorption coefficient (a(λ)), we used an integrating cavity absorption meter.

_{0}), we used the beam attenuation coefficient c(530) determined with the help of a PUM transparency meter, yielding b(530) = c(530) − a(530).

_{i}is the wavelength of the spectral bands of the satellite ocean color scanner, ρ(λ

_{i}) is the measured value of the subsurface reflectance, and $\widehat{\rho}\left({\lambda}_{i}\right)$ is the values of the same reflectance depending on parameters v

_{s}and v

_{l}calculated by solving RTE. For stations 7044, 7069, and 7091, we used a limited set of spectral channels without 412, 443, and 469 nm, as the values of ρ(λ

_{i}) for these wavelengths contradicted the results of shipboard measurements of the absorption coefficient. This may be the result of an erroneous atmospheric correction in the shortwave range at low solar elevations.

_{s},v

_{l}) on the only parameter, i.e., b

_{b}. In this regard, in order to determine the optimal values of v

_{s}and v

_{l}, we solved the problem of the extremum of function S under the following conditions imposed on the variables (v

_{s}and v

_{l}): b(530,v

_{s},v

_{l}) = c(530) − a(530), where c(530) and a(530) are measured values. The results of this algorithm are the profiles of apparent optical properties (AOPs) shown in Section 3.3 and Discussion.

_{s}, v

_{l}and the absorption coefficient (a(λ,z)).

_{d}(z) was possible within the framework of a simpler model, ‘case 1 new’ [4]. According to this model, all IOPs are uniquely determined through a single parameter, the chlorophyll concentration (Chl). In particular, the absorption coefficient is modeled as the sum of three components: $a\left(z,\lambda \right)={a}_{w}\left(\lambda \right)+{a}_{p}\left(z,\lambda \right)+{a}_{g}\left(z,\lambda \right)$, where a

_{w}is absorption by pure water, a

_{p}is absorption by particulate matter, and a

_{g}is absorption by yellow matter (Gelbstoff). For the parameter a

_{p}[52], ${a}_{p}\left(\lambda ,Chl\left(z\right)\right)=A\left(\lambda \right)Chl{\left(z\right)}^{E\left(\lambda \right)}$ was used; for the yellow matter absorption the following formula was applied [4]:

_{g}= 0.2, λ

_{0}= 440 nm, and S = 0.014 nm

^{−1}. A comparison of a

_{p}and a

_{g}values calculated from these formulae with the ICAM measurements showed that whereas this model may be a good approximation for a

_{p}, the values of a

_{g}calculated with the default (f

_{g}) are significantly lower than the ICAM results. In calculations according to this scheme, the measured values of the Chl concentration obtained at varying depths were used. This approach allows us to study the effect of taking into account the OAC stratification on the result of calculating underwater light fields.

_{p}(λ) values obtained using the integrating sphere.

#### 2.4. Satellite Data

_{rs}(λ) spectrum.

_{rs}(λ) spectra obtained from the MODIS satellite ocean color data with modeling results. Both absorption data measured with ICAM and model values for the selected Chl* concentrations were used for modeling (Section 3.2). Good agreement was achieved between the model and satellite spectra for the entire visible range for station 7013. For the other stations, significant differences are noticeable for the 412 nm band, which is associated with atmospheric correction errors. The differences between the model and satellite spectra for station 7044 arise because this station is located at the boundary of the area of increased Chl concentration (Figure 1). In addition, the difference in the time of shipboard and satellite measurements at this station was 32 h. For the wavelength of 530 nm used in our hydro-optical model (Section 2.3), the error between the model and satellite data does not exceed 8%.

#### 2.5. SIO RAS Regional Chl-Retrieval Alghorithm

_{rs}(531)/R

_{rs}(547)]

^{−7.76}.

_{rs}(λ) of MODIS Aqua/Terra ocean color scanners and shipboard Chl measurements (26 pairs, with a time interval between field and satellite measurements of less than 12 h). The average relative error (RE) of the B22 algorithm in this data set is 38%, the root mean square error (RMSE) is 0.21 mg m

^{−3}, the coefficient of determination is 0.32, p-value < 0.001, and the bias is −0.04 mg m

^{−3}. If the admissible time interval between satellite and field measurements is increased to 48 h (121 pairs), the RMSE will increase to 0.38 mg m

^{−3}, RE = 49%, and bias = −0.05 mg m

^{−3}correspondingly.

## 3. Results

#### 3.1. Validation of the SIO RAS Regional Chl-Retrieval Alghorithm

_{fl}> was equal to 0.44–0.50 mg m

^{−3}). In the case of AMK 68, the measurements were carried out in an area of strong coccolithophore bloom (according to direct measurements, the concentration of coccolithophores in the surface layer varied in the range of 1.4–6.3 million cells/L). The bloom can affect the accuracy of satellite algorithms with respect to estimations of Chl concentration. The Chl values there were noticeably higher (<Chl

_{fl}> = 1.27 mg m

^{−3}). To calibrate the fluorimeter data, we used Chl values measured at stations in the Barents Sea. The MODIS/Aqua data average daily composites (Figure 3A,B) were calculated, and data with the STRAYLIGHT flag were excluded to eliminate the distortion of satellite data near clouds.

^{−3}, RE = 23%, bias = +0.04 mg m

^{−3}) are somewhat lower than for June 12 (B22: RMSE = 0.17 mg m

^{−3}, RE = 32%, bias = +0.08 mg m

^{−3}).

^{−3}), then the regional algorithm yields estimates mainly in the range 1.5–2 mg m

^{−3}. This leads to a decrease in bias for the regional algorithm. If compared with the validation of the Chl retrieval algorithms in the absence of phytoplankton bloom, we note that in the case of coccolithophore bloom, the relative errors are approximately the same (24–28%), but the absolute errors are slightly higher (about 0.4 mg m

^{−3}). This could be the result of both errors, either in the calibration of the fluorimeter under the conditions of coccolithophore blooms, and the time difference between the fluorometric and satellite measurements (about a day).

#### 3.2. Chlorophyll Concentrations

#### 3.3. Validation of Instantaneous Irradiance Calculations

_{d}(530, z) vertical profiles, as well as the results of simulation performed under the assumption of the homogeneity of the upper layer and for pure water, are shown in Figure 6.

^{−3}) was obtained as a result of direct measurements. Corresponding curves are closest at station 7091, where the minimum Chl concentration (0.17 mg m

^{−3}) was recorded.

_{d_PAR}(z) for the PAR range calculated based on the data of direct determinations using LI-COR and modelling to verify the quality of the spectral model (Figure 7). The agreement between the results is acceptable: RE = 53%, 51%, 27%, and 7% for the selected stations, respectively. The best agreement between the data was obtained at stations 7069 and 7091, with good weather conditions during data collection. The bend in the measured vertical profile (K

_{d_PAR}(z)) at station 7069 in the region of 30 m, as well as the break in the corresponding profile for station 7044 near 10 m, are the result of the peculiarities of the OAC stratification, which are clearly distinguishable in the c(530, z) profiles (Figure 5). Section 4.2 is devoted to a possible approach to accounting for stratification.

## 4. Discussion

#### 4.1. The Influence of Chl Concentration on the Accuracy of Calculating the Seawater Energy Absorbed in the PAR Range

_{abs}(z)) was calculated using the data interpolated in depth with a step of dz = 1 m according to the following equation:

_{abs}(z) = E

_{d}(z) + E

_{u}(z + dz) − E

_{d}(z + dz) − E

_{u}(z),

_{abs}(z) depend on the lighting conditions, which are difficult to model under partial cloudiness. To optimally fit the results of in situ measurements, the model data were consistently shifted along the horizontal axis.

_{g}(443) from satellite data in the Arctic exceed the errors of satellite algorithms to estimate the Chl concentration [55], highlighting the primary role of CDOM in the absorption of solar energy by the seawater and making the development of methods for estimating a

_{g}(443) necessary. Such an improvement will entail a refinement of the seasonal estimates of radiance balance in the Barents Sea [56,57].

#### 4.2. The Impact of Considering IOP Stratification

_{d}(530, z) in comparison to the data obtained at station 7069. The Chl concentration was measured at the depths of 1, 6, 15, 22, 38, and 52 m. To carry out the calculations, the obtained Chl values were interpolated.

_{g}= 0.2 (see Equation (3)) differ significantly from the results of measurements at depths greater than 15 m (RE = 147%), whereas for f

_{g}= 1.2, we obtained excellent agreement between the calculation results and measurements (RE = 8%). Therefore, Morel’s ‘case 1 new’ model, with a slight modification, can take into account IOP stratification (Figure 5). Compared to calculations without stratification, this approach makes it possible to achieve improved agreement between the measured and calculated E

_{d}(530, z) profiles. Furthermore, it is of interest to study the influence of other factors vertical distribution, such as CDOM absorption and the particle-scattering coefficients. In this case, it is possible to use a special technique to calculate the vertical profile of CDOM absorption [58].

#### 4.3. An Example of Using OLCI Data

_{rs}MODIS spectra, which are affected by atmospheric correction errors, showed good agreement between the parameters of underwater light fields when compared to direct measurements. In this section, we consider the applicability of this approach in terms of using better quality satellite data. Take, for example, OLCI data of 9 August 2021, selected for station 7069. In comparison to the MODIS spectrum used in the main part of the work, the OLCI spectrum does not exhibit an unrealistic increase in R

_{rs}in short-wavelength channels, which contradicts to the data of direct determinations of the seawater absorption coefficient (Figure 10a). The results of model calculations are close to satellite data for the entire R

_{rs}OLCI spectrum, and for MODIS, the model spectrum of R

_{rs}makes it possible to avoid the influence of errors in shortwave channels. Such errors typical for the Arctic region lead to underestimated values of the CDOM absorption coefficient compared to those measured on the integrating sphere, leading to low accuracy of satellite algorithms in this region [55].

_{rs}spectra: full OLCI and shortened MODIS (488–667 nm). A small error (0–4%) arises due to the close values of R

_{rs}(530) used for the model setting.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Position of the stations of cruises 83 and 84 of the R/V ‘Akademik Mstislav Keldysh’ against the background of the averaged spatial distribution of chlorophyll-a concentration according to MODIS/Aqua and Terra (chlor_a) data: 7013—12 June 2021; 7044—26 July 2021; 7069—9 August 2021; 7090 and 7091—17 August 2021.

**Figure 3.**The spatial distributions of Chl concentration according to MODIS/Aqua data on 12 June (

**A**) and 14 June (

**B**), 2021, calculated using the B22 regional algorithm. The black line shows the ship’s route. Comparison of the Chl values calculated from satellite data on 12 June (

**C**) and 14 June (

**D**), 2021 and measured with a fluorimeter. The dotted line is the perfect fit (1:1).

**Figure 4.**Comparison of Chl values calculated based on satellite data obtained on 14–15 August 2017 and measured using a flow-through fluorimeter. The dashed line is the perfect fit (1:1), and the colored lines are linear regressions.

**Figure 6.**E

_{d}(530, z) vertical profiles from direct measurements of Ramses (black lines), from modeling data taking into account OAC (red lines), and for a hypothetical case of pure water (blue lines).

**Figure 7.**K

_{d_PAR}(z) vertical profiles in the PAR range based on data of direct determinations (black lines) and modeling (red lines).

**Figure 8.**Vertical distributions of solar energy absorbed in seawater in the PAR range drawn from direct measurements (black lines) and modeling based on in situ measurements (red lines), selected Chl* values (green dotted lines), and the pure water hypothesis (blue lines).

**Figure 9.**Comparison of downwelling irradiance E

_{d}(530, z) profiles measured with Ramses (black line) and calculated using the ‘case 1 new’ model for f

_{g}= 0.2 (red and yellow lines) and f

_{g}= 1.2 (green line) at station 7069. The red curve was calculated without taking into account stratification.

**Figure 10.**R

_{rs}spectra obtained from MODIS and OLCI data (solid lines) and as a result of modelling (dashed lines); the vertical dotted line shows the cutoff area of short-wavelength MODIS channels (

**a**); relative deviation of absorbed energy calculated using different R

_{rs}spectra: full OLCI and shortened MODIS (

**b**).

Station | Latitude, N | Longitude, E | Date | Time, UTC | Location |
---|---|---|---|---|---|

7013 | 70°25.6092′ | 33°49.061′ | 14 June 2021 | 11:07 | Southern part of the Barents Sea |

7044 | 74°57.03′ | 27°36.04′ | 28 July 2021 | 3:00 | Central part of the Barents Sea |

7069 | 80°27.02′ | 16°05.54′ | 9 August 2021 | 9:20 | NW of Svalbard |

7090 | 78°22.99′ | 25°51.93′ | 18 August 2021 | 14:00 | East of Svalbard |

7091 | 78°44.46′ | 24°28.38′ | 18 August 2021 | 19:20 | East of Svalbard |

**Table 2.**The correspondence parameters between the values of chlorophyll concentration measured with a fluorimeter and calculated based on MODIS data by standard and regional algorithms, depending on the data set.

Data Set | Algorithm | N | R^{2} | RMSE, mg m ^{−3} | RE, % | Bias, mg m ^{−3} |
---|---|---|---|---|---|---|

AMK 83, 12.06.21 | chlor_a | 421 | 0.28 | 0.23 | 37 | +0.12 |

B22 | 0.35 | 0.17 | 32 | +0.08 | ||

AMK 83, 14.06.21 | chlor_a | 271 | 0.36 | 0.19 | 25 | +0.01 |

B22 | 0.42 | 0.15 | 23 | +0.04 | ||

AMK 68, 14-15.08.17 | chlor_a | 259 | 0.70 | 0.40 | 28 | +0.34 |

B22 | 0.70 | 0.37 | 24 | +0.16 |

^{2}—coefficient of determination, RMSE—root mean square error, RE—average relative error.

**Table 3.**Chlorophyll concentrations calculated based on satellite data by various algorithms (chlor_a, B22) and measured in situ.

Station | Date and Time (UTC) of MODIS/Aqua Overpass (ΔT) | Chlorophyll Concentration, mg m^{−3} | |||
---|---|---|---|---|---|

In Situ | chlor_a | B22 | Chl* | ||

7013 | 12.06.21 10:35 (48 h) | 0.51 | 0.50 | 0.52 | 1 |

7044 | 26.07.21 11:00 (32 h) | 1.07 | 0.31 | 0.42 | 0.25 |

7069 | 09.08.21 11:15 (2 h) | 0.54 | 0.39 | 0.41 | 1 |

7091 | 17.08.21 8:50 (11 h) | 0.17 | 0.29 | 0.35 | 1 |

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**MDPI and ACS Style**

Glukhovets, D.; Sheberstov, S.; Vazyulya, S.; Yushmanova, A.; Salyuk, P.; Sahling, I.; Aglova, E.
Influence of the Accuracy of Chlorophyll-Retrieval Algorithms on the Estimation of Solar Radiation Absorbed in the Barents Sea. *Remote Sens.* **2022**, *14*, 4995.
https://doi.org/10.3390/rs14194995

**AMA Style**

Glukhovets D, Sheberstov S, Vazyulya S, Yushmanova A, Salyuk P, Sahling I, Aglova E.
Influence of the Accuracy of Chlorophyll-Retrieval Algorithms on the Estimation of Solar Radiation Absorbed in the Barents Sea. *Remote Sensing*. 2022; 14(19):4995.
https://doi.org/10.3390/rs14194995

**Chicago/Turabian Style**

Glukhovets, Dmitry, Sergey Sheberstov, Svetlana Vazyulya, Anna Yushmanova, Pavel Salyuk, Inna Sahling, and Evgeniia Aglova.
2022. "Influence of the Accuracy of Chlorophyll-Retrieval Algorithms on the Estimation of Solar Radiation Absorbed in the Barents Sea" *Remote Sensing* 14, no. 19: 4995.
https://doi.org/10.3390/rs14194995