Extreme weather and climate events can be catastrophic not only when a single climate variable approaches extreme levels, but also when rare combinations of multiple variables compound to produce dangerous conditions. For instance, heat waves are especially hazardous when high temperatures coincide with high relative humidity. Understanding the risk of such events necessitates developing statistical methods to capture the behavior of tails of multivariate distributions. Our research seeks to quantify uncertainty in estimates of the extreme p-isolines of bivariate probability distributions, that is, bivariate thresholds that are jointly exceeded with some small probability p.

Several methods to estimate such isolines given geophysical data exist, but little work has been done to quantify their uncertainty in a rigorous manner. Relying on isoline estimates without considering uncertainty may lead, for example, to overestimating the return time of lethal combinations of heat and humidity, leaving societies unprepared for the early arrival of a “once-per-thousand-years” heat wave event. We explain the theory behind our method, showcase preliminary simulation results demonstrating the desired coverage guarantees on known distributions, and discuss open theoretical and methodological challenges. We also describe potential uses of this method on real datasets, including the detection of climate-change-driven shifts in the severity of multivariate extreme weather and climate events.