Toward the assimilation of images

Abstract. The equations that govern geophysical fluids (namely atmosphere, ocean and rivers) are well known but their use for prediction requires the knowledge of the initial condition. In many practical cases, this initial condition is poorly known and the use of an imprecise initial guess is not sufficient to perform accurate forecasts because of the high sensitivity of these systems to small perturbations. As every situation is unique, the only additional information that can help to retrieve the initial condition are observations and statistics. The set of methods that combine these sources of heterogeneous information to construct such an initial condition are referred to as data assimilation. More and more images and sequences of images, of increasing resolution, are produced for scientific or technical studies. This is particularly true in the case of geophysical fluids that are permanently observed by remote sensors. However, the structured information contained in images or image sequences is not assimilated as regular observations: images are still (under-)utilized to produce qualitative analysis by experts. This paper deals with the quantitative assimilation of information provided in an image form into a numerical model of a dynamical system. We describe several possibilities for such assimilation and identify associated difficulties. Results from our ongoing research are used to illustrate the methods. The assimilation of image is a very general framework that can be transposed in several scientific domains

Coupling dynamic equations and satellite images for modelling ocean surface circulation

International audienceSatellite image sequences visualise the ocean surface and allow assessing its dynamics. Processing these data is then of major interest to get a better understanding of the observed processes. As demonstrated by state-of-the-art, image assimilation permits to retrieve surface motion, based on assumptions on the dynamics. In this paper, we demonstrate that a simple heuristics, such as the Lagrangian constancy of velocity, can be used and successfully replaces the complex physical properties described by the Navier-Stokes equations for assessing surface circulation from satellite images. A data assimilation method is proposed that adds an acceleration term a(t) to this Lagrangian constancy equation, which summarises all physical processes other than advection. A cost function is designed that quantifies discrepancy between satellite data and model values. This cost function is minimised by the BFGS solver with a dual method of data assimilation. The result is the initial motion field and the acceleration terms a(t) on the whole temporal interval. These values a(t) model the forces, other than advection, that contribute to surface circulation. Our approach was tested on synthetic data and with Sea Surface Temperature images acquired on Black Sea. Results are quantified and compared to those of state-of-the-art methods

Finite Rank Approximation based method for solving the RTE in stellar atmospheres and application to an inverse problem

The Finite Rank Approximation (FRA) based method is well known in operator approximation theory but it is also useful for suggesting numerical methods for solving integral equations. In this document we describe two FRA methods for the numerical resolution of the integral formulation of the 1D Radiative Transfer Equation (RTE) posed in a static slab; we browse some advantages of them (especially the possibility to control the error) and we give some reduction of computation technics (iterative refinement schemes) which can be used with these methods. Numerical results obtained for a realistic Sun atmosphere model are given. In the last section we give an example of an inverse problem associated to the RTE: we show the iterative recovering of the albedo from the measurement of the outgoing specific intensity at a surface of the considered domain

SCIENTIFIC COMMITTEE TENTH REGULAR SESSION

The SC acknowledge the projects and donors that are continuing to contribute to the development and application of SEAPODYM to the work programme of the WCPFC-SC and to endorse the inclusion of all presented projects within the scope of Project 62. The SC notes the 2014-2015 work plan for Project 62