## 1 Introduction  
The ocean epipelagic zone that extends from the surface to approximately 200 m depth is extremely important for ocean-atmosphere interactions with implications to climate and supporting life on Earth. Most solar radiation incident on the ocean is absorbed within this layer [1; 2]. In the euphotic layer that overlaps with the upper portion or the entire epipelagic zone in very clear ocean waters, there is enough light to support the process of photosynthesis, which contributes nearly half of the world's total biological primary production [3]. The studies of light propagation and light field characteristics are crucial for understanding many physical and biological processes in the upper ocean, which are driven by or depend on solar radiation. For example, for studying the heating rate, the radiometric quantities of spectral downward plane irradiance, \(E_{d}\)(z, \(\lambda\)), and the spectral upward plane irradiance, \(E_{u}\)(z, \(\lambda\)), are essential [4]. The symbols \(z\) (units of m) and \(\lambda\) (units of nm) stand for depth in the ocean and light wavelength in vacuum, respectively. In photosynthesis studies the key quantity of photosynthetically available radiation (PAR) is best represented on the basis of radiometric quantity of spectral scalar irradiance, \(E_{o}\)(z, \(\lambda\)), and its integration over the spectral range of 350-700 nm or 400-700 nm with conversion from energy units to quantum units [5; 6; 7; 8; 9]. This measure of PAR is hereafter referred to as the PAR quantum scalar irradiance, \(E_{oPAR}\). In the past, however, the PAR estimates in the ocean have been often based on the measurements of downward plane irradiance [10], so this measure of PAR will be referred to as PAR quantum downward irradiance, \(E_{dPAR}\). The PAR estimate in terms of \(E_{oPAR}\) is superior to \(E_{dPAR}\), mainly because it does not ignore the contribution of upwelling light to photosynthetically available radiation and the measurement of \(E_{o}\) with a spherical collector gives equal weight to quanta arriving at a point from all possible directions, in contrast to the cosine weighting in the measurement of \(E_{d}\) with a plane collector. For simplicity, the explicit dependence of optical quantities on \(z\) and \(\lambda\) is omitted hereafter unless causing ambiguity (symbols and definitions are summarized in Table 1, see also [9] for terminology and definitions used in hydrologic optics). Radiometric measurements in the ocean started in the early 1930s and a summary of pioneering work can be found in [11]. Example early studies include measurements of spectral irradiance, e.g., [12; 13] and the angular distribution of radiance, e.g., [14; 15; 16], and determinations of some apparent optical properties (AOPs) of the ocean from light measurements, e.g., [12; 17; 18]. Early reports on radiometric and other optical measurements in the ocean can be also found in the Russian literature, e.g., [19]. More recent studies have considerably expanded these early measurements by using advanced instrumentation and various deployment approaches, e.g., [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. Much research interest in recent decades has been concentrated on ocean reflectance in relation to applications of ocean color remote sensing. For these applications, many radiometric measurements have been collected for spectral upwelling (zenith) radiance, \(L_{u}\), and \(E_{d}\), and optionally also for \(E_{u}\)[33; 34; 32]. Note that the zenith radiance indicates that the measured light travels toward zenith. The analysis of radiometric measurements