NSFGEO-NERC: Multiscale Stochastic Modeling and Analysis of the Ocean Circulation

湍流洋流由复杂的运动组成--射流、漩涡和波浪，它们在非常不同的时空尺度上共存，但也没有明显的尺度分离。沿着在高数值分辨率下模拟多尺度海洋环流的计算挑战，以及由此导致的对多尺度流动的动力学和运动学理解的困难，自然地实际需要开发降低复杂性的预测模型，以再现跨尺度的湍流海洋运动的整体复杂性。本项目旨在通过动态，即，这些方法包括基于方程和统计数据驱动的简化方法，描述相对较少的（从几十到几百）时空模式的演变，并捕捉基本的多尺度洋流和分层的基本统计特性。它将结合联合收割机的发展和应用最先进的数据适应方法和严格的数学理论，在海洋模型的层次结构中进行动态和经验的简化。在这个项目中开发的方法是非常普遍的，可以很容易地扩展到流体力学和地球物理流动的其他问题。降阶随机模式在粗粒度意义上模拟湍流流动，可以作为大气环流模式的有效和低成本的海洋组件，可以改善气候变化的定量预测。该项目将促进美国和英国的研究合作，并提供在国际环境中进行交叉培训的机会。英国合作者将通过帝国理工学院EPSRC博士培训中心“行星地球数学”招募一名博士生，从事随机降阶海洋模型的开发和应用工作。该项目旨在开发通用和新颖的方法，用于构建复杂性降低的随机海洋仿真器，基于高端模型模拟或基础动力学方程，或两者兼而有之，以及捕捉不同尺度的海洋变化，从大尺度年代际变化到中尺度涡旋，以及由此产生的对多尺度流动的动力学和运动学理解。本项目的目标是：（i）扩展最近的理论结果，并模拟包括中尺度涡旋在内的全谱动力学重要尺度;（ii）证明随机流模拟器可以为多尺度瞬态流型及其相互作用的动力学和运动学特性提供基本的新见解，并寻求模式相互作用的动力学解释; ㈢将经验和动力还原方法推广到空间不均匀和紊流; ㈣在不同复杂程度和地理情况的海洋模式层次中考虑海洋环流的几种动态模拟的多尺度涡旋流，例如纬向流的各向异性湍流和西边界流的风力环流，（v）将随机流模拟器嵌入非涡动分辨动力学海洋模型中，作为涡动效应的有效参数化。

Turbulent oceanic flows consist of complex motions - jets, vortices and waves that co-exist on very different spatio-temporal scales but also without clear scale separation. Along with computational challenges to simulate multiscale oceanic circulation in high numerical resolution, as well as resulting difficulties in dynamically and kinematical understanding of multiscale flows, naturally goes practical need to develop prognostic models of reduced complexity that reproduce the whole complexity of turbulent oceanic motions across scales. This project aims to develop such reduced-order stochastic models by dynamical, i.e., equations-based as well as statistical data-driven reduction methods, describing the evolution of relatively few (from tens to hundreds) spatio-temporal modes and capturing essential statistical properties of the underlying multiscale oceanic flow and stratification. It will combine development and applications of state-of-the-art data-adaptive methods and rigorous mathematical theory for dynamical and empirical reduction in the hierarchy of oceanic models. The methods to be developed in this project are very general and can be easily extended to other problems in fluid mechanics and geophysical flows. The reduced-order stochastic models that emulate the turbulent flows in a coarse-grained sense can be adopted as efficient and low-cost oceanic components of general circulation models that could improve quantitative prediction of climate change. The Project will foster a USA-UK research collaboration and provide opportunities for cross-training in an international setting. The UK collaborator will recruit a PhD student via the EPSRC Centre for Doctoral Training "Mathematics of Planet Earth" at the Imperial College to work on development and applications of stochastic reduced-order ocean models.This Project aims to develop versatile and novel methods for constructing stochastic oceanic emulators of reduced complexity, based either on high-end model simulations or on underlying dynamical equations, or both, and for capturing oceanic variability across scales, i.e., from large-scale decadal variability to mesoscale eddies, and resulting dynamical and kinematical understanding of multiscale flows. The goals of this Project are (i) to extend recent theoretical results and to emulate the full spectrum of dynamically important scales including mesoscale eddies; (ii) to demonstrate that the stochastic flow emulators can provide fundamental novel insights into dynamical and kinematical properties of the multiscale transient flow patterns and their interactions, and to search for dynamical interpretations of mode interactions; (iii) to extend empirical and dynamical reduction methods to spatially inhomogeneous and turbulent flows; (iv) to consider several types of dynamically simulated eddying multiscale flows of the ocean circulation in the hierarchy of oceanic models of different complexity and geography, such as anisotropic turbulence on zonal currents and wind-driven gyres with western boundary currents, (v) to embed the stochastic flow emulators into non-eddy-resolving dynamical oceanic models as effective parameterizations of the eddy effects.