Estimation of the degree of polarization through computational sensing

The degree of polarization of a refected field from active laser illumination can be used for object identifcation and classifcation. The goal of this study is to investigate methods for estimating the degree of polarization for refected fields with active laser illumination, which involves the measurement and processing of two orthogonal field components (complex amplitudes), two orthogonal intensity components, and the total field intensity. We propose to replace interferometric optical apparatuses with a computational approach for estimating the degree of polarization from two orthogonal intensity data and total intensity data. Cramer-Rao bounds for each of the three sensing modalities with various noise models are computed. Algebraic estimators and maximum-likelihood (ML) estimators are proposed. Active-set algorithm and expectation-maximization (EM) algorithm are used to compute ML estimates. The performances of the estimators are compared with each other and with their corresponding Cramer-Rao bounds. Estimators for four-channel polarimeter (intensity interferometer) sensing have a better performance than orthogonal intensities estimators and total intensity estimators. Processing the four intensities data from polarimeter, however, requires complicated optical devices, alignment, and four CCD detectors. It only requires one or two detectors and a computer to process orthogonal intensities data and total intensity data, and the bounds and estimator performances demonstrate that reasonable estimates may still be obtained from orthogonal intensities or total intensity data. Computational sensing is a promising way to estimate the degree of polarization.

Development of a physically-based method for delineation of hydrologically homogeneous regions and flood quantile estimation in ungauged basins via the index flood method

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data is unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. It is generally accepted that hydrologic similarity results from similar physiographic characteristics, and thus these characteristics can be used to delineate regions and classify ungauged sites. However, as currently practiced, the delineation is highly subjective and dependent on the similarity measures and classification techniques employed. A standardized procedure for delineation of hydrologically homogeneous regions is presented herein. Key aspects are a new statistical metric to identify physically discordant sites, and the identification of an appropriate set of physically based measures of extreme hydrological similarity. A combination of multivariate statistical techniques applied to multiple flood statistics and basin characteristics for gauging stations in the Southeastern U.S. revealed that basin slope, elevation, and soil drainage largely determine the extreme hydrological behavior of a watershed. Use of these characteristics as similarity measures in the standardized approach for region delineation yields regions which are more homogeneous and more efficient for quantile estimation at ungauged sites than those delineated using alternative physically-based procedures typically employed in practice. The proposed methods and key physical characteristics are also shown to be efficient for region delineation and quantile development in alternative areas composed of watersheds with statistically different physical composition. In addition, the use of aggregated values of key watershed characteristics was found to be sufficient for the regionalization of flood data; the added time and computational effort required to derive spatially distributed watershed variables does not increase the accuracy of quantile estimators for ungauged sites. This dissertation also presents a methodology by which flood quantile estimates in Haiti can be derived using relationships developed for data rich regions of the U.S. As currently practiced, regional flood frequency techniques can only be applied within the predefined area used for model development. However, results presented herein demonstrate that the regional flood distribution can successfully be extrapolated to areas of similar physical composition located beyond the extent of that used for model development provided differences in precipitation are accounted for and the site in question can be appropriately classified within a delineated region.