This study advances nonstationary precipitation modeling by using single, flexible distributions to analyze trends across the full daily spectrum. We demonstrate that evolving shape parameters are critical for accurately capturing observed differential changes in low, medium, and extreme quantiles. This method ensures statistical consistency, providing reliable trend assessments over the two-component framework common in climate impact analysis. 

We derived a new statistical test that can compare climate models and observations more broadly than before, while allowing for both natural fluctuations and human influences. Tests on global temperature data show that most climate models differ from observations in important ways.

Standard algorithms for estimating the power spectral density of finite discrete data require interpolating missing samples, which usually produces biased estimates. An unbiased estimate can be obtained by taking the Fourier transform of the unbiased estimator of the circular autocorrelation, using only the available data. With missing samples, this estimator can produce negative power spectral densities, but converges to positive values when averaged over a sufficient number of realizations.

Using information derived from tree-rings, we reconstruct possible combinations of past temperatures and precipitation amounts.  This lets us put current changes in context and shows, for example, that the 1930s were likely the driest decade on record in central Kansas, while the late 20th century was likely the wettest period on record in the North American southwest.

We studied how small, short-lived ocean features in the Mediterranean Sea affect microscopic plant communities that support ocean life. Using a new statistical approach, we found strong evidence that these features can host unique communities not found in surrounding waters. This discovery helps us better understand the role of ocean dynamics in shaping marine ecosystems, even when data are limited and conditions vary widely.

Extreme precipitation probability estimation is vital for hazard protection design but has high uncertainty. We tested six statistical models using 2000 years of climate data. Our Bayesian hierarchical duration-dependent Generalized Extreme Value model shows the highest accuracy and robustness for sample sizes between 30 and 100 years, making it highly promising for use with limited observational records.