Mathematical and Computational Challenges in Earth System Modelling

点击翻译按钮获取中文摘要

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.