Mathematical and Computational Challenges in Earth System Modelling

地球系统建模中的数学和计算挑战

• 批准号: RGPIN-2020-04246
• 负责人: Khouider, Boualem
• 金额: $ 2.26万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=716856
• 关键词: Mathematical; Computational; Challenges; Earth; System

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.

我的研究计划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）的忠诚度。该提案的目的是使用已建立的随机多云模型（SMCM）进行对流参数化，并开发有效的海冰动力学方法。我将培训10个HQP，以了解及时寻找更好的气候变化预测的问题。由于人类活动，由于化石燃料燃烧，我们的星球正在变暖。对生态系统，世界经济和极端天气的巨大后果得到了广泛的记录和建立。但是，尽管ESM最近取得了巨大进展，但未来可以指导正确决策的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方面仍然存在很大的偏见。潮湿的对流和海冰是与这些偏见有关的最不确定的参数。 ESM基于大气和海洋动力学的广泛接受的流体方程，并与植被，土壤水分，冰和许多其他地球动态过程结合起来。由于计算能力有限，这些方程在水平和物理过程中以较小尺度的50-200 km和物理过程中的粗网层离散，由称为参数化的子网格模型表示。自开始以来，云和对流的参数化一直是反复挑战。 我的小组最近在基于SMCM（SMCPM）的质量流量框架中开发了一个随机羽流模型，统一了浅和深对流。 SMCPM已在单列（1D）NCAR社区ESM（CESM）中成功测试。该提案的第一部分将处理3D CESM中SMCPM的实施和测试。该项目的核心将是培训一个文档和一名博士生的基础。 博士学位将完善并使用贝叶斯参数推理技术，我们已经使用实际数据为统一SMCPM开发了SMCM。 最先进的ESM代表使用Hibler的粘性塑料方程（VPE）的海冰动力学。 VPE是高度非线性退化的椭圆形偏微分方程，在物理相关方面不适合。他们的数值解决方案一直是一个挑战，而是使用了修改的变体。借助我的主学生，我们努力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解决原始VPE，这是非常具有挑战性的。因此，是时候在框外思考了。 我将应用我们为Monge-Ampere方程开发的高效方法。通过这个项目，我将培训一位硕士和一名博士生。邮政DOC将在有或没有SMCPM的情况下，在CESM中测试新的Sea-Ice模型的项目。 这项研究还将参与5个本科生。