Diffuse attenuation in optically-shallow water: effects of bottom reflectance

It is well-known that in the ocean, where the depth of the ocean floor is large compared with the attenuation length of irradiance, the diffuse attenuation coefficients for vector and scalar irradiance (K-functions) are not affected by the optical properties or proximity of the ocean floor. This is the case of an optically deep ocean where the attenuation coefficients are determined solely by the inherent optical properties of the water and the distribution of radiance. Since, within optical-deep water, variability in the K- functions due to radiance distribution are small relative to the effects of the inherent optical properties of water, K- functions have been treated as quasi-inherent optical properties. Furthermore, when the depth of the ocean floor is shallow enough so that it becomes illuminated by down- welling irradiance, i.e. when the ocean is optically shallow, the in-water light field is modified by the optical properties of the ocean floor. The effect decreases with increasing depth and distance from the ocean floor. It is not generally appreciated, however, that the associated K- functions will also be affected by both the optical properties and the proximity of the ocean floor and, therefore, cannot be treated as quasi-inherent optical properties. If these effects are neglected, large errors, exceeding 25 percent in some cases, can result from modeling the optically shallow scalar irradiance profile as a function of a constant diffuse attenuation coefficient.