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

湍流海洋流动由复杂的运动组成--射流、漩涡和波浪在非常不同的时空尺度上共存，但也没有明确的尺度分离。随着以高数值分辨率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，自然需要开发仿真器，即降低复杂性的预报模型，以动态地再现跨尺度海洋湍流运动的全部复杂性。这一举措旨在通过数学方法，即基于方程和数据驱动的简化方法，开发这种模拟器，描述相对较少的(从几十个到数百个)时空模式的演变，并捕捉基本的多尺度海洋流动和层结的基本统计特性。它将结合最先进的数据自适应方法和严格的数学理论的发展和应用，从准地转到原始方程的海洋模式层级的动力学和经验约化。本建议的目标是(I)推广最新的理论结果，并模拟包括中尺度涡旋在内的所有动力重要尺度；(Ii)证明随机和非线性流动模拟器可以对多尺度瞬变流型及其相互作用的动力学和运动学性质提供基本的新见解，并寻求对非线性模式相互作用的动力学解释；(Iii)将经验和动力学约化方法扩展到空间非均匀和湍流；(4)在整个复杂和地理范围的海洋模式体系中考虑几种类型的海洋环流动态模拟涡流，从纬向流上的各向异性β平面湍流和具有西边界流的风生涡旋，到区域海洋模拟系统的综合解，从而开发有效的涡流多尺度流模拟器，(5)将随机和非线性流动模拟器嵌入非涡旋解析动力学海洋模式中，作为涡流效应的有效参数。该项目的智力优势在于开发通用和新颖的方法来构建复杂性较低的随机海洋仿真器，要么基于高端模式模拟，要么基于基本的动力学方程，或者两者兼而有之，并捕捉跨尺度的海洋动力学，即从大尺度的十年变率到中尺度的涡旋，以及由此产生的对多尺度流动的动力学和运动学理解。该项目的更广泛的影响在于开发非常通用的方法，可以很容易地应用于其他科学。在粗粒度意义上模拟湍流的统计模式可以作为大气环流模式中海洋分量的高效和低成本的模拟器。该项目代表着与NSF-NERC促进美英研究的计划目标的完美契合，也是博士后参与前沿国际研究的绝佳机会。涡流解析解决方案数据和软件将公之于众。

The 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 emulators, i.e. prognostic models of reduced complexity that would reproduce dynamically the whole complexity of turbulent oceanic motions across scales. This initiative aims to develop such emulators by mathematical, i.e. equations-based as well as data-driven reduction methods, describing 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 ofoceanic models from the quasi-geostrophic to primitive equations.The goals of this proposal 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 and nonlinear 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 nonlinear 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 flows of the ocean circulation in the hierarchy of oceanic models across full spectrum of complexity and geography, from anisotropic beta-plane turbulence on zonal currents, and wind-driven gyres with western boundary currents, to comprehensive solutions by Regional Oceanic Modeling System, and, thus, to develop efficient emulators for the eddying multiscale flows, (v) to embed the stochastic and nonlinear flow emulators into non-eddy-resolving dynamical oceanic models as effective parameterizations of the eddy effects. The intellectual merit of this project is in developing versatile and novel methods to construct stochastic oceanic emulators of reduced complexity, based either on high-end model simulations or underlying dynamical equations, or both, and capturing oceanic dynamics across scales, i.e., from large-scale decadal variability to mesoscale eddies, and resulting dynamical and kinematical understanding of multiscale flows.The project's broader impacts lie in developing methods that are very general and can be easily adopted to other sciences. The statistical models that emulate the turbulent flows in a coarse-grained sense can be adopted as efficient and low-cost emulators for oceanic components of general circulation models. The project represents perfect fit to NSF-NERC program goals of fostering USA-UK research and perfect opportunity for the postdocs to get engaged into the leading-edge international research. Eddy-resolving solutions data and software will be made public.