Characterizing diurnal and interannual variability in the atmosphere through physical and stochastic models

Mathematical models are commonplace in atmospheric science and continue to provide insight into processes across spatial and temporal scales. The study of climate dynamics relies on a spectrum of mathematical models, ranging from physical models based on the governing equations of fluid dynamics to statistical models that utilize probability to represent climate as the distribution of weather events. Hierarchical statistical models, which utilize multiple levels of conditional probability distributions, provide a framework for combining the principles or actual mathematical framework of physical models into statistical models. Development of computational tools for Bayesian analysis of hierarchical models has improved their utility, and spatio-temporal models are often implemented for climate applications. In three papers, this dissertation implements several physical and statistical models to investigate modes of variability in the climate system. The first paper develops statistical models for the diurnal cycle of relative humidity while accounting for spatial dependence in the observed realizations. The diurnal cycle varies stochastically from day to day through a dynamic model. The second study focuses on the interannual variability of large-scale stationary disturbances in the Northern Hemisphere winter circulation. The stationary waves are maintained by forcing mechanisms including anomalous heating patterns and the mean flow. Through an experiment with a numerical model, this study investigates the stationary wave response to variations in heating and the mean wind. The third component investigates the diurnal behavior of the atmospheric hydrological cycle. The study's analysis focuses on the conditional distributions of water vapor flux divergence given neighboring values. This aids the construction of a hierarchical spatial statistical model with random conditional variances. Bayesian analysis for a spatio-temporal version of the model includes posterior predictive diagnostics based on empirical conditional moments.