The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz ’96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.

响应理论的目标，在其许多统计力学公式中的每一个中，都是根据未受扰动状态和应用扰动的知识来预测系统的扰动响应。最近关于这个问题的一个新角度集中在提供一种方法来预测系统的一个可观测值的变化，使用第二个可观测值的变化作为实际强迫的替代。当只有不完整的信息可用时，这种观点试图解决复杂系统中因果关系的非常相关的问题。我们在此介绍了一种量化和排序可观测值的预测能力的方法，并使用它来研究范式空间扩展系统（Lorenz '96 模型）的响应。我们对系统进行局部扰动，然后研究给定的局部可观察量在多大程度上可以预测单独的局部可观察量的行为。我们表明，这种方法可以揭示信号在系统内传播的方式。我们还表明，如果将多个作用强迫以及相应的多个可观察量视为感兴趣的可观察量的预测因子，则该过程会变得更有效。