A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting

Abstract

Extreme streamflow is a key indicator of flood risk, and quantifying the changes in its distribution under non-stationary climate conditions is key to mitigating the impact of flooding events. We propose a non-stationary process mixture model (NPMM) for annual streamflow maxima over the central US (CUS) which uses downscaled climate model precipitation projections to forecast extremal streamflow. Spatial dependence for the model is specified as a convex combination of transformed Gaussian and max-stable processes, indexed by a weight parameter which identifies the asymptotic regime of the process. The weight parameter is modeled as a function of the annual precipitation for each of the two hydrologic regions within the CUS, introducing spatio-temporal non-stationarity within the model. The NPMM is flexible with desirable tail dependence properties, but yields an intractable likelihood. To address this, we embed a neural network within a density regression model which is used to learn a synthetic likelihood function using simulations from the NPMM with different parameter settings. Our model is fitted using observational data for 1972--2021, and inference carried out in a Bayesian framework. The two regions within the CUS are estimated to be in different asymptotic regimes based on the posterior distribution of the weight parameter. Annual streamflow maxima estimates based on global climate models for two representative climate pathway scenarios suggest an overall increase in the frequency and magnitude of extreme streamflow for 2006-2035 compared to the historical period of 1972-2005.

References in corpus (6)

• Stationary max-stable fields associated to negative definite functions
• A hierarchical max-stable spatial model for extreme precipitation
• On spatial extremes: with application to a rainfall problem
• Informed attribution of flood changes to decadal variation of atmospheric, catchment and river drivers in Upper Austria
• Bayesian spatio-temporal models for stream networks
• Neural Networks for Parameter Estimation in Intractable Models

Cited by in corpus (4)

• Flexible space-time models for extreme data
• Semi-parametric bulk and tail regression using spline-based neural networks
• Neural Bayes estimation and selection for complex bivariate extremal dependence models
• Using spatial extreme-value theory with machine learning to model and understand spatially compounding weather extremes