Section: New Results
Modeling for Oceanic and Atmospheric flows
Numerical Schemes for Ocean Modelling
Participants : Eric Blayo, Laurent Debreu, Florian Lemarié, Christopher Eldred, Farshid Nazari.
The increase of model resolution naturally leads to the representation of a wider energy spectrum. As a result, in recent years, the understanding of oceanic submesoscale dynamics has significantly improved. However, dissipation in submesoscale models remains dominated by numerical constraints rather than physical ones. Effective resolution is limited by the numerical dissipation range, which is a function of the model numerical filters (assuming that dispersive numerical modes are efficiently removed). A review paper on coastal ocean models has been written with German colleagues and will be published in Ocean Modelling early 2018 ().
Ocean models usually rely on a mode splitting procedure which separates the fast external gravity waves with the slower internal waves. A paper on the stability of the mode splitting has been submitted to Journal of Computational Physics ()
The team is involved in the HEAT (Highly Efficient ATmospheric Modelling) ANR project. This project aims at developing a new atmospheric dynamical core (DYNAMICO) discretized on an icosahedral grid. This project is in collaboration with Ecole Polytechnique, Meteo-France, LMD, LSCE and CERFACS. This year we worked on dispersion analysis of compatible Galerkin schemes for a 1D shallow water model ().
Coupling Methods for Oceanic and Atmospheric Models
Participants : Eric Blayo, Laurent Debreu, Florian Lemarié, Charles Pelletier, Antoine Rousseau, Sophie Thery.
Coupling methods routinely used in regional and global climate models do not provide the exact solution to the ocean-atmosphere problem, but an approximation of one . For the last few years we have been actively working on the analysis of ocean-atmosphere coupling both in terms of its continuous and numerical formulation.Our activities over the last few years can be divided into four general topics
Stability and consistency analysis of existing coupling methods: in  we showed that the usual methods used in the context of ocean-atmosphere coupling are prone to splitting errors because they correspond to only one iteration of an iterative process without reaching convergence. Moreover, those methods have an additional condition for the coupling to be stable even if unconditionally stable time stepping algorithms are used. This last remark was further studied recently in  and it turned out to be a major source of instability in atmosphere-snow coupling.
Study of physics-dynamics coupling: during the PhD-thesis of Charles Pelletier (funded by Inria) the scope is on including the formulation of physical parameterizations in the theoretical analysis of the coupling, in particular the parameterization schemes to compute air-sea fluxes . To do so, a metamodel representative of the behavior of the full parameterization but with a continuous form easier to manipulate has been derived thanks to a sensitivity analysis based on Sobol' indexes. This metamodel has the advantage to be more adequate to conduct the mathematical analysis of the coupling while being physically satisfactory. This work is in revision for publication in Quarterly Journal of the Royal Meteorological Society and has been presented in various conferences , , , . In parallel we have contributed to a general review gathering the main international specialists on the topic .
Design of a coupled single column model: in order to focus on specific problems of ocean-atmosphere coupling, a work on simplified equation sets has been started. The aim is to implement a one-dimensional (in the vertical direction) coupled model with physical parameterizations representative of those used in realistic models. Thanks to this simplified coupled model the objective is to develop a benchmark suite for coupled models evaluation. Last year the single column oceanic and atmospheric components have been developed and coupled during the PhD-thesis of Rémi Pellerej and in the framework of the SIMBAD project. A publication describing this model and its interfacing with the OOPS software to allow the implementation of various data assimilation techniques is currently in preparation for the Geoscientific Model Development journal.
Analysis of air-sea interactions in realistic high-resolution realistic simulations: part of our activity has been in collaboration with atmosphericists and physical oceanographers to study the impact on some modeling assumptions (e.g. ) in large-scale realistic ocean-atmosphere coupled simulations , , .
These four topics are addressed through strong collaborations between the applied mathematicians and the climate community.
Moreover a PPR (Projet à partenariat renforcé) called SIMBAD (SIMplified Boundary Atmospheric layer moDel for ocean modeling purposes) is funded by Mercator-Ocean for the next three years (from march 2015 to march 2018). The aim of this project in collaboration with Meteo-France, Ifremer, LMD, and LOCEAN is to derive a metamodel to force high-resolution oceanic operational models for which the use of a full atmospheric model is not possible due to a prohibitive computational cost. First results have been presented during international conferences ,  and a publication is currently in preparation. Another industrial contract named ALBATROS is also funded by (from June 2016 to June 2019) to couple SIMBAD with the NEMO global ocean model and a wave model called WW3.
An ANR project COCOA (COmprehensive Coupling approach for the Ocean and the Atmosphere, P.I.: E. Blayo) has been funded in 2016 and has officially start in January 2017.
Data assimilation for coupled models
In the context of operational meteorology and oceanography, forecast skills heavily rely on proper combination of model prediction and available observations via data assimilation techniques. Historically, numerical weather prediction is made separately for the ocean and the atmosphere in an uncoupled way. However, in recent years, fully coupled ocean-atmosphere models are increasingly used in operational centers to improve the reliability of seasonal forecasts and tropical cyclones predictions. For coupled problems, the use of separated data assimilation schemes in each medium is not satisfactory since the result of such assimilation process is generally inconsistent across the interface, thus leading to unacceptable artefacts. Hence, there is a strong need for adapting existing data assimilation techniques to the coupled framework. As part of our ERACLIM2 contribution, R. Pellerej started a PhD on that topic late 2014 and will defend it early 2018. So far, three general data assimilation algorithms, based on variational data assimilation techniques, have been developed and applied to a single column coupled model. The dynamical equations of the considered problem are coupled using an iterative Schwarz domain decomposition method. The aim is to properly take into account the coupling in the assimilation process in order to obtain a coupled solution close to the observations while satisfying the physical conditions across the air-sea interface. Preliminary results shows significant improvement compared to the usual approach on this simple system , . The aforementioned system has been coded within the OOPS framework (Object Oriented Prediction System) in order to ease the transfer to more complex/realistic models.
The second contribution to ERACLIM2 was to investigate the importance of the quality of the data assimilation scheme in the ocean in the coupled system. It led to the proposition of cost effective approximations either in term of resolution reduction or equation simplifications, along with a metric to asses the quality of said approximations 
Finally, CASIS, a new collaborative project with Mercator Océan has started late 2017 in order to extend developments to iterative Kalman smoother data assimilation scheme, in the framework of a coupled ocean-atmospheric boundary layer context.
Parameterizing subgrid scale eddy effects
Participant : Eugene Kazantsev.
Basing on the maximum entropy production principle, the influence of subgrid scales on the flow is presented as the harmonic dissipation accompanied by the backscattering of the dissipated energy. This parametrization is tested on the shallow water model in a square box. Two possible solutions of the closure problem are compared basing on the analysis of the energy dissipation-backscattering balance. Results of this model on the coarse resolution grid are compared with the reference simulation at four times higher resolution. It is shown that the mean flow is correctly recovered, as well as variability properties, such as eddy kinetic energy fields and its spectrum .