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来提高地球系统模型（ESM）的保真度。本文的目标是利用已建立的随机多云模型（SMCM）进行湿对流参数化，并开发有效的海冰动力学方法。我将在寻找更好的气候变化预测这一及时问题的前沿研究方面培训10名HQP。由于人类活动，我们的星球由于化石燃料的燃烧而变暖。气候变化对生态系统、世界经济和极端天气的巨大影响已被广泛记录和确立。然而，尽管esm最近取得了巨大进展，但未来的气候预测和归因仍然高度不确定，因为这些模式在模拟当前和过去气候方面仍然存在很大偏差。潮湿对流和海冰是与这些偏差相关的最不确定的参数。esm基于广泛接受的大气和海洋动力学流体方程，与植被、土壤水分、冰和许多其他地球动力学过程耦合。由于计算能力有限，这些方程被离散在50-200 km的水平粗网格上，而发生在较小尺度上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是一个反复出现的挑战。

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.