Severe thunderstorms cause substantial economic and human losses in the United States. Simultaneous high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are favorable to severe weather, and both they and the composite variable $\mathrm{PROD}=\sqrt{\mathrm{CAPE}} \times \mathrm{SRH}$ can be used as indicators of severe thunderstorm activity. Their extremal spatial dependence exhibits temporal non-stationarity due to seasonality and large-scale atmospheric signals such as El Ni\~no-Southern Oscillation (ENSO). In order to investigate this, we introduce a space-time model based on a max-stable, Brown--Resnick, field whose range depends on ENSO and on time through a tensor product spline. We also propose a max-stability test based on empirical likelihood and the bootstrap. The marginal and dependence parameters must be estimated separately owing to the complexity of the model, and we develop a bootstrap-based model selection criterion that accounts for the marginal uncertainty when choosing the dependence model. In the case study, the out-sample performance of our model is good. We find that extremes of PROD, CAPE and SRH are generally more localized in summer and, in some regions, less localized during El Ni\~no and La Ni\~na events, and give meteorological interpretations of these phenomena.

翻译：强雷暴在美国造成了巨大的经济和人员损失。对流有效位能（CAPE）和风暴相对螺旋度（SRH）同时达到高值有利于强天气的发生，两者及其复合变量 $\mathrm{PROD}=\sqrt{\mathrm{CAPE}} \times \mathrm{SRH}$ 可作为强雷暴活动的指示因子。受季节性和大尺度大气信号（如厄尔尼诺-南方涛动，ENSO）的影响，它们的极值空间依赖性表现出时间非平稳性。为研究这一现象，我们引入了一个基于最大稳定布朗-雷施尼克场的时空模型，其范围通过张量积样条依赖于ENSO和时间。我们还提出了一个基于经验似然和自助法的最大稳定性检验。由于模型复杂性，边际参数和依赖参数需分别估计，并开发了一个基于自助法的模型选择准则，在选取依赖模型时考虑边际不确定性。案例研究中，该模型的样本外表现良好。我们发现PROD、CAPE和SRH的极值在夏季通常更为局地化，而在某些区域，厄尔尼诺和拉尼娜事件期间局地化程度减弱，并给出了这些现象的气象学解释。