# Projects

# Stochastic reduced order models

for real-time data assimilation

for real-time data assimilation

**Project goal : **Development and applications of new mathematical and computational tools for real-time estimation and short-time prediction of 3D fluid flow, using limited computational resources. This is made possible by the coupling between data, physical models and sparse fluid flow measurements. Here, the term data refers to numerical simulation outputs.

**Methodology ****: **To achieve these goals, synthetic (i.e. simulated) data and intrusive surrogate models (ROM) drastically reduces the problem dimensionality. Errors induced by the dimension reduction are quantified by a multi-scale physically-based stochastic parameterization. This Uncertainty Quantification (UQ) enables simulation-measurement coupling through state-of-art data assimilation algorithms.

**Results ****:** Impressive numerical results have been obtained for a 3-dimensional wake flows at moderate Reynolds for up to 14 vortex shedding cycles after the learning window, using a single measurement point.

**Green innovations : **The software resulting from this project would allow, in real-time, the monitoring and optimization of the operation of wind turbines and boats equipped with foils.

**Some related publications & communications**

Resseguier, V., Ladvig, M., Heitz, D. (2022). "Real-time estimation and prediction of unsteady flows using reduced-order models coupled with few measurements". Journal of Computational Physics. [HAL][Preprint]

Resseguier, V., Picard, A. M., Mémin, E. & Chapron, B. (2021). Quantifying truncation-related uncertainties in unsteady fluid dynamics reduced order models. SIAM/ASA Journal on Uncertainty Quantification. [HAL][file]

Valentin Resseguier, Matheus Ladvig, Augustin Picard, Etienne Mémin, Bertrand Chapron (2020)

"Toward real-time embedded observer of unsteady fluid flow environment",

10th European Congress on Embedded Real Time Software and Systems (ERTS 2020). Toulouse.

[Conference poster]Matheus Ladvig, Agustin Martin Picard, Valentin Resseguier, Dominique Heitz, Etienne Mémin, Chapron Bertrand (2020)

"Real-time observer from stochastic reduced order model",

[Slides]

# Wave-turbulence interaction

**Project goal : **Simulate more precisely and at lower cost the interactions of surface currents on swells and better characterize these effects and their impacts (bias and variability) on satellite radar measurements.

**Methodology ****: **The small-scale currents being generally badly resolved by models and unobserved by altimetric measurements, we have developed stochastic multiscale self-similar and self-adaptive models to represent them and simulate their effects on swell spectra. From there, wave fields are emulated and radar measurements can be simulated.

**Results ****: **Self-similarity in both time and space ensures very good skills to our stochastic turbulence models in every simulated situations. In contrast, the usual time-decorrelation assumption is valid only for wavenumber larger than a threshold.

Heterogeneous oceanic currents like jets locally enhances wave energy, and this strengthens several biases on altimetric satellite measurements due to wave vertical asymmetries.

**Related publications & communications**

Resseguier, V., Hascoet, E., Chapron, B. (Submitted). "Random ocean swell-rays: a stochastic framework". STUOD Proceedings.

Valentin Resseguier, Erwan Hascoet, Bertrand Chapron, Baylor Fox-Kemper (2021) "Validity domains and parametrizations for white-noise and multiscale models in turbulence and wave-turbulence interactions". EGU [HAL][PICO slide]

# Models under location uncertainty

**Project goal : **Model the effect of unresolved turbulence and above all quantify the induced simulation model errors in order to improve ensemble-based data assimilation algorithms.

**Methodology ****: **Physically, the two central assumptions are the temporal decorrelation of small-scale turbulence and the transport of physical quantities by the partially random velocity of the fluid. Compared to classical fluid mechanics, three new terms appear in the equations: a multiplicative noise, a diffusion term, and a large-scale advecting velocity correction. For ensemble forecasts, we propose several parametrization choice (i.e. possibly heterogeneous spatial covariance) for the random turbulence.

**Results ****: **This framework enables new fluid dynamics model derivations and faster attractor visit. But more importantly, the dynamics under location uncertainty accurately quantifies model errors unlike traditional methods (e.g. random initial conditions).

**Related publications**

Resseguier, Long Li, Gabriel Jouan, Pierre Dérian, Etienne Mémin, Chapron Bertrand (2020)"New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics",Archives of Computational Methods in Engineering.[HAL][bibtex][file]

Valentin Resseguier, Wei Pan, Baylor Fox-Kemper (2020)"Data-driven versus self-similar parameterizations for Stochastic Advection by Lie Transport and Location Uncertainty",Nonlinear Processes in Geophysics.[HAL][bibtex][file] [github repo]

Bertrand Chapron, Pierre Dérian, Etienne Mémin, Valentin Resseguier (2018)"Large scale flows under location uncertainty: a consistent stochastic framework",Quarterly Journal of the Royal Meteorological Society.[HAL][bibtex][file]

Valentin Resseguier, Etienne Mémin, Bertrand Chapron (2017)"Geophysical flows under location uncertainty, Part III SQG and frontal dynamics under strong turbulence conditions",Geophysical and Astrophysical Fluid Dynamics.[HAL][bibtex][file]

Valentin Resseguier, Etienne Mémin, Bertrand Chapron (2017)"Geophysical flows under location uncertainty, Part II Quasi-geostrophy and efficient ensemble spreading",Geophysical and Astrophysical Fluid Dynamics.[HAL][bibtex][file] [github repo]

Valentin Resseguier, Etienne Mémin, Bertrand Chapron (2017)"Geophysical flows under location uncertainty, Part I Random transport and general models",Geophysical and Astrophysical Fluid Dynamics.[HAL][bibtex][file]

**Some r****elated communications**

Baylor Fox-Kemper, Darryl Holm, Wei Pan, Valentin Resseguier (2019)

"Stochastic transport to quantify errors in geophysical fluid dynamic simulations",

EGU 2019 (European Geophysical Union). Vienne, AT.[Slides]Valentin Resseguier, Long Li, Gabriel Jouan, Pierre Dérian, Etienne Mémin, Bertrand Chapron (2019)

"Dynamics under location uncertainty and other energy-related stochastic subgrid schemes",

2019 - Workshop Conservation Principles, Data and Uncertainty in Atmosphere-Ocean Modelling. Potsdam, DE.[Slides]

Valentin Resseguier, Etienne Mémin, Bertrand Chapron (2016)

"Likely chaotic transitions of large-scale fluid flows using a stochastic transport model",

9th Chaotic Modeling and Simulation International Conference (CHAOS2016). Londres, GB.[Slides]

Valentin Resseguier, Etienne Mémin, Bertrand Chapron (2016)

"Stochastic subgrid tensor for geophysical flow modeling",

8th European Postgraduate Fluid Dynamics Conference. Varsovie, PL.[Poster]

**Open-source codes**

SQGMU [github repo]

This MATLAB codes simulates deterministic or randomized version of the Surface Quasi-Geostrophic (SQG) model. The random dynamics is based on the transport under location uncertainty. It is associated to : "Geophysical flows under location uncertainty, Part II", V. Resseguier et al., 2017

LU_SALT_Selfsim [github repo]

This MATLAB codes simulates deterministic or randomized version of 2D Euler and Surface Quasi-Geostrophic (SQG) models. The random dynamics is based on LU and SALT frameworks. Several parameterisations are available. It is associated to : "Data-driven versus self-similar parameterizations for Stochastic Advection by Lie Transport and Location Uncertainty", V. Resseguier et al., 2020

# Fluid mixing

**Project goal : **Identify the Lagrangian coherent structures (i.e. the fluid subdomains which stay isolated from each other without mixing) but also understand and provide parametrization proxy for Lagragian-advection-based downscaling methods (e.g. Sutton et al., 1994, for the atmosphere or Desprès et al., 2011a,b for the ocean).

**Methodology ****:**

To identify Lagrangian coherent structures we simulate (or observe) streaklines from many source points, and then we compute the streaklines' tangents norm kurtosis (4th-order moment). This method detects streaklines breakings which occur at Lagrangian coherent structures boundaries.

Besides, oceanographic Lagragian-advection-based downscaling methods focus on the tracer “submesoscale” structures (≤10 km), created by mesoscale currents (∼100 km) indirectly measured by satellite. And in this case, we can assume these (Eulerian) currents as constant in time. Thus, the key mixing processes are only locally uniform shears and foldings around stationary convective cells. From there, we propose a pseudo-analytical deterministic model, inexpensive in computing power, to predict the deformations generated by the currents and the evolution of the tracer 2nd-order statistics after a finite time.

**Results ****: **

Our streaklines tangents kurtosis method successfully identify Lagrangian coherent structures. But, contrary to the state of the art (finite-time Lyapunov exponents, abbreviated FLTE), our method is not restricted by the weak precision of the spatial derivatives involved (finite differences).

For oceanographic Lagragian-advection-based downscaling methods, we successfully predict the evolution of spectral energy density of the tracer after a finite time, the effective diffusion coefficient and the optimal time to stop a downscaling, without needing any time integration.

**Related publications & communications**

**Valentin Resseguier,**Bertrand Chapron, Etienne Mémin (2022). "Effects of smooth divergence-free flows on tracer gradients and spectra: Eulerian prognosis description". Journal of Physical Oceanography. [HAL][file][github repo]

**Open-source codes**

Mixing [github repo]

Compute Lagrangian advection and several mixing diagnoses, from synthetic and real oceanographic data. For real satellite image tests, globcurrent data can be used. It is associated to : "Effects of smooth divergence-free flows on tracer gradients and spectra: Eulerian prognosis description", V. Resseguier et al., 2021