Collaborative Research: The Weak Temperature Gradient Equations for Tropical Atmosphere Dynamics

在这个项目中，气象学家和应用数学家们共同致力于研究大尺度热带大气动力学的“弱温度梯度”（WTG）方程。 WTG方程形成一个“平衡模型”，或一组奇异极限方程，渐近validin一个参数制度有关的热带大气。 WTG方程组的设计是为了便于研究热带气候问题的关键方面，如对流和其他非绝热过程的大尺度动力作用。 这一重点是通过消除其他过程，可以在解决方案中的原始方程，如重力波和斜压不稳定，以同样的方式消除重力波在extratrophic平衡模式，如准地转方程。 该项目的一个目标是通过研究风力发电机方程的性质来发展新的数学，另一个目标是在代表与真实的地球气候相关的理想化的几何、边界条件和强迫条件下求解方程，然后研究解对关键参数的敏感性。 这些目标的实现有望使人们更深入地了解真实的气候和更复杂的数学模型，如大气环流模型（GCM）。地球的气候系统是出了名的复杂。 许多不同的物理过程在一个错综复杂的反馈网络中相互作用，产生了我们观察到的动态和多变的气候。 与实验室科学不同，气象学和海洋学由于不可能进行受控实验而受到阻碍，这些实验可能会使关键机制得到全面揭示。 我们被困在我们生活的这个星球上，不能改变它的基本属性来看看会发生什么。 因此，科学的进展是通过观察和严重依赖于GCM的数值模拟，GCM是在最强大的计算机上运行的复杂计算机程序。 这些模拟提供了某种受控气候实验的可能性：我们可以在计算机上创建虚拟地球，控制它们的属性，并精确地观察它们的行为。 这种方法的一个明显的局限性是，模型是现实的不完美表现。 一个不太明显但同样重要的问题是模型的复杂性，它既限制了可以进行的模拟的数量和类型，又使得结果几乎和真实的气候系统一样难以理解。 由于这些问题，有必要用比GCM更简单的模型进行理论研究，以加强观测和GCM研究--如果不简单到允许用纸和纸解决，那么至少使用在PC上快速运行的非常简单的计算机程序。 在某种程度上，这些更简单的模式与真实的系统具有共同的关键特征，它们的简单性允许对气候基本动力学的更深层次的理解，并导致明确的假设，可以对观测和GCM模拟进行测试。 该项目利用气候科学家的物理洞察力和应用数学家的复杂方法来开发和研究专门用于代表地球气候系统中热带大气成分的简单模型。

In this project, meteorologists and applied mathematicians arecollaborating to study the "weak temperature gradient" (WTG) equations forlarge-scale tropical atmospheric dynamics. The WTG equations form a"balance model", or set of singular limit equations, asymptotically validin a parameter regime relevant to the tropical atmosphere. The WTGequations are designed to facilitate study of key aspects of the tropicalclimate problem, such as the large-scale dynamical roles of moistconvection and other diabatic processes. This focus is achieved byeliminating other processes which can be present in solutions to theprimitive equations, such as gravity waves and baroclinic instability, inthe same way as gravity waves are eliminated in extratropical balancemodels such as the quasi-geostrophic equations. One goal of this projectis to develop new mathematics by studying the WTG equations' properties.Another goal is to solve the equations under geometries, boundaryconditions and forcings which represent idealizations of those relevant tothe real earth's climate, and then to study the sensitivity of thesolutions to key parameters. Achievement of these goals is expected tolead to deeper understanding of both the real climate and more complexmathematical models of it, such as general circulation models (GCMs).The earth's climate system is notoriously complex. Many differentphysical processes interact in a tangled web of feedbacks to produce thedynamic and variable climate we observe. Unlike a laboratory science,meteorology and oceanography are hindered by the impossibility ofcontrolled experiments which might allow the key mechanisms to beconclusively revealed. We are stuck with the one planet on which we liveand cannot change its basic properties to see what happens. Consequently,the science proceeds by observation and by a heavy reliance on numericalsimulation with GCMs, which are sophisticated computer programs run on themost powerful computers available. These simulations offer thepossibility of a certain kind of controlled climate experiments: we cancreate virtual earths on the computer, control their properties, andobserve their behavior with precision. One obvious limitation of thisapproach is that the models are imperfect representations of reality. Aless obvious, but equally important problem is the models' complexity,which both limits the number and type of simulations which can be done andrenders the results nearly as difficult to understand as the real climatesystem. Because of these problems, there is a need to supplementobservational and GCM studies with theoretical studies using models thatare simpler than GCMs - if not simple enough to allow solution with penciland paper, then at least using very simple computer programs that runquickly on a PC. To the extent that these simpler models have keyfeatures in common with the real system, their simplicity allows a deeperlevel of understanding of the basic dynamics of climate and leads toexplicit hypotheses that can be tested against observations and GCMsimulations. This project harnesses the physical insight of climatescientists and the sophisticated methods of applied mathematicians todevelop and study simple models designed specifically to represent thetropical atmospheric component of the earth's climate system.