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

海洋湍流是由复杂的运动组成的--射流、漩涡和波浪，它们在不同的时空尺度上共存，但也没有明显的尺度分离。沿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，自然地实际需要开发仿真器，即降低复杂性的预测模型，其将动态地再现跨尺度湍流海洋运动的整个复杂性。这一举措旨在通过数学方法，即基于方程的方法以及数据驱动的简化方法，开发此类模拟器，描述相对较少的（从数十到数百）时空模式的演变，并捕捉基本的多尺度海洋流动和分层的基本统计特性。它将结合联合收割机发展和应用最先进的数据自适应方法和严格的数学理论，在海洋模式的层次中从准地转方程到原始方程进行动力和经验的简化。（ii）证明随机和非线性流动仿真器可以提供对多尺度瞬态流模式及其相互作用的动力学和运动学性质的基本新颖的见解，并寻找非线性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在海洋模式的层次结构中考虑几种类型的海洋环流的动态模拟涡流，这些模式涉及各种复杂性和地理情况，从纬向流上的各向异性β平面湍流，以及具有西部边界流的风力驱动的涡旋，到区域海洋模拟系统的综合解决方案，并因此开发用于涡旋多尺度流的有效模拟器，（v）将随机和非线性流动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。该项目的智力价值在于开发多功能和新颖的方法来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，并捕获跨尺度的海洋动力学，即，从大尺度年代际变率到中尺度涡旋，以及由此产生的对多尺度流动的动力学和运动学理解。该项目更广泛的影响在于开发了非常通用的方法，可以很容易地被其他科学采用。在粗粒度的意义上模拟湍流的统计模式可以被采用作为有效的和低成本的模拟器的海洋组件的大气环流模式。该项目非常适合NSF-NERC促进美英研究的计划目标，也是博士后参与前沿国际研究的绝佳机会。涡流解决方案的数据和软件将被公开。

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.