Étude de représentations parcimonieuses des statistiques d'erreur d'observation pour différentes métriques. Application à l'assimilation de données images

Vincent Chabot 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Recent decades have seen an increase in quantity and quality of satellite observations. Over the years, those observations has become increasingly important in numerical weather forecasting. Nowadays, these datas are crucial in order to determine optimally the state of the studied system. In particular, satellites can provide dense observations in areas poorly observed by conventionnal networks. However, the potential of such observations is clearly under-used in data assimilation: in order to avoid the management of observation errors, thinning methods are employed in association to variance inflation. In this thesis, we adress the problem of extracting information on the system dynamic from satellites images data during the variationnal assimilation process. This study is carried out in an academic context in order to quantify the influence of observation noise and of clouds on the performed analysis. When the noise is spatially correlated, it is hard to take into account such correlations by working in the pixel space. Indeed, it is necessary to invert the observation error covariance matrix (which turns out to be very huge) or make an approximation easily invertible of such a matrix. Analysing the information in an other space can make the job easier. In this manuscript, we propose to perform the analysis step in a wavelet basis or a curvelet frame. Indeed, in those structured spaces, a correlated noise does not affect in the same way the differents structures. It is then easier to take into account part of errors correlations : a suitable approximation of the covariance matrix is made by considering only how each kind of element is affected by a correlated noise. The benefit of this approach is demonstrated on different academic tests cases. However, when some data are missing one has to address the problem of adapting the way correlations are taken into account. This work is not an easy one : working in a different observation space for each image makes the use of easily invertible approximate covariance matrix very tricky. In this work a way to adapt the diagonal hypothesis of the covariance matrix in a wavelet basis, in order to take into account that images are partially hidden, is proposed. The interest of such an approach is presented in an idealised case.
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Submitted on : Friday, October 10, 2014 - 10:15:17 AM
Last modification on : Friday, December 28, 2018 - 10:27:55 AM
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Vincent Chabot. Étude de représentations parcimonieuses des statistiques d'erreur d'observation pour différentes métriques. Application à l'assimilation de données images. Traitement du signal et de l'image [eess.SP]. Université de Grenoble, 2014. Français. ⟨tel-01073582v1⟩

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