A Stochastic Approach to Representing Unresolved Mesoscales in Ocean Circulation Models

海洋模型是理解、估计和预测海洋动力学不可缺少的工具。构建准确的海洋模型的一个关键挑战是，计算资源排除了对所有物理尺度的直接分辨率；根据其预期用途，下一代全球海洋模型将具有从1度到1/10度的水平空间分辨率。这一范围较粗的模式支持较长期的集合预报(例如气候预报)和再分析应用程序，不能代表全球大区域上能量最强的动力--中尺度的规模。中尺度涡旋(约100公里)在热量和生物地球化学示踪物的传输中起着主导作用，其影响在全球海洋模式中的参数化由来已久。高分辨率模式支持对海洋动力过程的短期预报和研究，但对于长期或大型集合应用来说，它们过于昂贵。在海洋(和大气)模型中模拟未分辨尺度的影响的一个新范式是基于以下观察结果：未分辨小尺度动力学与可分辨动力学以不确定的方式相互作用；与这些未分辨尺度相关的净示踪剂输送是随机的，需要随机模型。构建准确的、随机的真实物理场模型是一个年轻的研究领域，将随机参数化为计算海洋模型的领域也是如此。该项目将把复杂的统计模型和系统的贝叶斯优化应用于海洋建模，从而大大扩展这两个领域。该项目还将为物理海洋学和应用数学交叉领域的博士后研究员提供培训。它将通过共同体地球系统模型海洋模型工作组(OMWG)加强大学研究人员与国家大气研究中心(NCAR)科学家之间的合作。将发展一个全球中尺度涡度场的随机模式。将在CESM版本3的海洋部分的1度版本中实现和测试中尺度涡旋的随机参数化。该项目旨在开发一个用于长期或大型集合应用的粗分辨率海洋模式设置中的示踪物输送的随机参数化的框架。与其他直接模拟输运的方法不同，随机方法直接模拟涡速和示踪剂异常场，并使用它们来构造真实的示踪剂通量。这一想法最近开始在允许涡流的海洋模型的背景下发展起来，以模拟激发部分分辨的中尺度涡旋的‘后向散射’，但直到过去一两年才开始在粗略模式情况下发展，这与允许涡流的情况有很大不同。然而，为粗略模式开发现实的随机参数尤其重要，因为这些粗略模式越来越多地被用于集合模拟场景，需要涡流驱动的大范围变率的现实模式。为了使这些研究的结论准确，必须将与中尺度涡旋输送有关的不确定性通过真实的随机参数包含在模式中。这种方法的一个好处是，涡旋场比输运更容易模拟和观察；该方法还可以得到真实的非高斯示踪通量分布。该方法在Gent-McWilliams(GM)框架内工作，并导致涡团速度的随机参数化。该项目有两个主要组成部分：(1)发展涡旋场的随机模式；(2)在气专委级别的全球气候模式中实施、彻底测试和验证相关的随机参数化。这两个组成部分都将涉及与NCAR的共同体地球系统模式海洋模式工作组的科学家密切合作。

Ocean models are indispensable tools for understanding, estimating, and predicting ocean dynamics. A key challenge in the construction of accurate ocean models is the fact that computational resources preclude direct resolution of all physical scales; depending on their intended use, the next generation of global ocean models will have horizontal spatial resolutions from 1 degree to 1/10 degree. Models at the coarser end of this range, which support longer-term ensemble forecasting (e.g. climate prediction) and reanalysis applications, are unable to represent the scale of the most energetic dynamics, the mesoscale, over large regions of the globe. Mesoscale eddies (on order 100 km) play a leading role in the transport of heat and biogeochemical tracers, and the parameterization of their effects in global ocean models has a long history. High-resolution models support shorter-term forecasting and studies of ocean dynamical processes, but they are too expensive for long-term or large-ensemble applications. An emerging paradigm in modeling the effects of unresolved scales in ocean (and atmosphere) models is based on the observation that unresolved small-scale dynamics interact with resolvable dynamics in a non-deterministic way; the net tracer transports associated with these unresolved scales are stochastic, and require stochastic models. The construction of accurate, stochastic models of real physical fields is a young field of research, as is the field of stochastic parameterization into computational ocean models. This project will significantly extend both these fields by bringing to bear sophisticated statistical models and systematic Bayesian optimization to ocean modeling. The project will also provide training for a post-doctoral fellow at the intersection of physical oceanography and applied mathematics. It will strengthen collaborations between university-based researchers and scientists at the National Center for Atmospheric Research (NCAR) through the Community Earth System Model (CESM) Ocean Model Working Group (OMWG). A stochastic model of the global mesoscale eddy field will be developed. A stochastic parameterization of mesoscale eddies will be implemented and tested in the 1-degree version of the ocean component of the CESM version 3.This project aims to develop a framework for stochastic parameterization of tracer transports in the coarse- resolution ocean model setting used for long-term or large ensemble applications. Unlike other approaches that model the transport directly, the stochastic approach models the eddy velocity and tracer anomaly fields directly, and uses them to construct realistic tracer fluxes. This idea has recently begun to be developed in the context of eddy-permitting ocean models to model 'backscatter' that energizes the partially resolved mesoscale eddies, but only in the past year or two has it begun to be developed in the coarse-model case, which is significantly different than the eddy-permitting case. It is particularly important to develop realistic stochastic parameterizations for coarse models though, because the ensemble-simulation scenarios for which these coarse models are increasingly used require realistic patterns of eddy-driven large-scale variability. The uncertainty associated with mesoscale eddy transports absolutely must be included in the models via realistic stochastic parameterizations for the conclusions of these studies to be accurate. A benefit of this approach is that the eddy fields are easier to model and observe than the transport; the approach also results in realistic non-Gaussian tracer flux distributions. The approach works within the Gent-McWilliams (GM) framework and results in a stochastic parameterization of the eddy bolus velocity. The project has two main components: (i) the development of a stochastic model of the eddy field, and (ii) the implementation, thorough testing, and validation of the associated stochastic parameterization in an IPCC-class global climate model. Both components will involve close collaboration with scientists in the Community Earth System Model (CESM) Ocean Model Working Group (OMWG) at NCAR.