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.

翻译：极端径流是洪水风险的关键指标，量化其在非平稳气候条件下的分布变化是减轻洪灾影响的核心。我们提出一种非平稳过程混合模型（NPMM），用于预测美国中部地区（CUS）的年径流极大值，该模型利用降尺度气候模型降水预测来预报极端径流。模型的空间依赖性通过变换高斯过程与最大稳定过程的凸组合来刻画，并由权重参数索引以识别过程的渐近分布类型。权重参数建模为CUS两个水文区各自年降水量的函数，从而在模型中引入时空非平稳性。NPMM具有灵活的尾部依赖特性，但其似然函数难以直接计算。为解决此问题，我们将神经网络嵌入密度回归模型，利用不同参数设置下NPMM的模拟结果学习合成似然函数。基于1972-2021年的观测数据进行模型拟合，并在贝叶斯框架下完成推断。根据权重参数的后验分布，CUS内两个区域被估计处于不同的渐近分布类型。基于两种代表性气候路径情景下全球气候模型的年径流极大值估算表明：与历史时期（1972-2005）相比，2006-2035年极端径流的频率和幅度总体呈上升趋势。