**Figure 1.**
The basic instruments for field measurements. Photos captured by A.V. Grigoriev (**A**–**D**,**F**) and D. I. Glukhovets (**E**), both from the Shirshov Institute of Oceanology (SIO RAS) used here with permission.

**Figure 1.**
The basic instruments for field measurements. Photos captured by A.V. Grigoriev (**A**–**D**,**F**) and D. I. Glukhovets (**E**), both from the Shirshov Institute of Oceanology (SIO RAS) used here with permission.

**Figure 2.**
The phase scattering function: (**A**) For the plated cell and coccolith; (**B**) For the non-coccolithophore particles in the Black Sea (red curve) and the Barents Sea (blue).

**Figure 2.**
The phase scattering function: (**A**) For the plated cell and coccolith; (**B**) For the non-coccolithophore particles in the Black Sea (red curve) and the Barents Sea (blue).

**Figure 3.**
Spectral values of the absorption coefficient (**A**,**B**) and the backscattering coefficient depending on the N_{coc} (10^{6} cell/L) concentration (**C**,**D**): A, C, the Black Sea; B, D, the Barents Sea. The curves 1 and 2 in Figures A and B relate to two values of the seawater absorption coefficient: A, a(440) = 0.09 m^{−1} and 0.53 m^{−1}, respectively; B, 0.18 and 0.53 m^{−1}, respectively.

**Figure 3.**
Spectral values of the absorption coefficient (**A**,**B**) and the backscattering coefficient depending on the N_{coc} (10^{6} cell/L) concentration (**C**,**D**): A, C, the Black Sea; B, D, the Barents Sea. The curves 1 and 2 in Figures A and B relate to two values of the seawater absorption coefficient: A, a(440) = 0.09 m^{−1} and 0.53 m^{−1}, respectively; B, 0.18 and 0.53 m^{−1}, respectively.

**Figure 4.**
Black Sea. The radiance distributions in the plane of the sun as a function of the viewing angle θ (the range of positive values of θ corresponds to the azimuthal viewing angle ϕ = 0°, the negative values ϕ = 180°; the downward radiance in the θ range of and −90° ÷ +90°, the upward radiances −180° ÷ (−90°) and 90° ÷ 180°). The left part shows the absorption a(440) = 0.09 m^{−1}, the right, a(440) = 0.53 m^{−1}. The numbers near the curves show the depth in meters. For θ_{0} = 25°, λ = 530 nm, wind speed 0 m/s.

**Figure 4.**
Black Sea. The radiance distributions in the plane of the sun as a function of the viewing angle θ (the range of positive values of θ corresponds to the azimuthal viewing angle ϕ = 0°, the negative values ϕ = 180°; the downward radiance in the θ range of and −90° ÷ +90°, the upward radiances −180° ÷ (−90°) and 90° ÷ 180°). The left part shows the absorption a(440) = 0.09 m^{−1}, the right, a(440) = 0.53 m^{−1}. The numbers near the curves show the depth in meters. For θ_{0} = 25°, λ = 530 nm, wind speed 0 m/s.

**Figure 5.**
Barents Sea. The same as in

Figure 4. (

**A**) N

_{coc} = 0 cell/L,

a(400) = 0.18 m

^{−1}; further respectively. (

**B**) 0, 0.53; (

**C**) 5 × 10

^{6}, 0.18; (

**D**) 5 × 10

^{6}, 0.53; (

**E**) 10

^{7}, 0.18; (

**F**) 10

^{7}, 0.53; θ

_{0} = 60°.

**Figure 5.**
Barents Sea. The same as in

Figure 4. (

**A**) N

_{coc} = 0 cell/L,

a(400) = 0.18 m

^{−1}; further respectively. (

**B**) 0, 0.53; (

**C**) 5 × 10

^{6}, 0.18; (

**D**) 5 × 10

^{6}, 0.53; (

**E**) 10

^{7}, 0.18; (

**F**) 10

^{7}, 0.53; θ

_{0} = 60°.

**Figure 6.**
Black Sea. The angular radiance distributions for different observation conditions. On the left, the solar zenith viewing angle θ

_{0} = 60°, on the right, overcast condition. All others are the same as in

Figure 4.

**Figure 6.**
Black Sea. The angular radiance distributions for different observation conditions. On the left, the solar zenith viewing angle θ

_{0} = 60°, on the right, overcast condition. All others are the same as in

Figure 4.

**Figure 7.**
Black Sea. Comparison of the radiance distributions for cases of smooth and rough surfaces;

a(440 ) = 0.09 m

^{−1}, θ

_{0} = 25°, λ = 530

HM,

N_{coc} = 5 10

^{6} cell/L. All others are the same as in

Figure 4.

**Figure 7.**
Black Sea. Comparison of the radiance distributions for cases of smooth and rough surfaces;

a(440 ) = 0.09 m

^{−1}, θ

_{0} = 25°, λ = 530

HM,

N_{coc} = 5 10

^{6} cell/L. All others are the same as in

Figure 4.

**Figure 8.**
Black Sea. The angular radiance distributions at 410 and 670 nm;

a(440) = 0.09 m

^{−1}, θ

_{0} = 25°, wind speed 0 m/s. All others are the same as in

Figure 4.

**Figure 8.**
Black Sea. The angular radiance distributions at 410 and 670 nm;

a(440) = 0.09 m

^{−1}, θ

_{0} = 25°, wind speed 0 m/s. All others are the same as in

Figure 4.

**Figure 9.**
The spectra of the radiance reflectance as a function of the concentration of coccolithophores for the Black Sea (**A**,**B**) and the Barents Sea (**C**,**D**); the values of the absorption coefficient a(440) equal A, 0.09 m^{−1}, B, 0.53 m^{−1}, C, 0.18 m^{−1}, D, 0.53 m^{−1}. For the Black Sea, solid lines, θ_{0} = 25°; dashed lines, θ_{0} = 60°; for the Barents Sea, solid lines, θ_{0} = 60°; dashed lines, overcast. The numbers near the curves indicate N_{coc}, 10^{6} cell/L.

**Figure 9.**
The spectra of the radiance reflectance as a function of the concentration of coccolithophores for the Black Sea (**A**,**B**) and the Barents Sea (**C**,**D**); the values of the absorption coefficient a(440) equal A, 0.09 m^{−1}, B, 0.53 m^{−1}, C, 0.18 m^{−1}, D, 0.53 m^{−1}. For the Black Sea, solid lines, θ_{0} = 25°; dashed lines, θ_{0} = 60°; for the Barents Sea, solid lines, θ_{0} = 60°; dashed lines, overcast. The numbers near the curves indicate N_{coc}, 10^{6} cell/L.

**Figure 10.**
The downward irradiance profiles calculated for the case of the Black Sea, λ = 500 nm and θ_{0} = 25°, depending on the coccolithophore concentration N_{coc} for the absorption coefficient a(440) = 0.09 m^{−1} (**a**) and 0.53 m^{−1} (**b**). The numbers near the curves indicate the N_{coc}, 10^{6} cell/L values.

**Figure 10.**
The downward irradiance profiles calculated for the case of the Black Sea, λ = 500 nm and θ_{0} = 25°, depending on the coccolithophore concentration N_{coc} for the absorption coefficient a(440) = 0.09 m^{−1} (**a**) and 0.53 m^{−1} (**b**). The numbers near the curves indicate the N_{coc}, 10^{6} cell/L values.

**Figure 11.**
The downward irradiance E_{d}(500) profiles for the case of the Black Sea and θ_{0} = 25°, depending on the coccolithophore concentration (N_{coc} = 0, blue curves; N_{coc} = 5 × 10^{6} cell/L, magenta) and the absorption coefficient (on (**a**) with a(440) = 0.09 m^{−1}, on (**b**), 0.53 m^{−1}). The solid line shows the results of numerical simulation, the dotted line shows calculation for K_{d} = K_{0} = const.

**Figure 11.**
The downward irradiance E_{d}(500) profiles for the case of the Black Sea and θ_{0} = 25°, depending on the coccolithophore concentration (N_{coc} = 0, blue curves; N_{coc} = 5 × 10^{6} cell/L, magenta) and the absorption coefficient (on (**a**) with a(440) = 0.09 m^{−1}, on (**b**), 0.53 m^{−1}). The solid line shows the results of numerical simulation, the dotted line shows calculation for K_{d} = K_{0} = const.

**Figure 12.**
The results of model simulation of the diffuse attenuation coefficient <K> for the photic layer as a function of N_{coc} (10^{6} cell/L) and the absorption coefficient a(440). The cases (**A**,**B**) are calculated for the Black Sea and θ_{0} = 25°; (**C**,**D**) For the Barents Sea and θ_{0} = 60°.

**Figure 12.**
The results of model simulation of the diffuse attenuation coefficient <K> for the photic layer as a function of N_{coc} (10^{6} cell/L) and the absorption coefficient a(440). The cases (**A**,**B**) are calculated for the Black Sea and θ_{0} = 25°; (**C**,**D**) For the Barents Sea and θ_{0} = 60°.

**Figure 13.**
Functions ρ(λ) according to Equations (7)–(10). Red line, Equation (7); Green, Equation (8); light blue, Equation (9); Blue, Equation (10).

**Figure 13.**
Functions ρ(λ) according to Equations (7)–(10). Red line, Equation (7); Green, Equation (8); light blue, Equation (9); Blue, Equation (10).

**Figure 14.**
Relative errors of Equations (7)–(10), depending on the parameter

u, taking into account the “non-coccolithophore” particles (dashed lines) and without it (solid lines). The color of the curves is the same as in

Figure 13.

**Figure 14.**
Relative errors of Equations (7)–(10), depending on the parameter

u, taking into account the “non-coccolithophore” particles (dashed lines) and without it (solid lines). The color of the curves is the same as in

Figure 13.

**Figure 15.**
Spectral values of ρ(λ) obtained for

N_{coc} = 10

^{7} cell/L by numerical simulation (black curves) and by using approximate formulas (the color of the curves corresponds to

Figure 13), in comparison with parameter

u (dashed purple lines and right axis). (

**A**) Black Sea,

a(440) = 0.09 m

^{−1}, θ

_{0} = 25°; (

**B**) Barents Sea,

a(440) = 0.18 m

^{−1}, θ

_{0} = 60°.

**Figure 15.**
Spectral values of ρ(λ) obtained for

N_{coc} = 10

^{7} cell/L by numerical simulation (black curves) and by using approximate formulas (the color of the curves corresponds to

Figure 13), in comparison with parameter

u (dashed purple lines and right axis). (

**A**) Black Sea,

a(440) = 0.09 m

^{−1}, θ

_{0} = 25°; (

**B**) Barents Sea,

a(440) = 0.18 m

^{−1}, θ

_{0} = 60°.

**Figure 16.**
Spectral values of the diffuse attenuation coefficient K_{d} in the Black Sea, θ_{0} = 25°, N_{coc} = 10^{7} cell/L (red curves) and N_{coc} = 0 (blue curves), a(440) = 0.09 m^{−1} (left column) and 0.53 m^{−1} (right column). The cases (**A**,**B**) are calculated for K_{0}, the all others for <K>; solid lines, by numerical calculations; dashed lines, with the approximated Equations; (**A,B**) and (**E**,**F)**, Equation (11), (**C**,**D**), Equation (12), (**G**,**H)**, Equation (13).

**Figure 16.**
Spectral values of the diffuse attenuation coefficient K_{d} in the Black Sea, θ_{0} = 25°, N_{coc} = 10^{7} cell/L (red curves) and N_{coc} = 0 (blue curves), a(440) = 0.09 m^{−1} (left column) and 0.53 m^{−1} (right column). The cases (**A**,**B**) are calculated for K_{0}, the all others for <K>; solid lines, by numerical calculations; dashed lines, with the approximated Equations; (**A,B**) and (**E**,**F)**, Equation (11), (**C**,**D**), Equation (12), (**G**,**H)**, Equation (13).

**Figure 17.**
Spectral values of the diffuse attenuation coefficient <K> depending on the N_{coc} (10^{6} cell/L), clear sky, θ_{0} = 60°. Solid lines, numerical simulation; dashed curves, the approximate formulas. (**A**,**C**), ICAM absorption a(440) = 0.18 m^{−1}; (**B**,**D**), the modeling absorption a(440) = 0.53 m^{−1}. (**A**,**B**), Equation (12); **C**, **D**, Equation (13).

**Figure 17.**
Spectral values of the diffuse attenuation coefficient <K> depending on the N_{coc} (10^{6} cell/L), clear sky, θ_{0} = 60°. Solid lines, numerical simulation; dashed curves, the approximate formulas. (**A**,**C**), ICAM absorption a(440) = 0.18 m^{−1}; (**B**,**D**), the modeling absorption a(440) = 0.53 m^{−1}. (**A**,**B**), Equation (12); **C**, **D**, Equation (13).

**Figure 18.**
Comparison between the radiance calculation results by Monte Carlo and discrete ordinate methods. Coccolithophore concentration 5⋅10^{6} cell/L, wavelength 410 nm, depths 0^{−} and 4 m. Red and blue lines present the Monte Carlo results; black and green, matrix operator method.

**Figure 18.**
Comparison between the radiance calculation results by Monte Carlo and discrete ordinate methods. Coccolithophore concentration 5⋅10^{6} cell/L, wavelength 410 nm, depths 0^{−} and 4 m. Red and blue lines present the Monte Carlo results; black and green, matrix operator method.

**Table 1.**
Measured and derived parameters ^{1} for modeling.

**Table 1.**
Measured and derived parameters ^{1} for modeling.

**Seawater Optical**
**Parameters** | absorption coefficients: seawater—a(λ), filtrate—a_{f}(λ), |

CDOM—ag(λ) = af(λ)−aw(λ), particulate—ap(λ); |

Beam attenuation coefficient—c(530); |

Scattering coefficient—b(530) = c(530)−a(530); |

Backscattering coefficient—b_{b}(λ) from ρ(λ); |

b(λ), β(λ), P(λ)—using model [40,41,42,43] |

**Coccolithophore**
**Parameters** | plated cell and coccolith concentration N_{coc} and N_{lith}—from direct determination or by setting for model; |

Optical characteristics—from [4,44]. |

**Non-coccolithophore Parameters** | particle scattering coefficients b_{p}(λ), β_{p}(λ), P_{p}(λ)—using model [40,41,42,43]; |

absorption coefficient from ICAM measurements as a(λ)−a_{w}(λ) or by setting for model; |

**Table 2.**
Set of optical characteristics * for the modeling.

**Table 2.**
Set of optical characteristics * for the modeling.

Input Parameters | Optical Characteristics |
---|

N_{coc} | a(440) | b(440) | ω_{0}(440) | b(555) | b_{b}(555) | ω_{0}(555) | ${\tilde{\mathit{b}}}_{\mathbf{b}}\left(555\right)$ | <cos> |
---|

**Black Sea** |

**0** | 0.09 | 0.60 | 0.87 | 0.48 | 0.008 | 0.864 | 0.017 | 0.922 |

**0** | 0.53 | 0.60 | 0.531 | 0.48 | 0.008 | 0.748 | 0.017 | 0.922 |

**5** | 0.09 | 3.82 | 0.977 | 2.81 | 0.075 | 0.974 | 0.027 | 0.895 |

**5** | 0.53 | 3.78 | 0.877 | 2.81 | 0.075 | 0.945 | 0.027 | 0.895 |

**10** | 0.09 | 6.83 | 0.987 | 5.13 | 0.141 | 0.985 | 0.027 | 0.892 |

**10** | 0.53 | 6.93 | 0.929 | 5.13 | 0.141 | 0.969 | 0.027 | 0.892 |

**Barents Sea** |

**0** | 0.18 | 2.55 | 0.934 | 2.18 | 0.02 | 0.943 | 0.0091 | 0.949 |

**0** | 0.53 | 2.53 | 0.827 | 2.18 | 0.02 | 0.93 | 0.0091 | 0.949 |

**5** | 0.18 | 5.63 | 0.969 | 4.37 | 0.082 | 0.971 | 0.0188 | 0.918 |

**5** | 0.53 | 5.56 | 0.913 | 4.37 | 0.082 | 0.964 | 0.0188 | 0.918 |

**10** | 0.18 | 8.39 | 0.979 | 6.56 | 0.145 | 0.985 | 0.0221 | 0.908 |

**10** | 0.53 | 8.61 | 0.942 | 6.56 | 0.145 | 0.975 | 0.0221 | 0.908 |

**Table 3.**
Normalized angular distributions of underwater radiance in the Black Sea and Barents Sea.

**Table 3.**
Normalized angular distributions of underwater radiance in the Black Sea and Barents Sea.

**Black Sea** |

**N**_{coc} = 5 × 10^{6} cell/L, a(440) = 0.09 m^{−1} | **N**_{coc} = 5 × 10^{6} cell/L, a(440) = 0.53 m^{−1} |

z, m | −90 | −45 | 0 | 45 | 90 | k * | z, m | −90 | −45 | 0 | 45 | 90 | k |

4 | 0.910 | 1.491 | 2.366 | 1.949 | 1 | - | 4 | 0.867 | 2.023 | 4.033 | 2.881 | 1 | |

6 | 0.967 | 1.680 | 2.301 | 1.844 | 1 | 0.281 | 6 | 0.946 | 2.366 | 3.975 | 2.708 | 1 | 0.485 |

10 | 0.996 | 1.777 | 2.292 | 1.795 | 1 | 0.264 | 10 | 0.993 | 2.570 | 3.986 | 2.616 | 1 | 0.471 |

14 | 1.000 | 1.788 | 2.293 | 1.790 | 1 | 0.260 | 14 | 0.999 | 2.598 | 3.993 | 2.604 | 1 | 0.467 |

**N**_{coc} = 10^{7} cell/L, a(440) = 0.09 m^{−1} | **N**_{coc} = 10^{7} cell/L, a(440) = 0.53 m^{−1} |

z, m | −90 | −45 | 0 | 45 | 90 | k | z, m | −90 | −45 | 0 | 45 | 90 | k |

4 | 0.990 | 1.499 | 1.831 | 1.547 | 1 | - | 4 | 0.981 | 1.956 | 2.746 | 2.057 | 1 | |

6 | 0.999 | 1.527 | 1.830 | 1.532 | 1 | 0.350 | 6 | 0.998 | 2.015 | 2.748 | 2.029 | 1 | 0.608 |

8 | 1.000 | 1.530 | 1.830 | 1.531 | 1 | 0.348 | 8 | 1.000 | 2.023 | 2.750 | 2.025 | 1 | 0.605 |

10 | 1.000 | 1.530 | 1.831 | 1.530 | 1 | 0.349 | 10 | 1.000 | 2.024 | 2.750 | 2.024 | 1 | 0.605 |

**Barents Sea** |

**N**_{coc} = 5 × 10^{6} cell/L, a(440) = 0.18 m^{−1} | **N**_{coc} = 5 × 10^{6} cell/L, a(440) = 0.53 m^{−1} |

z, m | −90 | −45 | 0 | 45 | 90 | k | z, m | −90 | −45 | 0 | 45 | 90 | k |

4 | 0.886 | 1.756 | 2.685 | 2.376 | 1 | - | 4 | 0.872 | 1.936 | 3.156 | 2.691 | 1 | |

6 | 0.969 | 2.029 | 2.904 | 2.194 | 1 | 0.406 | 6 | 0.964 | 2.268 | 3.446 | 2.475 | 1 | 0.485 |

10 | 0,996 | 1,777 | 2,292 | 1,795 | 1 | 0.417 | 10 | 0.997 | 2.399 | 3.529 | 2.414 | 1 | 0.497 |

14 | 1.000 | 1.788 | 2.293 | 1.790 | 1 | 0.418 | 14 | 1.000 | 2.409 | 3.534 | 2.410 | 1 | 0.499 |

**N**_{coc} = 10^{7} cell/L, a(440) = 0.18 m^{−1} | **N**_{coc} = 10^{7} cell/L, a(440) = 0.53 m^{−1} |

z, m | −90 | -45 | 0 | 45 | 90 | k | z, m | −90 | −45 | 0 | 45 | 90 | k |

4 | 0.977 | 1.755 | 2.290 | 1.824 | 1 | - | 4 | 0.983 | 0.983 | 2.618 | 2.006 | 1 | |

6 | 0.999 | 1.796 | 2.311 | 1.803 | 1 | 0.525 | 6 | 0.998 | 0.998 | 2.647 | 1.980 | 1 | 0.621 |

8 | 1.000 | 1.800 | 2.313 | 1.801 | 1 | 0.526 | 8 | 1.000 | 1.000 | 2.649 | 1.977 | 1 | 0.620 |

10 | 1.000 | 1.801 | 2.313 | 1.801 | 1 | 0.526 | 10 | 1.000 | 1.000 | 2.649 | 1.976 | 1 | 0.623 |

**Table 4.**
The changes in the ratio ρ(490)/ρ(550) depending on the N_{coc} concentration.

**Table 4.**
The changes in the ratio ρ(490)/ρ(550) depending on the N_{coc} concentration.

N_{coc}, 10^{6} cell/L | 0 | 1 | 3 | 5 | 10 |
---|

**Black Sea, a(440) = 0.09 m**^{−1}, θ_{0} = 25° | 1.9 | 1.7 | 1.5 | 1.4 | 1.3 |

**Black Sea, a(440) = 0.53 m**^{−1}, θ_{0} = 25° | 0.87 | 0.82 | 0.82 | 0.83 | 0.86 |

**Barents Sea, a(440) = 0.18 m**^{−1}, θ_{0} = 60° | 1.10 | 1.08 | 1.06 | 1.05 | 1.04 |

**Barents Sea, a(440) = 0.53 m**^{−1}, θ_{0} = 60° | 0.82 | 0.81 | 0.82 | 0.84 | 0.82 |

**Table 5.**
The depth of the photic layer Z_{1%} (m) for λ = 500 nm, in the cases of the Black Sea and Barents Sea, depending on the value of N_{coc}, the illumination conditions, and the absorption coefficient.

**Table 5.**
The depth of the photic layer Z_{1%} (m) for λ = 500 nm, in the cases of the Black Sea and Barents Sea, depending on the value of N_{coc}, the illumination conditions, and the absorption coefficient.

N_{coc}, 10^{6} cell/L | 0 | 5 | 10 | 0 | 5 | 10 |
---|

**Illumination Conditions** | **Black Sea, a(440) = 0.09 m**^{−1} | **Black Sea, a(440) = 0.53 m**^{−1} |

**Clear Sky,****θ**_{0} = 25° | >40 | 20.8 | 15.6 | 16.3 | 9.2 | 7.1 |

**Clear Sky,****θ**_{0} = 60° | >40 | 20.2 | 15.2 | 14.4 | 8.7 | 6.8 |

**Overcast** | >40 | 20.5 | 15.5 | 15.6 | 9.0 | 7.0 |

**Illumination Conditions** | **Barents Sea, a(440) = 0.18 m**^{−1} | **Barents Sea, a(440) = 0.53 m**^{−1} |

**Clear Sky,****θ**_{0} = 25° | 17.5 | 10.8 | 8.5 | 13.1 | 8.5 | 6.8 |

**Clear Sky,****θ**_{0} = 60° | 16.3 | 10.4 | 8.3 | 12.1 | 8.1 | 6.5 |

**Overcast** | 17.0 | 10.6 | 8.4 | 12.7 | 8.4 | 6.7 |

**Table 6.**
The value of <K> (500) m^{−1} for the cases of the Black Sea and Barents Sea, depending on the value of N_{coc}, illumination conditions, and the absorption coefficient.

**Table 6.**
The value of <K> (500) m^{−1} for the cases of the Black Sea and Barents Sea, depending on the value of N_{coc}, illumination conditions, and the absorption coefficient.

N_{coc}, 10^{6} cell/L | 0 | 5 | 10 | 0 | 5 | 10 |
---|

Illumination Conditions | Black Sea, a(440) = 0.09 m^{−1} | Black Sea, a(440) = 0.53 m^{−1} |

Clear Sky, θ_{0} = 25° | 0.094 | 0.224 | 0.304 | 0.272 | 0.487 | 0.639 |

Clear Sky, θ_{0} = 60° | 0.105 | 0.236 | 0.317 | 0.317 | 0.532 | 0.684 |

Overcast | 0.098 | 0.228 | 0.309 | 0.288 | 0.503 | 0.656 |

Illumination Conditions | Barents Sea, a(440) = 0.18 m^{−1} | Barents Sea, a(440) = 0.53 m^{−1} |

Clear Sky, θ_{0} = 25° | 0.252 | 0.411 | 0.525 | 0.335 | 0.520 | 0.661 |

Clear Sky, θ_{0} = 60° | 0.284 | 0.444 | 0.558 | 0.385 | 0.569 | 0.705 |

Overcast | 0.263 | 0.423 | 0.538 | 0.354 | 0.538 | 0.675 |

**Table 7.**
Absolute and relative errors of Equations (7–10), depending on the N_{coc} value and the solar zenith angle for the Black Sea, λ = 490 nm and a(440) = 0.09 m^{−1}. The value of parameter u is shown in the first column in brackets.

**Table 7.**
Absolute and relative errors of Equations (7–10), depending on the N_{coc} value and the solar zenith angle for the Black Sea, λ = 490 nm and a(440) = 0.09 m^{−1}. The value of parameter u is shown in the first column in brackets.

N_{coc}, 10^{6} Cells/L | θ_{0}, ° | Absolute Formula Errors | Relative Formula Errors |
---|

(7) | (8) | (9) | (10) | (7) | (8) | (9) | (10) |
---|

0 (0.17) | 25 | −0.004 | −0.004 | −0.005 | −0.004 | −6% | −6% | −8% | −6% |

60 | −0.008 | −0.008 | −0.010 | −0.009 | −12% | −12% | −14% | −13% |

1 (0.34) | 25 | 0.002 | 0.001 | −0.017 | −0.007 | 1% | 1% | −12% | −5% |

60 | −0.004 | −0.005 | −0.023 | −0.013 | −3% | −3% | −15% | −8% |

3 (0.53) | 25 | 0.064 | 0.014 | −0.035 | −0.004 | 24% | 5% | −13% | −2% |

60 | 0.059 | 0.009 | −0.039 | −0.009 | 22% | 4% | −15% | −3% |

5 (0.63) | 25 | 0.17 | 0.021 | −0.049 | −0.003 | 49% | 6% | −14% | −1% |

60 | 0.16 | 0.018 | −0.052 | −0.006 | 48% | 5% | −15% | −2% |

10 (0.77) | 25 | 0.50 | 0.020 | −0.080 | −0.011 | 109% | 4% | −18% | −2% |

60 | 0.50 | 0.021 | −0.079 | −0.009 | 109% | 5% | −17% | −2% |

**Table 8.**
The absolute errors (m^{−1}) of the Equations (11–13) for determining <K>, depending on the value of N_{coc} (10^{6} cell/L), the solar zenith angle θ_{0} (**°**), and the absorption coefficients a(440), m^{−1}.

**Table 8.**
The absolute errors (m^{−1}) of the Equations (11–13) for determining <K>, depending on the value of N_{coc} (10^{6} cell/L), the solar zenith angle θ_{0} (**°**), and the absorption coefficients a(440), m^{−1}.

a(440) | 0.09 | 0.53 |
---|

θ_{0} | 25 | 60 | 25 | 60 |
---|

λ, nm | (13) | (12) | (11) | (13) | (13) | (12) | (11) | (13) |
---|

**N**_{coc} = 0 |

**400** | −0.004 | −0.010 | −0.032 | −0.002 | 0.018 | −0.008 | 0.032 | 0.039 |

**450** | −0.002 | −0.012 | −0.029 | −0.004 | 0.006 | −0.001 | −0.007 | −0.001 |

**500** | −0.001 | −0.012 | −0.024 | −0.003 | 0.000 | −0.001 | −0.019 | −0.009 |

**550** | −0.003 | −0.007 | −0.021 | −0.007 | −0.001 | 0.000 | −0.017 | −0.010 |

**600** | 0.004 | 0.004 | −0.011 | −0.010 | 0.007 | 0.004 | −0.007 | −0.010 |

**650** | 0.011 | 0.005 | −0.001 | −0.010 | 0.013 | 0.004 | 0.001 | −0.010 |

**700** | 0.029 | 0.001 | 0.017 | −0.009 | 0.030 | 0.001 | 0.018 | −0.009 |

**N**_{coc} = 5 |

**400** | 0.11 | −0.09 | −0.16 | 0.11 | −0.001 | −0.08 | −0.22 | 0.01 |

**450** | 0.13 | −0.05 | −0.10 | 0.13 | 0.02 | −0.09 | −0.19 | 0.01 |

**500** | 0.13 | −0.03 | −0.07 | 0.13 | 0.05 | −0.08 | −0.15 | 0.04 |

**550** | 0.09 | −0.05 | −0.08 | 0.09 | 0.05 | −0.07 | −0.12 | 0.04 |

**600** | 0.03 | −0.07 | −0.13 | 0.01 | 0.02 | −0.07 | −0.13 | 0.002 |

**650** | 0.01 | −0.05 | −0.12 | −0.01 | 0.01 | −0.05 | −0.12 | −0.01 |

**700** | 0.02 | −0.03 | −0.11 | −0.03 | 0.02 | −0.03 | −0.11 | −0.03 |

**N**_{coc} = 10 |

**400** | 0.30 | −0.11 | −0.20 | 0.30 | 0.04 | −0.20 | −0.43 | 0.05 |

**450** | 0.33 | −0.03 | −0.10 | 0.33 | 0.11 | −0.17 | −0.31 | 0.10 |

**500** | 0.32 | −0.004 | −0.06 | 0.31 | 0.16 | −0.12 | −0.21 | 0.16 |

**550** | 0.23 | −0.04 | −0.10 | 0.23 | 0.15 | −0.10 | −0.18 | 0.14 |

**600** | 0.10 | −0.11 | −0.19 | 0.08 | 0.08 | −0.12 | −0.21 | 0.06 |

**650** | 0.06 | −0.11 | −0.21 | 0.03 | 0.05 | −0.11 | −0.21 | 0.02 |

**700** | 0.03 | −0.09 | −0.21 | -0.02 | 0.03 | −0.09 | −0.21 | −0.02 |