Collaborative Research: CMG: Predictability and Dynamics of Models of Quasigeostrophic Turbulence and Their Low-Dimensional Truncations

该项目将开发新的数学策略，用于量化复杂地理系统的可预测性。该项目的一部分将量化海洋和大气流动的双周期、两层表示的确定性截断的可预测性，并将其与完整的两层模型中的信息损失率进行比较。信息的损失将通过使用相对熵来度量。还将比较模型的李雅普诺夫指数谱的行为。这项研究将研究是否可以在完整的两层问题的解决方案中找到低维混沌结构的签名。相对熵的直接计算将与从矩得到的估计进行比较。该项目的第二部分将扩展这种类型的分析，以随机扩展的低维模型，以期寻找变化的可预测性和低维混沌结构的性质。该项目最后将进行进一步的统计测试，以描述气候变量的行为，例如检查制度之间的过渡路径。这项研究将增进对中纬度大气过程的认识和了解。基本的问题，如低维相空间结构的方式受到内在随机噪声的影响，以及如何开发减少模型，代表低频率的大气变化将得到解决。此外，还将开发适用于大气/海洋科学中各种模型的模拟和可预测性分析的新的数值方法。

This project will develop new mathematical strategies for quantifying the predictability of complex geosystems. One part of the project will quantify the predictability of deterministic truncations of the doubly-periodic, two-layer representations of oceanic and atmospheric flows, derived by Galerkin projections, and compare this to the rate of loss of information in the full two-layer model. Loss of information will be measured by using relative entropy. The behavior of the spectra of Lyapunov exponents of the models will also be compared. The study will examine whether signatures of low-dimensional chaotic structures can be found in solutions of the full two-layer problem. The direct calculation of relative entropy will be compared with estimates derived from moments. A second part of the project will extend this type of analysis to stochastic extensions of low-dimensional models with a view to searching for changes in predictability and in the nature of the low-dimensional chaotic structures. The project will conclude with further statistical tests to describe the behavior of climatological variables, e.g. to examine transition pathways between regimes. This research will advance knowledge and understanding of mid-latitude atmospheric processes. Fundamental questions such as the way in which low-dimensional phase space structures are affected by intrinsic stochastic noise and how to develop reduced models that represent low-frequency variability of the atmosphere will be addressed. In addition, novel numerical methods applicable to the simulation and predictability analysis of a wide range of models in atmosphere/ocean science will be developed.