Ocean color, a theoretical study using matrix operator theory

Abstract

Matrix Operator theory has been extended for application to "Ocean Color" related problems. Required to extend the theory, specialized quadrature methods and both reflection and transmission operators, representing the ocean's surface, were developed. Subsequently, Fortran programs to implement the modified Matrix Operator theory for inhomogenous atmosphere-ocean systems were written and tested. The modified technique was then used to examine the strength of currently used one-dimensional "Ocean Color" reflectance formulas. Predicted by one-dimensional reflectance formulas, functions of (rho) alone, both the "product" ambiguity and the "shape" ambiguity were examined in detail. As part of that examination, calculations for a wide variety of ocean characteristics were performed using an atmospheric model representing conditions of (lamda) = 0.55 (mu)m. One-dimensional ocean reflectance formulas were found to be inadequate in several ways. Not accounted for by one-dimensional theory, large "shape" related and "product" related reflectance variations were found to exist. The "shape" ambiguity predicted by one-dimensional formulas was shown not to exist. Further, it was discovered that one-dimensional "Ocean Color" reflectance formulas were more sensitive to error for (rho)/b(,b) < 1.