A Spatial Markov Model for Climate Extremes

Spatial climate data are often presented as summaries of areal regions such as grid cells, either because they are the output of numerical climate models or to facilitate comparison with numerical climate model output. Extreme value analysis can benefit greatly from spatial methods that borrow information across regions. For Gaussian outcomes, a host of methods that respect the areal nature of the data are available, including conditional and simultaneous autoregressive models. However, to our knowledge, there is no such method in the spatial extreme value analysis literature. In this article, we propose a new method for areal extremes that accounts for spatial dependence using latent clustering of neighboring regions. We show that the proposed model has desirable asymptotic dependence properties and leads to relatively simple computation. Applying the proposed method to North American climate data reveals several local and continental-scale changes in the distribution of precipitation and temperature extremes over time. Supplementary material for this article is available online.空间气候数据常以面域（如网格单元）的汇总形式呈现，这要么是因为其本身为数值气候模式的输出结果，要么是为了便于与数值气候模式的输出结果进行比对。极值分析能够从跨区域信息共享的空间方法中获益良多。对于服从高斯分布的响应变量而言，已有诸多尊重数据面域特性的方法，包括条件自回归与同时自回归模型。然而据我们所知，空间极值分析领域的现有文献中尚未出现此类方法。本文提出一种面向面域极值问题的新方法，该方法通过邻近区域的潜在聚类来刻画空间依赖性。我们证明所提模型具备理想的渐近依赖性特性，且计算过程相对简便。将所提方法应用于北美气候数据后，我们发现降水与气温极值的分布在时间维度上存在若干局地及大陆尺度的变化。本文的补充材料可在线获取。