Date of Award

Fall 2013

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Ernst Linder

Abstract

This work explores two applications of extreme value analysis. First, we apply EV techniques to traffic stream data to develop an accurate distribution of capacity. Data were collected by the NHDOT along Interstate I93, and two adjacent locations in Salem, NH were examined. Daily flow maxima were used to estimate capacity, and data not associated with daily breakdown were deemed censored values. Under this definition, capacity values are approximated by the generalized extreme value (GEV) distribution for block maxima. To address small sample sizes and the presence of censoring, a Bayesian framework using semi-informative priors was implemented. A simple cross validation procedure reveals the GEV model, using both censored and observed capacity data, is suitable for probabilistic prediction. To overcome the uncertainty associated with a high number of censored values at one location, a hierarchical model was developed to share information between locations and generally improve fitted results.

Next, we perform a statistical downscaling by applying a CDF transformation function to local-level daily precipitation extremes (from NCDC station data) and corresponding NARCCAP regional climate model (RCM) output to derive local-scale projections. These high-resolution projections are essential in assessing the impacts of projected climate change. The downscaling method is performed on 58 locations throughout New England, and from the projected distribution of extreme precipitation local-level 25-year return levels are calculated. To obtain uncertainty estimates for future return levels, both a parametric bootstrap and Bayesian procedure are implemented. The Bayesian method consists of a semi-parametric mixture model for daily precipitation where extremes are modeled parametrically using generalized Pareto distributions, and non-extremes are modeled non-parametrically using quantiles. We find that these Bayesian credibility intervals are generally larger than those obtained from a previously applied parametric Bootstrap procedure, indicating that projected trends in New England precipitation tend to be less significant than is hinted at in many studies.

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