by Arthur Vidard (Inria)
Ocean model developers from Inria teams, together with external partners from Shom, Brgm and Ifremer, are coming together to develop and improve ocean modelling capabilities from regional to nearshore.
The ocean plays a major role in global climate change; first, by acting as a moderator by absorbing around 30% of the excess anthropogenic carbon dioxide and more than 90% of the resulting additional energy. Second, this in turn dramatically affects ecosystems (through effects such as ocean acidification and temperature rises) and can create or aggravate severe weather conditions (e.g., hurricanes and coastal floods). This is particularly true for coastal areas directly threatened by such events and by sea level rises, and where about 60% of the world’s population lives.
Many human activities and associated problems, such as food production, trade, public safety and pollution, are directly linked to the ocean. Understanding and predicting complex phenomena at various scales (regional, coastal, littoral) is therefore of utmost importance. For models of these phenomena to function as analysis tools for policy makers, they also need to provide a measure of their associated uncertainties.
In this context, the SURF project [L1] aims to develop several solutions for ocean coastal modelling with significantly different approaches, both in terms of system of equations and discretization schemes. Purely from a modelling point of view there exist three main approaches: a fully depth-averaged PDE stand point in which all small scale effects are modelled; multi-layer approximations also based on some form of averaging/projection; full/direct discretization of primitive PDEs (full non-linear potential, Euler, or RANS) with another method.
Inria teams are contributing to a variety of such models. In particular, members of SURF are involved in: Croco, a community primitive equation model on structured grid; Uhaina, a Green-Naghdi-based unstructured near-shore wave model; Freshkiss3d, a finite volume code for the simulation of the 3D hydrostatic and incompressible Navier-Stokes equations; and SW2D, a finite volume, unstructured mesh shallow water. Different models work better in particular situations, depending on the geographic location and physical regime, and models need to be chosen accordingly.
By definition, models only partially represent reality and there are many sources of uncertainty. The common thread of SURF is the estimation, propagation, reduction and representation of uncertainties in coastal ocean modelling. It is possible to artificially distinguish two types uncertainties: epistemic uncertainties that are coming from approximations, unknown parameters or lack of physical knowledge, and random uncertainties coming from inherent variability of the system or external sources of uncertainties. Typically, the latter can be unresolved physical processes due to discretization (sub-grid scale processes) or uncertainties about external forcing, for instance. The former category can be related to crucial poorly known numerical or physical parameters of the model. We are addressing both types of uncertainty, either by estimating or reducing them. Additionally, satellite measurements are reaching a spatial resolution that is potentially finer than those of the current oceanic computational simulation capabilities. Even though they only measure part of the system (one quantity, at the surface only), this is a great opportunity to qualify our coupling of models and quantify and reduce uncertainties.
Within this framework, three research axes are being developed:
A simple way to combine different models is a pure statistical combination of part of their output. The difficulty here lies in the fact that the different model, despite being linked through mathematical properties, may not represent the same part of the reality. The other possibility is to mathematically couple the equation systems on respective areas of validity (different boxes in figure 1, ), but going beyond domain decomposition, with possibly moving boundaries and ensuring conservative properties wherever it proves feasible. The main outcome is to devise an optimal strategy for further developments for coastal ocean modelling at Inria, from regional to nearshore.
Figure 1: Target application: multiscale simulation around Gâvres Presque-isle. Different models will be valid on these different domains (courtesy BRGM).
Uncertainty reduction and numerical schemes
Ocean models are built on a combination of numerical schemes and choices of physical terms. The variety of available models in SURF makes it possible to understand the relative strengths and weaknesses of these combinations, and this could enable more appropriate choices to be designed. Moreover, some specific issues like how to best discretize vertically or how to properly deal with moving boundaries are still open questions .
A numerical forecast is most useful if associated to a measure of its uncertainties. This is commonly achieved using an ensemble of forecasts representing the range of possible future states. The key is to well represent this range. Inria recently developed a way to represent uncertainties associated to unresolved processes (processes that live at smaller scales than the discretization grid) through stochastic modelling. It is more consistent with the approximation actually made but requires the stochastic process at an early stage of the equations’ derivation . Within SURF, we first develop and validate this approach for our hierarchy of models and second use the same approach to describe the uncertainties associated to ocean atmosphere coupling processes.
With the multitude of scientific questions it raises, SURF is an ambitious research project that requires the mobilisation of varied skills and thus involves complementary Inria teams. Airsea (in Grenoble) will contribute its expertise on oceanic modelling and the coupling of models at very different spatial and temporal scales. Cardamom (in Bordeaux) will complete the numerical methods and the associated uncertainties for the models. Ange in Paris and Lemon in Sophia will be asked to model coastal flows in shallow waters, or on the coupling between ocean and river models. Fluminance (in Rennes) will develop statistical image processing techniques to supply the sub-mesh models. Finally, Defi in Saclay and Mingus in Rennes will contribute theoretical skills on the quantification of uncertainties and partial differential equations, respectively.
During the four years of the project, the Inria teams will also collaborate with experts from the Bureau of Geological and Mining Research (BRGM), the Hydrographic Service of the Navy (SHOM) and IFREMER on both coastal security issues and the development and validation of the models.
 M. Tayachi, et al.: “Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem”, Int. Journal for Numerical Methods in Fluids, Wiley, 2014, 75 (6).
 T. Song, et al.: “The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows”, Journal of Computational Physics, 369, 2018
 V. Resseguier, E. Mémin, B. Chapron: “Geophysical flows under location uncertainty”, Part I, II & III, Geophysical and Astrophysical Fluid Dynamics, 111 (3), pp.149-176, 2017.
Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, France