Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

首席研究员开发和研究对天气和气候重要的地球物理过程的数学模型。一个主要目标是更好地了解气候变率的来源及其影响的程度。这项工作涉及新的数学理论和技术，用于由一组偏微分方程描述的系统状态之间的动态转换，以及记忆效应——任何特定状态特征的差异取决于系统到达该状态的状态链。系统可以是确定性的，也可以是随机的。数学问题是由气候问题引起的，反过来，理论和技术被应用于理解气候动力学和预测的基本问题。这个项目可以提高对天气、气候和环境现象的预测和新见解，这些对我们的经济至关重要。厄尔尼诺-南方涛动（ENSO）是该项目的研究对象之一，它是年际气候变率的主要模式，对温度、降水、热带气旋、人类健康甚至冲突都有全球影响。该项目涉及相关科学学科的科学家和研究生。研究生也包括在该项目的工作中。主要研究方向为确定性偏微分方程和随机偏微分方程的动态转移理论，以及建立有效的非马尔可夫化简模型的理论和方法。目标是量化与气候低频变率的典型源相关的敏感性和动态转变。主要目标包括量化记忆效应所起的作用，确定低模式和高模式之间的关键非线性相互作用以及由噪声引起的记忆效应。将研究的气候变率的几个典型来源包括ENSO、热带对流和温盐环流。它们的变率，无论是独立的还是相互作用的，都可能在过去和未来的气候变化中发挥重要作用。该项目涉及与不同机构活跃的大气/海洋科学家的具体合作，研究生也包括在项目工作中。

The principal investigator develops and studies mathematical models of geophysical processes important for weather and climate. A major aim is to better understand sources of climate variability and the extent of their influences. The work involves new mathematical theory and techniques for dynamic transitions between states of a system described by a set of partial differential equations, and for memory effects -- differences in any particular state's features that depend on the chain of states through which the system arrives at that state. The system may be deterministic or stochastic. The mathematical issues are motivated by climate problems, and in turn the theory and the techniques are applied to the understanding of fundamental issues in climate dynamics and prediction. This project leads to improved predictions and new insights into weather, climate, and environmental phenomena of central importance to our economy. One such phenomenon to be studied in this project is the El Nino-Southern Oscillation (ENSO), which is the dominant mode of inter-annual climate variability, and which has global impacts on temperature, precipitation, tropical cyclones, human health, and even conflict. The project involves scientists as well as graduate students from the related scientific disciplines. Graduate students are included in the work of the project. The principal investigator and his collaborators work on dynamic transition theory for both deterministic partial differential equations and stochastic partial differential equations (SPDEs), and on developing theory and methods to establish effective non-Markovian reduced models for SPDEs. The goal is to quantify the sensitivity and dynamic transitions associated with typical sources of climate low frequency variability. Major goals include quantifying the role played by the memory effects, and identifying the key nonlinear interactions between low and high modes and the memory effects caused by noise. A few typical sources of climate variability that will be studied include ENSO, tropical convections, and the thermohaline circulations. Their variability, independently and interactively, may play a significant role in climate changes, past and future. The project involves specific collaborations with active atmosphere/ocean scientists in different institutions, and graduate students are included in the project work as well.