Date of Award

12-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Dr. Robert Lund

Committee Member

Dr. Colin Gallagher

Committee Member

Dr. Peter Kiessler

Committee Member

Dr. Xiaoqian Sun

Abstract

The first part of this dissertation studies genetic algorithms as a means of estimating the number of changepoints and their locations in a climatic time series. Such methods bypass classical subsegmentation algorithms, which sometimes yield suboptimal conclusions. Minimum description length techniques are introduced. These techniques require optimizing an objective function over all possible changepoint numbers and location times. Our general objective functions allow for correlated data, reference station aspects, and/or non-normal marginal distributions, all common features of climate time series. As an exhaustive evaluation of all changepoint configurations is not possible, the optimization is accomplished via a genetic algorithm that random walks through a subset of good models in an intelligent manner. The methods are applied in the analysis of 173 years of annual precipitation measurements from New Bedford, Massachusetts and the North Atlantic Basin's tropical cyclone record. In the second part, trend estimation techniques are developed for monthly maximum and minimum temperatures observed in the conterminous 48 United States over the last century. While most scientists concur that this region has warmed in aggregate, there is no a priori reason to believe that temporal trends in extremes will have same patterns as trends in average temperatures. Indeed, under minor regularity conditions, the sample partial sum and maximum of stationary time series are asymptotically independent. Climatologists have found that minimum temperatures are warming most rapidly; such an aspect can be investigated via our methods. Here, models with extreme value and changepoint features are used to estimate trend margins and their standard errors. A spatial smoothing is then done to extract general structure. The results show that monthly maximum temperatures are not significantly changing - perhaps surprisingly, in more cases than not, they are cooling. In contrast, the minimum temperatures show significant warming. Overall, the Southeastern United States shows the least warming (even some cooling) and the Western United States, Northern Midwest, and New England have experienced the most warming.

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