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

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics


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 of
oceanic 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.

Planned Impact

The developed data-driven and analytical methods are by nature very general and can be easily adopted to other sciences. The dynamical flow analyses can be adopted in other areas of fluid mechanics, while applications of emulators can be useful for other multiscale geophysical problems. From an educational perspective, the project will fund and train two postdoctoral scientists, one at UCLA and the other one at IC. The presence of proposing team members in many specialized meetings and summer schools will broaden the horizons and help cross-fertilization of research. The proposed 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. The software for constructing emulators and eddy-resolving solutions data will be made publicly available, similar to SSA-MTM Toolkit and ROMS, maintained by DK and JCM, respectively.

Milestones and Measures of Success:
A set of eddy-resolving solutions that can be used for other analyses and separate projects.
Publication of peer-reviewed journal articles.
Timely presentations of key results on international conferences and focused workshops, as well as at the leading UK oceanographic institutions.
High-quality training of the PDRA.
Training of 1-2 PhD students.
New research collaborations stemming from the Project.
Description The main goal of the research funded on this grant is to present a parameterisation scheme of unresolved processes that significantly improves the capabilities of ocean numerical low-resolution models in producing realistic long-time simulations. The unresolved processes are the ones governed by the intense interactions between transient features such as coherent meso-scale vortices. A stochastic data-driven approach is employed to tackle the problem. This means that the low-resolution model is augmented with the information statistically inferred from, in our case, a short high-resolution model solution, which features all the necessary transient dynamics that is deficient in the low-resolution solution. Making use of a statistical decomposition of the high-resolution solution into large-scale and small-scale fields, one then produces the effective forcing term. This forcing term is then supplied into the low-resolution model to produce a much improved solution. Our key findings are that although these kinds of statistical decomposition are not unique, the low-resolution model surprisingly well adjusts itself to the parameterised high-resolution forcing and remains stable for a wide range of the supplied forcing (produced with various decomposition parameters and from different high-resolution model runs). The produced parameterised low-resolution solution is found to be a substantial improvement over the non-parameterised low-resolution solution. The parameterised solution resembles key characteristics of the corresponding high-resolution solutions such as it features a similar idiosyncratic geometrical structure of the flow as well as a similar energy spectrum, which cannot be attained by solving the corresponding non-parameterised model. As a next step, the parametrisation approach has been significantly improved by reducing the amount of information needed from the high-resolution truth. Now, instead of utilising the full high-resolution data, we decompose it into physically meaningful fields and then make use only of the eddy fields, which correspond to transient high-frequency dynamics lacking in the coarse-resolution solutions. The eddy fields are statistically less involved compared to the full eddy forcing fields and thus are tenable to be emulated by reasonably complex stochastic models. This paves the way for formulating a comprehensive framework for utilising limited information from objective truth (wheater from expensive high-resolution simulations or observational data) to augment coarse-resolution, long-term ocean simulations.
Exploitation Route The findings may be useful for the ocean modelling community in that they provide evidence that the data-driven approach to parameterising unresolved processes can lead to more accurate outcomes of long-term ocean model runs. Another important finding is that in order to obtain necessary information from given data to supply it into low-resolution models, one first needs to accurately preprocess this data and to decompose it into physically important scales. This is necessitated by the fact that the unresolved processes in the low-resolution model should be prioritised whilst the resolved scales, oppositely, should be suppressed and not contributed twice to the integral dynamics. More evidence of the importance of physically correct scale decompositions in ocean flows has been obtained. The step is crucial for tempering parameterisation approaches towards a more profound understanding of underlying physics, which should be accounted for in the coarse-resolution models. We also established the minimal amount of true data needed to be fed into coarse-resolution models to nudge the coarse-resolution dynamics closer to the true reference solution. This involves knowledge of eddy fields that induce the peculiar geometrical structure of the resulting flow.
Sectors Environment