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Three chapters are included in this dissertation. Chapter 1 introduces the research herein. The societal impacts of future climate change depend on changes in temperature variability in addition to changes in mean temperatures. While general circulation models (GCMs) predict changes in both means and variability, GCMs cannot fully reproduce present-day temperature distributions. In Chapter 2, we address an ensuing need for simulations of future temperatures that combine the observational record and GCM projections of changes in means and variability. Our perspective is that such simulations should be based on transforming observations to account for GCM projected changes, in contrast transforming GCM output to correct for discrepancies with observations. Our methodology is designed for simulating transient (nonstationary) climates, which are evolving in response to changes in CO$_2$ concentrations (as is the Earth at present). Since the proposed simulation requires GCM projected changes in covariance, we describe a statistical model for the evolution of temporal covariances in a GCM, and apply this model to an ensemble of runs from one GCM, CCSM3. We find that, in CCSM3, changes in covariance can be explained as a function of the regional mean change in temperature and the rate of change of warming. This feature means that our statistical model can be used to emulate the evolving covariances in the GCM under scenarios for which the GCM has not been run. When combined with an emulator for mean temperature, our methodology can simulate temperatures under such scenarios. The emulator for variability changes is also of interest on its own as a summary of GCM projections of variability changes. Chapter 3 concerns modeling a bivariate meteorological process -- temperature and dew point -- measured at high temporal frequencies and given covariate information. Dew point is bounded above by temperature, so nonstandard methods are needed to characterize their bivariate distribution, especially at times when temperature approaches dew point (or equivalently when relative humidity approaches 100\%). The data analyzed are minute-to-minute measurements from early May from the years 2003 through 2012 at the Atmospheric Radiation Measurement (ARM) Program's Southern Great Plains (SGP) site in Northern Oklahoma, at the central facility near Lamont, OK. We find that, in addition to relative humidity, solar radiation and the magnitude of minute-to-minute changes in wind direction help explain aspects of the behavior of the bivariate process. We propose a parametric model for how the spectral matrix of a high-frequency component of the process varies with these covariates over time. The spectral approach allows for convenient and interpretable models of bivariate processes in time and our model captures many of observed features of the data.


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