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

本项目旨在建立并应用一个新的理论框架，以发展和评估数值模式中涡动输运的参数化。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，包括现存的和尚未制定的变体。这项工作将为从第一原理交叉评估现有或提议的参数化提供途径。从这项工作中产生的两个重要软件包是(i)用于在任意模型坐标系中实现涡流参数化和离散化选择的符号代数软件，以及（ii）用于模型实现中错误诊断的数值代码。明确的，随机的，坐标无关的（ESC）框架将包括：(i)明确和严格的滤波和平均操作定义；（ii）一种灵活的随机建模方法，可以放松现有参数化中对涡流路径平滑和对局部条件的依赖所隐含的不切实际的约束；（iii）使用与坐标无关的表示来表达参数化的物理本质，而不需要选择模型几何形状。这项工作将阐明参数化形式与守恒性质（能量、熵等）之间的联系；加速多模型系统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；并考虑了高频弹道行为观测范围对参数化结构的影响。该奖项反映了美国国家科学基金会的法定使命，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.