AI 中文总结
研究临界转变早期预警信号，提出基于特征向量旋转的EWS，通过时变参数卡尔曼滤波器估计\(\beta\)，测试发现其对扰动敏感度更高，能先于基于特征值的信号，在多区域数据和模拟系统中验证，或可作为通用跨系统EWS。
AI 中文摘要
临界转变的早期预警信号（EWS）主要基于系统雅可比矩阵主导特征值的变化，如方差上升和滞后1自相关（AR(1)）。然而，基于特征值的EWS对扰动的敏感度为\(O(\Delta\theta^2)\)，限制了其提前时间。我们引入了一种基于特征向量旋转的互补EWS，通过时变参数卡尔曼滤波器在对数-对数空间中估计时变弹性\(\beta(t)=d\log y / d\log x\)来衡量。由于特征向量敏感度为\(O(\Delta\theta)\)，预计\(\beta\)会先于基于特征值的信号。我们在24年的美国国家航空航天局（NASA）Airs月度数据（2002 - 2026年，284次观测）上对三个气候不同的区域（北极65 - 90N、热带10S - 10N、印度季风区）进行测试，使用温度（\(T\)）和比湿（\(q\)）作为耦合变量。\(\beta\)在所有区域与AR(1)正交（皮尔逊\(r\approx0\)，无显著性），证实了其独特的信息内容。系统的超前-滞后分析表明，\(\beta\)比AR(1)提前14 - 24个月，与\(O(\Delta\theta)>O(\Delta\theta^2)\)机制一致。六个具有已知临界点的模拟系统（斯托默尔大西洋经向翻转环流模型、折叠分岔、逻辑斯谛映射、临界减缓）进一步验证，当转变涉及耦合退化时，\(\beta\)比AR(1)提前39 - 153个时间步长。\(\beta\)的无量纲性质（无标度对数-对数指数）表明它可能作为一种通用的跨系统EWS，类似于临界现象中的标度指数。
英文摘要
Early-warning signals (EWS) for critical transitions are predominantly based on changes in the dominant eigenvalue of the system's Jacobian-rising variance and lag-1 autocorrelation (AR(1)). However, eigenvalue-based EWS have $O(delta theta^2)$ sensitivity to perturbations, limiting their lead time. We introduce a complementary EWS based on eigenvector rotation, measured by the time-varying elasticity $beta(t) = d log y / d log x$ estimated via a TVP-Kalman filter in log-log space. Since eigenvector sensitivity is $O(delta theta)$, $beta$ is predicted to precede eigenvalue-based signals. We test this hypothesis on 24 years of monthly NASA AIRS data (2002--2026, 284 observations) across three climatically distinct regions (Arctic 65-90N, Tropics 10S-10N, Indian Monsoon), using temperature ($T$) and specific humidity ($q$) as the coupled variables. $beta$ is orthogonal to AR(1) in all regions (Pearson $r approx 0$, n.s.), confirming the distinct information content. Systematic lead-lag analysis reveals that $beta$ precedes AR(1) by 14--24 months, consistent with the $O(delta theta) > O(delta theta^2)$ mechanism. Six simulated systems with known tipping points (Stommel AMOC model, fold bifurcation, logistic map, critical slowing down) further validate that $beta$ leads AR(1) by 39-153 timesteps when the transition involves coupling degradation. The dimensionless nature of $beta$ (scale-free log-log exponent) suggests it may serve as a universal, cross-system EWS, analogous to scaling exponents in critical phenomena.
