Stochastic reduced order models
for real-time data assimilation

Project goal : Real-time estimation and short-time prediction of 3D fluid flow, using few sensors and limited computational resources. This is made possible by the coupling between synthetic data, physical models and sensors' measurements.

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 control of wind turbines, boats equipped with foils, and antifreeze towers in vineyards.

Some related publications & communications

Open-source code

The python code performs the data assimilation using precomputed ROM coefficients and ROM noise statistics.

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


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

Some related communications

Open-source codes

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

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 :  


Related publications & communications

Open-source codes

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