  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.
