Modeling the vertical distributions of downwelling plane irradiance and diffuse attenuation coefficient in optically deep waters

Abstract

The diffuse attenuation coefficient (Kd) is critical to understand the vertical distribution of underwater downwelling irradiance (Ed). Theoretically Ed is composed of the direct solar beam and the diffuse sky irradiance. Applying the statistical results from Hydrolight radiative transfer simulations, Kd is expressed into a mathematical equation (named as PZ06) integrated from the contribution of direct solar beam and diffuse sky irradiance with the knowledge of sky and water conditions. The percent root mean square errors (RMSE) for the vertical distribution of Ed(z) under various sky and water conditions between PZ06 and Hydrolight results are typically less than 4%. Field observations from the southern Middle Atlantic Bight (SMAB) and global in situ data set (NOMAD) also confirmed the validity of PZ06 in reproducing Kd. PZ06 provides an alternative and improvement to the simpler models (e.g., Gordon, 1989; and Kirk, 1991) and an operational ocean color algorithm, while the latter two kinds of models are valid to limited sky and water conditions. PZ06 can be applied to study Kd from satellite remotely sensed images and seems to improve Kd derivation over current operational ocean color algorithm.