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

本项目旨在创建和应用一个新的理论框架，用于开发和评估数值模式中涡流传输的参数化。该框架构成了一套原则，将物理意义与参数化形式联系起来，包括现存的以及尚未制定的变化。这项工作将提供一个途径，交叉评价现有的或拟议的参数化从第一原则。这一工作将产生两个重要的软件包：（i）用于在任意模式坐标系中实现涡参数化和选择离散化的符号代数软件，（ii）用于模式实现中的误差诊断的数值代码。（ii）一个灵活的方法来随机建模，放松不切实际的约束隐含在现有的参数化涡流路径的平滑度和依赖当地条件;及（iii）使用坐标独立的表示来表达的物理本质的参数化模型的几何形状的选择自由。这项工作将澄清参数化形式与守恒性质（能量、涡度拟能等）之间的联系;加速多模型系统中离散化误差的识别和评估;唯一地识别跨实现的参数化通量的平流和扩散分量;并解释了所观察到的高-该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

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.