Collaborative Research: A Coordinate-Free Framework for Improving Eddy Parameterizations

本项目旨在建立和应用一个新的理论框架，用于发展和评估数值模式中的涡旋输送的参数化。该框架构成了一套将物理意义与参数化形式联系起来的原则，包括现有的和尚未制定的变体。这项工作将为根据第一原则对现有的或拟议的参数进行交叉评价提供一条途径。这项工作将产生两个重要的软件包：(I)符号代数软件，用于在任意模型坐标系中实现涡流参数化和离散化的选择，以及(Ii)用于模型实施中的错误诊断的数值代码。显式、随机、坐标无关(ESC)框架将包括：(I)过滤和平均操作的显式和严格的定义；(Ii)灵活的随机建模方法，其放松了现有参数化中隐含的对涡流路径光滑性和对局部条件的依赖的不切实际的约束；以及(Iii)使用与坐标无关的表示来表达与选择模型几何无关的参数化的物理本质。这项工作将澄清参数化形式和守恒性质(能量、能化等)之间的联系；加快多模式系统中离散化误差的识别和评估；独特地识别跨实施的参数化通量的平流和扩散分量；并说明观察到的高频轨迹行为范围对参数化结构的影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project is to create and apply a new theoretical framework for developing and assessing parameterizations of eddy transport in numerical models. The framework constitutes a set of principles linking physical meaning to parameterization form, including extant as well as yet-unformulated variations. This work will provide an avenue for the cross-evaluation of existing or proposed parameterizations from first principles. Two significant software packages that will result from this work are (i) symbolic algebra software for implementing eddy parameterizations in an arbitary model coordinate system and choice of discretization, and (ii) numerical code for error diagnostics in model implementation.The Explicit, Stochastic, Coordinate-independent (ESC) framework will incorporate: (i) explicit and rigorous definitions for filtering and averaging operations; (ii) a flexible approach to stochastic modeling that relaxes the unrealistic constraints implicit in existing parameterizations on eddy path smoothness and dependence on local conditions; and (iii) the use of coordinate-independent representations to express the physical essence of parameterizations free from choice of model geometry. This work will clarify the link between parameterization forms and conserved properties (energy, enstrophy, etc.); speed the identification and assessment of discretization errors in multiple model systems; uniquely identify the advective and diffusive components of parameterized fluxes across implementations; and account for the impact of the observed range of high-frequency trajectory behavior on parameterization structure.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.