Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process

TL;DR

This paper introduces a novel deep learning-based spatial model for extreme streamflow analysis, combining Gaussian and max-stable processes to better capture tail dependence and detect changes over time.

Contribution

It develops a process mixture model with neural network-based likelihood approximation, enabling scalable analysis of spatial extremes in large datasets.

Findings

Identified regions with increasing extreme streamflow in the US.

Demonstrated the model's ability to capture realistic tail dependence.

Provided a scalable approach for large-scale spatial extreme value analysis.

Abstract

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly suited for modeling extreme events. Spatial extreme value models with more realistic tail dependence characteristics are under active development. They are theoretically justified, but give intractable likelihoods, making computation challenging for small datasets and prohibitive for continental-scale studies. We propose a process mixture model (PMM) which specifies spatial dependence in extreme values as a convex combination of a Gaussian process and a max-stable process, yielding desirable tail dependence properties but intractable likelihoods. To address this, we employ a unique computational strategy where a feed-forward neural network is embedded in a density regression model to approximate the conditional distribution at one spatial location given a set of neighbors. We then use this univariate density function to approximate the joint likelihood for all locations by way of a Vecchia approximation. The PMM is used to analyze changes in annual maximum streamflow within the US over the last 50 years, and is able to detect areas which show increases in extreme streamflow over time.