# Evaluation of the CDOM Absorption Coefficient in the Arctic Seas Based on Sentinel-3 OLCI Data

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## Abstract

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## 1. Introduction

_{g}(λ), which can be obtained with acceptable accuracy using optical methods, both contact and remote [3,4]. We have to consider the CDOM absorption when calculating the visible solar radiation entering the water column in a wavelength range of 400–700 nm, called photosynthetically available radiation (PAR), a fundamental factor for ocean primary bio-productivity. The visible radiation entering the water column contributes to the ocean heat budget [5], determines underwater visibility, and practical use of various equipment for activity, studying, and monitoring of the marine environment.

_{rs}in the shortwave bands (the wavelengths <488 nm). This algorithm gives good results in the Kara Sea but can be applied to other seas as well. In the Barents Sea, coccolithophore blooms may interfere with standard algorithms for determining the a

_{g}values. The blooms occur in July–September and lead to a significant change in the spectral water-leaving radiance [3,4]. Not all algorithms cope with these changes. The solution to the atmospheric correction problem is beyond this work; our task is to assess the results of its application.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field Measurements

#### 2.2.1. Measurements of the Spectral Absorption Coefficients

^{−1}[31].

#### 2.2.2. Floating and Deck Spectroradiometers

_{rs}. During the measurements at drift stations, the device floats off the ship at a distance of 0–50 m to avoid shading and reflection. Depending on weather conditions, 20–50 spectral scans are averaged during processing, using a specially developed algorithm. The subsurface radiance reflectance ρ(λ) is calculated as ρ(λ) = πL

_{u}(λ)/E

_{d}(λ), where L

_{u}(λ) and E

_{d}(λ) are the upwelling radiance and the downwelling irradiance just beneath the sea surface, respectively. A particular deck sensor, installed on the open deck in a place free from shading, performs the continuous monitoring of changes in surface irradiance during measurements.

#### 2.2.3. Measurements of the Diffuse Attenuation Coefficient K_{d}

_{d}(z, λ) measured by two irradiance meters BIC and RAMSES to calculate the diffuse attenuation coefficient.

_{d}(z, λ) values allow us to compute the diffuse attenuation coefficients K

_{d}(λ) for underwater irradiance, assuming the exponential law E

_{d}(z) = E

_{d}(0

^{−}) exp[–K

_{d}× z], and omitting wavelength λ for simplicity. In this work, we used K

_{d}(λ) values for the upper uniform layer, the thickness of which varied from 10 to 30 m.

_{d}[36]. From our field measurements, K

_{d}(490) varied from 0.03 to 0.34 m

^{−1}for the Norwegian and Barents seas and within 0.06–0.36 m

^{−1}for the Kara Sea. Hence, the informative satellite depth Z* was within 2.8–16 m in the Kara Sea and 3.0–33 m in the Norwegian and Barents seas. Usually, the thickness of the layer, where the K

_{d}values were measured, exceeded the Z* value; only in the clear waters of the Barents Sea (stations 5557 and 5560 of AMK-68),the Z* value was higher.

#### 2.2.4. The Beam Attenuation Coefficient Measurements

_{bp}calculated from in situ measured R

_{rs}and the satellite color scanner data (see Section 3.3). The values of the beam attenuation coefficient were measured by a PUM-A transparency meter in the laboratory mode—on water samples or as a part of a shipboard flow-through system [37]. The device measures the beam attenuation coefficient at 530 nm in a range of 0.050–1.0 m

^{−1}with an error of 0.005 m

^{−1}.

^{−1}. To verify the results, we also carried out the inter-calibration of the laboratory PUM-A device with a submersible PUM transparency meter. The beam attenuation coefficient values of the water sample from the bottle, measured by PUM-A in a cuvette, were compared with the PUM data at the same depth. The difference did not exceed 0.01 m

^{−1}.

#### 2.3. Satellite Data and Algorithms

#### 2.3.1. Satellite Data and Software

_{d}. When processing, the following data flags were used: OLCI_LAND, OLCI_CLOUD, OLCI_CLOUD_AMBIGUOUS, OLCI_CLOUD_MARGIN. For map building, we binned the data on a 3 × 3 km grid.

_{rs}and the diffuse attenuation coefficients K

_{d}(490). Using the values of R

_{rs}, the absorption coefficients of yellow substance a

_{g}and the particle backscattering coefficients [4] were calculated for the field stations where the time difference between satellite and field measurements was no more 24 h. Since the algorithms for these products were developed for MODIS color scanners, we interpolated the VIIRS R

_{rs}to MODIS wavelengths. When calculating the parameters, the pixels flagged with LAND, CLDICE, SEAICE, and STRAYLIGHT were filtered out.

#### 2.3.2. Algorithms

_{bp}and the TSM concentration, we used the algorithms listed below.

#### OLCI NN

_{rs}. The standard atmospheric correction also derives the Rrs spectral values.

#### GIOP

_{rs}(λ) in the visible range of the spectrum and can derive the absorption coefficients of colored dissolved organic matter a

_{g}(λ) and of phytoplankton pigments a

_{ph}(λ), as well as the particle backscattering coefficient b

_{bp}(λ). Based on the obtained data on the remote sensing reflectance R

_{rs}(λ), the model performs an inversion to find the optimal set of the bio-optical characteristics of the water column, which minimizes the difference between the simulated and the measured values. The model provides the possibility of adjusting input parameters (such as chlorophyll concentration, the spectral slope for yellow substance absorption).

#### The Quasi-Analytical Algorithm (QAA)

_{rs}(λ) as a result of analysis of several empirical, analytical, and semi-analytical models, in particular, Gordon et al. [43] and Lee et al. [44]. The generally utilized expression [45,46] presents the spectral b

_{b}(λ) values.

_{b}(λ), the QAA algorithm can derive the seawater absorption coefficient and estimate the values of the detrit-gelbstoff and the phytoplankton pigment absorption coefficients. The ESA Ocean Colour Climate Change Initiative selected the QAA algorithm to derive b

_{bp}for creating a long-term series of satellite ocean color products.

#### Regional Semi-Analytical Algorithm (RSA)

_{g}, particle backscattering coefficient b

_{bp,}and diffuse attenuation coefficient K

_{d}(λ) in four spectral channels 443, 490, 555, and 625 nm in the Kara and White seas using MODIS satellite data [23]. It uses the R

_{rs}data for the wavelength range ≥488 nm. The above-surface remote-sensing reflectances R

_{rs}(412) and R

_{rs}(443) are not used due to the high probability of the atmospheric correction errors. In the present work, we modified the RSA algorithm to the OLCI spectral channels, and now it uses the R

_{rs}data for the wavelength range greater than or equal to 490 nm.

_{b}(λ) is solved using the low-parametric models representing the seawater coefficients as a superposition of the contributions of the main components. The absorption coefficient a(λ) is defined as the sum of the absorption of pure sea water, yellow substance or CDOM, and the phytoplankton pigments, while b

_{b}(λ) is defined as the superposition of the backscattering by pure seawater and the suspended particles. The contribution of chlorophyll is accounted for using a regional algorithm for the Kara Sea [47]. An iterative approach was used to improve the accuracy while estimating the slope of the absorption spectrum. As a result of solving the inverse problem, two parameters are defined: a

_{g}(443) and b

_{bp}(555). These parameters also allow to calculate the K

_{d}(λ) value using Gordon’s formula [48]. The RSA algorithm was validated using the shipboard data, measured with a floating spectroradiometer [34] and free from errors of atmospheric correction. The algorithm was also tested on satellite data and showed acceptable results [23].

#### Algorithm for Determining b_{bp} and TSM

_{bp}= b

_{bp}(555), the diffuse attenuation coefficient K

_{d}(555) and the parameter X(555) = b

_{b}(555)/[a(555) + b

_{b}(555)] are calculated. The value of X(555) is determined through the value of the normalized water-leaving radiances L

_{wn}(555), K

_{d}(555) using the ratio L

_{wn}(510)/L

_{wn}(555). The value [a(555) + b

_{b}(555)] can be obtained from K

_{d}(555) using Gordon’s formula [48]; the backscattering coefficient b

_{bp}as the difference between the seawater b

_{b}and the known pure water backscattering coefficient b

_{bw}. We adapted this algorithm to the MODIS, OLCI, and VIIRS spectral channels.

_{wn}by a floating spectroradiometer and TSM were used to derive the regression equation TSM vs. b

_{bp}: TSM = 73.5 b

_{bp}+ 0.016, where b

_{bp}, m

^{−1}and TSM, mg/L. The average error in determining the concentration of suspended matter is about 30%.

#### 2.3.3. Error Estimates

_{i}indicates fit values, and$\mathsf{\sigma}$ is the standard deviation.

## 3. Results

_{g}_olci_C2RCC values using the SNAP program C2RCC processor with default parameters [40].

_{rs}(λ) measured by floating or deck spectroradiometers, the spectral diffuse attenuation coefficient of the underwater irradiance K

_{d}(λ), the beam attenuation coefficient c, as well as data from other satellite ocean color scanners and results of calculations by various algorithms (see Section 2.2 and Section 2.3).

#### 3.1. Validation and Analysis of the ADG_443_NN Values Derived from OLCI Data

_{g}_olci_std) is available as a Level 2 standard product of the OLCI instrument on the Sentinel 3A, B satellites (see Section 2.2). Figure 3 presents the results of comparing a

_{g}_olci_std with the data of direct absorption measurements by the ICAM technique (a

_{g}_icam).

_{g}_olci_std and a

_{g}_icam values can be more than 30-fold. Comparing Figure 3b,d, one can see that the real uncertainties are significantly (≥100%) higher than the calculated errors of the ADG443_NN_err (~10%).

_{rs}data measured by the floating (or deck) spectroradiometer are incomparably better (see below).

^{2}turned out to be large enough for all the algorithms used: 0.656 for RSA, 0.922 for QAA, 0.960 for GIOP.

_{g}_olci_C2RCC values were calculated from the L1 level OLCI data by the C2RCC processor [40]. All algorithms, except for neural networks, gave negative values in the calculations for some individual flybys, which caused the difference in the number of data pairs (Table 2). We consider the atmospheric correction errors in more detail in Section 3.2.

_{g}_olci_std and a

_{g}_olci_C2RCC versus the measured values of a

_{g}_icam; Table 3 presents the regression parameters.

_{g}_olci_C2RCC values, a significant relationship is observed for both seas, and even better for the Kara Sea.

_{g}_olci_std values, and the retrieval of the absorption coefficient values is practically possible only with the C2RCC processor data.

_{g}spatial distributions using the derived equation for the Barents Sea. Figure 6 shows the ADG_443_NN spatial distributions in the Barents and partly in the Norwegian seas built with standard a

_{g}_olci_std and corrected a

_{g}_corr data for AMK-65 and AMK-68 cruises. Adjusted distributions look more plausible; the vast white area between 30° and 50° E in Figure 6B is due to a lack of satellite data due to cloudiness.

#### 3.2. Results of Atmospheric Correction

_{rs}as a reference to compare the values of the spectral radiance reflectance directly above the sea surface.

_{rs}on the above difference (Figure 7A) and the solar zenith angle (SZA) (Figure 7B). Spectral R

_{rs}standard errors are significantly wavelength-dependent; they increase in the shortwave region of the visible spectrum [28].

^{2}= 0.043 for the module of the time interval at a significance level of p = 0.004, compared with R

^{2}= 0.016, p = 0.083 for the solar zenith angle. The independence of the error value from the time interval between shipboard and satellite data points out the stability of the measurement conditions determined by the hydrometeorological factors and oceanological processes prevailing in the period under consideration. Nevertheless, at intervals exceeding 20 h, the errors increase by a factor of 1.5 (RMSE for time difference >20 h equals 0.0036 while the mean RMSE = 0.0024, N = 48). That may relate to the surface water dynamics [50].

_{rs}spectra measured at Station 6240 in the Kara Sea on 14 July 2019. For this station, we collected the most significant amount of satellite data—23 files. The colors show the various sensors; black line—the result of direct determinations; gray lines—the spectra with RMSE > 0.001.

^{−1}correspond to the waters of the surface desalinated layer formed in the summer season by the Ob and Yenisei river runoff [51]. The lower salinity and a high content of colored dissolved organic matter are typical for this water compared to waters outside the influence of river runoff [50]. Station 6240 is located in the area where waters with different optical characteristics come into contact, which causes the observed differences in the values of the absorption coefficient, calculated with different algorithms and dates.

#### 3.3. OLCI Estimates of the Particle Backscattering Coefficient

#### 3.3.1. In Situ Measurements in the Barents Sea

_{bp}values in our field studies. These values were calculated using the R

_{rs}values, measured by floating (AMK-65) and deck (AMK-68) spectroradiometers. We calculated the b

_{bp}(555) for a wavelength of 555 nm using the different algorithms described in Section 2.2.2: the simplified regression algorithm (SRA) [23], a quasi-analytical algorithm QAA [22], and the GIOP model [41,42].

_{bp}(555) values for the selected stations with the beam attenuation coefficient c(530) for the subsurface layer (5 m) measured by the PUM-A device (Section 2). Such a comparison makes clear physical sense because TSM mainly determines both the beam attenuation and backscattering coefficients. Figure 12 shows the comparison results.

_{bp}(555) vs. c(530) with different algorithms.

#### 3.3.2. Comparison between the Particle Backscattering Coefficient Values Derived from Field and OLCI Satellite Data

_{bp}data derived from field and OLCI satellite data. The selected stations included the data from a floating or a deck spectroradiometer, satellite data from OLCI, MODIS, and VIIRS, and absorption data measured by ICAM. For OLCI data, the calculation was performed using the R

_{rs}values available as a result of the BAC (standard) and AAC (NN) atmospheric correction. In the last case, the R

_{rs}Level 2 data were derived from the TOA Level 1 radiance data, using the C2RCC processor [40]. For the calculations in the Kara Sea, we used the regional semi-analytical RSA. Figure 13 shows the regression lines for the Barents, Kara, and Laptev seas. Table 7 presents the regression parameters for different regions, algorithms, and satellites.

^{2}> 0.3 is observed only in the case of the C2RCC processor, the QAA algorithm. That may be due to the strong influence of river runoff in this region. A better correlation is obtained for stations in the Barents Sea. For example, for standard OLCI Level 2 data using the GIOP algorithm, R

^{2}= 0.92.

#### 3.4. Diffuse Attenuation Coefficient

#### 3.4.1. Comparison of a_{g} and K_{d} Measured In Situ

_{g}(443) and K

_{d}(443) measured in situ, separately for the Barents and Norwegian seas (AMK 68—Figure 14A) and the Kara Sea (AMK 72 and 76—Figure 14B). The a

_{g}coefficient was measured using ICAM, K

_{d}calculated from the data of the underwater irradiance measured by two instruments (BIC and Ramses) in the upper homogeneous layer. We determined the K

_{d}coefficient as the average between the measurements if they were made with both devices.

_{g}(443) and K

_{d}(443). One can see a reasonably good correlation for the Kara Sea, with data from the AMK 72 and AMK 76 voyages: the coefficient of determination R

^{2}= 0.73. We also obtained a high correlation (R

^{2}= 0.72) for the Barents Sea, but the regression equations in these two seas differ significantly. The stations with coccolithophore blooms (see Figure 14A) fit well into the obtained regression. For the waters of the Norwegian Sea, there is no stable relationship between a

_{g}(443) and K

_{d}(443): R

^{2}= 0.21, but the resulting regression equation does not differ much from that obtained for the Barents Sea. The results obtained indicate the consistency of measurements of a

_{g}and K

_{d}.

#### 3.4.2. Consistency between the Data Derived from Field Measurements

_{d}using a simple formula: K

_{d}= (1 + 0.005 θ

_{0}) a + 3.47 b

_{b}, where a and b

_{b}—the seawater absorption and backscattering coefficients, θ

_{0}—the solar zenith angle [52]. This formula provides reasonable accuracy for waters with coccolithophore blooms and no bloom [53].

_{bp}was calculated from the in situ measured spectra R

_{rs}(λ) using algorithm [49].

_{d}values for two wavelengths, 443 and 490 nm, calculated by formula [52], and from in situ measurements of underwater irradiance at 18 stations in the Barents Sea (AMK 68). It is seen an excellent agreement of the K

_{d}estimates obtained for both spectral channels: the coefficient of determination is R

^{2}= 0.98; the RMSE equals 0.028 and 0.035 m

^{−1}for 443 and 490 nm, respectively. The stations with coccolithophore blooms do not worsen the obtained correspondence. That proves a good agreement between the data of our field measurements of the absorption coefficient a(λ), remote sensing reflectance spectra R

_{rs}(λ), and the diffuse attenuation coefficient K

_{d}(λ).

#### 3.4.3. Comparison of K_{d}(490) Values from Satellite and Field Data (Standard Algorithms)

_{d}(490) calculated from the data of field measurements and the OLCI Level 2 standard product. We used the K

_{d}(490) value for the nearest pixel, but only for those satellite overpasses with the number of valid pixels being at least 17 out of the 25 closest. Some stations have more overpasses than others; the maximum number equal to 9 was for station 6239 in the Kara Sea (AMK 76, K

_{d}(490) = 0.32 m

^{−1}according to in situ data). As seen, almost all OLCI flights resulted in underestimated K

_{d}(490) values (0.10–0.15 m

^{−1}); only the OLCI flight, closest by the time of the field measurements (less than four hours), gave K

_{d}(490) = 0.39 m

^{−1}.

_{d}(490) calculated from field measurements and satellite MODIS and VIIRS data. As in the OLCI case, we took the K

_{d}(490) values from Level 2 files in the nearest pixel, so they were the standard product of these scanners. Since the overpass of the considered satellites differs, the set of presented data for each scanner is different. For MODIS and VIIRS scanners, we managed to obtain data for station 5580 in the Barents Sea with an intense coccolithophore bloom; the directly measured coccolithophore plated cell concentration was approximately 5 × 10

^{6}cell/L, the detached coccoliths 1.5 × 10

^{8}cell/L, and K

_{d}(490) = 0.34 m

^{−1}.

_{d}(490) values calculated from satellite and field data (the nearest pixel). As seen from Figure 16A and Table 9, a good agreement between OLCI and field data is observed for the Barents Sea (AMK 68): coefficient of determination R

^{2}= 0.80, standard error RMSE = 0.05 m

^{−1}, relative error RE = 20%. However, these calculations were only for four stations. The stations with coccolithophore blooms did not show much difference from other stations in this region. In the Kara Sea (AMK 72 and 76), the OLCI estimates of K

_{d}(490), in general, are approximately two times lower than K

_{d}(490) from in situ measurements: the ratio of the mean values is 0.51, RE = 45%, but for stations in clear waters with K

_{d}(490) < 0.1 m

^{−1}, satellite data errors do not exceed 15%.

_{d}(490) estimates from satellite and the field data in clear waters (K

_{d}(490) < 0.2 m

^{−1}). In more turbid waters, the satellite K

_{d}(490) values were underestimated by about a factor of 2. The intense coccolithophore bloom in the Barents Sea and the river runoff in the Kara Sea cause such turbid waters.

## 4. Discussion

_{p}at 443 and 670 nm as a proxy of chlorophyll concentration; they presented almost no results on the CDOM absorption. The authors mentioned the factors limiting ocean color remote sensing capability in the Nordic Seas (low sun zenith angle, persistent cloudiness, and fog) without focusing on them.

_{d}(489), the particle scattering coefficient at 443 nm, and the product “iop_adg” (the sum of organic detritus and gelbstoff absorption at 443 nm). They statistically compared the satellite Level 2 products with the in situ data from several validation campaigns in 2016–2018. In particular, the authors presented estimates for “iop_adg”—a mean normalized bias 8%, root-mean-square error 56%, average absolute percentage 54%, N = 18.

_{g}.

^{−1}as an absolute error for the ag_olci_std values, which is less than 0.1 m

^{−1}, and 20% as a relative error for the values exceeding 0.1 m

^{−1}, we must reject more than a half of the total number of pairs (Figure 3a). The main reason for the appearance of poor points is unsatisfactory atmospheric correction. In Section 3.2, we considered this problem in detail. As a parameter for analysis of the atmospheric correction errors, we used the values of the remote sensing reflectance R

_{rs}. We built the dependences of the RMSE values on the time difference and from the solar zenith angle. Analysis of these dependencies allowed us to present the reasonable limitations of using the satellite R

_{rs}spectra: RMSE ≤ 0.001. This value is not a strict requirement; at present, we consider it a reference point.

## 5. Conclusions

_{g}, directly measured by the ICAM spectrophotometer, has shown that the real uncertainties are quite different from the calculated errors, ADG443_NN_err. The former can exceed 100%, while the latter, even for a single OLCI file, is ~10%. The main reason is the unsatisfactory atmospheric correction.

_{rs}directly measured above the sea surface as a reference. The standard error RMSE increases weakly with increasing time difference between the in situ measurement and the satellite overpass and the solar zenith angle. However, the RMSE values can be about 0.001 even with a time difference of more than 20 h and solar zenith angles greater than 70°. Conversely, errors exceeding 0.004 can be detected with a time difference of fewer than five hours and angles less than 50°. The other factors that affected RMSE are the azimuth angle difference and the surface water layer condition.

^{2}= 0.670, the regression error s

_{regr}= 0.010 m

^{−1}, and the relative error (variation coefficient) RE = 17%. For the Kara Sea, the absorption coefficient values were calculated with the C2RCC processor: R

^{2}= 0.624, s

_{reg}= 0.045 m

^{−1}, RE = 30%. Statistical support for the derived equations is insufficient, and it is too early to present the derived equations for practical use.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Perovich, D.K.; Nghiem, S.V.; Markus, T.; Schweiger, A.J. Seasonal evolution and interannual variability of the local solar energy absorbed by the Arctic sea ice–ocean system. J. Geophys. Res.
**2007**, 112, C03005. [Google Scholar] [CrossRef] - Perovich, D.K.; Jones, K.F.; Light, B.; Eicken, H.; Markus, T.; Stroeve, J.; Lindsay, R. Solar partitioning in a changing Arctic sea-ice cover. Ann. Glaciol.
**2011**, 52, 192–196. [Google Scholar] [CrossRef] [Green Version] - Kopelevich, O.V.; Sahling, I.V.; Vazyulya, S.V.; Glukhovets, D.I.; Sheberstov, S.V.; Burenkov, V.I.; Karalli, P.G.; Yushmanova, A.V. Bio-Optical Characteristics of the Seas, Surrounding the Western Part of Russia, from Data of the Satellite Ocean Color Scanners of 1998–2017; VASh FORMAT, OOO: Moscow, Russia, 2018. [Google Scholar]
- Kopelevich, O.V.; Sahling, I.V.; Vazyulya, S.V.; Glukhovets, D.I.; Sheberstov, S.V.; Burenkov, V.I.; Karalli, P.G.; Yushmanova, A.V. Electronic Atlas. Bio-Optical Characteristics of the Seas, Surrounding the Western Part of Russia, from Data of the Satellite Ocean Color Scanners of 1998–2018. Available online: http://optics.ocean.ru/ (accessed on 31 July 2020).
- Kopelevich, O.V.; Sheberstov, S.V.; Burenkov, V.I.; Vazyulya, S.V.; Likhacheva, M.V. Assessment of underwater irradiance and absorption of solar radiation at water column from satellite data. In Remote Sensing, Laser Probing, and Imagery in Natural Waters, edited by Iosif M. Levin, Gary D. Gilbert, Charles C. Trees, Proceeding of SPIE Vol.6615; SPIE: Bellingham, WA, USA, 2007; p. 661507. [Google Scholar]
- Amon, R.M.W. The role of dissolved organic matter for the organic carbon cycle in the Arctic Ocean. In The Organic Carbon Cycle in the Arctic Ocean; Stein, R., MacDonald, R., Eds.; Springer: Berlin, Germany, 2003; pp. 83–99. [Google Scholar] [CrossRef]
- Miller, W.L.; Moran, M.; Sheldon, W.M.; Zepp, R.G.; Opsahl, S. Determination of apparent quantum yield spectra for the formation of biologically labile photoproducts. Limnol. Oceanogr.
**2002**, 47, 343–352. [Google Scholar] [CrossRef] - Pugach, S.P.; Pipko, I.I.; Shakhova, N.E.; Shirshin, E.A.; Perminova, I.V.; Gustafsson, Ö.; Bondur, V.G.; Ruban, A.S.; Semiletov, I.P. Dissolved organic matter and its optical characteristics in the Laptev and East Siberian seas: Spatial distribution and interannual variability (2003–2011). Ocean Sci.
**2018**, 14, 87. [Google Scholar] [CrossRef] [Green Version] - Matsuoka, A.; Ortega-Retuerta, E.; Bricaud, A.; Arrigo, K.R.; Babin, M. Characteristics of colored dissolved organic matter (CDOM) in the Western Arctic Ocean: Relationships with microbial activities. Deep Sea Res. Part II Top. Stud. Oceanogr.
**2015**, 118, 44–52. [Google Scholar] [CrossRef] [Green Version] - Gonçalves-Araujo, R.; Stedmon, C.A.; Heim, B.; Dubinenkov, I.; Kraberg, A.; Moiseev, D.; Bracher, A. From fresh to marine waters: Characterization and fate of dissolved organic matter in the Lena River Delta region, Siberia. Front. Mar. Sci.
**2015**, 2, 108. [Google Scholar] [CrossRef] [Green Version] - Matsuoka, A.; Boss, E.; Babin, M.; Karp-Boss, L.; Hafez, M.; Chekalyuk, A.; Proctor, C.W.; Werdell, P.J.; Bricaud, A. Pan-Arctic optical characteristics of colored dissolved organic matter: Tracing dissolved organic carbon in changing Arctic waters using satellite ocean color data. Remote Sens. Environ.
**2017**, 200, 89–101. [Google Scholar] [CrossRef] - Fichot, C.G.; Kaiser, K.; Hooker, S.B.; Amon, R.M.W.; Babin, M.; Bélanger, S.; Walker, S.; Benner, R. Pan-Arctic distributions of continental runoff in the Arctic Ocean. Sci. Rep.
**2013**, 3, 1053. [Google Scholar] [CrossRef] [Green Version] - Matsuoka, A.; Bricaud, A.; Benner, R.; Para, J.; Sempéré, R.; Prieur, L.; Bélanger, S.; Babin, M. Tracing the transport of colored dissolved organic matter in water masses of the Southern Beaufort Sea: Relationship with hydrographic characteristics. Biogeosciences
**2012**, 9, 925. [Google Scholar] [CrossRef] [Green Version] - Brezonik, P.; Menken, K.D.; Bauer, M. Landsat-based remote sensing of lake water quality characteristics, including chlorophyll and colored dissolved organic matter (CDOM). Lake Reserv. Manag.
**2005**, 21, 373–382. [Google Scholar] [CrossRef] - Aiken, G.R.; Gilmour, C.C.; Krabbenhoft, D.P.; Orem, W. Dissolved organic matter in the Florida Everglades: Implications for ecosystem restoration. Crit. Rev. Environ. Sci. Technol.
**2011**, 41, 217–248. [Google Scholar] [CrossRef] - Kothawala, D. Dissolved Organic Matter in Inland Waters and Its Impacts on Drinking Water Quality. 2019. Available online: https://kalendarium.uu.se/event/?eventId=43238 (accessed on 30 July 2020).
- Kuznetsova, O.A.; Kopelevich, O.V.; Sheberstov, S.V.; Burenkov, V.I.; Mosharov, S.A.; Demidov, A.B. Assessment of chlorophyll concentration in the Kara Sea based on the data of satellite scanner MODIS–AQUA. Curr. Probl. Remote Sens. Earth Space
**2013**, 5, 21–31. [Google Scholar] - Glukhovets, D.I.; Goldin, Y.A. Research of the relationship between salinity and yellow substance fluorescence in the Kara Sea. Fundamentalnaya i Prikladnaya Gidrofizika
**2018**, 11, 34–39. [Google Scholar] [CrossRef] - Kubryakov, A.; Stanichny, S.; Zatsepin, A. River plume dynamics in the Kara Sea from altimetry-based lagrangian model, satellite salinity and chlorophyll data. Remote Sens. Environ.
**2016**, 176, 177–187. [Google Scholar] [CrossRef] - Zavialov, P.O.; Izhitskiy, A.S.; Osadchiev, A.A.; Pelevin, V.V.; Grabovskiy, A.B. The structure of thermohaline and bio-optical fields in the surface layer of the Kara Sea in September 2011. Oceanology
**2015**, 55, 461–471. [Google Scholar] [CrossRef] - Burenkov, V.I.; Goldin, Y.A.; Artem’ev, V.A.; Sheberstov, S.V. Optical characteristics of the Kara Sea derived from shipborne and satellite data. Oceanology
**2010**, 50, 675–687. [Google Scholar] [CrossRef] - Lee, Z.; Carder, K.; Arnone, R. Deriving inherent optical properties from water color: A multiband quasi-analytical algorithm for optically deep waters. Appl. Opt.
**2002**, 41, 5755–5772. [Google Scholar] [CrossRef] - Vazyulya, S.V.; Kopelevich, O.V.; Sheberstov, S.V.; Artemiev, V.A. Satellite estimation of the coefficients of CDOM absorption and diffuse attenuation in the White and Kara seas. Curr. Probl. Remote Sens. Earth Space
**2014**, 11, 31–41. [Google Scholar] - Konik, M.; Kowalczuk, P.; Zabłocka, M.; Makarewicz, A.; Meler, J.; Zdun, A.; Darecki, M. Empirical Relationships between Remote-Sensing Reflectance and Selected Inherent Optical Properties in Nordic Sea Surface Waters for the MODIS and OLCI Ocean Colour Sensors. Remote Sens.
**2020**, 12, 2774. [Google Scholar] [CrossRef] - Lamquin, N.; Clerc, S.; Bourg, L.; Donlon, C. OLCI A/B Tandem Phase Analysis, Part 1: Level 1 Homogenisation and Harmonisation. Remote Sens.
**2020**, 12, 1804. [Google Scholar] [CrossRef] - Lamquin, N.; Déru, A.; Clerc, S.; Bourg, L.; Donlon, C. OLCI A/B Tandem Phase Analysis, Part 2: Benefits of Sensors Harmonisation for Level 2 Products. Remote Sens.
**2020**, 12, 2702. [Google Scholar] [CrossRef] - Clerc, S.; Donlon, C.; Borde, F.; Lamquin, N.; Hunt, S.E.; Smith, D.; McMillan, M.; Mittaz, J.; Woolliams, E.; Hammond, M.; et al. Benefits and Lessons Learned from the Sentinel-3 Tandem Phase. Remote Sens.
**2020**, 12, 2668. [Google Scholar] [CrossRef] - Mograne, M.A.; Jamet, C.; Loisel, H.; Vantrepotte, V.; Mériaux, X.; Cauvin, A. Evaluation of Five Atmospheric Correction Algorithms over French Optically-Complex Waters for the Sentinel-3A OLCI Ocean Color Sensor. Remote Sens.
**2019**, 11, 668. [Google Scholar] [CrossRef] [Green Version] - Kyryliuk, D.; Kratzer, S. Evaluation of Sentinel-3A OLCI Products Derived Using the Case-2 Regional CoastColour Processor over the Baltic Sea. Sensors
**2019**, 19, 3609. [Google Scholar] [CrossRef] [Green Version] - Pogosyan, S.I.; Durgaryan, A.M.; Konyukhov, I.V.; Chivkunova, O.B.; Merzlyak, M.N. Absorption spectroscopy of microalgae, cyanobacteria, and dissolved organic matter: Measurements in an integrating sphere cavity. Oceanology
**2009**, 49, 866–871. [Google Scholar] [CrossRef] - Glukhovets, D.I.; Sheberstov, S.V.; Kopelevich, O.V.; Zaytseva, A.F.; Pogosyan, S.I. Measuring the sea water absorption factor using integrating sphere. Light Eng.
**2018**, 26, 120–126. [Google Scholar] [CrossRef] - Pope, R.M.; Fry, E.S. Absorption spectrum (380–700 nm) of pure water. I. Integrating cavity measurements. Appl. Opt.
**1997**, 36, 8710–8723. [Google Scholar] [CrossRef] - Yushmanova, A.V.; Kopelevich, O.V.; Vazyulya, S.V.; Sahling, I.V. Inter-annual variability of the seawater light absorption in surface layer of the northeastern Black Sea in connection with hydrometeorological factors. J. Mar. Sci. Eng.
**2019**, 7, 326. [Google Scholar] [CrossRef] [Green Version] - Artemiev, V.A.; Burenkov, V.I.; Vortman, M.I.; Grigoriev, A.V.; Kopelevich, O.V.; Khrapko, A.N. Sea-truth measurements of ocean color: A new floating spectroradiometer and its metrology. Oceanology
**2000**, 40, 139–145. [Google Scholar] - Li, M.E.; Shibanov, E.B.; Martynov, O.V.; Korchemkina, E.N. Determination of the impurities concentration in the sea water on the range of the rising radiation brightness. Morskoi Gidrofizicheskii Zhurnal
**2015**, 186, 17–33. [Google Scholar] - Gordon, H.R.; McCluney, W.R. Estimation of the depth of sunlight penetration in the sea for remote sensing. Appl. Opt.
**1975**, 14, 413–416. [Google Scholar] [CrossRef] [PubMed] - Goldin, Y.A.; Glukhovets, D.I.; Gureev, B.A.; Grigoriev, A.V.; Artemiev, V.A. Shipboard flow-through complex for measuring bio-optical and hydrological seawater characteristics. Oceanology
**2020**, 60, 713–720. [Google Scholar] - Sheberstov, S.V. A system of batch processing of oceanological satellite data. Curr. Probl. Remote Sens. Earth Space
**2015**, 12, 154–161. [Google Scholar] - Doerffer, R.; Schiller, H. The MERIS case 2 water algorithm. Int. J. Remote Sens.
**2007**, 28, 517–535. [Google Scholar] [CrossRef] - Brockmann, C.; Doerffer, R.; Peters, M.; Stelzer, K.; Embacher, S.; Ruescas, A. Evolution of the C2RCC neural network for Sentinel 2 and 3 for the retrieval of ocean colour products in normal and extreme optically complex waters. In Proceedings of the Living Planet Symposium, Prague, Czech Republic, 9–13 May 2016. ESA SP-740. [Google Scholar]
- Werdell, P.J.; Franz, B.A.; Bailey, S.W.; Feldman, G.C.; Boss, E.; Brando, V.E.; Mangin, A. Generalized ocean color inversion model for retrieving marine inherent optical properties. Appl. Opt.
**2013**, 52, 2019–2037. [Google Scholar] [CrossRef] - Werdell, P.J.; McKinna, L.I.W.; Boss, E.; Ackleson, S.G.; Craig, S.E.; Gregg, W.W.; Lee, Z.; Maritorena, S.; Roesler, C.S.; Rousseaux, C.S.; et al. An overview of approaches and challenges for retrieving marine inherent optical properties from ocean color remote sensing. Prog. Oceanogr.
**2018**, 160, 186–212. [Google Scholar] [CrossRef] - Gordon, H.R.; Brown, O.B.; Evans, R.H.; Brown, J.W.; Smith, R.C.; Baker, K.S.; Clark, D.K. A semianalytical radiance model of ocean color. J. Geophys. Res.
**1988**, 93, 10909–10924. [Google Scholar] [CrossRef] - Lee, Z.; Carder, K.L.; Mobley, C.D.; Steward, R.G.; Patch, J.S. Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization. Appl. Opt.
**1999**, 38, 3831–3843. [Google Scholar] [CrossRef] [Green Version] - Gordon, H.R.; Morel, A. Remote assessing of ocean color for interpretation of satellite visible imagery: A review. Lect. Notes Coast. Estuar. Stud.
**1983**, 4, 44. [Google Scholar] - Smith, R.C.; Baker, K.S. Optical properties of the clearest natural waters. Appl. Opt.
**1981**, 20, 177–184. [Google Scholar] [CrossRef] - Demidov, A.B.; Kopelevich, O.V.; Mosharov, S.A.; Sheberstov, S.V.; Vazyulya, S.V. Modelling Kara Sea phytoplankton primary production: Development and skill assessment of regional algorithms. J. Sea Res.
**2017**, 125, 1–17. [Google Scholar] [CrossRef] - Gordon, H.R. Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water? Limnol. Oceanogr.
**1989**, 34, 1389–1409. [Google Scholar] [CrossRef] - Burenkov, V.I.; Ershova, S.V.; Kopelevich, O.V.; Sheberstov, S.V.; Shevchenko, V.P. An Estimate of the Distribution of Suspended Matter in the Barents Sea Waters on the Basis of the SeaWiFS Satellite Ocean Color Scanner. Oceanology
**2001**, 41, 622–628. [Google Scholar] - Glukhovets, D.I.; Goldin, Y.A. Surface desalinated layer distribution in the Kara Sea determined by shipboard and satellite data. Oceanologia
**2020**, 62, 364–373. [Google Scholar] [CrossRef] - Zatsepin, A.G.; Zavialov, P.O.; Kremenetskiy, V.V.; Poyarkov, S.G.; Soloviev, D.M. The upper desalinated layer in the Kara Sea. Oceanology
**2010**, 50, 657–667. [Google Scholar] [CrossRef] - Lee, Z.-P.; Du, K.-P.; Arnone, R. A model for the diffuse attenuation coefficient of downwelling irradiance. J. Geophys. Res.
**2005**, 110, 02016. [Google Scholar] [CrossRef] - Kopelevich, O.; Sheberstov, S.; Vazyulya, S. Effect of a Coccolithophore Bloom on the Underwater Light Field and the Albedo of the Water Column. J. Mar. Sci. Eng.
**2020**, 8, 456. [Google Scholar] [CrossRef]

**Figure 1.**Location of the selected stations: (

**a**)—AMK-65 (blue), AMK-68 (red), AMK-71 (black), AMK-76 (green), (

**b**)—AMK-72 (magenta).

**Figure 2.**Distributions of the number of days with data per bin (

**a**,

**c**,

**e**; scale 1) and cloud coverage according to OLCI_CLOUD flag data (

**b**,

**d**,

**f**; scale 2). AMK-65: (

**a**,

**b**); AMK-68: (

**c**,

**d**); AMK-71: (

**e**,

**f**), AMK-72: (

**g**,

**h**), AMK-76: (

**i**,

**j**).

**Figure 3.**Top: scatter plots of the in situ measured and satellite derived a

_{g}(443) values: (

**a**)—complete dataset; (

**b**)—river estuary data excluded. The Barents Sea points are shown in orange, the Kara and Laptev seas are shown in turquoise. Various cruises are represented by symbols. The dotted line is the correlation across all data. Bottom: the standard product errors ADG_443_NN_err in comparison with the ADG_443_NN values for OLCI Level 2 file S3A_OL_2_WFR_20170814T091713; (

**c**) complete dataset; (

**d**) the same in the enlarged scale. The Barents Sea, 14 August 2017.

**Figure 4.**Comparison of the absorption values calculated from the R

_{rs}measurements by the floating (or deck) spectroradiometer using different algorithms with the values measured by the ICAM device for 13 stations. The solid line is 1:1 dependency. (

**a**)—RSA algorithm (RMSE = 0.042, RE = 40%); (

**b**) QAA (RMSE = 0.04, RE = 38%); (

**c**)—GIOP (RMSE = 0.045, RE = 36%) (see Section 2.3).

**Figure 5.**Regressions of satellite values a

_{g}_olci_std (

**a**) and a

_{g}_olci_C2RCC (

**b**) vs. measured values a

_{g}_icam. The dotted lines represent the correlations for the corresponding seas.

**Figure 6.**The ADG_443_NN distributions based on standard OLCI data a

_{g}_olci_std (

**a**,

**c**) and corrected ag_corr data (

**b**,

**d**) for the AMK-65 (

**a**,

**b**) and AMK-68 (

**c**,

**d**) cruises.

**Figure 7.**Dependences of the average RMSE of the R

_{rs}values on the absolute difference between the time of the in situ and the satellite measurements (

**A**) and on the zenith angle of the sun (

**B**). The blue lines show the trend assessment.

**Figure 8.**R

_{rs}(λ) values obtained from the shipboard (black line) and satellite measurements (colored lines: red—OLCI BAC, orange—OLCI AAC, blue—MODIS Aqua, brown—MODIS Terra, green—VIIRS SNPP, purple—VIIRS NOAA-20). The grey color shows data for which the RMSE values obtained by comparing shipboard and satellite data were greater than 0.001. Station 6240, Kara Sea, 14 July 2019.

**Figure 9.**RMSE (top row) and maximum error (bottom row) values obtained when comparing shipboard and satellite data depending on the sun zenith angle (left column) and the time interval between data (right column). The colors of the circles correspond to the colors of the lines in Figure 1. The gray circles show the data for which the RMSE values exceed 0.001. The red dotted line on the right side of the figure corresponds to RMSE = 0.001. Station 6240, Kara Sea, 14 July 2019.

**Figure 10.**Spatial distribution of the beam attenuation coefficient c measured in the Kara Sea on 14 July 2019. The dotted line shows the position of station 6240.

**Figure 11.**Average RMSE values obtained by comparing shipboard and satellite data for 15 ship stations and 27 OLCI spectra calculated using the C2RCC processor, depending on the solar zenith angle (left), observation zenith angle (center), and the absolute values of azimuth angle differences (right). Gray circles indicate the cloud risk flag, red asterisks—glint risk, black crosses—any other flag, colored circles—data without flags.

**Figure 12.**Comparison of the particle backscattering coefficient b

_{bp}(555) with the beam attenuation coefficient c(530) for the Barents Sea. Red circles—SRA algorithm, blue—QAA algorithm, green—GIOP algorithm. The black line is a correlation based on SRA, black dotted line—correlation based on QAA data, dash-dotted line – based on GIOP data.

**Figure 13.**Scatterplots of in situ b

_{bp}(555) data and data from satellite calculations for the Barents Sea (

**a**), the Kara Sea, and the Laptev Sea (

**b**). Red circles—RSA algorithm for the Level 2 data, red crosses—RSA_C2RCC algorithm; blue circles—QAA algorithm for the Level 2 data, blue crosses—QAA_C2RCC algorithm; green circles—GIOP algorithm for the Level 2 data, green crosses—GIOP _C2RCC algorithm; yellow circles—SRA. Dashed lines—1: 1 match.

**Figure 14.**Comparison of the yellow substance absorption coefficient a

_{g}(443) and the diffuse attenuation coefficient K

_{d}(443) measured in situ: (

**A**) for the Barents and Norwegian seas (AMK 68); (

**B**) the Kara Sea (AMK 72 and 76). The solid black line is the regression line for all AMK 68 data; blue dotted line—the Barents Sea, AMK 68; red dotted line—the Norwegian Sea, AMK 68; purple dotted line—the Kara Sea, AMK 72 and 76. Green circles show the stations with coccolithophore blooms.

**Figure 15.**Scatterplot of the diffuse attenuation coefficient K

_{d}for the wavelengths 443 (

**A**) and 490 (

**B**) nm calculated by formula [52], and from in situ measurements of underwater irradiance at 18 stations in the Barents Sea (AMK 68). Solid black line—perfect correspondence 1:1; dotted black line—linear regression. Green circles show the stations with coccolithophore blooms.

**Figure 16.**Scatterplot of the diffuse attenuation coefficient K

_{d}(490) values calculated from field measurements and satellite data (standard algorithm, nearest pixel): (

**A**) OLCI; (

**B**) MODIS; (

**C**) VIIRS. Solid black line—perfect correspondence 1:1; dotted blue line—the regression line for the Barents Sea, AMK 68; dotted red line—the Kara Sea, AMK 72, and 76. Green circles show the stations with coccolithophore blooms.

Cruise and Vessel | Region | Measurement Period | Number of Stations |
---|---|---|---|

AMK-65 | Norwegian and Barents Seas | 29 June–9 July 2016 | 14 |

AMK-68 | North Atlantic (60°N section), Barents Sea | 30 June–7 August 2017 | 72 |

AMK-71 | North Atlantic (60°N section), Norwegian and Barents seas | 28 June–13 August 2018 | 75 |

AMK-72 | Kara Sea and Laptev Sea | 20 August–16 September 2018 | 105 |

AMK-76 | Kara Sea | 7–28 July 2019 | 47 |

**Table 2.**Regression parameters between the absorption values derived from satellite and in situ data for various algorithms and neural networks (NN) OLCI. N is the number of pairs to calculate the regression, R

^{2}is the coefficient of determination.

MODIS | VIIRS | OLCI | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Aqua | Terra | SNPP | NOAA-20 | Standard | C2RCC | |||||||

N * | R^{2} | N | R^{2} | N | R^{2} | N | R^{2} | N | R^{2} | N | R^{2} | |

RSA | 21 | 0.52 | 23 | 0.44 | 23 | 0.38 | 12 | 0.29 | 18 | 0.04 | 14 | 0.24 |

QAA | 21 | 0.27 | 15 | 0.03 | 20 | 0.55 | 8 | 0.13 | 18 | 0 | 19 | 0.47 |

GIOP | 24 | 0.02 | 30 | 0.2 | 30 | 0.08 | 13 | 0.02 | 19 | 0.08 | 19 | 0.33 |

NN | 19 | 0.04 | 19 | 0.03 |

^{2}, the coefficient of determination.

Sea | N | Regression Equation | <X> | <Y> | R^{2} | S_{regr} | RE *, % |
---|---|---|---|---|---|---|---|

OLCI_standard vs. a_{g}_ICAM | |||||||

Barents | 10 | Y = 1.48 X − 0.008 | 0.06 | 0.08 | 0.670 | 0.023 | 28 |

Kara | 9 | Y = 0.037 X + 0.032 | 0.147 | 0.038 | 0.035 | insignificant | - |

OLCI_C2RCC vs. a_{g}_ICAM | |||||||

Barents | 10 | Y = 1.19 X − 0.017 | 0.06 | 0.054 | 0.430 | 0.03 | 56 |

Kara | 9 | Y = 0.178 X + 0.007 | 0.147 | 0.033 | 0.624 | 0.012 | 38 |

Sea | N | Regression Equation | <X> | <Y> | R^{2} | s_regr. | RE, % |
---|---|---|---|---|---|---|---|

a_{g}_corr vs. OLCI_standard | |||||||

Barents | 10 | Y = 0.67 X + 0.020 | 0.06 | 0.06 | 0.670 | 0.010 | 17 |

a_{g}_corr vs. OLCI_C2RCC | |||||||

Barents | 10 | Y = 0.43 X + 0.034 | 0.06 | 0.06 | 0.430 | 0.011 | 18 |

Kara | 9 | Y = 0.62 X + 0.055 | 0.147 | 0.147 | 0.624 | 0.045 | 30 |

**Table 5.**The total number of satellite data points for 15 stations with shipboard reflectance measurements and their number with RMSE ≤ 0.001. AAC—Alternative Atmospheric Correction, BAC—Baseline Atmospheric Correction.

Sensor | All Data | RMSE ≤ 0.001 |
---|---|---|

OLCI BAC | 27 | 3 |

OLCI AAC | 27 | 13 |

MODIS Aqua | 36 | 16 |

MODIS Terra | 40 | 13 |

VIIRS SNPP | 37 | 14 |

VIIRS NOAA-20 | 22 | 18 |

**Table 6.**The statistical parameters of the regression bbp(555) (Y) vs. c(530) (X) with different algorithms.

Algorithm | N | Regression | <X> | <Y> | R^{2} | RMSE, m^{−1} | RE, % |
---|---|---|---|---|---|---|---|

SRA | 31 | Y = 0.01 X − 0.004 | 0.78 | 0.01 | 0.96 | 0.0020 | 29 |

QAA | 31 | Y = 0.014 X − 0.005 | 0.78 | 0.01 | 0.95 | 0.0026 | 40 |

GIOP | 29 | Y = 0.02 X − 0.006 | 0.75 | 0.005 | 0.94 | 0.0031 | 51 |

^{2}—determination coefficient, RMSE—Root Mean Square Error, RE—average relative error.

**Table 7.**Regression parameters between b

_{bp}(555) from satellite (Y) and in situ (X) data for different algorithms (only cases where the values of the coefficient of determination exceed 0.3).

Algorithm X | Algorithm Y | Seas | N | Regression | <X> | <Y> | R^{2} | RMSE, m^{−1} | RE, % |
---|---|---|---|---|---|---|---|---|---|

QAA | Standard | Barents | 11 | Y = 1.01 X + 0.01 | 0.02 | 0.03 | 0.87 | 0.0072 | 28 |

QAA | C2RCC | Barents | 11 | Y = 0.21 X + 0.002 | 0.02 | 0.005 | 0.61 | 0.0031 | 54 |

QAA | C2RCC | Kara and Laptev | 9 | Y = −0.11 X + 0.001 | 0.003 | 0.0003 | 0.33 | 0.0002 | 56 |

GIOP | Standard | Barents | 11 | Y = 0.89 X + 0.01 | 0.02 | 0.02 | 0.92 | 0.0059 | 26 |

GIOP | C2RCC | Barents | 11 | Y = 0.52 X + 0.01 | 0.02 | 0.02 | 0.56 | 0.0102 | 54 |

SRA | SRA | Barents | 11 | Y = 0.86 X + 0.01 | 0.02 | 0.03 | 0.75 | 0.0084 | 32 |

**Table 8.**Regression parameters between values of a

_{g}and K

_{d}measured in situ at a wavelength of 443 nm.

Data Set | N | Regression Equation | R^{2} |
---|---|---|---|

Barents Sea, AMK 68 | 20 | a_{g} = 0.16 K_{d} ^{0.44} | 0.72 |

Norwegian Sea, AMK 68 | 10 | a_{g} = 0.18 K_{d} ^{0.46} | 0.21 |

all AMK 68 data | 30 | a_{g} = 0.16 K_{d} ^{0.44} | 0.56 |

Kara Sea, AMK 72 and 76 | 31 | a_{g} = 0.55 K_{d} ^{0.94} | 0.73 |

**Table 9.**Correspondence parameters between the K

_{d}(490) values obtained from field measurements (X) and satellite data (Y). Satellite data for the nearest pixel.

Data Set | Regression Equation | N * | R^{2} | <Y>/<X> | RMSE | RE |
---|---|---|---|---|---|---|

OLCI | ||||||

AMK 68 | Y = 0.61 X + 0.03 | 4 | 0.80 | 0.76 | 0.05 | 20% |

AMK 72 and 76 | Y = 0.31 X + 0.04 | 24 | 0.24 | 0.51 | 0.14 | 45% |

MODIS | ||||||

AMK 68 | Y = 0.25 X + 0.08 | 13 | 0.48 | 0.63 | 0.11 | 26% |

AMK 72 and 76 | Y = 0.25 X + 0.09 | 32 | 0.09 | 0.74 | 0.09 | 33% |

VIIRS | ||||||

AMK 68 | Y = 0.22 X + 0.07 | 7 | 0.91 | 0.55 | 0.13 | 36% |

AMK 72 and 76 | Y = 0.25 X + 0.06 | 49 | 0.31 | 0.58 | 0.14 | 47% |

^{2}, the coefficient of determination; <Y>/<X>, the ratio of the mean K

_{d}(490) values; RMSE, the root mean squared error, m

^{−1}; RE, the relative error.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Glukhovets, D.; Kopelevich, O.; Yushmanova, A.; Vazyulya, S.; Sheberstov, S.; Karalli, P.; Sahling, I.
Evaluation of the CDOM Absorption Coefficient in the Arctic Seas Based on Sentinel-3 OLCI Data. *Remote Sens.* **2020**, *12*, 3210.
https://doi.org/10.3390/rs12193210

**AMA Style**

Glukhovets D, Kopelevich O, Yushmanova A, Vazyulya S, Sheberstov S, Karalli P, Sahling I.
Evaluation of the CDOM Absorption Coefficient in the Arctic Seas Based on Sentinel-3 OLCI Data. *Remote Sensing*. 2020; 12(19):3210.
https://doi.org/10.3390/rs12193210

**Chicago/Turabian Style**

Glukhovets, Dmitry, Oleg Kopelevich, Anna Yushmanova, Svetlana Vazyulya, Sergey Sheberstov, Polina Karalli, and Inna Sahling.
2020. "Evaluation of the CDOM Absorption Coefficient in the Arctic Seas Based on Sentinel-3 OLCI Data" *Remote Sensing* 12, no. 19: 3210.
https://doi.org/10.3390/rs12193210