Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order 4D-Var prior to the incremental 4D-Var in the full space in order to achieve faster convergence. An application performed in the tropical Pacific Ocean, with assimilation of TAO temperature data, shows the method to be both feasible and efficient. It allows the global cost of the assimilation to be reduced by a factor of 2 without affecting the quality of the solution

Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error

Assessment of the ocean circulation in the Azores region as predicted by a numerical model assimilating altimeter data from Topex/Poseidon and ERS-1 satellites

International audienceTwo years of altimetric data from Topex/Poseidon (October 1992-September 1994) and ERS-1 (October 1992-December 1993) were assimilated into a numerical model of the North Atlantic. The results of these simulations are analysed in the Azores region to assess the performance of our model in this particular region. Maps of instantaneous dynamic topography and transports show that the model performs well in reproducing the velocities and transports of the Azores Front. Drifter data from the Semaphore experiment are also used to study the correlation between the drifter velocities and the corresponding model velocities. Some interesting oceanographic results are also obtained by examining the seasonal and interannual variability of the circulation and the influence of bathymetry on the variability of the Azores Front. Thus, on the basis of our two year experiment, it is possible to confirm the circulation patterns proposed by previous studies regarding the seasonal variations in the origin of the Azores Current. Moreover, it is shown that the Azores Current is quite narrow in the first year of assimilation (1992-1993), but becomes much wider in the second year (1993-1994). The role of the bathymetry appears important in this area since the mesoscale activity is shown to be strongly related to the presence of topographic slopes. Finally, spectral analyses of sea-level changes over time and space are used to identify two types of wave already noticed in other studies: a wave with (300 km)-1 wave number and (120 days)-1 frequency, which is characteristic of mesoscale undulation, and a wave with (600 km)-1 wave number and (250 days)-1 frequency which probably corresponds to a Rossby wave generated in the east of the basin

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

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

Building Generalized Open Boundary Conditions for Fluid Dynamics Problems

International audienceThis paper deals with the design of an efficient open boundary condition (OBC) for fluid dynamics problems. Such problematics arise, for instance, when one solves a local model on a fine grid that is nested in a coarser one of greater extent. Usually the local solution $U^{\hbox{\scriptsize loc}}$ is computed from the coarse solution $U^{\hbox{\scriptsize ext}}$ thanks to an OBC formulated as $B_hU^{\hbox{\scriptsize loc}}=B_HU^{\hbox{\scriptsize ext}}$, where $B_h$ and $B_H$ are discretizations of the same differential operator ${\cal B}$ ($B_h$ being defined on the fine grid and $B_H$ on the coarse grid). In this paper we show that such an OBC cannot lead to the exact solution, and we propose a generalized formulation $B_hU^{{\hbox{\scriptsize loc}}}=B_HU^{\hbox{\scriptsize ext}}+g$, where $g$ is a correction term. When $B_h$ and $B_H$ are discretizations of a transparent operator, $g$ can be computed analytically, at least for simple equations. Otherwise we propose to approximate $g$ by a Richardson extrapolation procedure. Numerical test cases on a 1-D Laplace equation and on a 1-D shallow water system illustrate the improved efficiency of such a generalized OBC compared to usual ones

Lateral Boundary Conditions at the staircase-like boundary of ocean models

National audienceA 4D-Var data assimilation technique is applied to a rectangular-box configuration of the NEMO in order to analyze the optimal parametrization of boun\-dary conditions at lateral boundaries. The impact of staircase-shaped coastlines is studied by rotating the model grid around the center of the box. Rotations on $30^\circ$ and $45^\circ$ are studied with single and double gyre forcing patterns. It is shown that optimized boundary conditions compensate the errors induced by the staircase-like approximation of the coastline

Compact finite difference schemes for shallow-water ocean model

In this paper, we test some high order numerical schemes on simple oceanic models. We first compare fourth-order and sixth-order compact schemes with the classical second-order centered scheme on the system of equations describing the inertia-gravity waves, and then we focus on the performances of the fourth-order compact scheme on oceanic typical processes, such as Munk boundary layer and shallow-water physics. Numerical analysis of the schemes, and many computational results are presented

Approximation explicite des formules "bulks" en vue du développement d'un couplage océan-atmosphère cohérent

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