2022 Volume 83 Issue 3 Pages 171-195
Secchi depth (SD) of pure water is the basic value required for quantitative analysis of the SD in of other water bodies. However, it is difficult to determine this value directly through experiments and, to date, no universal value has been theoretically obtained. Previously, we reported an estimation of this value by observing a calculated image of a first-order approximation of light scattering by water molecules, with a focus on improving accuracy. Therefore, in this study, we analogized the nth-order approximation of the luminance formula for light scattering by water molecules, based on first- to fourth-order approximations, to improve accuracy. The calculation time increased with an increase in the order of approximation. We then evaluated the pure water SDs by observing the calculated first- to second-order and first- to third-order approximated images with a realistically possible calculation time.
For incident angles of 0°, 10°, 20°, …, 80°, and 89°, the color image SDs (CISDs) observed for the first- to third-order approximated tristimulus values for light arriving from the direction of a Secchi disk and the background were in the range of 94.2 ± 2.1 m to 114 ± 6.1 m; at this order, they were considered to have almost converged. The monochromatic image SDs (MISDs) obtained by third-order approximation were in the range of 83.5 ± 1.5 m to 106 ± 4.4 m. As the MISDs were smaller than the CISDs at the angle of incidence, it can be said that our observations of pure water SDs tended to be judged by the color difference rather than contrast.
The root mean squares of the relative errors of the automatically determined SDs based on the color difference threshold to the CISDs, and similarly determined SDs based on the contrast threshold to the MISDs, were 6.1% and 3.0%, respectively.
