Discrete Angle Radiative Transfer in Uniform and Extremely Variable Clouds.
The transfer of radiant energy in highly inhomogeneous media is a difficult problem that is encountered in many geophysical applications. It is the purpose of this thesis to study some problems connected with the scattering of solar radiation in natural clouds. Extreme variability in the optical density of these clouds is often believed to occur regularly. In order to facilitate study of very inhomogeneous optical media such as clouds, the difficult angular part of radiative transfer calculations is simplified by considering a series of models in which conservative scattering only occurs in discrete directions. Analytic and numerical results for the radiative properties of these Discrete Angle Radiative Transfer (DART) systems are obtained in the limits of both optically thin and thick media. Specific results include: (a) In thick homogeneous media, the albedo (reflection coefficient), unlike the transmission, cannot be obtained by a diffusion equation. (b) With the aid of an exact analogy with an early model of conductor/superconductor mixtures, it is argued that inhomogeneous media with embedded holes, neither the transmission, nor the albedo can be described by diffusive random walks. (c) Using renormalization methods, it is shown that thin cloud behaviour is sensitive to the scattering phase functions since it is associated with a repelling fixed point, whereas, the thick cloud limit is universal in that it is phase function independent, and associated with an attracting fixed point. (d) In fractal media, the optical thickness required for a given albedo or transmission can differ by large factors from that required in the corresponding plane parallel geometry. The relevant scaling exponents have been calculated in a very simple example. (e) Important global meteorological and climatological implications of the above are discussed when applied to the scattering of visible light in clouds. In the remote sensing context, an analysis of satellite data reveals that augmenting a satellite's resolution reveals increasingly detailed structures that are found to occupy a decreasing fraction of the image, while simultaneously brightening to compensate. By systematically degrading the resolution of visible and infra red satellite cloud and surface data as well as radar rain data, resolution -independent co-dimension functions were defined which were useful in describing the spatial distribution of image features as well as the resolution dependence of the intensities themselves. The scale invariant functions so obtained fit into theoretically predicted functional forms. These multifractal techniques have implications for our ability to meaningfully estimate cloud brightness fraction, total cloud amount, as well as other remotely sensed quantities.
- Pub Date:
- Physics: Atmospheric Science