FY 1988

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

Mobley, C.D., and R.W. Preisendorfer

NOAA Tech. Memo. ERL PMEL-75, NTIS: PB88-192703, 195 pp (1988)

This report is a repository of the details of derivation of a numerical procedure to determine the unpolarized radiance distribution as a function of depth, direction, and wavelength, in a natural hydrosol such as a lake or sea. The input to the model consists of (i) the incidence radiance distribution at the air-water surface, (ii) the state of randomness of the air-water surface as a function of wind speed, (iii) the volume scattering and volume attenuation function of the medium as a function of depth and wavelength, and (iv) the type of bottom boundary. The fundamental mathematical operation in the development of the numerical model is the discretization over direction space of the continuous radiative transfer equation. The directionally discretized radiances, called quad-averaged radiances, are the averages over a finite set of solid angles of the directionally continuous radiance. The quad-averaged equations are azimuthally decomposed using standard Fourier analysis to obtain equations for the quad-averaged radiance amplitudes. These amplitude equations are then developed in terms of reflectance and transmittance functions. The reflectances and transmittances are continuous functions of depth and are governed by a set of Riccati equations which is easily integrated. The depth-dependent, quad-averaged radiances are assembled from the solution reflectances and transmittances of the water body, in combination with the boundary conditions. The model has an expandable library of derived quantities that are of use in various applications of optics to natural waters, such as marine biological studies, underwater visual search tasks, remote sensing, and climatology.