Understanding and mapping extreme heat is critical for risk management and public health planning, particularly in regions with complex terrain and heterogeneous climate. We present a case study of extreme heat in the Four Corners region of the United States, using high-resolution surface skin temperature data from the North American Land Data Assimilation System to characterize spatially heterogeneous and seasonally varying extremes across complex terrain, and to assess their implications for heat-related public health risks. Spatial extremes exhibit complex dependencies across geographic regions, which require sophisticated statistical models to capture. While recent advances in spatial extreme value modeling provide flexible representations of joint tail dependencies, statistical inference remains computationally demanding, especially for datasets with a large number of locations. To address this, we propose a random scale mixture process that facilitates Bayesian inference of spatial extremes, and develop scalable inference strategies that leverage advances in spatial modeling and amortized learning. We evaluate the proposed inference methods through large-scale simulation studies, representing the first such extensive study in spatial extremes, and a high-resolution surface skin temperature application in the Four Corners region. Surface skin temperature is particularly useful as a predictor for air temperature, for studying heatwaves and related environmental phenomena, and to calculate heat indices reflecting downstream health risks at any location. Our findings provide insights into efficient, data-driven approaches for modeling spatial extremes, and serve as guidelines for practitioners in the fields of climate science, environmental risk assessment, and beyond.

翻译：理解并绘制极端高温分布对风险管理和公共卫生规划至关重要，尤其在复杂地形与气候异质性区域。本研究以美国四角地区为案例，利用北美陆面数据同化系统的高分辨率地表皮肤温度数据，刻画复杂地形下空间异质性且季节性变化的极端事件，并评估其对高温相关公共卫生风险的影响。空间极端事件在地理区域间表现出复杂的依赖关系，需借助复杂统计模型进行捕捉。尽管空间极值模型的近期进展提供了联合尾部分布的灵活表达，但统计推断仍面临巨大计算挑战，尤其是针对大样本位置数据集。为此，我们提出一种随机尺度混合过程以促进空间极值的贝叶斯推断，并开发可扩展的推断策略，结合空间建模与摊销学习的进展。通过大规模模拟研究（该领域首次此类系统性研究）及四角地区高分辨率地表皮肤温度应用，我们评估了所提推断方法。地表皮肤温度作为气温预测因子，在研究热浪及相关环境现象、计算反映下游健康风险的任何地点的热指数方面具有独特价值。本研究为空间极值建模提供了高效数据驱动方法，并为气候科学、环境风险评估等领域的实践者提供指导。