Projecting Flood Frequency Curves Under a Changing Climate Using Spatial Extreme Value Analysis

Climate change is often described in terms of the mean, but it will be felt most acutely in terms of extreme events. In particular, the International Panel of Climate Change’s recent Sixth Assessment warns of an increase in the likelihood and magnitude of extreme flooding events in upcoming decades. Understanding the spatiotemporal variability of these changes is critical to mitigating their impact.

However, current methods for spatial extreme value analysis are limited in their modeling flexibility and computational capabilities, and thus methodological work is required to analyze extreme events across the United States. Therefore, in this project, the investigators will develop new methodological and computational tools for spatial extreme value analysis and apply them to forecasting flood risk under a changing climate.

The project team is comprised of an interdisciplinary group of statisticians and hydrologists to accomplish these ambitious objectives and ensure that the results are disseminated to the appropriate communities. The analysis combines fifty years of annual maximum streamflow observations at hundreds of gauges provided by the United States Geological Survey with CMIP6 climate model output produced under different climate scenarios.

This analysis will provide high-resolution maps of anticipated change in flood risk and local flood frequency curves to inform water infrastructure projects. A highlight of the project is a workshop that will foster synergy between statisticians and hydrologists by encouraging the sharing of ideas, approaches and solutions to flood risk prediction, and aid in the formulation of a common language shared by statisticians and hydrologists for successful transfer of knowledge across disciplines. The overall objective is to improve resiliency to extreme flooding events in the United States.

This project will result in major advances in both spatial extreme value analysis and hydrology. The investigators will pursue two methods that exploit recent developments in distributed computing, machine learning and artificial intelligence, respectively, to improve computation for spatial extreme value analysis. Computation for spatial extremes is challenging because the most common model is the max-stable process, and this model gives an intractable likelihood function and is thus not conducive to direct application of maximum likelihood or Bayesian analysis.

To overcome this difficulty, this project will develop a divide-and-conquer method that analyzes data separately by subregion and then combines the results using generalized method of moments techniques. It is shown that this procedure has desirable theoretical properties and gives substantial performance gain over state-of-the-art methods. The project also develops a new method under the Bayesian framework that is preferred for uncertainty quantification.

The new method decomposes the intractable likelihood function into a sequence of simpler functions, and uses deep-learning distribution regression to approximate these simpler functions. This approximation can be arbitrarily precise with computational requirements that scale linearly with the number of spatial locations, facilitating analysis of large datasets.

The project culminates with the analysis of flood-frequency curves across the US. Compared to current methods, by using spatial extreme value analysis the analysis borrows information across space to improve estimation of small probabilities and estimate the probability of multiple locations simultaneously experiencing an extreme event. This project will produce new software for extreme value analysis and also train two graduate students in theoretical, computational and applied extreme value analysis in hydrology with a strong emphasis on interdisciplinary collaboration.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.