## 1 Introduction
In some studies, however, for example in the work of [PERSON] [10; 47], the average cosines are considered just as simple parameters that specify the angular structure of the light field, and not AOPs. In this paper, we choose to refer to the average cosines as AOPs, which is consistent with the traditional view [9; 46; 48] and simplifies the narrative structure of the presentation of our results for the three classes of parameters (i.e., \(K\)-coefficients, reflectances, and average cosines) which are derived from radiometric quantities. The issue of whether or not we refer to the average cosines as AOPs has no impact on the presented results. The scarcity of simultaneous measurements of \(E\) and \(E_{o}\) has also greatly limited the potential use of the so-called Gershun equation [49] for estimating the absorption coefficient of seawater, \(a\), from radiometric measurements or AOPs. This equation can be derived directly from the 1-D scalar (i.e., depth dependence only and no consideration of polarization of light) radiative transfer equation (RTE) for radiance, and takes a simple form \(a=K_{E}\cdot\overline{\mu}\) when the inelastic radiative processes and internal sources are ignored [9]. The inelastic processes in the ocean include Raman scattering by water molecules, fluorescence by phytoplankton pigments, especially chlorophyll-\(a\), and fluorescence by colored dissolved organic matter (CDOM). Few experimental studies have incorporated measurements of both spectral plane and scalar irradiances [18; 44] or derived the irradiance quartet from radiance measurements limited to a single or a few wavebands [20; 29; 31; 50] to examine the application of [PERSON]'s equation. [PERSON] [51] demonstrated that the irradiances involved in [PERSON]'s equation, \(E\) and \(E_{o}\), can be measured with two irradiance sensors equipped with spherical collectors oriented in upward and downward looking directions and masked so that they each collect light over a hemispherical portion of the collector. This latter approach was also used by [PERSON] and [PERSON] [52] to determine the absorption coefficient of seawater from [PERSON]'s equation. In principle, theoretical simulations of radiative transfer (RT) in the ocean enable the analysis of essentially all radiometric quantities of underwater light field and AOPs for various pre-defined scenarios of input data of inherent optical properties (IOPs) of seawater and boundary conditions at the sea surface and ocean bottom. There is a large body of literature in this area with a great majority of studies focusing on the so-called inverse problem or developing methods for estimatingIOPs from radiometric measurements of natural light field or AOPs in a water body (see [53] for a review of this topic). In general, the limitations of such RT models are set by the assumptions used in their development, which include the assumptions regarding the vertical structure of IOPs and inelastic processes. The RT simulations have usually assumed a homogeneous water column and ignored all or some inelastic processes [47; 54; 55; 56; 57; 58; 59; 60]. If included, the vertical stratification normally requires some idealized parameterization of the depth profile of IOPs, e.g., [61; 62; 63; 64]. The models based on such simplifying assumptions can be satisfactory within certain limitations for the purposes of their development, for example the retrieval of average IOPs in the near-surface ocean layer. Notwithstanding the simplifying assumptions about the ocean environment, the RT modeling has provided insights into the complexity of the effects of the vertical inhomogeneity of the water column [60; 62; 63; 65; 66] and inelastic processes [67; 68; 69; 70; 71; 72; 73; 74; 75] on in-water and water-leaving light fields as well as AOPs.