## 3 Results and Discussion
### Application of [PERSON]'s Equation  
The underwater radiometric measurements in conjunction with the use of [PERSON]'s equation provide a method for determining the absorption coefficient of seawater, \(a(\lambda,\,z)\), as a product of \(K_{E}(\lambda,\,z)\) and \(\overline{\mu}(\lambda,\,z)\). The main limitation of this radiometric method is that [PERSON]'s equation was derived from a simplified radiative transfer equation that ignores inelastic processes of Raman scattering and fluorescence and internal sources (i.e., true light emission) such as bioluminescence, e.g., [9; 11; 49]. Therefore, in principle, this method can work satisfactorily only for cases in which the contributions of inelastic processes and internal sources are negligible. Because bioluminescence is typically intermittent and discrete under natural conditions in the ocean, the primary limitation of the applicability of [PERSON]'s equation in the upper ocean or euphotic layer is associated with the presence of inelastic processes. In spite of these limitations, this radiometric method offers a unique benefit resulting from the estimation of the absorption coefficient that is representative of relatively large volume of seawater. This is because the radiometric measurements and AOPs are representative of much larger volumes of water compared with small volumes involved in direct IOP measurements including in situ absorption meters. We examined the applicability of the radiometric method using our data collected at two stations, one in the Carmen Basin and another in the Farallon Basin (see Figure 1), where concurrent radiometric and ac-9 measurements were made. In this analysis, we compare the values of the absorption coefficient, \(a_{ac9}(z,\,\lambda)\), measured with the ac-9 instrument with those derived from [PERSON]'s equation, i.e., \(a_{AOP}(z,\,\lambda)=K_{E}(z,\,\lambda)\cdot\overline{\mu}(z,\,\lambda)\). In order to enable such comparison, the data of \(a_{ac9}(z,\,\lambda)\) and \(\overline{\mu}(z,\,\lambda)\) were adjusted to common depths corresponding to the determinations of \(K_{E}(z,\,\lambda)\). Specifically, \(\overline{\mu}(z,\,\lambda)\) was linearly interpolated to obtain the values for depths at which \(K_{E}(z,\,\lambda)\) was determined, i.e., the mid-points between the discrete depths (see Equation (1)) where the radiometric measurements, and hence \(\overline{\mu}(z,\,\lambda)\), were made. The high depth resolution ac-9 data required only minor interpolation to these mid-point depths. In addition, the high spectral resolution data of \(K_{E}(z,\,\lambda)\) and \(\overline{\mu}(z,\,\lambda)\) were linearly interpolated to ac-9 wavelengths. Our comparative analysis of \(a_{AOP}(z,\,\lambda)\) and \(a_{ac9}(z,\,\lambda)\) is focused on five ac-9 wavelengths, 440, 488, 555, 650, and 676 nm. In addition to the effects of inelastic processes and mismatch of spatial scales of AOP and ac-9 measurements, it is noteworthy to mention other sources of uncertainty that can affect the comparisons of \(a_{ac9}(z,\,\lambda)\) and \(a_{AOP}(z,\,\lambda)\). The accurate direct in situ measurements of \(a(z,\,\lambda)\) with instruments such as ac-9 are difficult, mainly because of scattering error and stringent calibration requirements [112; 113; 114]. The determinations of \(K_{E}(z,\,\lambda)\) and \(\overline{\mu}(z,\,\lambda)\) require measurements with four (\(E_{d},\,E_{u},\,E_{ad},\,E_{ou}\)) or at least three (\(E_{d},\,E_{u},\,E_{o}\)) radiometric sensors, so these determinations are critically dependent on accurate calibrations of multiple sensors. The accuracy of determinations of \(K_{E}(z,\,\lambda)\) for specific depths can be also affected by relatively low depth resolution of radiometric measurements that were taken at several discrete depths in our study. In spite of multiple sources of uncertainty, we found reasonably good agreement between \(a_{AOP}\) and \(a_{ac9}\) throughout the euphotic layer for the blue and green spectral regions where the effects of inelastic processes were relatively weak (Figure 14a-c).