## 1 Introduction
\begin{table}
\begin{tabular}{c l c} \hline \hline
**Symbol** & \multicolumn{1}{c}{**Description**} & **Units** \\ \hline \(\lambda\) & Light wavelength in vacuum & nm \\ \(z\) & Depth in water & m \\ \(\theta_{s}\) & Solar zenith angle & degree \\ \(a\) & Absorption coefficient & m\({}^{-1}\) \\ \(b\) & Scattering coefficient & m\({}^{-1}\) \\ \(c\) & Beam attenuation coefficient (sum of \(a\) and \(b\)) & m\({}^{-1}\) \\ \(L_{u}\) & Spectral upwelling radiance at zenith direction & W m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) \\ \(E_{d}\), \(E_{u}\) & Spectral downwelling and upwelling plane irradiances & W m\({}^{-2}\) nm\({}^{-1}\) \\ \(E_{o}\), \(E_{d}\), \(E_{u}\) & Spectral total, downwelling, and upwelling scalar irradiances & W m\({}^{-2}\) nm\({}^{-1}\) \\ \(K_{x}\) & Diffuse attenuation coefficients for irradiance or radiance \(x\) & m\({}^{-1}\) \\ \(\overline{\mu}\), \(\overline{\mu}_{d}\), \(\overline{\mu}_{u}\) & Average cosines of total, down- and upwelling light fields & dimensionless \\ \(R\) & Irradiance reflectance & dimensionless \\ \(\mathcal{Ch}l\) & Chlorophyll-\(a\) concentration & mg m\({}^{-3}\) \\
**Subscripts** & & \\ \(w\) & Water & \\ \(p\) & Suspended particulate matter & \\ \(g\) & Colored dissolved organic matter (CDOM) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols of basic variables used in this study. driven by the interest in ocean color has been typically focused on near-surface layer, approximately the top 10-20 m. With regard to AOPs, most experimental efforts have been placed on the determinations of (i) the spectral diffuse attenuation coefficients \(K_{d}\), \(K_{u}\), and \(K_{Lu}\) for \(E_{d}\), \(E_{u}\), and \(L_{u}\), respectively; (ii) the spectral irradiance reflectance, \(R=E_{u}/E_{d}\); and (iii) the spectral remote-sensing reflectance just above the sea surface, \(R_{rs}(z=0^{+})=L_{\omega}(z=0^{+})/E_{d}(z=0^{+})\) where \(L_{\omega}\) is the spectral water-leaving radiance and \(z=0^{+}\) is just above the sea surface, e.g., [32; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43]. Note also that the measurements of both \(E_{d}\) and \(E_{u}\) allow for determination of the net irradiance, \(E=E_{d}-E_{u}\), and the diffuse attenuation coefficient for net irradiance, \(K_{E}\). In contrast to the plane irradiances \(E_{d}\) and \(E_{u}\), the measurements of spectral scalar irradiance, \(E_{o}\), including its downward, \(E_{od}\), and upward, \(E_{ou}\), components have seldom been conducted. In particular, simultaneous measurements of the irradiance quartet that includes \(E_{d}\), \(E_{u}\), \(E_{od}\), and \(E_{ou}\) have been very rare [44] and we are unaware of explicit presentation of experimental data of the complete irradiance quartet in the literature. This greatly limits the availability of experimental data of the average cosines that provide a simple way of specifying the angular structure of the light field. The average cosines include: (i) the average cosine for the downwelling light field, \(\overline{\mu}_{d}=E_{d}/E_{od}\); (ii) the average cosine for the upwelling light field, \(\overline{\mu}_{u}=E_{u}/E_{ou}\); and (iii) the average cosine for the entire light field, \(\overline{\mu}=(E_{d}-E_{u})/(E_{od}+E_{ou})\equiv E/E_{o}\)[8; 9]. We note that according to the original concept and definition of AOPs introduced by [PERSON] [45; 46], the average cosines (and the reciprocal of the average cosines referred to as the distribution functions) can be considered AOPs. [PERSON] [46] provides the following definition of AOPs: \"The apparent optical properties of a natural hydosch are those radiometrically determined scattering- and absorbing-induced quantities which generally depend on the geometrical structure of the light field (i.e., whether the light field is more or less collimated or diffuse) but which have enough regular features and enough stability to be entitled to the appellation optical property\".