Inverse Problems in Hydrologic Radiative Transfer

Abstract

The long-term scientific goal of my research is to better understand the distribution of phytoplankton in the world's oceans through remote sensing their influence on the optical properties of the water. OBJECTIVESOptically, phytoplankton reveal their presence through their influence on the inherent optical properties (IOP's) of the water. The main effect of phytoplankton is to increase the absorption of light by virtue of the strong absorption by their photosynthetic (chlorophyll a) and accessory pigments. A secondary effect is to increase the backscattering coefficient of the medium in a manner that depends on the concentration of pigments. Although techniques for measuring the absorption coefficient directly (e.g., in-situ AC9 measurements or in-vitro filterpad absorption) are becoming accepted by the scientific community, laboratory techniques for measuring backscattering are tedious and subject to error, and in-situ techniques for backscattering are in their infancy. In addition, in most in-situ measurements the volume of medium that is sampled is small and may not be representative of the whole water body, even in a homogeneous medium. Thus, in the past, there has been considerable effort devoted toward indirectly inferring these IOP's by virtue of their affect on the apparent optical properties (AOP's), e.g., the diffuse reflectance of the water (the color of the water) or the downwelling irradiance attenuation coefficient. These AOP's are perhaps the most frequently measured quantities in hydrologic optics. Clearly, interpretation of such observations requires a detailed understanding of the influence of phytoplankton on the IOP's, and their link to the AOP's.The IOP ↔ AOP link forms the focus of the present research. In particular, our research is centered on deriving the IOP's from measurements of the AOP's. This is an example of the inverse problem of radiative transfer. It is important in that IOP's determined from AOP's are, by definition, sampled at a scale appropriate for radiative transfer, and for remote sensing. Also, the retrieved IOP's possess the attribute that when combined with the radiative transfer equation, they reproduce the measured AOP's. The table below summarizes in matrix form inverse problems relevant to hydrologic optics. Our goal is to fill in the uncompleted elements of the matrix.