Collaborative Research: Non-Markovian Reduction of Nonlinear Stochastic Partial Differential Equations, and Applications to Climate Dynamics

合作研究：非线性随机偏微分方程的非马尔可夫约简及其在气候动力学中的应用

• 批准号: 1616450
• 负责人: Honghu Liu
• 金额: $ 21.45万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1616450&HistoricalAwards=false
• 关键词: Collaborative; Research; Non; Markovian; Reduction

Liu, DMS-1616450Chekroun, DMS-1616981 The dynamics of the atmosphere and oceans exhibits several recurrent large-scale patterns, which include the well-known El Nino-Southern Oscillation (ENSO) as a prominent example. The variability of such irregular climate patterns has always had a large impact on humans; some possible disastrous consequences include heavy flooding or extended drought in different regions, collapse of fisheries, plagues, and crop failure. To understand the time variability and to provide robust prediction of such climate patterns are thus of vital importance -- both for our economy and for society. These tasks are, however, long-standing challenges in geosciences due to the complexity of our climate system. In this project, the investigators and their colleagues study a factor important for such predictive understandings: the effect of ubiquitous random fluctuations on the dynamics of some fundamental climate models. In particular, the mechanism of extreme El Nino warming events such as the 2015-2016 one is explored from the perspective of noise-induced phenomena. The approach relies crucially on a novel dimension reduction methodology developed recently by the investigators and their colleagues. The knowledge gained in this project is expected to bring new insights into the design of better prediction methods for the evolution of large-scale climate patterns. Graduate students are involved in the work of the project. The dimension reduction methodology adopted and further developed in this project is based on a new stochastic parameterization technique for the unresolved small-scale dynamics of the underlying nonlinear stochastic partial differential equations. The approach has several distinctive features: (i) The parameterization is pathwise in nature. It is very well suited for cases when one is not only interested in statistical quantities but also trajectory-wise dynamical behaviors, which is the case for the applications to climate dynamics. (ii) The parameterization of the small-scale dynamics leads in particular to exogenous memory effects in the reduced systems. This non-Markovian feature can help achieve good modeling performance even in situations that are known to be challenging for other traditional methods to operate. (iii) A practical way to construct different parameterizations is also offered within the approach, and a simple non-dimensional quantity is designed to compare objectively the skills of these parameterizations prior to numerical simulations of the corresponding reduced systems. The developed framework can be applied to deterministic partial differential equations as well; and the method has already been successfully used in several applications including the study of phase transitions, optimal control, and the analysis of noise-induced phenomena. For the applications to climate dynamics, the goals are: (i) to develop useful and easy-to-use low-dimensional reduced models for ENSO based on stochastic versions of some sophisticated coupled ocean-atmosphere models, and (ii) to use these reduced models to investigate the impact of different types of noise on the irregularity of ENSO dynamics. The challenges inherent to this study of climate models help provide new directions for the development of the methodology as well as of parameterization schemes in general. The theoretical and computational tools developed in this project are general, flexible, and have a broad range of applications in nonlinear sciences and engineering. Graduate students are involved in the work of the project.

Liu，DMS-1616450Chekroun，DMS-1616981大气和海洋的动力学表现出几种复发的大规模模式，其中包括众所周知的El Nino-Southern振荡（ENSO），这是一个重要的例子。 这种不规则的气候模式的变化一直对人类产生很大的影响。一些可能的灾难性后果包括在不同地区进行严重的洪水或延长的干旱，渔业，瘟疫和作物衰竭的崩溃。 因此，要了解时间变异性并提供对这种气候模式的强大预测至关重要 - 无论是对我们的经济和社会而言。 但是，由于我们的气候系统的复杂性，这些任务是地球科学的长期挑战。 在这个项目中，研究人员及其同事研究了对这种预测理解的重要因素：无处不在的随机波动对某些基本气候模型的动力学的影响。 特别是，从噪声引起的现象的角度探索了极端的El Nino变暖事件（例如2015 - 2016年）的机制。 该方法至关重要地依赖于研究人员及其同事最近开发的一种新颖的降低方法。 预计该项目中获得的知识将为大规模气候模式的发展提供更好的预测方法的设计。 研究生参与了该项目的工作。 该项目中采用和进一步开发的尺寸减小方法基于一种新的随机参数化技术，用于基础非线性非线性随机偏微分方程的未解决的小规模动力学。 该方法具有几个独特的特征：（i）参数化本质上是路径方向的。 它非常适合当一个人不仅对统计数量感兴趣，还对轨迹的动力学行为感兴趣，这是气候动力学应用的情况。 （ii）小规模动力学的参数化尤其导致还原系统中的外源记忆效应。 即使在众所周知，对于其他传统方法，即使在众所周知，这种非马克维亚功能也可以帮助实现良好的建模性能。 （iii）在该方法中还提供了一种构造不同参数化的实用方法，并且在数值模拟相应减少的系统之前，设计了一个简单的非二维数量来客观地比较这些参数化的技能。 开发的框架也可以应用于确定性的部分微分方程。该方法已经成功地用于多种应用中，包括研究相变，最佳控制和噪声诱导现象的分析。 对于气候动态的应用，目标是：（i）基于某些复杂的耦合海洋 - 大气模型的随机版本，为ENSO开发有用且易于使用的低维度降低模型，以及（ii）使用这些简化模型来研究不同类型的噪声对ENSO动力学不正理性的影响。 这项气候模型研究固有的挑战有助于为方法论的发展以及一般的参数化方案提供新的方向。 该项目中开发的理论和计算工具是一般，灵活的，并且在非线性科学和工程中具有广泛的应用。 研究生参与了该项目的工作。