Extreme weather events are rare, but disproportionately important for societal and economic risk. Estimating their likelihood is therefore central to applications ranging from infrastructure design to financial risk management. This task is fundamentally constrained by limited data. Observational records are often too short to robustly characterize rare events, while the underlying climate system is changing in ways that can alter the behavior of extremes. At the same time, statistical approaches for estimating extreme event probabilities and physical studies of the processes that generate extremes are often developed separately, limiting our ability to interpret risk in a coherent framework. This thesis investigates how statistical limitations and physical climate processes jointly shape the estimation and interpretation of extreme events under limited data conditions. Using a combination of idealized climate model simulations, observational datasets, and statistical analysis, I examine both the reliability of extreme value estimates and the mechanisms that influence climate extremes, with a focus on extreme heat. I show that short climate records can lead to systematic underestimation of rare event probabilities and large uncertainty in return level estimates. These results quantify how sample size and tail behavior constrain the reliability of statistical inference and provide guidance for identifying when available data are insufficient for robust estimation, including under climate change imposing unknown trends. I also demonstrate that observed changes in the frequency of extreme heat are, to first order, consistent with shifts in the underlying temperature distribution. A novel statistical method of isolating low-frequency variability from noisy climate data yields a simple and generalizable interpretation of observed temperature trends. Finally, I show that in regions with strong land–atmosphere coupling, such as the Central United States, soil moisture deficits and atmospheric circulation patterns can amplify extreme heat beyond what occurs on typical days. These nonlinear processes influence extreme events in a way that may be challenging to anticipate at long timescales in the future. These results highlight both the limits of statistical inference for rare events and the role of physical mechanisms in shaping extreme behavior. This dissertation provides practical and conceptual tools for interpreting and quantifying extremes under limited data in a changing climate.
Ronak Nishesh Patel (Mon,) studied this question.