arXiv subjects

Eric Blayo

Publications and source records attributed to Eric Blayo.

7 recordsLinked to original sources

arXiv2023

Towards a finite volume discretization of the atmospheric surface layer consistent with physical theory

We study an atmospheric column and its discretization. Because of numerical considerations, the column must be divided into two parts: (1) a surface layer, excluded from the computational domain and parameterized, and (2) the rest of the column, which reacts more slowly to variations in surface conditions. A usual practice in atmospheric models is to parameterize the surface layer without excluding it from the computational domain, leading to possible consistency issues. We propose here to unify the two representations in a Finite Volume discretization. In order to do so, the reconstruction inside the first grid cell is performed using the particular functions involved in the parameterizations and not only with polynomials. Using a consistency criterion, surface layer management strategies are compared in different physical situations.

math.NA↗

arXiv2021

Discrete analysis of Schwarz Waveform Relaxation for a simplified air-sea coupling problem with nonlinear transmission conditions

In this study we present a non-overlapping Schwarz waveform relaxation (SWR) method applied to a one dimensional model problem representative of the coupling between the ocean and the atmosphere. This problem includes nonlinear interface conditions analogous to a quadratic friction law. We study the convergence of the corresponding SWR at a semi-discrete level for a linear friction and for a linearized quadratic friction at the interface. Using numerical experiments we show that the convergence properties in the linearized quadratic friction case are very close to the ones obtained with the full nonlinear problem for the range of parameter values of interest. We investigate the possibility to improve the convergence speed by adding a relaxation parameter at the interface.

math.AP↗

arXiv2017

Recent progress and review of issues related to Physics Dynamics Coupling in geophysical models

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example. Hence, coupling between these physics parameterizations and the resolved fluid dynamics and also between the dynamics of the air and water, is necessary. In this paper weather and climate models are used to illustrate the problems. Nevertheless the same applies to other geophysical models. This coupling is an important aspect of geophysical models. However, often model development is strictly segregated into either physics or dynamics. As a consequence, this area has many unanswered questions. Recent developments in the design of dynamical cores, extended process physics and predicted future changes of the computational infrastructure are increasing complexity. This paper reviews the state-of-the-art of the physics-dynamics coupling in geophysical models, surveys the analysis techniques, and illustrates open questions in this field. This paper focuses on two objectives: To illustrate the phenomenology of the coupling problem with references to examples in the literature and to show how the problem can be analysed. Proposals are made on how to advance the understanding and upcoming challenges with emerging modeling strategies. This paper is of interest to model developers who aim to improve the models and have to make choices on and test new implementations, to users who have to understand choices presented to them and finally users of outputs, who have to distinguish physical features from numerical problems in the model data.

physics.ao-ph↗

arXiv2012

Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem

In the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D Laplace equation. We will first show how to obtain the 1-D model from the 2-D one by integration along one direction, by analogy with the link between shallow water equations and the Navier-Stokes system. Then, we will focus on the design of an Schwarz-like iterative coupling method. We will discuss the choice of boundary conditions at coupling interfaces. We will prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and the control of the difference between a global 2-D reference solution and the 2-D coupled one. These theoretical results will be illustrated numerically.

math.AP↗

arXiv2007

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.

physics.geo-ph↗

arXiv2007

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.

physics.geo-ph↗

arXiv2007

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method.

physics.geo-ph↗