Mathematical and Computational Challenges in Earth System Modelling

我的研究计划旨在开发和使用基于物理的地球模型和高效的计算技术，以提高地球系统模型(ESM)的保真度。这项提议的目标是使用已建立的用于湿对流和参数化的随机多云模式(SMCM)，并开发有效的海冰动力学方法。我将培训10名总部基地人员，在寻找更好的气候变化预测的及时问题上进行尖端研究。对生态系统、世界经济和极端天气的戏剧性后果被广泛记录和确立。然而，尽管最近在ESM方面取得了巨大的进展，但未来的气候预测和可以指导适当决策的属性仍然高度不确定，因为这些模型在模拟当前和过去的气候方面仍然存在很大的偏差。湿对流和海冰是与这些偏差相关的最不确定的参数之一。这些ESM基于广泛接受的大气和海洋动力学的流体方程，与植被、土壤水分、冰和许多其他地球动力学过程相耦合。由于计算能力有限，这些方程在50-200公里的粗网格上离散，而发生在较小尺度上的水平和物理过程由称为参数化子网格模型表示。云和对流的参数化从一开始就是一个反复出现的挑战。我的团队最近开发了一个随机羽流模型，在基于SMCM(SMCPM)的质量通量框架中统一了浅对流和深对流。SMCPM已在单列(1D)NCAR的社区ESM(CESM)中成功测试。提案的第一部分将涉及在3D CESM中实施和测试SMCPM。该项目的核心将是为培养一名博士后和一名博士生奠定基础。博士将改进和使用我们为SMCM开发的贝叶斯参数推理技术，以统一的SMCPM为例，使用真实数据。最先进的ESM使用Hibler的粘塑性方程(VPE)来表示海冰的动力学。VPE是高度非线性的退化椭圆型偏微分方程，在物理上相关的区域是不适定的。但它们的数值解一直是一个挑战，取而代之的是修改的变体。和我硕士的学生一起，我们致力于改进一种现有的方法，试图使用传统的牛顿法直接求解原始的VPE，事实证明这是非常具有挑战性的。因此，现在是跳出框框思考的时候了。我将应用我们为Monge-Ampere方程开发的一种高效方法。通过这个项目，我将培养一名硕士和一名博士生。一名博士后将承担在CESM中测试新的海冰模型的项目，包括使用和不使用SMCPM。这5名本科生也将参与这项研究。

My research program aims at developing and using physically based models and efficient computing techniques to improve the fidelity of earth system models (ESM). The goal of this proposal is to use an established stochastic multicloud model (SMCM) for moist convection parameterization, and develop efficient methods for sea-ice dynamics. I will train 10 HQP in cutting edge research on the timely issue of searching for better climate change projections. Because of human activity, our planet is warming due to fossil fuel burning. The dramatic consequences on ecosystems, the world economy and weather extremes are widely documented and established. However, future climate projections and attributions that can guide proper decision making, remain highly uncertain despite the tremendous recent progress in ESMs, as these models still have large biases in simulating the current and past climates. Moist convection and sea-ice are among the most uncertain parameters, associated with these biases. ESMs are based on the widely accepted fluid equations for the atmosphere and ocean dynamics, coupled to vegetation, soil moisture, ice, and many other earth's dynamical processes. Because of limited computing power, these equations are discretized on coarse meshes of 50-200 km in the horizontal and physical processes occurring on smaller scales are represented by sub-grid models known as parameterizations. The parametrization of clouds and convection has been a recurrent challenge since the start.  My group has recently developed a stochastic plume model, unifying shallow and deep convection, in a mass-flux framework based on the SMCM (SMCPM). The SMCPM has been successfully tested in the single column (1D) NCAR's Community ESM (CESM). The first part of the proposal will deal with the implementation and testing of the SMCPM in the 3D CESM. The core of this project will be the basis for  training one post doc and one PhD student.  The PhD will refine and use a Bayesian parameter inference technique, we have developed for the SMCM, to the case of the unified SMCPM, using real data.  State-of-the-art ESMs represent sea-ice dynamics using the viscous-plastic equations (VPEs) of Hibler. The VPEs are highly nonlinear degenerate elliptic partial differential equations that are ill posed in physically relevant regimes. Their numerical solution has been a challenge and modified variants were used instead. With my master's student, we worked on improving one existing method which attempts to solve the original VPEs directly, using the traditional Newton method, which turned out to be very challenging. It is therefore time to think outside the box.  I will apply a highly efficient method that we developed for the Monge-Ampere equation. Through this project, I will train one master and one PhD student. A post doc will undertake the project of testing the new sea-ice model in CESM both with and without the SMCPM.  5 undergrads will also be involved in this research.