Collaborative Research: Energetically consistent, resolution aware, parameterization of meso-scale eddies in the ocean

该项目的目的是开发一个框架来参数化涡旋效应，它可以在高和低模式分辨率下应用。虽然模拟小组为提高海洋气候模型的空间分辨率付出了巨大的努力，但长期的全球气候模拟才刚刚开始进入“允许涡流”的状态。在可预见的未来，许多理想化的研究以及古气候模拟将继续依赖分辨率更低的模式。因此，在“非涡旋”和“允许涡旋”两种分辨率下，充分的参数化表示子网格涡旋效应对于我们产生充分的海洋气候模拟的能力至关重要。此外，在本项目中进行的理想化模型研究将为中尺度涡流和湍流能量循环的特性提供有价值的见解。这项工作进一步为本科生实习生、研究生和博士后研究员提供了宝贵的培训。他们将接触到海洋湍流理论，数值模式的开发和模拟，以及大数据集的分析，包括数值模式输出和观测数据。最后，该项目支持一位早期职业生涯的PI，他正在芝加哥大学（重新）建立物理海洋学研究和教育。为了实现广泛适用的参数化，本研究将结合Eden and Greatbatch（2008）和Jansen and Held（2014）的思想，对亚网格涡流动能进行显式预算。这允许闭合子网格涡旋效应，这与当前对湍流涡旋能量循环的理解是一致的，同时它足够简单和通用，可以很容易地在一系列海洋气候模型中实施，而不会增加显著的计算成本。亚网格尺度通过斜压不稳定性的参数化以及动能和熵的湍流级联与已分解的气流交换能量。正如Jansen和Held（2014）所讨论的那样，要充分表示湍流能量和熵级联，需要将能量从亚网格尺度“后向散射”包含到已分解的流动中，这一点迄今为止从未包含在现实的海洋模型中。本研究主要有三个方面：(1)针对斜压不稳定性尚未完全解决的非旋转模型，开发基于eke预算的涡参数化方法。(2)针对“允许涡旋”的分辨率，发展基于eke预算的涡旋参数化，其中合理的涡旋扰动可以明确模拟，但分辨率仍然不足以完全解决中尺度涡旋。(3)将两种极限情况合并为一个广义框架，该框架适用于广泛的分辨率。最后一步至关重要，因为给定分辨率的模型在海洋的某些部分可能是“允许涡流的”，而在海洋的其他部分则是“不允许涡流的”（Hallberg, 2013）。基于eke预算的方法自然提供了一种能够在这两种制度之间充分过渡的参数化方法。该项目的目标将通过一系列模型来实现，从理想化的过程研究到现实的全球海洋模型。这一层次结构将使该团队能够基于对相关物理过程的基本理解开发一种参数化方法，同时也适用于最先进的复杂气候模型。通过将理想化的数值模拟与更高分辨率的参考模拟进行比较，并最终通过显示全球海洋模式在再现海洋观测方面的改进能力来衡量是否成功。

The aim of this project is to develop a framework to parameterize eddy effects, which can be applied at both high and low model resolutions. While modeling groups put significant effort into increasing the spatial resolution of ocean climate models, longer-term global climate simulations are only starting to enter the "eddy-permitting" regime. Many idealized studies, as well as paleoclimate simulations, will continue to rely on models with even coarser resolutions for the foreseeable future. Adequate parameterizations representing sub-grid eddy effects at both "non-eddying" and "eddy-permitting" resolutions are thus crucial for our ability to produce adequate ocean climate simulations. Moreover, idealized modeling studies, performed in this project, will provide valuable insight about properties of mesoscale eddies and the turbulent energy cycle. This work further provides valuable training for an undergraduate intern, a graduate student and a postdoctoral researcher. They will be exposed to the theory of ocean turbulence, numerical model development and simulation, as well as analysis of big data sets, including both numerical model output and observational data. Finally, the project supports an early career PI, who is (re-)establishing physical oceanography research and education at The University of Chicago.To achieve a broadly applicable parameterization, this study will make use of an explicit budget for the sub-grid eddy kinetic energy, which combines ideas of Eden and Greatbatch (2008) and Jansen and Held (2014). This allows for a closure of sub-grid eddy effects that is consistent with the current understanding of the turbulent eddy energy cycle, while being simple and general enough to be readily implemented in a range of ocean climate models without adding significant computational cost. The sub-grid scales exchange energy with the resolved flow via parameterizations of baroclinic instability, as well as the turbulent cascade of kinetic energy and enstrophy. As discussed in Jansen and Held (2014), an adequate representation of the turbulent energy and enstrophy cascade requires the inclusion of energy "backscatter" from the subgrid-scales to the resolved flow, which so far has never been included in a realistic ocean model. This research is organized along three main thrusts: (1) Develop an EKE-budget-based eddy parameterization for non-eddying models, where baroclinic instability remains entirely unresolved. (2) Develop an EKE-budget-based eddy parameterization for "eddy-permitting" resolutions, where reasonable eddy-like disturbances can be simulated explicitly, but the resolution remains insufficient to fully resolve mesoscale eddies. (3) Combine the two limit cases into a generalized framework, which is applicable over a wide range of resolutions. The last step is crucial in light of the fact that models of a given resolution may be "eddy-permitting" in some parts of the ocean, while they are "non-eddying" in other parts of the ocean (Hallberg, 2013). The EKE-budget based approach naturally offers itself to the formulation of a parameterization that can adequately transition between these two regimes. The project goal will be achieved using a hierarchy of models, ranging from idealized process studies, to realistic global ocean models. This hierarchy will allow the team to develop a parameterization that is based in a fundamental understanding of the relevant physical processes, while also being applicable in complex state-of-the-art climate models. Success will be gauged by comparing the idealized numerical simulations to much higher resolution reference simulations, and ultimately by showing the global ocean models' improved ability to reproduce ocean observations.