Moving Towards Dynamic/Causal Process Models for Spatio-Temporal Extremes

The last decade has seen a large number of severe heatwaves that were unprecedented in the observational record, highlighting the challenges associated with accurately quantifying the likelihood and magnitude of future extreme events. An alternative to such probabilistic assessments is identification of upper bounds that quantify the hottest surface air temperatures that can possibly be achieved by the end of the 21st century. Theory, simulations, and observational analyses support the existence of a finite upper bound for surface air temperature; however, estimates for future upper-bound values that are realistic and usable for planning remain unavailable. Here, we use atmospheric theory to constrain statistical estimates of surface air temperature upper bounds in the Northern Hemisphere midlatitudes where convection is the limiting mechanism for surface heating. We find that by incorporating atmospheric dynamics within a flexible spatial extremes copula, we can anticipate the most extreme heatwave events over the last four decades. Furthermore, surface and atmospheric humidity play an important role in modulating best- and worst-case upper bound estimates by accounting for the effect of dry-air entrainment. Ultimately, our results provide an important bridge between data-driven (purely statistical) and data-agnostic (purely theoretical) upper bound estimates of surface air temperature. 

We propose a new model and estimation framework for spatiotemporal streamflow outcomes that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture of Gaussian and max-stable spatial and temporal random variables. A censoring mechanism allows us to leverage observations in the bulk to improve modeling of the tail. As the likelihood is intractable, we develop a deep Vecchia approximation to the likelihood using neural networks to fit a flexible quantile regression model with monotonic splines. Simulations and modeling of streamflow data from the U.S. Geological Survey illustrate the feasibility and practicality of our approach. 

Decision-makers use projections from computer models to prepare for natural hazards including wildfires and floods. Understanding how the computer model inputs influence its projections is a key step in this process. Sobol' sensitivity analysis quantifies the importance of uncertain computer model inputs and their interactions. Performing Sobol' sensitivity analysis can be computationally costly. Replacing the computer model with an emulator reduces the computational burden (Roth et al., 2025). The Bayesian adaptive spline surface (BASS) emulator (1) efficiently handles high-dimensional input spaces and (2) provides Sobol' sensitivity indices without evaluating the emulator (Francom et al., 2018). Strategically adding data points to train the emulator (via adaptive sampling) can further reduce the computational burden by reducing the amount of training data required. We propose an adaptive sampling approach to train the BASS emulator that exploits the Monte Carlo error-free sensitivity indices provided to guide the sampling process. Our process can be tailored to various goals for Sobol' sensitivity analysis, including screening (identifying a set of low sensitivity inputs), ranking (ordering inputs by their relative impact on the model output), and factor mapping (identifying areas of the input space that lead to critical model output values). By drastically reducing computational costs, our approach enables Sobol' sensitivity analysis on a limited computational budget for slow, high-dimensional computer models. Therefore, our approach has the potential to improve understanding of high-dimensional complex systems, such as the reliability of power systems to natural hazards. 

Clusters of extremes in space such as floods and wildfires are ubiquitous in the environment. These spatial clusters of extreme events vary over time as well. Environmental processes are governed by underlying dynamical/mechanistic relationships that concern many variables that can interact both linearly and non-linearly. Indeed, the mechanistic dynamics of such processes can produce extremes through internal sources (e.g., transient growth) and via external forcing. In this research, we build a statistical modeling framework that can include a spatio-temporal dynamics but allows for different types of forcing (extremes and non-extremes). That is, this model should allow for "typical" behavior in the bulk of the marginal distribution but allow for non-trivial extremes (i.e., asymptotic dependence/independence) in either tail.  We use real data to demonstrate that this method can also allow for the modeling of event-level data without having to extract maxima or threshold exceedances.