Wednesday, 17 January 2007: 1:30 PM
Assimilation of images in geophysical models
210B (Henry B. Gonzalez Convention Center)
Since ten years the number of observations provided by the observation of the Earth has been mutiplied by more than 20, but only a small amount ( less than 4% ) is used in the numerical assimilation. Nevertheless it is clear that the dynamics of the images has an important informative content . The quesstion is how to use these images in data assimilation? We will discuss about two possible approaches capable to be implemented within a variational framework. The firs approach is to associate to the images some simple conservative properties (e.g. luminance) then by carrying out a variational annalysis extracts some pseudo i nformation which will be used in a conventional variational annalysis. The second approach is to consider the images as geophysical objects imbedded in metric spaces. An observation operator is defined from the space of the state variables of the model toward the space of images in order to compare observed and calculated images.. The cost function of the variational assimilation will include such term. A major problem is the choice of the space of images. We will present some results based on the a space of curvlets. The difficulties encountered will be discussed and some numreical results will be presented.