Modelling the Climate and Weather of a 2D Lagrangian-Averaged Euler-Boussinesq Equation with Transport Noise
Modelling the Climate and Weather of a 2D Lagrangian-Averaged Euler-Boussinesq Equation with Transport Noise
复制标题
使用传输噪声对二维拉格朗日平均 Euler-Boussinesq 方程的气候和天气进行建模
DOI：
10.1007/s10955-019-02443-9
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发表时间：
2020
影响因子：
1.6
通讯作者：
Alonso-Orán D
中科院分区：
文献类型：
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作者：
Alonso-Orán D
气候变化及其对极端天气事件的影响的预测是我们这个时代最大的社会和智力挑战之一。问题的第一部分是区分天气和气候。第二部分是了解物理变量波动的动态。第三部分是预测波动的方差如何受到波动动态中的统计相关性的影响。本文研究了一个名为 LA SALT 的框架，该框架可以应对气候变化问题挑战的所有三个部分。作为该框架的一个易于处理的示例，我们考虑在没有其他外力的情况下在垂直平面内重力作用下不可压缩分层流体的欧拉-布辛斯克 (EB) 方程。本例中问题的所有三个部分都得到了解决。事实上，对于这个问题，该框架还提供了物理变量动力学的全局适定性及其波动时刻的闭合动力学方程。因此，在适定的数学环境中，本文开发的框架表明，平均场动力学与波动动力学中复杂的相关性阵列相结合，驱动平均统计量的演化。 2D EB 模型分析框架的结果定义了气候以及气候变化、天气动态和天气统计变化，所有这些都在具有独特的全球强大解决方案的 SPDE 模型系统的背景下进行。
The prediction of climate change and its impact on extreme weather events is one of the great societal and intellectual challenges of our time. The first part of the problem is to make the distinction between weather and climate. The second part is to understand the dynamics of the fluctuations of the physical variables. The third part is to predict how the variances of the fluctuations are affected by statistical correlations in their fluctuating dynamics. This paper investigates a framework called LA SALT which can meet all three parts of the challenge for the problem of climate change. As a tractable example of this framework, we consider the Euler–Boussinesq (EB) equations for an incompressible stratified fluid flowing under gravity in a vertical plane with no other external forcing. All three parts of the problem are solved for this case. In fact, for this problem, the framework also delivers global well-posedness of the dynamics of the physical variables and closed dynamical equations for the moments of their fluctuations. Thus, in a well-posed mathematical setting, the framework developed in this paper shows that the mean field dynamics combines with an intricate array of correlations in the fluctuation dynamics to drive the evolution of the mean statistics. The results of the framework for 2D EB model analysis define its climate, as well as climate change, weather dynamics, and change of weather statistics, all in the context of a model system of SPDEs with unique global strong solutions.