Statistics of Extremes with Applications in Climate

Whitney K Huang, Purdue University

Abstract

Extreme events such as heatwaves and hurricanes can produce huge damages to both human society as well as the environmental systems. Thus, it is important to estimate the magnitude of future extreme events along with estimation uncertainty. In this dissertation, we present three studies ranging from estimating temperature extremes (e.g. 50-year return level of annual maximum temperature) and developing statistical methods to better characterize upper tail of the precipitation distributions to modeling spatial nonstationary covariance structure that commonly arises in environmental processes in a global scale. In the first study, we make use of millennial runs of climate simulations and model the temperature extremes (annual maxima/minima) using the generalized extreme value distribution. We investigate how temperature extremes might change and how well these changes can be estimated as a function of data length. The exceptionally long climate simulations (1000 years of daily output) used here not only enable us to estimate the changes in temperature extremes precisely but also allow for thorough assessments of the commonly made assumption in extreme value analysis. Furthermore, we demonstrate the danger of using short time series to estimate the changes in temperature extremes and we discuss the implications in the context of climate change. The Log-Histospline method is developed and presented in the second study of the dissertation. The method aims to achieve a flexible modeling for the bulk part of the data while maintaining accurate estimation in the upper tail of a distribution. Combining ideas from data transformation, spline smoothing, and penalized Poisson regression, we demonstrate the usefulness of our proposed method through simulation studies and we discuss an application of estimating precipitation extremes. The third study of the dissertation is focused on modeling the nonstationary spatial covariance structure. We adopt a spatial basis function approach by projecting the sample covariance matrix into a low-dimensional space. By regularizing sample covariance matrix, we are able to preserve the long range dependence structure observed in the data while making the inference reliable by exploiting the spatial structure. We illustrate the method by analyzing the country-wise growing season temperature on the global. The results show that the proposed model can capture the teleconnections well.

Degree

Ph.D.

Advisors

Zhang, Purdue University.

Subject Area

Climate Change|Statistics

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