Extreme weather events, such as windstorms and heatwaves, are driven by persistent atmospheric circulation patterns that evolve over several consecutive days. While traditional circulation-based studies often focus on instantaneous atmospheric states, capturing the temporal evolution, or trajectory, of these spatial fields is essential for characterizing rare and potentially impactful atmospheric behavior. However, performing an exhaustive similarity search on multi-decadal, continental-scale gridded datasets presents significant computational and memory challenges. In this paper, we propose TRAKNN (TRajectory Aware KNN), a fully unsupervised and data-agnostic framework for detecting geometrically rare short trajectories in spatio-temporal data with an exact kNN approach. TRAKNN leverages a recurrence-based algorithm that decouples computational complexity from trajectory length and efficient batch operations, maximizing computational intensity. These optimizations enable exhaustive analysis on standard workstations, either on CPU or on GPU. We evaluate our approach on 75 years of daily European sea-level pressure data. Our results illustrate that rare trajectories identified by TRAKNN correspond to physically coherent atmospheric anomalies and align with independent extreme-event databases.

翻译：极端天气事件（如风暴和热浪）通常由持续数日的稳定大气环流模式所驱动。尽管传统的环流研究多关注瞬时大气状态，但捕捉这些空间场的时间演化（即轨迹）对于表征罕见且可能具有重大影响的大气行为至关重要。然而，对跨越数十年、大陆尺度的网格化数据集进行详尽的相似性搜索，面临着巨大的计算与内存挑战。本文提出TRAKNN（轨迹感知KNN），一种完全无监督且与数据无关的框架，通过精确kNN方法检测时空数据中几何意义上罕见的短轨迹。TRAKNN采用基于递归的算法，将计算复杂度与轨迹长度解耦，并利用高效的批量操作最大化计算强度。这些优化使得在标准工作站（CPU或GPU）上进行详尽分析成为可能。我们在75年的欧洲日平均海平面气压数据上评估了该方法。结果表明，TRAKNN识别的罕见轨迹对应着物理上连贯的大气异常，并与独立的极端事件数据库相吻合。