标题： 数据缺口和异常值对恢复力指标的影响 显示英文标题

标题： The influence of data gaps and outliers on resilience indicators

摘要： 地球系统主要组成部分的韧性或稳定性正越来越多地受到人为压力的威胁，迫切需要可靠的早期预警信号以应对突发且不可逆的制度转变。广泛使用的数据驱动韧性指标基于方差和自相关性检测“临界减速”，这是稳定性下降的一个标志。然而，这些指标的解释因相互依赖关系理解不足以及对常见数据问题（如缺失值和异常值）的敏感性而受阻。在这里，我们建立了基于方差和自相关的韧性指标之间统计依赖性的严格数学分析，揭示了它们的一致性从根本上由时间序列的初始数据点驱动。使用合成数据和实际数据，我们证明缺失值显著削弱了指标的一致性，而异常值引入了系统偏差，导致基于时间自相关的韧性被高估。我们的研究结果为处理策略和准确性评估提供了必要且严格的理论基础，适用于越来越多利用现实世界数据推断系统韧性变化的学科。 显示英文摘要

摘要： The resilience, or stability, of major Earth system components is increasingly threatened by anthropogenic pressures, demanding reliable early warning signals for abrupt and irreversible regime shifts. Widely used data-driven resilience indicators based on variance and autocorrelation detect `critical slowing down', a signature of decreasing stability. However, the interpretation of these indicators is hampered by poorly understood interdependencies and their susceptibility to common data issues such as missing values and outliers. Here, we establish a rigorous mathematical analysis of the statistical dependency between variance- and autocorrelation-based resilience indicators, revealing that their agreement is fundamentally driven by the time series' initial data point. Using synthetic and empirical data, we demonstrate that missing values substantially weaken indicator agreement, while outliers introduce systematic biases that lead to overestimation of resilience based on temporal autocorrelation. Our results provide a necessary and rigorous foundation for preprocessing strategies and accuracy assessments across the growing number of disciplines that use real-world data to infer changes in system resilience.