A Study on the Blue Coloration of Ao-ike Pond, Aomori Prefecture, Japan: Formulation of a Physical Model in Terms of Radiance and Image Analyses

Abstract

The blue coloration model of a closed pond, Ao-ike Pond, Aomori Prefecture, Japan, was formulated in terms of radiance by applying a theory of observation devices proposed by Szirmay-Kalos (2008) and Hanaishi’s reverse ray tracing method. In this model, three potential contributions to the coloration were considered; irregular reflection at the Lambertian pond bottom, density fluctuation scattering by water, and Mie scattering by suspended solids. By utilizing model formulas for these mechanisms, some parameters were determined in order to duplicate the images of the pond surface without solar shading by tree leaves above the pond surface, in addition to the images with sunbeam trajectories by solar radiations passing through tree leaves, which are emitted from the water and visible on the surface. Simulating the pictures of the pond surface and the sun-beam-image analyses revealed that the blue colorations of Ao-ike Pond are mainly produced (1) by the density fluctuation scattering of water itself and the white Mie scattering by suspended solids and (2) by the red-light absorption by water in the optical paths before and after the two scatterings. Then, the density fluctuation scattering of water and the Mie scattering by suspended solids ex-hibited contributions of almost equal magnitude. The contribution of irregular reflections at the pond bottom was judged to be relatively small.