International audienceWe present a Lagrangian data assimilation experiment in an open channel flow above a broad-crested weir. The observations consist of trajectories of particles transported by the flow and extracted from a video film, in addition to classical water level measurements. However, the presence of vertical recirculations on both sides of the weir actually conducts to the identification of an equivalent topography corresponding to the lower limit of a surface jet. In addition, results on the identification of the Manning coefficient may allow to detect the presence of bottom recirculations
We tackle the problem of coupling a geophysical simulation model with data coming from image processing. It needs to define the image observation space and to design an operator to transform results from the image space to the model space. In this study, we use a shallow-water oceanographic circulation model developed at MHI. We propose a processing chain first based on an image processing step relying on a dedicated motion estimation operator, and then a data assimilation step of the estimated velocity. We illustrate the method on different results without and with assimilation. OBJECTIVESIn the framework of numerical forecasting for the evolution of geophysical fluid, we are interested in the assimilation of data coming from images. In order to forecast the behavior of geophysical fluids we need: a forecast model to describe the evolution of a state variable (generally it is a non-linear PDE system) and observations spatially and temporally distributed. Data assimilation provides a mathematical solution to combine data and models. During last decades model quality increased significantly. But forecast quality is not directly linked to model quality. To increase forecast quality it is also necessary to increase the amount and the quality of observations. Therefore, images -particularly images coming from spatial remote sensing -provide a huge amount of information. Using images in a data assimilation framework raises several difficulties:1. First it is necessary to define which image space is relevant according to model specialists.2. Then, it is necessary to construct an image operator dedicated to the problematic and coherent to the physical behavior. Moreover it is necessary to define a set of norm in order to quantify the influence of image information along the assimilation process.3. And finally, it is necessary to construct an operator to compare image space and model space.In the study presented in this paper, we are interested in oceanographic circulation forecasting. Oceanographic circulation is ruled by fluid mechanic. Most of oceanographic circulation models are heavy 3D models based on primitive equations [1]. They correspond to an approximation of Navier-Stokes equation associated to a nonlinear state equation coupling salinity, temperature and 3D velocity. Nevertheless, it exists simplified models based on shallow-water approximation [2,3]. They rely on a so called 1.5 layer representation of the ocean: the sea surface is represented by a mixed layer interfaced to the atmosphere and a deeper layer. Equation ruling the circulation are then:
International audienceThe general problem of surface matching is taken up in this study. The process described in this work hinges on a geodesic distance equation for a family of surfaces embedded in the graph of a cost function. The cost function represents the geometrical matching criterion between the two 3D surfaces. This graph is a hypersurface in 4-dimensional space, and the theory presented herein is a generalization of the geodesic curve evolution method introduced by R. Kimmel et al [12]. It also generalizes a 2D matching process developed in [4]. An Eulerian level-set formulation of the geodesic surface evolution is also used, leading to a numerical scheme for solving partial differential equations originating from hyperbolic conservation laws [17], which has proven to be very robust and stable. The method is applied on examples showing both small and large deformations, and arbitrary topological changes
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