Research themes
The SURF project federates the research activities carried out at Inria on the modelling of coastal and littoral ocean flows. It focuses on 3 research areas
Model coupling
A simple way to combine different models is a pure statistical combination of (part of) their results. The difficulty here lies in the fact that the different models, even if they are linked by mathematical properties, may not all represent the same part of reality. This can be very useful to better understand the relative merits of the models considered and the associated uncertainties. The other possibility is to couple mathematically the systems of equations on the respective domains of validity, but going beyond the domain decomposition, with possibly moving boundaries and ensuring conservation properties wherever possible. An alternative (but not exclusive) approach is to couple the models at the data assimilation level. Indeed, the recent development of very high resolution observation leads to a loss of information compared to coarser models. It would clearly be advantageous to use simpler but higher resolution models to represent the evolution of observed quantities. For example, gravity-based models could potentially better represent the altimeter data at a much lower computational cost. Such an approach requires careful preliminary theoretical study as it may lead to convergence and stability problems.
Quantification, reduction and propagation of uncertainties
As numerical flow models covering the entire hydrodynamic scale – ranging from the forcing scale (∼ 1000 km) to the dissipation scale (∼1 mm) – are largely beyond the reach of computers, only large-scale modelling can be addressed. In general, these unresolved processes are simulated by ad-hoc parameterisation, or more recently by stochastic modelling. However, it should be possible to design multi-layered models, or hierarchies of models that incrementally mimic the loss of resolution, accuracy and order of numerical schemes and physical truncations through randomisation.
For their action to be relevant, these parameterisations must be finely tuned and evaluated. Over the last decade, the availability of new observation networks (new generation satellites and radars, coastal video, …) with a much higher resolution has provided a large amount of information on small ocean scales and their effect on larger scales. The optimal way to use this data remains an open question, the current solution being to degrade the information to make it manageable, losing in the process the small-scale information that really interests us.
Numerical methods
Another way to reduce uncertainty is to include more physical terms in the equations of numerical models. This also involves working on improving the numerical schemes.
In this respect, we have identified three crucial points for the improvement of ocean models:
1- Vertical discretization of the fluid mechanics equations: there are several systems for representing the vertical velocity distribution in the Navier-Stokes system, namely the isopycnal coordinates (rho), the terrain coordinates (sigma) and the geopotential coordinates (z). While the rho description suffers from physical limitations and the transformation of the sigma coordinates leads to numerical difficulties, we propose to improve the z-coordinate system or the associated descriptions, e.g. the tilde formalism, by a cross-comparison with the multilayer approach
2- For hyperbolic systems, the stability of the spatial discretization often leads to an upwinding leading to a numerical dissipation of the scheme. While upwinding ensures stability, it also has a negative impact on accuracy. As simulations in ocean modelling cover large spatial and temporal domains, minimal numerical dissipation is required in order to use coarse meshes. The trade-off between stability and accuracy involves analysing both spatial and temporal patterns since centred patterns can be effective when coupled with dissipative temporal patterns.
3- When non-hydrostatic (dispersive) effects are taken into account in the models, numerical analysis becomes an acute problem and the models exhibit various instabilities not present in hydrostatic and quasi-hydrostatic systems. In addition, the computational costs due to the non-local elliptic operator to be inverted become prohibitive. Again, the strategy is to optimise the coupling between the hyperbolic and dispersive parts of the numerical scheme. This is important for our targeted applications, because for wave propagation and coastal impact, several aspects need to be paid special attention. The most important ones are the ability to take into account dispersive effects, active at depth-dependent wavelengths/frequencies, the ability to correctly model the formation of the large-scale circulation and the propagation of vorticity, as well as the possibility to integrate wave breaking effects.
Software developments
In particular, research and development are centred around the numerical models developed or co-developed by the DEFI teams
Croco [Link]
CROCO is an oceanic modeling system resolving very fine scales (especially in the coastal area), and their interactions with larger scales.
Uhaina [Link]
UHAINA is a phase-resolving free surface wave model for coastal engineering problems.
Freshkiss3d [Link]
Freshkiss3D is a software solving the 3D hydrostatic and incompressible Navier-Stokes equations with free surface and variable density.
SW2D [Link]
SW2D (Shallow Water 2D) is a C++ package dedicated to shallow water modeling with additional features such as porosity modeling (upscaling), passive transport, multi-layer models.
