标题： 临界转变的早期预警：区分临界点与图灵不稳定化 显示英文标题

标题： Early warning of critical transitions: distinguishing tipping points from Turing destabilizations

摘要： 当前临界点的早期预警信号往往无法区分灾难性转变和不太显著的状态变化，例如空间模式形成。 本文介绍了一种新方法，通过从空间均匀系统状态开始，提供有关正在接近的分岔类型的更多信息，从而解决这一局限性。 该方法依赖于从噪声时空数据中估计的色散关系，这可以揭示系统是否接近空间均匀（临界）或空间不均匀（图灵模式）的分岔。 我们使用修改后的Klausmeier模型，在合成数据上验证了该方法，探讨了在不同条件下的性能，包括噪声特性以及与分岔的距离。 我们还确定了实现最佳性能的数据需求。 我们的结果表明，基于这种方法的新空间早期预警系统有望改善许多气候子系统和生态系统未来转变的预测，这对于在快速变化的世界中有效保护和管理至关重要。 显示英文摘要

摘要： Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by providing more information about the type of bifurcation being approached starting from a spatially homogeneous system state. This method relies on estimates of the dispersion relation from noisy spatio-temporal data, which reveals whether the system is approaching a spatially homogeneous (tipping) or spatially heterogeneous (Turing patterning) bifurcation. Using a modified Klausmeier model, we validate this method on synthetic data, exploring its performance under varying conditions including noise properties and distance to bifurcation. We also determine the data requirements for optimal performance. Our results indicate the promise of a new spatial early warning system built on this method to improve predictions of future transitions in many climate subsystems and ecosystems, which is critical for effective conservation and management in a rapidly changing world.