Size distributions of atmospheric particles: Scale dependence, scattering properties of nonspherical particles and retrieval by inversion of spectral optical depth

As an investigation into size distributions of cloud particles from both the theoretical and instrumental points of view, this dissertation is mainly concerned with four topics. First, a systems theory is developed to study size distributions based on Shannon's maximum entropy principle and an energy barrier argument. This new theory reveals the scale-dependence of size distributions and provides an explanation for the long-existing discrepancy between observed and model-predicted size distributions. The scale-dependent behavior has many important implications for theoretical study as well as for instrumentation used in measuring size distributions. Second, a new methodology is developed to formulate the anomalous diffraction theory (ADT) for arbitrarily shaped particles. The ADT for finite circular cylinders is derived as a special application. Comparisons of ADT solutions with the rigorous T-matrix calculations are presented. The results show that the differences in extinction between ADT and exact solutions generally decrease with particle nonsphericity. A similar decrease occurs for absorption at wavelengths of relatively strong absorption, including the Christiansen bands (where the real part of the refractive index approaches unity). The results also suggest that ADT may provide an alternative to the widely used Mie theory in parameterization and remote sensing of cirrus clouds at certain wavelengths. Third, the illposedness and solution ambiguity of retrieving size distribution from multispectral extinction measurements are discussed. A new retrieval algorithm is developed to solve the illposed inverse problem; it is evaluated by comparison with an iterative algorithm and the method of truncated singular value decomposition. The influences of particle shapes and refractive indices on size distribution retrieval are investigated using the new retrieval algorithm. The effects of both the Mie theory and the new developed ADT approximation to light scattering by nonspherical particles are found to cause serious distortions of the retrieved size distributions. Similar distortions are also found when incorrect refractive indices are used. Fourth, the effects of the different factors discussed in previous chapters on size distribution retrievals are addressed. Implications for instrumentation and theoretical models are explored. The overall results of this research suggest that precautions need to be taken due to the scale-mismatch when (1) comparing observations with model predictions, (2){A0}comparing measurements with instruments of different sampling scales, (3){A0}coupling models that describe phenomena of different scales. Size distribution measurements should be interpreted with caution when nonspherical particles and/or refractive index errors exist. The new results also provide useful information to guide and orient future research on instrumentation as well as theoretical models of size distributions.