This paper presents a novel study on boxplot-valued data in climatological applications. Our methodologies are applied to the Berkeley Earth Surface Temperature Study. We validate our approaches through comprehensive simulations, comparing Bayesian and frequentist estimators for efficiency and accuracy. The results provide robust insights into climatic trends, particularly summer average temperatures across European countries. 

Drought frequently affects southern Ethiopia, and inadequate rainfall data complicate monitoring. Satellite data from three sources were evaluated for accuracy, showing the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) to be the most reliable. We assessed drought severity using the standardized precipitation index, aligning results with historical drought patterns. The study emphasizes that the CHIRPS enhances drought monitoring and early-warning systems in the region.

Correctly forecasting weather is crucial for decision-making in various fields. Standard multivariate verification tools have limitations, and a single tool cannot fully characterize predictive performance. We formalize a framework based on aggregation and transformation to build interpretable verification tools. These tools target specific features of forecasts, improving predictive performance characterization and bridging the gap between theoretical and physics-based tools.

We investigate how to make statistical predictions of extreme weather such that events predicted to occur with a probability of 1 % will occur 1 % of the time. We apply the methods we describe to a standard extreme weather attribution example from the recent climate literature. We find that the methods we describe imply that extremes are roughly twice as likely as when estimated using maximum likelihood. We have developed a software package to make it easy to apply these methods.