7.1.1 AGRIF

• Name: Adaptive Grid Refinement In Fortran
• Keyword: Mesh refinement
• Scientific Description: AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• Functional Description: AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• News of the Year: In 2019, a new contract has been signed with CMEMS (Copernicus Marine Environment Moniroting Service) in order to extent the multiresolution capabilities of the AGRIF and its integration into the NEMO ocean system.
• URL: https://gitlab.inria.fr/ldebreu/agrif
• Publications: tel-01546328, hal-00387435
• Contact: Laurent Debreu
• Participants: Roland Patoum, Laurent Debreu

7.1.2 BALAISE

• Name: Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement
• Keywords: Multi-scale analysis, Data assimilation, Optimal control
• Functional Description: BALAISE (Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement) is a test bed for image data assimilation. It includes a shallow water model, a multi-scale decomposition library and an assimilation suite.
• Contact: Arthur Vidard

7.1.3 NEMOVAR

• Name: Variational data assimilation for NEMO
• Keywords: Oceanography, Data assimilation, Adjoint method, Optimal control
• Functional Description: NEMOVAR is a state-of-the-art multi-incremental variational data assimilation system with both 3D and 4D var capabilities, and which is designed to work with NEMO on the native ORCA grids. The background error covariance matrix is modelled using balance operators for the multivariate component and a diffusion operator for the univariate component. It can also be formulated as a linear combination of covariance models to take into account multiple correlation length scales associated with ocean variability on different scales. NEMOVAR has recently been enhanced with the addition of ensemble data assimilation and multi-grid assimilation capabilities. It is used operationnaly in both ECMWF and the Met Office (UK)
• Contact: Arthur Vidard
• Partners: CERFACS, ECMWF, Met Office

7.1.4 Sensitivity

• Functional Description: This package is useful for conducting sensitivity analysis of complex computer codes.
• URL: https://cran.r-project.org/web/packages/sensitivity/index.html
• Contact: Laurent Gilquin

8.1.1 Numerical Schemes for Ocean Modelling

Participants: Eric Blayo, Matthieu Brachet, Laurent Debreu, Nicolas Ducousso, Emilie Duval, Florian Lemarié, Gurvan Madec, Antoine Nasser.

With the increase of resolution, the hydrostatic assumption becomes less valid and the AIRSEA group also works on the development of non-hydrostatic ocean models. The treatment of non-hydrostatic incompressible flows leads to a 3D elliptic system for pressure that can be ill conditioned in particular with non geopotential vertical coordinates. That is why we favour the use of the non-hydrostatic compressible equations that removes the need for a 3D resolution at the price of reincluding acoustic waves 17.

A comparison between 2D and 3D simulations of non hydrostatic surface waves has been performed in 44.

In addition, Emilie Duval started her PhD in September 2018 on the coupling between the hydrostatic incompressible and non-hydrostatic compressible equations. A detailed analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean is presented in 35.

Accurate and stable implementation of bathymetry boundary conditions in ocean models remains a challenging problem. The dynamics of ocean flow often depend sensitively on satisfying bathymetry boundary conditions and correctly representing their complex geometry. Generalized (e.g. ) terrain-following coordinates are often used in ocean models, but they require smoothing the bathymetry to reduce pressure gradient errors. Geopotential -coordinates are a common alternative that avoid pressure gradient and numerical diapycnal diffusion errors, but they generate spurious flow due to their “staircase” geometry. In 9, we introduce a new Brinkman volume penalization to approximate the no-slip boundary condition and complex geometry of bathymetry in ocean models. This approach corrects the staircase effect of -coordinates, does not introduce any new stability constraints on the geometry of the bathymetry and is easy to implement in an existing ocean model. The porosity parameter allows modelling subgrid scale details of the geometry. We illustrate the penalization and confirm its accuracy by applying it to three standard test flows: upwelling over a sloping bottom, resting state over a seamount and internal tides over highly peaked bathymetry features. Figure (1) shows strong improvements obtained when the penalization method is used in comparison with traditional terrain following $\sigma$ simulations. At 6 km resolution, the penalization methods (Figure (1) d)), that takes into account details of bathymetry, allows to recover internal tide wave beams closed to the 3 km simulation. (Figure (1) a)). Following this work, Antoine Nasser started his PhD in October 2019 on penalization methods. One of the objectives is to study the representation of overflows in global ocean model. The NEMO ocean model will be used for the applications.

In the context of the H2020 IMMERSE project, the AIRSEA team is in charge of the development of a new time stepping strategy for the NEMO ocean model. Nicolas Ducousso works particularly on the design of Runge Kutta schemes for ocean models, taking into account the splitting between barotropic and baroclinic models. The team also studies the use of exponential time integrators (40) for ocean models.

8.1.2 Coupling Methods for Oceanic and Atmospheric Models and Representation of the Air-Sea Interface

Participants: Eric Blayo, Florian Lemarié, Sophie Thery, Simon Clément, Manolis Perot.

1. Continuous and discrete analysis of Schwarz algorithms for OA coupling: we have been developing coupling approaches for several years, based on so-called Schwarz algorithms. Schwarz-like domain decomposition methods are very popular in mathematics, computational sciences and engineering notably for the implementation of coupling strategies. However, for complex applications (like in OA coupling) it is challenging to have an a priori knowledge of the convergence properties of such methods. Indeed coupled problems arising in Earth system modeling often exhibit sharp turbulent boundary layers whose parameterizations lead to peculiar transmission conditions and diffusion coefficients. In the framework of S. Thery PhD (defended in February 2021) the well-posedness of the non-linear coupling problem including parameterizations has been addressed and a detailed continuous analysis of the convergence properties of the Schwarz methods has been pursued to entangle the impact of the different parameters at play in such coupling problem 45. During the first year of C. Simon PhD, a general framework has been proposed to study the convergence properties at a (semi)-discrete level to allow a systematic comparison with the results obtained from the continuous problem.

   Within the COCOA project, a Schwarz-like iterative method has been applied in a state-of-the-art Earth-System model to evaluate the consequences of inaccuracies in the usual ad-hoc ocean-atmosphere coupling algorithms used in realistic models 20. Numerical results obtained with an iterative process show large differences at sunrise and sunset compared to usual ad-hoc algorithms thus showing that synchrony errors inherent to ad-hoc coupling methods can be significant.

2. Representation of the air-sea interface in coupled models: During the PhD-thesis of Charles Pelletier the scope was on including the formulation of physical parameterizations in the theoretical analysis of the coupling, in particular the parameterization schemes to compute air-sea fluxes. Following this work, a novel and rigorous framework for a consistent two-sided modeling of the surface boundary layer has been proposed 22. This framework allows for a more general representation of the vertical physics at the air-sea interface while improving the mathematical regularity of the numerical solutions. Moreover, it is flexible enough to include additional physical parameters for example to account for the effect of surface waves in the turbulent flux computation. This work is the first step toward more adequate discretization methods for the parameterization of surface and planetary boundary layers in climate models 3162 (PhD-thesis of C. Simon). The problem of interest takes the form of an nonstationary nonlinear parabolic equation. The objective is to derive a discretization for which we could prove nonlinear stability criteria and show robustness to large variations in parabolic Courant number while being consistent with our knowledge of the underlying physical principles (e.g. the Monin-Obukhov theory in the surface layer).This work will be carried out in the framework of a project funded by SHOM (contract 19CP07).

   Lately, in the framework of the M. Perrot internship, we have been working in collaboration with Etienne Mémin (Fluminance project team) to investigate the possibility to derive a stochastic representation of the atmospheric surface layer dynamics and thermodynamics based on a modeling under location uncertainty. Efforts in this direction will be pursued.

3. A simplified atmospheric boundary layer model for oceanic purposes: Part of our activities within the IMMERSE project is dedicated to the development of a simplified model of the marine atmospheric boundary layer (called ABL1d) of intermediate complexity between a bulk parameterization and a full three-dimensional atmospheric model and to its integration to the NEMO general circulation model 19. A constraint in the conception of such a simplified model is to allow an apt representation of the downward momentum mixing mechanism and partial re-energization of the ocean by the atmosphere while keeping the computational efficiency and flexibility inherent to ocean only modeling. First realistic applications of the coupled NEMO-ABL1d modeling system have been carried out 6.
4. Analysis and improvement of air-sea-wave interactions in realistic simulations: part of our activity has been in collaboration with atmosphericists and physical oceanographers to study the impact on some modeling assumptions in realistic ocean-atmosphere coupled simulations 13, 70, 65. At a more fundamental level, in collaboration with A. Wirth, we have studied turbulent fluctuations in a coupled Ekman layer problem with randomized drag coefficient 27. Moreover, within the ALBATROS project 63, we have contributed to the development of a 2-way coupling between an ocean global circulation model (NEMO) with a surface wave model (WW3). Such coupling is not straightforward to implement since it requires modifications of the governing equations, boundary conditions and subgrid scale closures in the oceanic model 8.

These topics are addressed through strong collaborations between the applied mathematicians and the climate and operational community (Meteo-France, Ifremer, SHOM, Mercator-Ocean, LMD, and LOCEAN). Our work on ocean-atmosphere coupling has steadily matured over the last few years and has reached a point where it triggered interest from the physicists. Through the funding of the the projects ANR COCOA (started in January 2017, PI: E. Blayo) and SHOM 19CP07 (started in January 2020, PI: F. Lemarié), Airsea team members play a major role in the structuration of a multi-disciplinary scientific community working on ocean-atmosphere coupling spanning a broad range from mathematical theory to practical implementations in climate and operational models. An expected outcome of those projects should be the design of a benchmark suite of idealized coupled test cases representative of known issues in coupled models. Such idealized test cases should motivate further collaborations at an international level. In this context, a single-column version of the CNRM climate models has been designed and several coupling algorithms have been implemented (work done by S. Valcke, CERFACS). This model will be used to illustrate the relevance of our theoretical work in a semi-realistic context.

8.1.3 Nonhydrostatic Modeling

Participant: Eric Blayo, Laurent Debreu, Emilie Duval.

In the context of the French initiative CROCO (Coastal and Regional Ocean COmmunity model, https://www.croco-ocean.org) for the development of a new oceanic modeling system, Emilie Duval is working on the design of methods to couple local nonhydrostatic models to larger scale hydrostatic ones (PhD started in Oct. 2018). Such a coupling is quite delicate from a mathematical point of view, due to the different nature of hydrostatic and nonhydrostatic equations (where the vertical velocity is either a diagnostic or a prognostic variable). A thorough analysis of the different families of waves that can be present in these equations was performed. A prototype has been implemented, which allows for analytical solutions in simplified configurations and makes it possible to test different numerical approaches.

8.1.4 Machine learning for reconstruction of model parameters.

Participants: Laurent Debreu, Eugene Kazantsev, Arthur Vidard, Olivier Zahm.

8.2.1 Direct assimilation of image sequences

At the present time the observation of Earth from space is done by more than thirty satellites. These platforms provide two kinds of observational information:

• Eulerian information as radiance measurements: the radiative properties of the earth and its fluid envelops. These data can be plugged into numerical models by solving some inverse problems.
• Lagrangian information: the movement of fronts and vortices give information on the dynamics of the fluid. Presently this information is scarcely used in meteorology by following small cumulus clouds and using them as Lagrangian tracers, but the selection of these clouds must be done by hand and the altitude of the selected clouds must be known. This is done by using the temperature of the top of the cloud.

Our current developments are targeted at the use of learning methods methods to describe the evolution of the images. This approach is being applied to the tracking of oceanic oil spills in the framework of a Long Li's Phd in co-supervision with Jianwei Ma.

8.2.2 Observation error representation

Accounting for realistic observations errors is a known bottleneck in data assimilation, because dealing with error correlations is complex. Following a previous study on this subject, we propose to use multiscale modelling, more precisely wavelet transform, to address this question. In 7 we investigate the problem further by addressing two issues arising in real-life data assimilation: how to deal with partially missing data (e.g., concealed by an obstacle between the sensor and the observed system); how to solve convergence issues associated to complex observation error covariance matrices? Two adjustments relying on wavelets modelling are proposed to deal with those, and offer significant improvements. The first one consists in adjusting the variance coefficients in the frequency domain to account for masked information. The second one consists in a gradual assimilation of frequencies. Both of these fully rely on the multiscale properties associated with wavelet covariance modelling.

A collaborative project started with C. Lauvernet (IRSTEA) in order to make use of this kind of assimilation strategies on the control of pesticide transfer and it led to the co supervision of E. Rouzies PhD, started in Dec 2019.

8.3.1 Parameter space dimension reduction and Model order reduction

Participants: Mohamed Reda El Amri, Arthur Macherey, Youssef Marzouk, Clémentine Prieur, Alessio Spantini, Ricardo Baptista, Daniele Bigoni, Olivier Zahm.

Numerical models describing the evolution of the system (ocean + atmosphere) contain a large number of parameters which are generally poorly known. The reliability of the numerical simulations strongly depends on the identification and calibration of these parameters from observed data. In this context, it seems important to understand the kinds of low-dimensional structure that may be present in geophysical models and to exploit this low-dimensional structure with appropriate algorithms. We focus in the team, on parameter space dimension reduction techniques, low-rank structures and transport maps techniques for probability measure approximation.

In 29, we propose a framework for the greedy approximation of high-dimensional Bayesian inference problems, through the composition of multiple low-dimensional transport maps or flows. Our framework operates recursively on a sequence of “residual” distributions, given by pulling back the posterior through the previously computed transport maps. The action of each map is confined to a low-dimensional subspace that we identify by minimizing an error bound. At each step, our approach thus identifies (i) a relevant subspace of the residual distribution, and (ii) a low-dimensional transformation between a restriction of the residual onto this sub-space and a standard Gaussian. We prove weak convergence of the approach to the posterior distribution, and we demonstrate the algorithm on a range of challenging inference problems in differential equations and spatial statistics.

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. The article 41 introduces a novel gradient-based dimension reduction method in which the informed subspace does not depend on the data. This permits online-offline computational strategy where the expensive low-dimensional structure of the problem is detected in an offline phase, meaning before observing the data. This strategy is particularly relevant for multiple inversion problems as the same informed subspace can be reused. The proposed approach allows to control the approximation error (in expectation over the data) of the posterior distribution. We also present sampling strategies which exploit the informed subspace to draw efficiently samples from the exact posterior distribution. The method is successfully illustrated on two numerical examples: a PDE-based inverse problem and a tomography problem with Poisson data.

In 36 we propose to robustly characterize joint and conditional probability distributions via transport maps. Transport maps or "flows" deterministically couple two distributions via an expressive monotone transformation. Yet, learning the parameters of such transformations in high dimensions is challenging given few samples from the unknown target distribution, and structural choices for these transformations can have a significant impact on performance. Here we formulate a systematic framework for representing and learning monotone maps, via invertible transformations of smooth functions, and demonstrate that the associated minimization problem has a unique global optimum. Given a hierarchical basis for the appropriate function space, we propose a sample-efficient adaptive algorithm that estimates a sparse approximation for the map. We demonstrate how this framework can learn densities with stable generalization performance across a wide range of sample sizes on real-world datasets.

In 38 we introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{ℝ}^d\to ℝ$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{ℝ}^d\to {ℝ}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{ℝ}^m\to ℝ$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm makes use of a sample ${\{x^{\left(i\right)},u\left(x^{\left(i\right)}\right),\nabla u\left(x^{\left(i\right)}\right)\}}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

The paper 43 is concerned with minimizing a sum of rational functions over a compact set of high-dimension. This work is motivated by the paper 38 in which one needs to optimze the sum of Rayleigh quotients. The proposed approach relies on the second Lasserre's hierarchy (also known as the upper bounds hierarchy) formulated on the pushforward measure in order to work in a space of smaller dimension. We show that in the general case the minimum can be approximated as closely as desired from above with a hierarchy of semidefinite programs problems or, in the particular case of a single fraction, with a hierarchy of generalized eigenvalue problems. We numerically illustrate the potential of using the pushforward measure rather than the standard upper bounds hierarchy. In our opinion, this potential should be a strong incentive to investigate a related challenging problem interesting in its own; namely integrating an arbitrary power of a given polynomial on a simple set (e.g., unit box or unit sphere) with respect to Lebesgue or Haar measure.

In the framework of Arthur Macherey’s PhD, we have proposed algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation 49. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. We are now interested in solving parametrized PDE with stochastic algorithms in the framework of potentially high dimensional parameter space. A preliminary step was the development of a PAC algorithm in relative precision for bandit problem with costly sampling 39.

Reduced models are also developed In the framework of robust inversion. In 55, we have combined a new greedy algorithm for functional quantization with a Stepwise Uncertainty Reduction strategy to solve a robust inversion problem under functional uncertainties. In a more recent work, we further reduced the number of simulations required to solve the same robust inversion problem, based on Gaussian process meta-modeling on the joint input space of deterministic control parameters and functional uncertain variable 34. These results are applied to automotive depollution. This research axis was conducted in the framework of the Chair OQUAIDO.

Scientific context

Forecasting geophysical  systems require complex models, which sometimes need to be coupled, and which make use of data assimilation. The objective of this project is, for a given output of such a system, to identify the most influential parameters, and to evaluate the effect of uncertainty in input parameters on model output. Existing stochastic tools are not well suited for high dimension problems (in particular time-dependent problems), while deterministic tools are fully applicable but only provide limited information. So the challenge is to gather expertise on one hand on numerical approximation and control of Partial Differential Equations, and on the other hand on stochastic methods for sensitivity analysis, in order to develop and design innovative stochastic solutions to study high dimension models and to propose new hybrid approaches combining the stochastic and deterministic methods. We took part to the writing of a position paper on the futur of sensitivity analysis 23.

8.4.1 Global sensitivity analysis

Participants: Elise Arnaud, Eric Blayo, Laurent Gilquin, Maria Belén Heredia, Adrien Hirvoas, Alexandre Janon, Henri Mermoz Kouye, Clémentine Prieur, Laurence Viry, Arthur Vidard, Emilie Rouzies.

8.4.2 Global sensitivity analysis with dependent inputs

An important challenge for stochastic sensitivity analysis is to develop methodologies which work for dependent inputs. Recently, the Shapley value, from econometrics, was proposed as an alternative to quantify the importance of random input variables to a function. Owen 67 derived Shapley value importance for independent inputs and showed that it is bracketed between two different Sobol' indices. Song et al. 71 recently advocated the use of Shapley value for the case of dependent inputs. In a recent work 66, in collaboration with Art Owen (Standford's University), we show that Shapley value removes the conceptual problems of functional ANOVA for dependent inputs. We do this with some simple examples where Shapley value leads to intuitively reasonable nearly closed form values. We also investigated further the properties of Shapley effects in 58.

8.4.3 Iterative estimation of Sobol’ indices

Participants: Elise Arnaud, Laurent Gilquin, Clémentine Prieur.

In the field of sensitivity analysis, Sobol’ indices are widely used to assess the importance of the inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol’ estimates. We proposed to tackle this issue by rendering the replication procedure iterative 14. The idea is to enable the addition of new model evaluations to progressively increase the accuracy of the estimates. These evaluations are done at points located in under-explored regions of the experimental designs, but preserving their characteristics. The key feature of this approach is the construction of nested space-filling designs. For the estimation of first-order indices, a nested Latin hypercube design is used. For the estimation of closed second-order indices, two constructions of a nested orthogonal array design are proposed. Regularity and uniformity properties of the nested designs are studied.

8.4.4 Green sensitivity for multivariate and functional outputs

Participants: María Belén Heredia, Clémentine Prieur.

Another research direction for global SA algorithm starts with the report that most of the algorithms to compute sensitivity measures require special sampling schemes or additional model evaluations so that available data from previous model runs (e.g., from an uncertainty analysis based on Latin Hypercube Sampling) cannot be reused. One challenging task for estimating global sensitivity measures consists in recycling an available finite set of input/output data. Green sensitivity, by recycling, avoids wasting. These given data have been discussed, e.g., in 68, 69. Most of the given data procedures depend on parameters (number of bins, truncation argument…) not easy to calibrate with a bias-variance compromise perspective. Adaptive selection of these parameters remains a challenging issue for most of these given-data algorithms. In the context of María Belén Heredia’s PhD thesis, we have proposed 2 a non-parametric given data estimator for aggregated Sobol’ indices, introduced in 60 and further developed in 56 for multivariate or functional outputs. We also introduced aggregated Shapley effects and we have extended a nearest neighbor estimation procedure to estimate these indices 37.

8.4.5 Global sensitivity analysis for parametrized stochastic differential equations

Participants: Henri Mermoz Kouye, Clémentine Prieur.

Many models are stochastic in nature, and some of them may be driven by parametrized stochastic differential equations. It is important for applications to propose a strategy to perform global sensitivity analysis (GSA) for such models, in presence of uncertainties on the parameters. In collaboration with Pierre Etoré (DATA department in Grenoble), Clémentine Prieur proposed an approach based on Feynman-Kac formulas 12. The research on GSA for stochastic simulators is still ongoing, first in the context of the MATH-AmSud project FANTASTIC (Statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations) with Chile and Uruguay, secondly through the PhD thesis of Henri Mermoz Kouye, co-supervised by Clémentine Prieur, in collaboration with INRA Jouy.

8.4.6 Sensitivity analysis in pesticide transfer models

Participants: Arthur Vidard, Emilie Rouzies.

Pesticide transfer models are valuable tools to predict and prevent pollution of water bodies. However, using such models in operational contexts requires a strong knowledge of their structure including influential parameters. This project aims at performing global sensitivity analysis (GSA) of the PESHMELBA model (pesticide and hydrology: modelling at the catchment scale). This work is made hard due to the modular, complex structure of the model that couples different physical processes. It results in a large input space dimension and a high computational cost that limits the number of available runs. Using classical GSA tools such as Sobol' indices is thus not feasible. In order to circumvect those limitations, alternative techniques such as HSIC dependence measure or Random Forest metamodel are explored in 33 and 48. Additionally, the use of such methods in the specific context of spatially distributed output is explored in a paper to be submitted soon.

8.5.1 Bayesian calibration

Physically-based avalanche propagation models must still be locally calibrated to provide robust predictions, e.g. in long-term forecasting and subsequent risk assessment. Friction parameters cannot be measured directly and need to be estimated from observations. Rich and diverse data is now increasingly available from test-sites, but for measurements made along ow propagation, potential autocorrelation should be explicitly accounted for. In the context of María Belén Heredia’s PhD, in collaboration with IRSTEA Grenoble, we have proposed in 57 a comprehensive Bayesian calibration and statistical model selection framework with application to an avalanche sliding block model with the standard Voellmy friction law and high rate photogrammetric images. An avalanche released at the Lautaret test-site and a synthetic data set based on the avalanche were used to test the approach. Results have demonstrated i) the efficiency of the proposed calibration scheme, and ii) that including autocorrelation in the statistical modelling definitely improves the accuracy of both parameter estimation and velocity predictions. In the context of the energy transition, wind power generation is developing rapidly in France and worldwide. Research and innovation on wind resource characterisation, turbin control, coupled mechanical modelling of wind systems or technological development of offshore wind turbines floaters are current research topics. In particular, the monitoring and the maintenance of wind turbine is becoming a major issue. Current solutions do not take full advantage of the large amount of data provided by sensors placed on modern wind turbines in production. These data could be advantageously used in order to refine the predictions of production, the life of the structure, the control strategies and the planning of maintenance. In this context, it is interesting to optimally combine production data and numerical models  in order to obtain highly reliable models of wind turbines. This process is of interest to many industrial and academic groups and is known in many fields of the industry, including the wind industry, as "digital twin”. The objective of Adrien Hirvoas's PhD work is to develop of data assimilation methodology to build the "digital twin" of an onshore wind turbine. Based on measurements, the data assimilation should allow to reduce the uncertainties of the physical parameters of the numerical model developed during the design phase to obtain a highly reliable model. Various ensemble data assimilation approches are currently under consideration to address the problem.  In the context of this work, it is necessary to develop algorithms of identification quantifying and ranking all the uncertainty sources. This work in done in collaboration with IFPEN. A first paper has been accepted for publication 42.

8.5.2 Simulation & Estimation of EPIdemics with Algorithms

Participants: Clémentine Prieur.

Due to the sanitary context, Clémentine Prieur decided to join a working group, SEEPIA Simulation & Estimation of EPIdemics with Algorithms, animated by Didier Georges (Gipsa-lab). A first work has been published 15. An extension of the classical pandemic SIRD model was considered for the regional spread of COVID-19 in France under lockdown strategies. This compartment model divides the infected and the recovered individuals into undetected and detected compartments respectively. By fitting the extended model to the real detected data during the lockdown, an optimization algorithm was used to derive the optimal parameters, the initial condition and the epidemics start date of regions in France. Considering all the age classes together, a network model of the pandemic transport between regions in France was presented on the basis of the regional extended model and was simulated to reveal the transport effect of COVID-19 pandemic after lockdown. Using the the measured values of displacement of people mobilizing between each city, the pandemic network of all cities in France was simulated by using the same model and method as the pandemic network of regions. Finally, a discussion on an integro-differential equation was given and a new model for the network pandemic model of each age was provided.

8.5.3 Non-Parametric statistical inference for Kinetic Diffusions

Participants: Clémentine Prieur, Jose Raphael Leon Ramos.

This research is the subject of a collaboration with Chile and Uruguay. More precisely, we started working with Venezuela. Due to the crisis in Venezuela, our main collaborator on that topic moved to Uruguay.

We are focusing our attention on models derived from the linear Fokker-Planck equation. From a probabilistic viewpoint, these models have received particular attention in recent years, since they are a basic example for hypercoercivity. In fact, even though completely degenerated, these models are hypoelliptic and still verify some properties  of coercivity, in a broad sense of the word. Such models often appear in the fields of mechanics, finance and even biology. For such models we believe it appropriate  to build statistical non-parametric estimation tools. Initial results have been obtained for the estimation of invariant density, in conditions guaranteeing its existence and unicity 51 and when only partial observational data are available. A paper on the non parametric estimation of the drift has been accepted recently 52 (see Samson et al., 2012, for results for parametric models). As far as the estimation of the diffusion term is concerned, a paper has been accepted 52, in collaboration with J.R. Leon (Montevideo, Uruguay) and P. Cattiaux (Toulouse). Recursive estimators have been also proposed by the same authors in 53, also recently accepted. In a recent collaboration with Adeline Samson from the statistics department in the Lab, we considered adaptive estimation, that is we proposed a data-driven procedure for the choice of the bandwidth parameters.

In 50, we focused on damping Hamiltonian systems under the so-called fluctuation-dissipation condition. Idea in that paper were re-used with applications to neuroscience in 64.

Note that Professor Jose R. Leon (Caracas, Venezuela, Montevideo, Uruguay) was funded by an international Inria Chair, allowing to collaborate further on parameter estimation.

We recently proposed a paper on the use of the Euler scheme for inference purposes, considering reflected diffusions. This paper could be extended to the hypoelliptic framework.

We also have a collaboration with Karine Bertin (Valparaiso, Chile), Nicolas Klutchnikoff (Université Rennes) and Jose R. León (Montevideo, Uruguay) funded by a MATHAMSUD project (2016-2017) and by the LIA/CNRS (2018). We are interested in new adaptive estimators for invariant densities on bounded domains 3, and would like to extend that results to hypo-elliptic diffusions.

8.5.4 Parameter control in presence of uncertainties: robust estimation of bottom friction

Participants: Victor Trappler, Arthur Vidard, Elise Arnaud, Laurent Debreu.

Many physical phenomena are modelled numerically in order to better understand and/or to predict their behaviour. However, some complex and small scale phenomena can not be fully represented in the models. The introduction of ad-hoc correcting terms, can represent these unresolved processes, but they need to be properly estimated.

A good example of this type of problem is the estimation of bottom friction parameters of the ocean floor. This is important because it affects the general circulation. This is particularly the case in coastal areas, especially for its influence on wave breaking. Because of its strong spatial disparity, it is impossible to estimate the bottom friction by direct observation, so it requires to do so indirectly by observing its effects on surface movement. This task is further complicated by the presence of uncertainty in certain other characteristics linking the bottom and the surface (eg boundary conditions). The techniques currently used to adjust these settings are very basic and do not take into account these uncertainties, thereby increasing the error in this estimate.

Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of uncertainties, the minimisation is not straightforward, as the output of the model depends on those uncontrolled inputs and on the control parameter as well. That is why we will aim at minimising the objective function, to get an estimation of the control parameter that is robust to the uncertainties.

The definition of robustness differs depending of the context in which it is used. In this work, two different notions of robustness are considered: robustness by minimising the mean and variance, and robustness based on the distribution of the minimisers of the function. This information on the location of the minimisers is not a novel idea, as it had been applied as a criterion in sequential Bayesian optimisation. However, the constraint of optimality is here relaxed to define a new estimate. To evaluate this estimation, a toy model of a coastal area has been implemented. The control parameter is the bottom friction, upon which classical methods of estimation are applied in a simulation-estimation experiment. The model is then modified to include uncertainties on the boundary conditions in order to apply robust control methods. This has been published in 26

10.1.1 Inria associate team not involved in an IIL

10.1.2 Inria international partners

10.2.1 FP7 & H2020 Projects

10.2.2 Collaborations in European programs, except FP7 and H2020

• Program: C3S
• Project acronym: ERGO
• Project title: Enabling an Ensemble of Data Assimilation for the Ocean
• Duration: Février 2019 - juillet 2021
• Coordinator: Arthur Vidard
• Other partners: Cerfacs (France), Met Office (U.K.), CMRE (int, Italie)
• Abstract: The scope of this contract is to improve ocean data assimilation capabilities at ECMWF, used in both initialization of seasonal forecasts and generation of coupled Earth System reanalyses. In particular it shall focus on i) improving ensemble capabilities in NEMO and NEMOVAR and the use of their information to represent background error statistics; ii) extend NEMOVAR capabilities to allow for multiple resolution in multi-incremental 3D-Var; iii) make better use of ocean surface observations. It shall also involve performing scout experiments and providing relevant diagnostics to evaluate the benefit coming from the proposed developments.

10.2.3 Collaborations with major European organizations

• Partner: European Center for Medium Range Weather Forecast. Reading (UK)
• World leading Numerical Weather Center, that include an ocean analysis section in order to provide ocean initial condition for the coupled ocean atmosphere forecast. They play a significant role in the NEMOVAR project in which we are also partner.

• Partner: Met Office (U.K) National British Numerical Weather and Oceanographic service. Exceter (UK).
• We do have a strong collaboration with their ocean initialization team through both our NEMO, NEMO-ASSIM and NEMOVAR activities. They also are our partner in the NEMOVAR consortium.

• Partner : SAMO board

• SAMO board is in charge of the organization of the SAMO (sensitivity analysis of model outputs) conferences, every three years. It is strongly supported by the Joint Research Center of the European Commission.

  In 2019, Clémentine Prieur, which is part of this board, as also co-chair of a satellite event on the future of sensitivity analysis. A position paper 23 has been published, as a synthesis of the discussions hold in Barcelona (autumn 2019).

10.3.1 ANR

• A 4-year contract : ANR COCOA (COmprehensive Coupling approach for the Ocean and the Atmosphere). PI: E. Blayo. (Jan. 2017 - Jun. 2021). Other partners: Laboratoire des Sciences du Climat et de l'Environnement (UMR8212, Gif-sur-Yvette), Laboratoire de Météorologie Dynamique (UMR8539, Paris), Laboratoire d'Océanographie Physique et Spatiale (UMR6523, Brest), Centre National de Recherche Météorologique (UMR3589, Toulouse), Cerfacs (Toulouse). This project aims at revisiting the overall representation of air-sea interactions in coupled ocean-atmosphere models, and particularly in climate models, by coherently considering physical, mathematical, numerical and algorithmic aspects.
• A 4-year contract : ANR ADOM (Asynchronous Domain decomposition methods) https://anr.fr/Projet-ANR-18-CE46-0008
• A 5-year contract : ANR MELODY (Bridging geophysics and MachinE Learning for the modeling, simulation and reconstruction of Ocean DYnamic) https://anr.fr/Projet-ANR-19-CE46-0011
• A 5-year contract with the French Navy (SHOM) on the improvment of the CROCO ocean model http://www.croco-ocean.org.
• C. Prieur and E. Arnaud are involved as experts in project High-Tune http://www.agence-nationale-recherche.fr/Projet-ANR-16-CE01-0010 funded by ANR.

10.3.2 Inria Challenge

• Sea Uncertainty Representation and Forecast (SURF),
• Coord : Airsea (A. Vidard),
• Partenaires Inria : Ange, Cardamom, Fluminance, Lemon, Mingus, Defi
• Partenaires extérieurs: BRGM, Ifremer, SHOM

10.3.3 Other Initiatives

• A. Vidard leads a group of projects gathering multiple partners in France and UK on the topic "Variational Data Assimilation for the NEMO/OPA9 Ocean Model", see 7.1.3.
• LEFE/GMMC CASIS, Coupled Assimilation Strategies for the Initialisation of an ocean- atmospheric boundary layer System, A. Vidard en collaboration avec Mercator océan
• C. Prieur is co-advising the PhD thesis of Henri Mermoz Kouye, in the framework of the Inria-INRA collaboration.  
• C. Prieur chaired GdR MASCOT NUM 2010-2017, in which are also involved M. Nodet, E. Blayo, C. Helbert, E. Arnaud, L. Viry, S. Nanty, L. Gilquin. She is still strong involved in the group (co-chair). In particular, she will co-chair next GdR annual meeting in Aussois (May 2020, reported to April 2021). https://www.gdr-mascotnum.fr/.

11.1.1 Scientific Events: Selection

11.1.2 Journal

11.1.3 Invited Talks

• F. Lemarié: Ocean Modeling for Predictions Workshop (online workshop which took place on June 29-30) 32

11.1.4 Leadership within the Scientific Community

• L. Debreu is the chair of the CNRS-INSU research program LEFE-MANU on mathematical and numerical methods for ocean and atmosphere https://insu.cnrs.fr/fr/methodes-mathematiques-et-numeriques-manu since April 2018.
• L. Debreu is the coordinator of the national group COMODO (Numerical Models in Oceanography).
• L. Debreu is a member of the steering committee of the CROCO ocean model https://www.croco-ocean.org

11.1.5 Scientific Expertise

• F. Lemarié is a member of the CROCO (https://www.croco-ocean.org/) scientific committee in charge of the « numerical methods » topic.
• F. Lemarié is a member of the NEMO (https://www.nemo-ocean.eu/) Developers Committee as external expert.

11.1.6 Research Administration

• E. Blayo is a deputy director of the Jean Kuntzmann Lab.
• C. Prieur is a  member  of the Scientific Council   of  the Mathematical Society of France (SMF).
• C. Prieur is a member of the Research Council of UGA.
• E. Arnaud is in charge of the AMAC (Algorithmes, Modeles, Analyses, Calcul) department of the Jean Kuntzmann Lab.
• E. Arnaud : member of PhD recruitment committee CORDI-S
• E. Arnaud : in charge of ATER recruitment committee in computer science at Univ Grenoble Alpes
• E. Arnaud : in charge of the parity commission at Jean Kuntzmann Lab.

11.2.1 Teaching

• Licence (ou équivalent) : E. Blayo, Mathematical analysis, 80h, L1, University Grenoble Alpes, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques, outils pour les sciences et l'Ingenierie, 100h, L1, UGA, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques pour les sciences de l'ingénieur, 66h, L2, UGA, France
• Master (ou équivalent) : E. Blayo, Partial Differential Equations, 45h, M1, University Grenoble Alpes, France

11.2.2 Supervision

• Intern : Camille Saint Martin, Couches absorbantes parfaitement adaptées pour un modèle d’écoulement océanique non-hydrostatique compressible, M2R, applied mathematics, Univ. Montpellier, 5 months, E. Blayo.
• PhD in progress: Sophie Théry, Numerical study of coupling algorithms and boundary layer parameterizations in climate models. October 2017, E. Blayo and F. Lemarié.
• PhD in progress: Emilie Duval, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2018, L. Debreu and E. Blayo.
• PhD in progress: Victor Trappler, Parameter control in presence of uncertainties, October 2017, E. Arnaud, L. Debreu and A. Vidard.
• PhD in progress: Rishabh Batth, Asynchronousparallel in time schemes for data assimilation, December 2019, L. Debreu and A. Vidard.
• PhD in progress: Simon Clément, Numerical analysis for reconciling in space and time the air-sea exchanges and their parameterization. October 2019, E. Blayo and F. Lemarié.
• PhD in progress: Adrien Hirvoas, Development of a data assimilation method for the calibration and continuous update of wind turbines digital twins, May 2018, E. Arnaud, C. Prieur, F. Caleyron
• PhD in progress : Antoine Nasser, Volume penalization methods for the representation of flows along topography in 3D ocean models, October 2019, L. Debreu and G. Madec.
• Post Doc in progress : Anass El Aouni, Multi-resolution techniques for ocean data assimilation, October 2019, A. Vidard

11.2.3 Juries

• Arthur Vidard
  • Jury Ingénieur de recherche UGA 2020.
• E. Blayo:
  • Jul. 17, 2020: PhD thesis of Beatriz-Ixetl Garçia Gomez, University Grenoble Alpes (president)
  • Sep. 29, 2020: PhD thesis of Laura Gómez Navarro, University Grenoble Alpes (president)
  • Nov. 10, 2020: HDR thesis of Laure Raynaud, University of Toulouse (reporter)
  • Nov. 18, 2020: PhD thesis of Sibo Cheng, University Paris Saclay (reporter)

11.3.1 Internal or external Inria responsibilities

• F. Lemarié is a member of the local "comité des emplois scientifiques" (CES) (since Sept 2019)
• F. Lemarié is the local scientific correspondent for national calls for projects (since July 2020)
• E.Kazantsev is a member of the Local Commission for Permanent Formation of Inria Grenoble - Rhône-Alpes.

11.3.2 Articles and contents

• E. Blayo, L. Debreu et C. Kazantsev, 2020 : Les modèles de climat. Maths Express : les maths, oui ça sert !, juin 2020. Publication du Comité International des Jeux Mathématiques.
• Blayo E. et C. Kazantsev, 2020 : Le projet de la Grange des Maths. La Gazette des Mathématiciens, 166, 65-71, octobre 2020.

11.3.3 Communication to the press

• C. Prieur was placed on a list of experts who could answer questions on various aspects of the news related to the ongoing Covid-19 epidemic by the CNRS press office. This list is made available to journalists in order to direct them to the appropriate interlocutors according to the angle of their questions.

11.3.4 Creation of media or tools for science outreach

• E. Arnaud, in charge of the pedagogic platform math@uga : implementation of a collaborative moodle platform http://math.u-ga.fr to share pedagogical resources within teachers and towards students.
• C.Kazantsev participated in the edition of the Teachers notebooks which explain and advise how to use the "La Grange Suitcases" (sets of mathematical games, problems and animations) destined for primary and secondary schools teachers as well as for the general public.
• C.Kazantsev participated in the creation of mathematical activities that can be autonomously used by schoolchildren of primary and secondary schools and by the general public.

11.3.5 Education

• Ch. Kazantsev and E. Blayo are strongly involved in the creation and dissemination of pedagogic suitcases with mathematical activities designed for primary and secondary schools used by 10,000 – 12,000 pupils in 2018-2019. This is done in collaboration with the Rectorat de Grenoble. This action received the prize Jacqueline Ferrand 2020 from the French Mathematical Society for educational innovation.
• C. Kazantsev is a member of an IREM group for creation of scientific activities for professional development of secondary schools teachers.
• C. Kazantsev is a member of an International Inter-IREM commission, which work on the multi-languages problem for children in the mathematical learning. Three meetings take place in Paris during the year, the first was on September 28.
• E. Arnaud has given a Seminar and training day, "(se) tromper avec les chiffres", formation esprit critique, with La maison pour la sciences
• E. Arnaud, C. Kazantzev have visited the Varces prison in france of an action of the "La grange des maths" to show the interest of mathematics to young prisonners.

11.3.6 Interventions

• E. Blayo gave several outreach talks, in particular for middle school and high school students, and for more general audiences.
• Ch. Kazantsev and E. Blayo are strongly involved in the creation of "La Grange des maths", a science popularization center that will be located in Varces (south of Grenoble), which will offer a huge variety of mathematical hands-on exhibits. See http://www.la-grange-des-maths.fr/

International journals

• 1 articleZinebZ. Abidi, KhalidK. Minaoui, AnassA. El Aouni, AyoubA. Tamim and HichamH. Laanaya. An Efficient Detection of Moroccan Coastal Upwelling Based on Fusion of Chlorophyll-a and Sea Surface Temperature Images With a New Validation IndexIEEE Geoscience and Remote Sensing LettersJune 2020, 1-5
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• 2 article MaríaM. Belén Heredia, ClémentineC. Prieur and NicolasN. Eckert. Nonparametric estimation of aggregated Sobol' indices: application to a depth averaged snow avalanche model International Journal of Reliability, Quality and Safety Engineering January 2020
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• 3 articleKarineK. Bertin, NicolasN. Klutchnikoff, JoséJ. León and ClémentineC. Prieur. Adaptive density estimation on bounded domains under mixing conditionsElectronic journal of statistics1412020, 2198-2237
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• 4 articleMatthieuM. Brachet and Jean-PaulJ.-P. Chehab. Fast and Stable Schemes for Phase Fields ModelsComputers and Mathematics with Applications806September 2020, 1683-1713
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• 5 article MatthieuM. Brachet and Jean-PierreJ.-P. Croisille. Spherical Shallow Water Waves Waves Simulation by a Cubed Sphere Finite Difference Solver Quaterly Journal of the Royal Meteorological Society November 2020
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• 6 article ThéoT. Brivoal, GuillaumeG. Samson, HervéH. Giordani, RomainR. Bourdallé-Badie, FlorianF. Lemarié and GurvanG. Madec. Impact of the current feedback on kinetic energy over the North-East Atlantic from a coupled ocean/atmospheric boundary layer model Ocean Science Discussions August 2020
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• 7 articleVincentV. Chabot, MaëlleM. Nodet and ArthurA. Vidard. Multiscale Representation of Observation Error Statistics in Data AssimilationSensors205March 2020, 1-20
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• 8 articleXavierX. Couvelard, FlorianF. Lemarié, GuillaumeG. Samson, Jean-LucJ.-L. Redelsperger, FabriceF. Ardhuin, RachidR. Benshila and GurvanG. Madec. Development of a 2-way coupled ocean-wave model: assessment on a global NEMO(v3.6)-WW3(v6.02) coupled configurationGeoscientific Model Development13July 2020, 3067–3090
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• 9 articleLaurentL. Debreu, Nicholas K.-R.N.-R. Kevlahan and PatrickP. Marchesiello. Brinkman volume penalization for bathymetry in three-dimensional ocean modelsOcean Modelling145January 2020, 1-13
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• 10 articleMohamed RedaM. El Amri, CelineC. Helbert, OlivierO. Lepreux, Miguel MunozM. Zuniga, ClémentineC. Prieur and DelphineD. Sinoquet. Data-driven stochastic inversion via functional quantizationStatistics and Computing303May 2020, 525-541
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• 11 articleAnassA. El Aouni. A hybrid identification and tracking of Lagrangian mesoscale eddiesPhysics of Fluids333March 2021, 036604
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• 12 articlePierreP. Etoré, ClémentineC. Prieur, Dang KhoiD. Pham and LongL. Li. Global sensitivity analysis for models described by stochastic differential equationsMethodology and Computing in Applied Probability22June 2020, 803-831
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• 13 articleGilesG. Fearon, StevenS. Herbette, JenniferJ. Veitch, GildasG. Cambon, Andrew JA. Lucas, FlorianF. Lemarié and MarcelloM. Vichi. Enhanced vertical mixing in coastal upwelling systems driven by diurnal-inertial resonance: numerical experimentsJournal of Geophysical Research. Oceans1259September 2020, e2020JC016208
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• 14 article LaurentL. Gilquin, ClémentineC. Prieur, EliseE. Arnaud and HerveH. Monod. Iterative estimation of Sobol’ indices based on replicated designs Computational and Applied Mathematics 40 18 January 2021
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• 15 articleLinaL. Guan, ChristopheC. Prieur, LiguoL. Zhang, ClémentineC. Prieur, DidierD. Georges and PascalP. Bellemain. Transport effect of COVID-19 pandemic in FranceAnnual Reviews in Control502020, 394-408
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• 16 articleUteU. Hausmann, Jean-BaptisteJ.-B. Sallée, NicolasN. Jourdain, PierreP. Mathiot, ClémentC. Rousset, GurvanG. Madec, JulieJ. Deshayes and ToreT. Hattermann. The Role of Tides in Ocean‐Ice Shelf Interactions in the Southwestern Weddell SeaJournal of Geophysical Research. Oceans1256June 2020, e2019JC015847
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• 17 articleMargauxM. Hilt, LaurentL. Roblou, CyrilC. Nguyen, PatrickP. Marchesiello, FlorianF. Lemarié, SwenS. Jullien, FranckF. Dumas, LaurentL. Debreu, XavierX. Capet, LucieL. Bordois, RachidR. Benshila and FrancisF. Auclair. Numerical modeling of hydraulic control, solitary waves and primary instabilities in the Strait of GibraltarOcean Modelling155July 2020, 101642
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• 18 articleRémiR. Lam, OlivierO. Zahm, YoussefY. Marzouk and KarenK. Willcox. Multifidelity Dimension Reduction via Active SubspacesSIAM Journal on Scientific Computing422April 2020, A929-A956
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• 19 articleFlorianF. Lemarié, GuillaumeG. Samson, Jean-LucJ.-L. Redelsperger, HervéH. Giordani, ThéoT. Brivoal and GurvanG. Madec. A simplified atmospheric boundary layer model for an improved representation of air-sea interactions in eddying oceanic models: implementation and first evaluation in NEMO (4.0)Geoscientific Model Development14December 2020, 543 - 572
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• 20 article OlivierO. Marti, SébastienS. Nguyen, PascaleP. Braconnot, SophieS. Valcke, FlorianF. Lemarié and EricE. Blayo. A Schwarz iterative method to evaluate ocean- atmosphere coupling schemes. Implementation and diagnostics in IPSL-CM6-SW-VLR Geoscientific Model Development Discussions December 2020
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• 21 articleEtienneE. Pauthenet, FabienF. Roquet, GurvanG. Madec, Jean-BaptisteJ.-B. Sallée and DavidD. Nerini. The Thermohaline Modes of the Global OceanJournal of Physical Oceanography49November 2020, 2535 - 2552
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• 22 article CharlesC. Pelletier, FlorianF. Lemarié, EricE. Blayo, Marie-NoëlleM.-N. Bouin and Jean-LucJ.-L. Redelsperger. Two-sided turbulent surface layer parameterizations for computing air-sea fluxes Quarterly Journal of the Royal Meteorological Society February 2021
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• 23 articleSamanS. Razavi, Anthony J.A. Jakeman, AndreaA. Saltelli, ClémentineC. Prieur, BertrandB. Iooss, EmanueleE. Borgonovo, ElmarE. Plischke, SamueleS. Lo Piano, TakuyaT. Iwanaga, WilliamW. Becker, StefanoS. Tarantola, Joseph H.A.J. Guillaume, JohnJ. Jakeman, HoshinH. Gupta, NicolaN. Melillo, GiovanniG. Rabitti, VincentV. Chabridon, QingyunQ. Duan, XifuX. Sun, StefanS. Smith, RaziR. Sheikholeslami, NasimN. Hosseini, MasoudM. Asadzadeh, ArnaldA. Puy, SergeiS. Kucherenko and Holger R.H. Maier. Position Paper: The Future of Sensitivity Analysis: An Essential Discipline for Systems Modelling and Policy MakingEnvironmental Modelling and Software137March 2021, 104954
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• 24 articleVictorV. Shutyaev, François-XavierF.-X. Le Dimet and EugeneE. Parmuzin. Sensitivity of response functions in variational data assimilation for joint parameter and initial state estimationJournal of Computational and Applied Mathematics373August 2020, 112368:1-14
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• 25 article KathrinK. Smetana and OlivierO. Zahm. Randomized residual-based error estimators for the Proper Generalized Decomposition approximation of parametrized problems International Journal for Numerical Methods in Engineering 2020
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• 26 articleVictorV. Trappler, EliseE. Arnaud, ArthurA. Vidard and LaurentL. Debreu. Robust calibration of numerical models based on relative regretJournal of Computational PhysicsNovember 2020, 109952
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• 27 article AchimA. Wirth and FlorianF. Lemarié. Jarzynski equality and Crooks relation for local models of air-sea interaction Earth System Dynamics Discussions December 2020
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• 28 articleOlivierO. Zahm, PaulP. Constantine, ClementineC. Prieur and YoussefY. Marzouk. Gradient-based dimension reduction of multivariate vector-valued functionsSIAM Journal on Scientific Computing421February 2020, A929-A956
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International peer-reviewed conferences

• 29 inproceedings MichaelM. Brennan, DanieleD. Bigoni, OlivierO. Zahm, AlessioA. Spantini and YoussefY. Marzouk. Greedy inference with structure-exploiting lazy maps NeurIPS Virtual, Canada December 2020
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Conferences without proceedings

• 30 inproceedings FlorianF. Lemarié, JérémieJ. Demange, LaurentL. Debreu, NicolasN. Ducousso and PatrickP. Marchesiello. Numerical representation of internal gravity waves propagation 2nd COMMODORE Workshop Hamburg, Germany January 2020
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• 31 inproceedings FlorianF. Lemarié. On the spatial and temporal discretization of vertical diffusion in the turbulent planetary boundary layer AGU Ocean Sciences Meeting San Diego, United States February 2020
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• 32 inproceedings FlorianF. Lemarié. Recent evolution and challenges for oceanic dynamical cores across all scales Ocean Modeling for Predictions Workshop Toulouse, France June 2020
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• 33 inproceedings EmilieE. Rouzies, ClaireC. Lauvernet, BrunoB. Sudret, ClémentineC. Prieur, RobertR. Faivre and ArthurA. Vidard. Sensitivity analysis to evaluate a new spatialized process-oriented model of water and pesticide transfers at the catchment scale 10th iEMSs Conference 2020 International Environmental Modelling and Software Society Brussels, Belgium September 2020
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Reports & preprints

• 34 misc Reda ElR. Amri, CélineC. Helbert, MiguelM. Munoz Zuniga, ClémentineC. Prieur and DelphineD. Sinoquet. Set inversion under functional uncertainties with joint meta-models 2020
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• 35 misc FrancisF. Auclair, LaurentL. Debreu, EmilieE. Duval, PatrickP. Marchesiello, EricE. Blayo and MargotM. Hilt. Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean October 2020
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• 36 misc RicardoR. Baptista, OlivierO. Zahm and YoussefY. Marzouk. An adaptive transport framework for joint and conditional density estimation December 2020
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• 37 misc MaríaM. Belén Heredia, ClémentineC. Prieur and NicolasN. Eckert. Aggregated Shapley effects: nearest-neighbor estimation procedure and confidence intervals. Application to snow avalanche modeling July 2020
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• 38 misc DanieleD. Bigoni, YoussefY. Marzouk, ClémentineC. Prieur and OlivierO. Zahm. Nonlinear dimension reduction for surrogate modeling using gradient information February 2021
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• 39 misc MarieM. Billaud-Friess, ArthurA. Macherey, AnthonyA. Nouy and ClémentineC. Prieur. A PAC algorithm in relative precision for bandit problem with costly sampling February 2021
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• 40 misc MatthieuM. Brachet, LaurentL. Debreu and ChristopherC. Eldred. Comparaison of Exponential integrators and traditional time integration schemes for the Shallow Water equations April 2020
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• 41 misc TiangangT. Cui and OlivierO. Zahm. Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems March 2021
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• 42 misc AdrienA. Hirvoas, ClémentineC. Prieur, EliseE. Arnaud, FabienF. Caleyron and Miguel MunozM. Zuniga. Quantification and reduction of uncertainties in a wind turbine numerical model based on global sensitivity analysis and recursive Bayesian inference approach June 2020
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• 43 misc Jean BernardJ. Lasserre, VictorV. Magron, SwannS. Marx and OlivierO. Zahm. Minimizing rational functions: a hierarchy of approximations via pushforward measures December 2020
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• 44 misc PatrickP. Marchesiello, FrancisF. Auclair, LaurentL. Debreu, James C.J. Mcwilliams, RafaelR. Almar, RachidR. Benshila and FranckF. Dumas. Tridimensional nonhydrostatic transient rip currents in a wave-resolving model October 2020
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• 45 misc SophieS. Thery, CharlesC. Pelletier, FlorianF. Lemarié and EricE. Blayo. Analysis of Schwarz Waveform Relaxation for the Coupled Ekman Boundary Layer Problem with Continuously Variable Coefficients April 2020
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• 46 misc OlivierO. Zahm, TiangangT. Cui, KodyK. Law, AlessioA. Spantini and YoussefY. Marzouk. Certified dimension reduction in nonlinear Bayesian inverse problems March 2021
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Other scientific publications

• 47 misc MargauxM. Hilt, LaurentL. Roblou, CyrilC. Nguyen, PatrickP. Marchesiello, FlorianF. Lemarié, SwenS. Jullien, FranckF. Dumas, LaurentL. Debreu, XavierX. Capet, LucieL. Bordois, RachidR. Benshila and FrancisF. Auclair. LES Modelling of the Impact of the Topography on Large-scale Exchange Flow in the Strait of Gibraltar San Diego, United States 2020
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• 48 misc EmilieE. Rouzies, ClaireC. Lauvernet and ArthurA. Vidard. How can we quantify and reduce the uncertainty of a watershed-scale pesticide transfer model? A comparison of several approaches. Online, United States December 2020
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