Novel Spatio-Temporal Models with Applications in Wind Forecasting

Abstract

This research asserts the benefits of incorporating atmospheric regimes from large-scale reanalysis datasets and accounting for regime- and region-specific prevailing winds in covariance models for accurate short-term wind forecasts at multiple weather stations. Extending from classic time series models, regime-switching autoregressive and vector autoregressive models, alongside their mixture counterparts, are utilized first to model short-term wind speed to 6 hours ahead at 23 weather stations across Alberta. The results underscore the advantages of simultaneous modelling of multiple locations and the integration of atmospheric information for short-term wind forecasting. Expanding our scope, we employ spatio-temporal covariance models to model wind speed at 131 weather stations in Alberta. Specifically, the Gneiting class is adopted for capturing the fully symmetrical features of the empirical correlation. To address the underfitting concerns of this model, theoretical foundations are laid for relaxing constraints on the interaction parameter via a discrete spatial grid. Moreover, to account for both prevailing wind speed and direction, we propose a novel form of Lagrangian covariance function and prove its validity under any finite-dimensional Euclidean space. Furthermore, we propose a regime-switching covariance model to enable the prevailing winds in the Lagrangian covariance function to vary by regime. This model is essentially a p-th order Markov chain Gaussian field with the Markov property held in the time domain. We investigate its limiting behaviour as well as its convergence rate and present a parameter estimation method. The superior performance of the proposed models is observed for both observed and unobserved weather stations, highlighting their utility for future wind farm site planning. The thesis concludes by exploring options for allowing regime-specific prevailing winds to vary by region, resulting in region-specific prevailing winds under each regime. This approach is motivated by the spatially varying benefits of modelling prevailing winds. New methods are proposed for estimating and incorporating regime-dependent prevailing winds into regime-switching covariance models, resulting in improved predictive performance for forecasting hourly wind speed at 142 weather stations in Alberta.