Date of Award
Doctor of Philosophy (PhD)
Andrew D. Brown
Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. This dissertation aims to provide a modeling framework for studying the variation of wind speed and wind direction. To this end, three projects are conducted to address some of the key issues for modeling wind vectors.\\
First, a conditional decomposition approach is developed to model the joint distribution of wind speed and direction. Specifically, the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. Von Mises mixture model is used to accommodate the circular nature of wind direction. The conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the functional dependence of the Weibull parameters on wind direction. The conditional decomposition approach allows the modeling of complex distributions with relatively simple and flexible univariate models. Moreover, by studying the variations of wind speed with respect to wind direction, we gain valuable insights that would be overlooked if we solely focused on studying wind speed alone. These insights have significant implications for a wide range of applications involving wind data. This conditional modeling framework is further extended to investigate the potential enhancement of estimating extreme wind speeds. Specifically, parametric extreme value modeling approaches, including block maxima, peaks-over-thresholds, and point process methods, are utilized to model the upper tail of its conditional distribution. The purpose of this extension is to avoid misspecification issues associated with the Weibull model and to improve estimation efficiency. Simulation studies, analysis of output from climate model simulation, and model comparisons are discussed.\\
A key feature of the wind field data is its complicated temporal and spatial structure. Therefore, the final goal of this dissertation involves the spatio-temporal modeling of wind speed. The proposed model captures the seasonal variation and temporal and spatial variability by decomposing the wind speed process into the ``global structure'' of the spatio-temporal mean component, the ``local structure'' that consists of a combination of time varying empirical orthogonal functions (EOFs), and a first-order dynamical spatial Gaussian process (GP). A crucial element of the proposed decomposition is leveraging the inherent circularity of the annual seasonal cycle to create effective replications in time. This enables us to employ more flexible nonstationary space-time modeling through EOF analysis and enhance computation efficiency using dynamical GPs.
Murphy, Eva, "A Framework for Statistical Modeling of Wind Speed and Wind Direction" (2023). All Dissertations. 3418.