CMG COLLABORATIVE RESEARCH: Development of New Statistical Learning Theory and Techniques for Improvement of Convection Parameterization in Climate Models

这项建议的重点是两个相互联系和同样重要的问题。其中第一个是发展一种新的统计学习理论（SLT），致力于对特定的复杂系统进行建模。二是为数值气候模式发展一种新的对流表示。了解气候和天气对科学、社会和经济都很重要。我们关注的过程（云，尤其是对流）对气候和天气至关重要。该建议涉及一种改进这些进程的代表性的新方法。我们的目标是将具有SLT专业知识的数学科学家团队和具有云模拟和气候系统建模专业知识的大气科学家团队结合起来，在用于数值天气预报和气候变化研究的大气模型中产生对流的创新表示。该项目将开发一个SLT系统，该系统可以在各种云系统中模拟更现实但非常昂贵的高分辨率云系统解析模型（CSRM）的统计行为。在大型模型中使用这些CSRM框架中最简单的框架也会增加今天的成本？这使得它们在许多研究中不切实际。通过在大尺度模型中模拟这些更现实的框架的行为，我们开发了一种新的SLT参数化，大大降低了模型对流更现实表示的成本，并提供了一个解决目前在科学界被视为关键问题的机会。通过开发面向应用的slt，我们希望使目前正在探索的更现实的云和对流公式在计算上可行，并在气候模式中使用它们。该提案将计算统计科学界的研究与气候科学相结合。气候系统最重要的组成部分之一是云的表示。它们控制着进入和离开气候系统的能量和热量的许多方面，它们与地球系统的许多组成部分（农业、天气、社会和经济）相互作用。但是云是如此复杂，以至于不能在用来理解气候和天气的模型中非常精确地处理它们。表示云所需的方程式是如此复杂，以至于精确的处理将使当前模型的速度减慢数千或数百万倍。目前的计算气候和天气模式不能提供云的精确表示，因此需要更快的云的近似处理。传统的气候和天气模式中的云表示不够准确，并且在改进这些模式组件方面进展缓慢。该建议采用先进的统计数学方法来试图改善这种情况。这些方法（称为统计学习理论或SLT）允许人们用精确、快速的近似值来表示非常复杂的系统。我们将尝试使用SLT来近似非常详细、复杂和昂贵的对流云模型，以产生一个精确的云近似，目标是使用这个近似（这些近似在气候和天气模型中经常被称为参数化）。该研究将推动SLT社区和气候社区使用的知识库的发展。

This proposal focuses upon two interconnected and equally important problems. The first of them is developing a new Statistical Learning Theory (SLT) dedicated to modeling specific complex systems. The second one is to develop a new convection representation for numerical climate models. Understanding climate and weather is important to science, society and the economy. The processes we focus upon (clouds, and particularly convection) are critical to climate and weather. The proposal involves a novel approach to improving the representation of those processes. Our goal is to combine a team of mathematical scientists with expertise in SLT, and atmospheric scientists with expertise in cloud modeling and climate system modeling to produce an innovative representation for convection in the atmospheric models used for numerical weather prediction and climate change studies. The project will develop an SLT system that emulates the statistical behavior of a more realistic but very expensive high resolution Cloud System Resolving Model (CSRM) in a variety of cloud regimes. Employing even the simplest of these CSRM frameworks in a large scale model increases the cost of today?s atmospheric models by factors of thousands, which make their use impractical for many studies. By emulating the behavior of these more realistic frameworks in a large scale model we develop a new SLT parameterization, dramatically reducing the cost of the more realistic representations of model convection, and providing an opportunity to address problems currently viewed as critical within the scientific community. By developing the application-oriented SLTs we hope to make the more realistic cloud and convective formulations currently being explored, computationally feasible and use them in climate models. This proposal combines research used in the computational statistics scientific community with climate science. One of the most important components of the climate system is the representation of clouds. They control many aspects of the energy and heat that enter and leave the climate system, and they interact with many components of the earth system (agriculture, weather, society, and the economy). But clouds are so complex that they can not be treated very precisely in models that are used for understanding climate and weather. The equations required to represent clouds are so complex that a precise treatment would slow down current models by factors of thousands or millions. Current computational climate and weather models cannot afford a precise representation of clouds so faster approximate treatments of clouds are needed. Traditional representations for clouds in climate and weather models are not sufficiently accurate, and progress has been slow in improving these model components. This proposal employs advanced statistical-mathematical methods to try and improve the situation. These methods (called Statistical Learning Theory or SLT) allow one to represent very complex systems with accurate, and very fast approximations. We are going to try to approximate very detailed, complex and expensive models of convective clouds using SLT to produce an accurate approximation for clouds with the goal of using this approximation (these approximations are frequently called a parameterization in climate and weather models). This research will push forward the knowledge base used in both the SLT community, and the climate community.