Analysis of ocean-atmosphere coupling algorithms : consistency and stability

International audienceThis paper is focused on the numerical and computational issues associated to ocean-atmosphere coupling. It is shown that usual coupling methods do not provide the solution to the correct problem, but to an approaching one since they are equivalent to performing one single iteration of an iterative coupling method. The stability analysis of these ad-hoc methods is presented, and we motivate and propose the adaptation of a Schwarz domain decomposition method to ocean-atmosphere coupling to obtain a stable and consistent coupling method

Robust calibration of numerical models based on relative regret

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 random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced. In this paper, we are going to present how to take into account those uncertainties by defining a family of calibration objectives based on the notion of relative-regret with respect to the best attainable performance given the uncertainties and compare it with the minimum in the mean sense, and the minimum of variance

AGRIF: Adaptive Grid Refinement In Fortran

This report presents AGRIF a Fortran90 package for the integration of adaptive mesh refinement (AMR) features within a finite difference numerical model. The package mainly consists in two parts. It first provides model-indep- endent Fortran90 procedures containing the different parts of an AMR process: time integration algorithm of the grid hierarchy, clustering algorithm, refinement algorithm, interpolation procedures... In a second part, a Fortran90 model-dependent code is created via the analysis of an entry file written by the user. Both model-dependent and model-independent parts are then linked into a library. Since the work of Berger and Oliger , adaptive mesh refinement (AMR) for structured grids has become very popular. Its domains of application are numerous and its efficiency has been clearly demonstrated. However dealing with AMR is a difficult task, which often keeps people from investigating the power of the method. As a matter of fact, AMR is intrinsically a dynamic method which requires dynamic memory management and structured types.AMRCLAW is a Fortran77 AMR package for conservation laws that was developed upon the Berger's AMR algorithms and the CLAWPACK package of R. LeVeque, and which incorporates all the primary features of the method proposed by Berger. However, with the quite recent apparition of object oriented languages, programming AMR methods has become simpler, and several AMR packages have then been developped. Most of them are implemented in C++, which appeared before Fortran 90. We can cite for instance Overture a C++ package subtitled Object-Oriented Tools for Solving CFD and Combustion Problems in Complex Moving Geometry, and DAGH (Distributed Adaptive Grid Hierarchy ).Concerning similar tools in Fortran90, we can cite PARAMESH , a package actually doing cells refinement, and which differs quite a lot from the original idea of Berger. There exist also AMR packages which actually try to implement C++ features in Fortran 90.In this paper, we present a new idea for implementing AMR features in an existing numerical model written in Fortran (77 or 90). This package uses the full compatibility between Fortran77 and Fortran90, and thus eliminates all kind of interfaces.The paper is organized as follows. The main operations involved in an AMR process are briefly reminded in section 2. Then the basic ideas of the package are presented in section 3, and section 4 explains how to use the program which produces the model-dependent Fortran code. Finally, an example is treated in section 5

Introducing time parallelisation within data assimilation using parareal method

Forecasts made by 4-D Var involves forward integration of model before proceeding for the minimisation process. While one reaches saturation in space parallelisation we try to obtain some speedup by integrating our model using the Parareal method. Our setting ensures that the minimum is obtained by solving a linear symmetric system. We use a modified version of the inexact conjugate gradient method where the matrix-vector multiplication is supplied by the parareal. This helps us to determine a specific stopping criterion for the parareal. The results are demonstrated by considering a 1-D linear shallow water model. Our method produces a speedup factor of 3 using fewer parareal iterations as compared to the same results obtained by the exact conjugate gradient method

Stability and accuracy of Runge-Kutta based split-explicit time-stepping algorithms for free-surface ocean models

International audienceBecause of the Boussinesq assumption employed in the vast majority of oceanic models, the acoustic waves are filtered and the fast dynamics corresponds to the external gravity-wave propagation which is much faster than other (internal) processes. The fast and slow dynamics are traditionally split into separate subproblems where the fast motions are nearly independent of depth. It is thus natural to model these motions with a two-dimensional (barotropic) system of equations while the slow processes are modeled with a three-dimensional (baroclinic) system. However such splitting is inexact, the barotropic mode is not strictly depth-independent meaning that the separation of slow and fast modes is non-orthogonal, even in the linear case. A consequence is that there are some fast components contained in the slow motions which induce instabilities controlled by time filtering of the fast mode. In this talk we present an analysis of the stability and accuracy of the barotropic–baroclinic mode splitting in the case where the baroclinic mode is integrated using a Runge-Kutta scheme and the barotropic mode is integrated explicitly (i.e. the so-called split-explicit approach). By referring to the theoretical framework developed by Demange et al. (2019), the analysis is based on an eigenvector decomposition using the true (depth-dependent) barotropic mode. We investigate several strategies to achieve stable integrations whose performance is assessed first on a theoretical ground and then by idealized linear and nonlinear numerical experiments

Challenges and prospects for dynamical cores of oceanic models across all scales

International audienceThis poster outlines an initiative to bring together the world-wide leading researchers actively contributing to the development of oceanic model dynamical cores irrespective of target applications (regional, coastal, or global). The first community for the numerical modeling ofthe global, regional and coastal ocean (COMMODORE) workshop (https://commodore2018.sciencesconf.org/) has been organized in Paris in September 2018 [1]. In total, the participants represented 15 oceanic dynamical cores among the most widely used by the research and operational community. The present poster summarizes the challenges and prospects for oceanic numerical cores across all scales discussed during the workshop. In particular, identified challenges to be addressed include strategies for multi-resolution, energy consistency and resolved/unresolved scales coupling, the design of vertical coordinates and their link with spurious numerical mixing, the inclusion of non-hydrostatic pressure contribution within existing primitive equations models, and the proper treatment of wetting and drying

Sliding or stumbling on the staircase: numerics of ocean circulation along piecewise-constant coastlines

Coastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase-like coastlines is a long-standing issue in ocean modelling. Pioneering work by Adcroft and Marshall (1998) revealed that artificial indentation of model coastlines, obtained by rotating the numerical mesh within an idealized square basin, generates a \textit{spurious form drag} that slows down the circulation. Here, we revisit this problem and show how this spurious drag may be eliminated. First, we find that \textit{physical} convergence (i.e. the main characteristics of the flow are insensitive to the increase of the mesh resolution) allows simulations to become independent of the mesh orientation. An advection scheme with a wider stencil also reduces sensitivity to mesh orientation from coarser resolution. Second, we show that indented coastlines behave as straight and slippery shores when a true mirror boundary condition on the flow is imposed. This finding applies to both symmetric and rotational-divergence formulations of the stress tensor, and to both flux and vector-invariant forms of the equations. Finally, we demonstrate that the detachment of a vortex flowing past an outgoing corner of the coastline is faithfully simulated with exclusive implementation of impermeability conditions. These results provide guidance for a better numerical treatment of coastlines (and isobaths) in ocean general circulation models

Two-way nesting

International audienc

Schwarz waveform relaxation for heterogeneous cluster computing: Application to numerical weather prediction

International audienceThis presentation deals with the numerical simulation of partial differential equations on highly heterogeneous computing platforms both in terms of computing power and speed of communication. These difficulties are even stronger when the initial problem is not easily decomposable into independent tasks, and when other issues such as fault tolerance come into play. We show that the Schwarz waveform relaxation methods may prove to be the right tool to address all these issues. After explaining the benefits of these methods on a simple 2D advection equation, we present preliminary results of running the weather research and forecasting (WRF) model on the Amazon EC2 computing platform. The main open problems are finally outlined