Global climate is changing at an alarming rate, with an increase in heat waves, wildfires, extreme weather events, and rising sea levels, which could cost the United States billions of dollars in lost labor, reduced crop yields, flooding, health problems, and crumbling infrastructure. Reports by hundreds of US climate scientists from 13 federal agencies in the Fourth National Climate Assessment (2018) predict that the US economy will shrink by as much as 10% by the end of the century if global warming continues with current trends. Extreme precipitation, in particular, has led to significant damage through flooding, bridge scouring, land-slides, etc.; therefore, it is critical to develop accurate and reliable methods for future extreme precipitation projection. This dissertation proposes new methods of improved projections of such extremes by appropriately accounting for a changing climate.

First, this dissertation studies how to model extreme precipitation using Markov Chains and dynamic optimization. By incorporating day-to-day serial dependency and dynamic optimization, the model improves the accuracy of extreme precipitation analysis significantly.

The dissertation also examines future projections of extreme precipitation. State-of-the-art methods for future precipitation projections are based on downscaled Global Climate Models (GCMs), which are not always accurate for extreme precipitation projection. This work studies accuracy when using downscaled GCMs for extreme precipitation and designed new methods based on copulas to improve the accuracy.

Finally, the above methods are applied to the analysis of future trends of intensity-duration-frequency (IDF) curves, which, in turn, have extensive applications in designing drainage systems. To incorporate geographic influence on local areas, a machine-learning-based solution is proposed and validated. The results show that the gradient boosting tree can be used to accurately project future IDF curves for short durations. It is also projected that short-duration intensity will increase up to 23% for the selected representative stations in this century.

In summary, this dissertation systemically studies different aspects of improvements and applications of extreme precipitation projection. By using mathematical models, such as copula and Markov Chains as well as various machine-learning models (i.e., gradient boosting tree), extreme precipitation projection can be made significantly more reliable for use.