## 3 Results and Discussion
### Overall Variability and Relationships Involving the Apparent Optical Properties
#### 3.2.2 Irradiance Reflectance  
Similar to the average cosines, the variations in the irradiance reflectance, \(R\), throughout the euphotic layer are characterized by a much broader range in the red spectral region where the effects of inelastic processes are very strong compared with the blue-green part of the spectrum where these effects are much weaker. Our data of \(R\) in the blue-green ranged from 0.006 to 0.056, whereas in the red from 0.0015 near the surface to 0.75 around \(z_{chlmax}\). The observed range in the blue-green is similar to that of 0.006-0.063 based on \(E_{d}\) and \(E_{u}\) measurements reported by [PERSON] [18] for 427, 477, 532, and 572 nm between the surface and -70 m. The \(R\) values at 633 nm in [PERSON]'s dataset range from 0.001 to 0.004, but these values were determined only at shallow depths, typically less than 5 m. Our data in the red extend to much higher values within the euphotic layer owing to strong inelastic effects in this spectral region, which is consistent with a few measurements from undisclosed locations reported by [PERSON] and [PERSON] [37]. As emphasized before, the increasing role of inelastic processes with increasing depth is most significant in the long-wavelength part of the spectrum. This effect is clearly seen in our data of  
Figure 10: Relationships between average cosines based on measurements from all stations and depths. Data for (**a**) \(\overline{\mu}\) vs. \(\overline{\mu}_{d}\) and (**b**) \(\overline{\mu}_{u}\) vs. \(\overline{\mu}_{d}\) are shown for selected light wavelengths as indicated in panel (**a**). In (**a**) data points for the blue and green (440 nm and 550 nm) were combined to determine the best-fit regression function (blue line) and data points for the red (650 nm and 683 nm) were combined to determine the best-fit regression function (red line). plotted as a function of depth for wavelengths of 650 and 683 nm (Figure 11). Both \(R(650)\) and \(R(683)\) showed gradual increase from the values of the order of \(10^{-3}\) near the surface to more than 0.1 within the mid- to deep portions of the examined water column. These data suggest that depth can serve as a useful proxy for the vertical changes in \(R\) in the red part of the spectrum. The best-fit exponential functions to the data are:  
\[R(650)=10^{0.7633\ln(z)-3.6633}\quad(r^{2}=\ 0.820,RMSE=\ 0.331,N=\ 74) \tag{5a}\] \[R(683)=10^{0.7690\ln(z)-3.2582}\quad(r^{2}=\ 0.794,RMSE=\ 0.362,N=\ 74). \tag{5b}\]  
Whereas these vertical trends in \(R\) reflect primarily the increasing effect of Raman scattering with depth, the effects of chlorophyll-\(a\) fluorescence were also evident within the 683 nm band. The values of \(R(683)\) were comparable to \(R(650)\) near the surface but increased faster with depth owing to increasing \(Chl\) and associated fluorescence until the \(Chl_{max}\) was reached. Consequently, \(R(683)\) tended to have the highest values at depths close to \(z_{Chlmax}\), which was about 30 m for most investigated stations in this study. The dominant role of Raman scattering and additional complexities caused by chlorophyll-\(a\) fluorescence emission in the red spectral region indicate that this part of the spectrum is not well suited for establishing a relationship between \(R\) and \(Chl\) within the euphotic layer. The analysis of our entire dataset including all measurement depths confirmed the lack of relationship between \(R\) in the red and \(Chl\) (not shown). For example, a very low determination coefficient (\(r^{2}\) in the range of \(\sim\)0.091-0.155) was found between the log-transformed data of red (650 or 683 nm)-to-green (550 nm) reflectance ratios and \(Chl\). In contrast, our data of the blue-to-green reflectance ratio, \(R(440)/R(550)\), and \(Chl\) collected at all measurement depths exhibited a relationship with significantly higher determination coefficient of 0.608 (not shown).