Secchi disk depth: A new theory and mechanistic model for underwater visibility

Secchi disk depth (ZSD) is a measure of water transparency, whose interpretation has wide applications from diver visibility to studies of climate change. This transparency has been explained in the past 60 + years with the underwater visibility theory, the branch of the general visibility theory for visual ranging in water. However, through a thorough review of the physical processes involved in visual ranging in water, we show that this theory may not exactly represent the sighting of a Secchi disk by a human eye. Further, we update the Law of Contrast Reduction, a key concept in visibility theory, and develop a new theoretical model to interpret ZSD. Unlike the classical model that relies strongly on the beam attenuation coefficient, the new model relies only on the diffuse attenuation coefficient at a wavelength corresponding to the maximum transparency for such interpretations. This model is subsequently validated using a large (N = 338) dataset of independent measurements covering oceanic, coastal, and lake waters, with results showing excellent agreement (~ 18% average absolute difference, R2 = 0.96) between measured and theoretically predicted ZSD ranging from < 1 m to > 30 m without regional tuning of any model parameters. This study provides a more generalized view of visual ranging, and the mechanistic model is expected to significantly improve the current capacity in monitoring water transparency of the global aquatic environments via satellite remote sensing.