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.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

DEVELOPMENT AND VALIDATION OF THE ANTERIOR CRUCIATE LIGAMENT INJURY-RISK-ESTIMATION QUIZ (ACL-IQ)

Over 2 million Anterior Cruciate Ligament (ACL) injuries occur annually worldwide resulting in considerable economic and health burdens (e.g., suffering, surgery, loss of function, risk for re-injury, and osteoarthritis). Current screening methods are effective but they generally rely on expensive and time-consuming biomechanical movement analysis, and thus are impractical solutions. In this dissertation, I report on a series of studies that begins to investigate one potentially efficient alternative to biomechanical screening, namely skilled observational risk assessment (e.g., having experts estimate risk based on observations of athletes movements). Specifically, in Study 1 I discovered that ACL injury risk can be accurately and reliably estimated with nearly instantaneous visual inspection when observed by skilled and knowledgeable professionals. Modern psychometric optimization techniques were then used to develop a robust and efficient 5-item test of ACL injury risk prediction skill—i.e., the ACL Injury-Risk-Estimation Quiz or ACL-IQ. Study 2 cross-validated the results from Study 1 in a larger representative sample of both skilled (Exercise Science/Sports Medicine) and un-skilled (General Population) groups. In accord with research on human expertise, quantitative structural and process modeling of risk estimation indicated that superior performance was largely mediated by specific strategies and skills (e.g., ignoring irrelevant information), independent of domain general cognitive abilities (e.g., metal rotation, general decision skill). These cognitive models suggest that ACL-IQ is a trainable skill, providing a foundation for future research and applications in training, decision support, and ultimately clinical screening investigations. Overall, I present the first evidence that observational ACL injury risk prediction is possible including a robust technology for fast, accurate and reliable measurement—i.e., the ACL-IQ. Discussion focuses on applications and outreach including a web platform that was developed to house the test, provide a repository for further data collection, and increase public and professional awareness and outreach (www.ACL-IQ.org). Future directions and general applications of the skilled movement analysis approach are also discussed.