The relationships between the apparent optical properties (AOP's) and the inherent optical properties (IOP's) of oceanic water bodies have been reinvestigated by solution of the radiative transfer equation. This reexamination deals specifically with oceanic case 1 waters (those for which phytoplankton and their associated particles or substances control their inherent optical properties). In such waters, when the chlorophyll content is low enough tin most of the entire ocean), the influence of molecular scattering by water molecules is not negligible, leading to a gradual change in the shape of the phase function. The effect of this change on the AOP's is analyzed. The effect of the existence of diffuse sky radiation in addition to the direct solar radiation on AOP-IOP relationships is also examined. Practical parameterizations are proposed to predict in case 1 waters, and at various depths, the vertical attenuation coefficient for downward irradiance (K-d) as a function of the IOP's and solar angle. These parameterizations are valid for the spectral domain where inelastic scattering does not significantly occur (wavelengths below 590 nm). (C) 1998 Optical Society of America.