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来量化复杂地球系统的可预测性。该项目的一部分将量化由伽辽金预测得出的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测量。还将比较模型的李雅普诺夫指数谱的行为。该研究将检验低维混沌结构的特征是否可以在全两层问题的解中找到。直接计算的相对熵将与从矩中得到的估计进行比较。该项目的第二部分将把这种类型的分析扩展到低维模型的随机扩展，以期寻找可预测性和低维混沌结构性质的变化。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途径。这项研究将促进对中纬度大气过程的认识和理解。诸如低维相空间结构受固有随机噪声影响的方式以及如何开发代表大气低频变异性的简化模型等基本问题将得到解决。此外，将发展新的数值方法，适用于大气/海洋科学中各种模式的模拟和可预测性分析。

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.