Geophysical systems are inherently complex and span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially pronounced for extreme events, which are primarily governed by their instantaneous properties rather than their average characteristics. Advances in dynamical systems theory, including the development of local dynamical indices such as local dimension and inverse persistence, have provided powerful tools for studying these short-lasting phenomena. However, existing applications of such indices often rely on predefined fixed spatial domains and scales, with limited discussion on the influence of spatial scales on the results. In this work, we present a novel spatially multiscale methodology that applies a sliding window method to compute dynamical indices, enabling the exploration of scale-dependent properties. Applying this framework to high-impact European summertime heatwaves, we reconcile previously different perspectives, thereby underscoring the importance of spatial scales in such analyses. Furthermore, we emphasize that our novel methodology has broad applicability to other atmospheric phenomena, as well as to other geophysical and spatio-temporal systems.

翻译：地球物理系统本质上是复杂的，跨越多个空间和时间尺度，使其动力学难以理解和预测。这一挑战对于极端事件尤为突出，因为极端事件主要受其瞬时属性而非平均特征所支配。动力学系统理论的进展，包括局部维度与逆持久性等局部动力学指数的发展，为研究这些短暂现象提供了有力工具。然而，此类指数的现有应用通常依赖于预定义的固定空间域和尺度，关于空间尺度对结果影响的讨论有限。在本研究中，我们提出了一种新颖的空间多尺度方法，该方法应用滑动窗口计算动力学指数，从而能够探索尺度依赖性特征。将此框架应用于欧洲夏季高影响热浪事件，我们调和了先前不同的观点，从而强调了空间尺度在此类分析中的重要性。此外，我们强调，我们的新方法对其他大气现象以及其他地球物理和时空系统具有广泛的适用性。