Diffuse attenuation coefficient of photosynthetically available radiation (PAR), K_PAR, is a key product of ocean color remote sensing. Current ocean color algorithms generally detect only the average K_PAR within one optical depth, $K_{PAR}^{RS}$. Due to the marked vertical variations of K_PAR, knowledge of $K_{PAR}^{RS}$ is insufficient to accurately evaluate the submarine light field. By using field in situ observations, a two-step approach, based on the development of an ocean color algorithm for $K_{PAR}^{RS}$ and the relationships between $K_{PAR}^{RS}$ and the average K_PAR from the surface down to depth Z (${\overline{K}}_{PAR}^Z$), was developed to remotely estimate the vertical variations in ${\overline{K}}_{PAR}^Z$ in the North Pacific from the MODerate-resolution Imaging Spectrometer (MODIS) imagery. The root mean square difference of log(${\overline{K}}_{PAR}^Z$) in depths within the euphotic zone was around ±0.059 (in unit of m⁻¹ for ${\overline{K}}_{PAR}^Z$), which corresponded to a deviation of ±15% for the estimated ${\overline{K}}_{PAR}^Z$ and the penetration depths of PAR. Our study may provide a promising approach to detect the vertical variations of ${\overline{K}}_{PAR}^Z$ and underwater PAR distributions in the North Pacific Ocean.

The quanta-to-energy ratio plays a crucial role in converting energy units to quantum units in the context of photosynthetically active radiation (PAR). Despite its widespread use, the effects of atmospheric particles and solar zenith angle (SZA) on the quanta-to-energy ratio remain unclear. In this study, both simulation and observation data revealed that the principal wavelength, which can be transformed into the quanta-to-energy ratio using a constant, exhibits a slow initial growth, followed by a rapid increase beyond 60° solar zenith angles and a subsequent dramatic decrease after reaching its maximum value. The measured quanta-to-energy ratio demonstrates a variable range of less than 3% for SZA under 70° in a cloudless atmosphere, with significant changes only occurring at zenith angles above 80°. Simulation data indicate that ozone, wind speed, surface-level pressure, surface air temperature, and relative humidity have negligible effects on the quanta-to-energy ratio. The Ångstrom exponent exerts a minor influence on the quanta-to-energy ratio by affecting diffuse radiation. Visibility, however, is found to have a substantial impact on the quanta-to-energy ratio. As a result, two relationships are established, linking the principal wavelength to visibility and the diffuse fraction of PAR. The principal wavelength serves as an effective measure of solar spectrum variability, remaining unaffected by radiation energy. This implies that atmospheric parameters which do not alter the solar spectrum will not influence the principal wavelength. The strong correlations between the principal wavelength, visibility, and the diffuse fraction of PAR suggest a broader range of applications for the principal wavelength in various research domains, opening up new avenues for exploration and potential contributions to numerous fields.