Graduation Year

2006

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mathematics and Statistics

Major Professor

Christopher P. Tsokos, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Marcus McWaters, Ph.D.

Committee Member

Charles Connor, Ph.D.

Keywords

Parametric Analysis, Extreme Value Distribution, Linear and Non-linear Modeling, Prediction and Forecasting

Abstract

This study consists of developing descriptive, parametric, linear and non-linear statistical models for such natural phenomena as hurricanes, lightning, flooding, red tide and volcanic fallout. In the present study, the focus of research is determining the stochastic nature of phenomena in the environment. These statistical models are necessary to address the variability of nature and the misgivings of the deterministic models, particularly when considering the necessity for man to estimate the occurrence and prepare for the aftermath.

The relationship between statistics and physics looking at the correlation between wind speed and pressure versus wind speed and temperature play a significant role in hurricane prediction. Contrary to previous studies, this study indicates that a drop in pressure is a result of the storm and less a cause. It shows that temperature is a key indicator that a storm will form in conjunction with a drop in pressure.

This study demonstrates a model that estimates the wind speed within a storm with a high degree of accuracy. With the verified model, we can perform surface response analysis to estimate the conditions under which the wind speed is maximized or minimized. Additional studies introduce a model that estimates the number of lightning strikes dependent on significantly contributing factors such as precipitable water, the temperatures within a column of air and the temperature range. Using extreme value distribution and historical data we can best fit flood stages, and obtain profiling estimate return periods.

The natural logarithmic count of Karenia Brevis was used to homogenize the variance and create the base for an index of the magnitude of an outbreak of Red Tide. We have introduced a logistic growth model that addresses the subject behavior as a function of time and characterizes the growth rate of Red Tide. This information can be used to develop strategic plans with respect to the health of citizens and to minimize the economic impact.

Studying the bivariate nature of tephra fallout from volcanoes, we analyze the correlation between the northern and eastern directions of a topological map to find the best possible probabilistic characterization of the subject data.

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