The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.

# Ocean & coupled ocean

Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres. Fluids [Internet]. 2018;3 (1) :21. Publisher's VersionAbstract

.
The Mathematics of Climate Change and of its Impacts. Workshop on "Mathematical Approaches to Climate Change Impacts - MAC2I" at the Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM), Italy [Internet]. 2017. Workshop websiteAbstract

.
The atmosphere and oceans as unsteady flows: Intrinsic variability and time-dependent forcing. BIRS Workshop 17w5048 - Transport in Unsteady Flows: from Deterministic Structures to Stochastic Models and Back Again [Internet]. 2017. Workshop websiteAbstract

.
Interannual variability in the North Atlantic ocean’s temperature field and its association with the wind stress forcing. Journal of Climate. 2017;30 (7) :2655-2678.Abstract

.
The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem. Discrete and Continuous Dynamical Systems - A. 2017;37 (1) :189-228.Abstract

.
Interannual variability in the North Atlantic SST and wind forcing. Seminar at International Research Institute for Climate and Society, Columbia. 2014.Abstract

.
Interannual Variability in North Atlantic Weather: Data Analysis and a Quasigeostrophic Model. Journal of the Atmospheric Sciences. 2016;73 (8) :3227-3248.Abstract

.
Data Assimilation for the Atmosphere, Ocean, Climate and Space Plasmas: Some Recent Results. Dept. of Meteorology, University of Reading and the NERC Data Assimilation Research Centre (DARC). 2007.Abstract

.
Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation. Nonlinear Processes in Geophysics. 1995;2 :241–268.Abstract

.
Multiple Equilibria, Periodic, and Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model. Journal of Physical Oceanography. 1995;25 (5) :764–786.Abstract

.
Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front. Journal of the Atmospheric Sciences. 2004;61 (9) :961–981.Abstract

.
Low-frequency variability and heat transport in a low-order nonlinear coupled ocean–atmosphere model. Physica D: Nonlinear Phenomena. 2015;309 :71–85.Abstract

.
Bifurcation analysis of ocean, atmosphere, and climate models. In: Handbook of numerical analysis. Vol. 14. Elsevier ; 2009. pp. 187–229.

.