A numerical model for the computation of radiance distributions in natural waters with wind‐roughened surfaces

A numerical technique is presented for computing radiance distributions in natural waters that have wind-blown surfaces and depth-dependent inherent optical properties. Input to the numerical model consists of the radiance distribution incident on the air-water surface from above, the wind velocity, which specifies the state of randomness of the air-water surface via a wind speed-wave slope spectrum, the volume scattering and volume attenuation functions of the water body as functions of depth and wavelength, and the type of bottom boundary. Primary output from the model consists of directionallv discretized radiances as functions of wavelength, direction, and depth throughout and above the water body. General knowledge of the radiance distribution in a water body is a prerequisite for solving more specific problems, such as those occurring in studies of underwater visibility, remote sensing of the oceans from aircraft or satellites, heating of the upper layers of the oceans, or photosynthesis. Moreover, since radiance is the fundamental radiometric quantity, if the radiance is known then all other quantities of interest, such as the irradiance, are easily obtained. Unfortunately, measurement of radiance is a difficult and expensive task in the ocean environment, and few systematic studies of radiance have been made in natural waters. However, a numerical model has been developed for computing radiance distributions in natural hydrosols, such as lakes and seas, given the inherent optical properties of the hydrosol itself and appropriate boundary conditions at the surface and bottom of the water body, along with the radiance incident on the water surface. This