## 3 Results and Discussion
### Application of [PERSON]'s Equation
As shown for the example data collected in the Farallon Basin, the applicability of [PERSON]'s equation within the examined water column extends from the short-wavelength portion of the spectrum to about 580 nm, as indicated by the vertical dotted line in Figure 14a. At longer wavelengths this application failed owing to stronger effects of Raman scattering and chlorophyll-\(a\) fluorescence, even at the shallowest depth of 7.2 m examined in this case (Figure 14a,b). As the Raman scattering effects continue to accumulate with increasing depth the short-wavelength boundary of the affected spectral region is expected to shift towards shorter wavelengths [60; 64; 73]. Therefore, one can expect that at depths greater than those examined in our study the application of [PERSON]'s equation may fail for wavelengths shorter than \(\sim\)580 nm. Figure 14b also shows that somewhat larger discrepancy between \(a_{AOP}\) and \(a_{ac9}\) at 440 nm was observed within the \(Chl_{max}\) layer around the depth of \(z_{Chlmax}\). This may be associated with the limitation that the radiometric measurements were taken at discrete depths with relatively low depthresolution (i.e., 10 m below \(z=20\) m), as opposed to nearly continuous depth profiles which would be required for better determinations of \(K_{E}(z,\lambda)\) within the optically heterogeneous layer. Figure 14c shows that \(a_{AOP}\) and \(a_{ac9}\) compare favorably for the combined dataset from the two stations, which includes data points for the three wavelengths from the blue-green spectral region (440, 488, and 555 nm) and all discrete depths included in this analysis (i.e., where \(K_{E}\) was determined). The best linear fit to the data is very close to the 1:1 line and the correlation is strong (\(r^{2}=0.750\)). This was the only case in this study when Model II regression analysis was applied (see Section 2.6). If the ac-9-measured values are tentatively assumed to represent true values, then the  
Figure 14: Comparison of the absorption coefficient of seawater measured with an ac-9 instrument (\(a_{ac9}\)) and estimated from AOPs using the irradiance quartet measurements and Gershun’s equation (\(a_{AOP}\)). (**a**) Spectra of absorption coefficient at depths for which the determinations of \(K_{E}\) were made on the basis of radiometric measurements taken at one station in the Carmen Basin where ac-9 measurements were made during the 2011 cruise. The vertical dotted line indicates the transition region to long-wavelength portion of the spectrum where the use of Gershun’s is inadequate because of the effects of inelastic processes. (**b**) Vertical profiles of absorption coefficient measured with the ac-9 instrument (solid lines) and estimated from AOPs (dashed lines) at selected light wavelengths as indicated. Data were collected at the same station as in panel (**a**). (**c**) Direct comparison between \(a_{AOP}\) and \(a_{ac9}\) at selected blue and green spectral bands as indicated. Data were collected at one station in the Guaymas Basin and one station in the Carmen Basin where ac-9 measurements were made during the 2011 cruise. (**d**) Relationship between \(K_{E}\)\(\cdot\overline{\mu}\) and \(K_{d}\)\(\cdot\overline{\mu}_{d}\) for the blue-green spectral regions based on data at the three selected light wavelengths as indicated. Solid lines in (**c**,**d**) represent the best-fit regression functions and dashed lines the 1:1 agreement between the variables. statistical indicators suggest a very small bias of \(a_{AOP}\) estimates as the median value for the ratio of \(a_{AOP}/a_{ac9}\) is very close to 1 (0.989) and the mean difference between \(a_{AOP}\) and \(a_{ac9}\) is very small (\(-0.0016\) m\({}^{-1}\)). The median absolute percent difference between \(a_{AOP}\) and \(a_{ac9}\) is 12.4% and the root mean square deviation is 0.0116 m\({}^{-1}\).