A Stochastic Approach to Representing Unresolved Mesoscales in Ocean Circulation Models

海洋模式是理解、估计和预测海洋动力学不可或缺的工具。建立精确海洋模型的一个关键挑战是，计算资源无法直接分辨所有物理尺度;根据其预期用途，下一代全球海洋模型的水平空间分辨率将从1度到1/10度不等。在这一范围较粗一端的模型支持较长期的集合预报（例如气候预报）和再分析应用，但无法代表地球仪大区域上最活跃的动力学尺度，即中尺度。中尺度涡旋（100公里量级）在热量和地球化学示踪剂的输送中起着主导作用，全球海洋模式中对其影响的参数化有着悠久的历史。高分辨率模式支持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）模型中未解决的尺度的影响建模的一个新兴的范例是基于观察未解决的小尺度动力学与可解决的动力学相互作用的非确定性的方式，与这些未解决的尺度的净示踪剂运输是随机的，需要随机模型。建立精确的、随机的真实的物理场模型是一个年轻的研究领域，将随机参数化引入计算海洋模型也是如此。该项目将通过将复杂的统计模型和系统的贝叶斯优化引入海洋建模，大大扩展这两个领域。该项目还将为一名博士后研究员提供物理海洋学和应用数学交叉方面的培训。它将通过社区地球系统模型（CESM）海洋模型工作组（OMWG）加强大学研究人员和国家大气研究中心（NCAR）科学家之间的合作。将建立一个全球中尺度涡动场的随机模式。在CESM第三版的1度海洋分量中，将实现中尺度涡旋的随机参数化，并进行试验。本项目旨在建立一个用于长期或大型集合应用的粗分辨率海洋模式中示踪剂输运随机参数化框架。与其他直接模拟输运的方法不同，随机方法直接模拟涡流速度和示踪剂异常场，并使用它们来构建逼真的示踪剂通量。这个想法最近开始发展的背景下，允许涡流的海洋模型模型的“后向散射”，激励部分解决中尺度涡旋，但只有在过去的一两年中，它开始在粗模型的情况下，这是显着不同的涡流允许的情况下，开发。然而，为粗糙模型开发现实的随机参数化尤为重要，因为越来越多地使用这些粗糙模型的集合模拟场景需要涡驱动的大尺度变化的现实模式。与中尺度涡旋输送相关的不确定性必须通过现实的随机参数化包含在模式中，以使这些研究的结论准确。这种方法的一个好处是，涡流场比运输更容易建模和观察;这种方法也会导致现实的非高斯示踪剂通量分布。该方法的Gent-McWilliams（GM）的框架内，并在一个随机参数化的涡团速度的结果。该项目有两个主要组成部分：（i）开发涡旋场的随机模型，以及（ii）在IPCC级全球气候模型中实施、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社区地球系统模型（CESM）海洋模型工作组（OMWG）的科学家的密切合作。

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.