Extremal dependence or independence may occur among the components of univariate or bivariate random vectors. Assessing which asymptotic regime occurs and also its extent are crucial tasks when such vectors are used as statistical models for risk assessment in the field of Climatology under climate change conditions. Motivated by the poor resolution of current global climate models in North Atlantic Small Islands, the extremal dependence between a North Atlantic Oscillation index (NAOI) and rainfall was considered at multi-year dominance of negative and positive NAOI, i.e., −NAOI and +NAOI dominance subperiods, respectively. The datasets used (from 1948–2017) were daily NAOI, and three daily weighted regionalised rainfall series computed based on factor analysis and the Voronoi polygons method from 40 rain gauges in the small island of Madeira (∼740 km2), Portugal. The extremogram technique was applied for measuring the extremal dependence within the NAOI univariate series. The cross-extremogram determined the dependence between the upper tail of the weighted regionalised rainfalls, and the upper and lower tails of daily NAOI. Throughout the 70-year period, the results suggest systematic evidence of statistical dependence over Madeira between exceptionally −NAOI records and extreme rainfalls, which is stronger in the −NAOI dominance subperiods. The extremal dependence for +NAOI records is only significant in recent years, however, with a still unclear +NAOI dominance.

中文翻译：

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使用极值图的小岛每日北大西洋振荡指数 (NAOI) 和加权区域降雨量的显着极值依赖性

单变量或双变量随机向量的分量之间可能出现极值依赖性或独立性。当这些向量被用作气候变化条件下气候学领域风险评估的统计模型时，评估出现哪种渐近机制及其范围是至关重要的任务。由于北大西洋小岛屿当前全球气候模型分辨率低，北大西洋涛动指数 (NAOI) 和降雨量之间的极值依赖被认为是负和正 NAOI 的多年主导地位，即 -NAOI 和 +NAOI分别占主导地位的子时期。使用的数据集（从 1948 年到 2017 年）是每日 NAOI，基于因子分析和 Voronoi 多边形方法从葡萄牙马德拉岛（约 740 平方公里）的 40 个雨量计计算出的三个每日加权区域化降雨系列。极值图技术用于测量 NAOI 单变量系列中的极值依赖性。交叉极值图确定了加权区域化降雨的上尾与每日 NAOI 的上尾和下尾之间的相关性。在整个 70 年期间，结果表明在异常 -NAOI 记录和极端降雨之间对马德拉的统计依赖性的系统证据，这在 -NAOI 优势子时期更强。然而，+NAOI 记录的极值依赖性仅在最近几年才显着，+NAOI 的主导地位仍不清楚。极值图技术用于测量 NAOI 单变量系列中的极值依赖性。交叉极值图确定了加权区域化降雨的上尾与每日 NAOI 的上尾和下尾之间的相关性。在整个 70 年期间，结果表明在异常 -NAOI 记录和极端降雨之间对马德拉的统计依赖性的系统证据，这在 -NAOI 优势子时期更强。然而，+NAOI 记录的极值依赖性仅在最近几年才显着，+NAOI 的主导地位仍不清楚。极值图技术用于测量 NAOI 单变量系列中的极值依赖性。交叉极值图确定了加权区域化降雨的上尾与每日 NAOI 的上尾和下尾之间的相关性。在整个 70 年期间，结果表明在异常 -NAOI 记录和极端降雨之间对马德拉的统计依赖性的系统证据，这在 -NAOI 优势子时期更强。然而，+NAOI 记录的极值依赖性仅在最近几年才显着，+NAOI 的主导地位仍不清楚。在整个 70 年期间，结果表明在异常 -NAOI 记录和极端降雨之间对马德拉的统计依赖性的系统证据，这在 -NAOI 优势子时期更强。然而，+NAOI 记录的极值依赖性仅在最近几年才显着，+NAOI 的主导地位仍不清楚。在整个 70 年期间，结果表明在异常 -NAOI 记录和极端降雨之间对马德拉的统计依赖性的系统证据，这在 -NAOI 优势子时期更强。然而，+NAOI 记录的极值依赖性仅在最近几年才显着，+NAOI 的主导地位仍不清楚。