Geometric foundation of invariant and conservative parameterization schemes

不变保守参数化方案的几何基础

基本信息

  • 批准号:
    RGPIN-2016-06457
  • 负责人:
  • 金额:
    $ 1.68万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2016
  • 资助国家:
    加拿大
  • 起止时间:
    2016-01-01 至 2017-12-31
  • 项目状态:
    已结题

项目摘要

The overarching goal of my research program is to advance the field of geometric parameterization. My research area lies at the intersection of applied mathematics, numerical analysis, fluid mechanics and meteorology. Numerical models are the prime source of reliable weather and climate predictions. With increase in computational power, models become more accurate and are capable of resolving a wider range of spatial and temporal scales than ever before. Despite this, even the most advanced numerical Earth models cannot resolve all processes that are important for precise weather and climate predictions. Since these unresolved processes cannot be omitted, they have to be incorporated into the model in an approximate manner. This is referred to as parameterization. Parameterization is important to close a numerical model for the atmosphere-ocean system and thus one of the main research directions in modern meteorology and oceanography. I propose a novel framework for developing physical parameterization schemes. The key paradigm is to use the geometric properties of the original governing equations of hydro-thermodynamics to formulate parameterization schemes that preserve these properties in the approximated equations. This will then form the basis for numerical models. These properties will include both symmetries and conservation laws, which are among the most important features of any physical model. The construction of geometry-preserving parameterization schemes will mainly rely on methods from the group analysis of differential equations. While the main emphasis of this research program will be the development of mathematical techniques that can be used for finding geometry-preserving parameterization schemes, we will also illustrate these techniques by constructing several closure models for important physical processes, including turbulence, eddies in the ocean, and atmospheric convection. This research program will provide the necessary tools for constructing physically and mathematically consistent parameterization schemes for a variety of processes that traditionally have to be parameterized in numerical models. This will provide a basis for the improvement of future weather and climate models. As symmetries and conservation laws are of central relevance in physics, engineering and the mathematical sciences, progress anticipated will advance these fields as well. This research program will also train several undergraduate and graduate students at the intersection of applied and computational mathematics, thus providing them with the opportunity to learn a wide variety of mathematical and technical skills equally important to excel in both academia and industry.
我的研究计划的首要目标是推进几何参数化领域。我的研究领域是应用数学、数值分析、流体力学和气象学的交叉领域。 数值模式是可靠的天气和气候预测的主要来源。随着计算能力的提高,模型变得更加准确,并且能够解决比以往更广泛的空间和时间尺度。尽管如此,即使是最先进的数值地球模型也无法解决所有对精确天气和气候预测至关重要的过程。由于这些未解决的过程不能省略,它们必须以近似的方式纳入模型。这被称为参数化。参数化是海洋-大气系统数值模式闭合的重要环节,也是现代气象学和海洋学的主要研究方向之一。 我提出了一个新的框架,开发物理参数化方案。关键的范例是使用的几何性质的原始控制方程的流体热力学制定参数化方案,保持这些属性的近似方程。这将成为数字模型的基础。这些性质将包括对称性和守恒定律,这是任何物理模型最重要的特征之一。保几何参数化方案的构造主要依赖于微分方程组分析的方法。 虽然这项研究计划的主要重点将是数学技术的发展,可用于寻找几何保持参数化方案,我们也将说明这些技术,通过构建几个封闭模型的重要物理过程,包括湍流,海洋中的涡旋,和大气对流。 该研究计划将提供必要的工具,为传统上必须在数值模型中参数化的各种过程构建物理和数学上一致的参数化方案。这将为未来天气和气候模式的改进提供基础。由于对称性和守恒定律在物理学、工程学和数学科学中具有核心意义,预期的进展也将推动这些领域的发展。该研究计划还将培养应用数学和计算数学交叉点的几名本科生和研究生,从而为他们提供学习各种数学和技术技能的机会,这些技能对于在学术界和工业界脱颖而出同样重要。

项目成果

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Bihlo, Alexander其他文献

Group classification of linear evolution equations

Bihlo, Alexander的其他文献

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{{ truncateString('Bihlo, Alexander', 18)}}的其他基金

Geometric foundation of invariant and conservative parameterization schemes
不变保守参数化方案的几何基础
  • 批准号:
    RGPIN-2016-06457
  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Numerical Analysis and Scientific Computing
数值分析与科学计算
  • 批准号:
    CRC-2020-00002
  • 财政年份:
    2022
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Numerical Analysis And Scientific Computing
数值分析与科学计算
  • 批准号:
    CRC-2020-00002
  • 财政年份:
    2021
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Geometric foundation of invariant and conservative parameterization schemes
不变保守参数化方案的几何基础
  • 批准号:
    RGPIN-2016-06457
  • 财政年份:
    2021
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Numerical analysis and scientific computing
数值分析和科学计算
  • 批准号:
    1000230772-2015
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Numerical Analysis and Scientific Computing
数值分析与科学计算
  • 批准号:
    1000233102-2019
  • 财政年份:
    2020
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Geometric foundation of invariant and conservative parameterization schemes
不变保守参数化方案的几何基础
  • 批准号:
    RGPIN-2016-06457
  • 财政年份:
    2019
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Numerical analysis and scientific computing
数值分析和科学计算
  • 批准号:
    1000230772-2015
  • 财政年份:
    2019
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs
Geometric foundation of invariant and conservative parameterization schemes
不变保守参数化方案的几何基础
  • 批准号:
    RGPIN-2016-06457
  • 财政年份:
    2018
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Discovery Grants Program - Individual
Numerical analysis and scientific computing
数值分析和科学计算
  • 批准号:
    1000230772-2015
  • 财政年份:
    2018
  • 资助金额:
    $ 1.68万
  • 项目类别:
    Canada Research Chairs

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