We present a new framework for analyzing the evolution of information in geophysical systems. Understanding how information, and its counterpart, uncertainty, propagates is central to predictability studies and has significant implications for applications such as forecast uncertainty quantification and risk management. It also offers valuable insight into the underlying physics of the system. Information propagation is closely linked to causality: how one part of a system influences another, and how some regions remain dynamically isolated. We apply this framework to the one-dimensional, highly nonlinear Kuramoto-Sivashinsky model and to the shallow-water equations, representing a mid-latitude atmospheric strip. Notably, we observe that information can propagate against the fluid flow, and that different model variables exhibit distinct patterns of information evolution. For example, pressure-related information propagates differently from relative vorticity, reflecting the influence of gravity waves versus balanced flow dynamics. This new framework offers a promising addition to the diagnostic tools available for studying complex dynamical systems.

翻译：我们提出了一个分析地球物理系统中信息演化的新框架。理解信息及其对应物——不确定性如何传播，是预测性研究的核心，并对预报不确定性量化和风险管理等应用具有重要影响。该框架也为理解系统的底层物理机制提供了宝贵见解。信息传播与因果关系紧密相连：系统的一部分如何影响另一部分，以及某些区域如何保持动态隔离。我们将此框架应用于一维高度非线性的Kuramoto-Sivashinsky模型和代表中纬度大气带的浅水方程。值得注意的是，我们观察到信息可以逆流体流动方向传播，且不同模型变量展现出截然不同的信息演化模式。例如，与压力相关的信息传播方式不同于相对涡度，这反映了重力波与平衡流动力学的影响差异。这一新框架为研究复杂动力系统提供了前景广阔的诊断工具补充。