Mathematical and Computational Challenges in Earth System Modelling

我的研究项目旨在开发和使用基于物理的模型和有效的计算技术，以提高地球系统模型（ESM）的保真度。本建议的目标是使用一个已建立的随机多云模式（SMCM）的湿对流参数化，并开发有效的方法海冰动力学。我将对10名HQP进行前沿研究方面的培训，以及时解决寻找更好的气候变化预测的问题。由于人类活动，我们的星球正在因化石燃料燃烧而变暖。气候变化对生态系统、世界经济和极端天气造成的严重后果已得到广泛记载和证实。然而，尽管最近在ESM方面取得了巨大进展，但可以指导正确决策的未来气候预测和归因仍然高度不确定，因为这些模型在模拟当前和过去的气候时仍然存在很大的偏差。湿对流和海冰是最不确定的参数，与这些偏差。ESM基于广泛接受的大气和海洋动力学流体方程，结合植被，土壤水分，冰和许多其他地球动力学过程。由于计算能力有限，这些方程在水平方向上在50-200公里的粗网格上离散化，在较小尺度上发生的物理过程由称为参数化的子网格模型表示。云和对流的参数化从一开始就一直是一个反复出现的挑战。 我的小组最近开发了一个随机烟羽模式，统一浅对流和深对流，在一个质量通量框架的SMCM（SMCPM）的基础上。SMCPM已在单列（1D）NCAR的Community ESM（CESM）中成功测试。该提案的第一部分将涉及SMCPM在3D CESM中的实施和测试。本项目的核心内容将作为培养一名博士后和一名博士生的基础。 博士将完善和使用贝叶斯参数推断技术，我们已经开发的SMCM，统一的SMCPM的情况下，使用真实的数据。 最先进的ESM使用Hibler的粘塑性方程（VPE）表示海冰动力学。VPE是高度非线性退化椭圆型偏微分方程，在物理相关的制度不适定。他们的数值解一直是一个挑战，并使用修改后的变体代替。和我的硕士生一起，我们致力于改进一种现有的方法，该方法试图使用传统的牛顿方法直接求解原始的VPE，结果证明这是非常具有挑战性的。因此，是时候跳出框框思考了。 我将应用我们为蒙日-安培方程开发的一种高效方法。通过这个项目，我将培养一名硕士生和一名博士生。一名博士后将承担在CESM中测试新海冰模型的项目，包括SMCPM和没有SMCPM。 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.