CMG: Unstable Periodic Solutions for Models of Atmospheric Dynamics

该项目使用不稳定周期轨道分析，应用于大气动力学的简化模型，以研究随时间变化的大气动力学的性质。 技术的选择是基于这样一种想法，即许多复发性循环模式在一段时间内表现出连贯的、有组织的行为。 这项研究将确定这种分析是否可以深入了解可能发生的模式以及原因，揭示不同大气状态之间过渡的性质，并帮助确定什么类型的模型状态最适合长期预测。 然后，我们将用这种方法来研究大气的这些性质如何对外部强迫的变化作出反应。我们将研究的两个模式是正压模式和两层准地转模式。 该项目的第一部分将涉及在其他领域对不稳定周期轨道的研究的基础上，试验成功地在这种模型中找到不稳定周期轨道的方法。 一旦发现不稳定的周期轨道，将与太平洋-北美模式和北大西洋涛动等主要环流模式的非周期生命周期进行比较。 该项目将继续尝试使用不稳定周期轨道的扩展来近似描述大气模型对外部强迫微小变化的敏感性的响应算子。 将结果与从波动耗散定理导出的近似响应算子进行比较。 最后，最不稳定的周期轨道上的点附近的状态的可预报性将被检查，以确定这些状态是否有异常的可预报性，如果成功的话，这项工作可能有助于了解在长期大气强迫的可预报性的变化，并提供在某些类型的长期预报的不确定性更好的理解。

This project uses an unstable periodic orbit analysis, applied to simplified models of atmospheric dynamics, to investigate the nature of time-dependent atmospheric dynamics. The choice of technique is based on the idea that many recurrent circulation patterns exhibit coherent, organized behavior for some period of time. The investigation will determine whether such an analysis can provide insights into what patterns are likely to occur and why, shed light on the nature of transitions between different atmospheric states, and help identify what type of model states should be most amenable to long-range prediction. The approach will then be used to examine how such properties of the atmosphere react to changes in external forcing.The two models that will be investigated are a barotropic model and a two-level quasigeostrophic model. The first part of the project will involve experimenting with ways of successfully finding unstable periodic orbits in such models, building on studies of unstable periodic orbits that have been made in other fields. Once found, the unstable periodic orbits will be compared with the aperiodic life-cycles of prominent circulation patterns such as the Pacific-North American pattern and the North Atlantic Oscillation. The project will continue with an attempt to use an expansion in unstable periodic orbits to approximate the response operator that describes the sensitivity of the atmospheric model to small changes in external forcing. The results will be compared with the approximate response operator derived from the fluctuation-dissipation theorem. Lastly, the predictability of states close to points on the least unstable periodic orbits will be examined with the intent of determining whether such states have anomalous predictability.If successful, the work may help understand variations in predictability in long-range atmospheric forcing, and provide a better understanding of uncertainty in some types of long-range forecasts.