Spatio-Temporal Statistical Modeling with Application to Wind Energy Assessment in Saudi Arabia

Abstract

Saudi Arabia has been trying to change its long tradition of relying on fossil fuels and seek renewable energy sources such as wind power. In this thesis, I firstly provide a comprehensive assessment of wind energy resources and associated spatio-temporal patterns over Saudi Arabia in both current and future climate conditions, based on a Regional Climate Model output. A high wind energy potential exists and is likely to persist at least until 2050 over a vast area ofWestern Saudi Arabia, particularly in the region between Medina and the Red Sea coast and during Summer months. Since an accurate assessment of wind extremes is crucial for risk management purposes, I then present the first high-resolution risk assessment of wind extremes over Saudi Arabia. Under the Bayesian framework, I measure the uncertainty of return levels and produce risk maps of wind extremes, which show that locations in the South of Saudi Arabia and near the Red Sea and the Persian Gulf are at very high risk of disruption of wind turbine operations. In order to perform spatial predictions of the bivariate wind random field for efficient turbine control, I propose parametric variogram matrix (function) models for cokriging, which have the advantage of allowing for a smooth transition between a joint second-order and intrinsically stationary vector random field. Under Gaussianity, the covariance function is central to spatio-temporal modeling, which is useful to understand the dynamics of winds in space and time. I review the various space-time covariance structures and models, some of which are visualized with animations, and associated tests. I also discuss inference issues and a case study based on a high-resolution wind-speed dataset. The Gaussian assumption commonly made in statistics needs to be validated, and I show that tests for independently and identically distributed data cannot be used directly for spatial data. I then propose a new multivariate test for spatial data by accounting for the spatial dependence. The new test is easy to compute, has a chi-square null distribution, and has a good control of the type I error and a high empirical power.