应数学系马坚伟教授邀请，国际著名数据同化专家，法国Grenoble第一大学数学系Francois-Xavier Le Dimet教授将于近日访问我系，并将做关于数据同化方面的学术报告，欢迎大家参加。

时    间：6月17号14:00-15:00，

地    点：格物楼503。

题    目：ASSIMILATION OF IMAGES: AN APPLICATION TO OIL SPILLS

摘要：Predicting the evolution is based on the integration of physical laws governing the flow. Basically we have a set on nonlinear equations based on conservation laws, the system is of order one with respect to time. Therefore we have to provide an initial condition in agreement with the physical properties of the flow and observational data. We propose to use variational methods, based on the theory of optimal control.

The method has been tested in operational centers since several decades.

Recently two problems have been raised:

- Geophysical fluids are not only air and oceanic water but the ocean and the atmosphere contain many pollutants having a strong interaction with the basic variables especially from the climatological point of view.

- There are many data on the fluids issued from routine observation but there are more and mote unconventional data under the form of images and their dynamics, mainly observed by satellites.

In this talk, we will be in the framework of the following remark. The contaminant is oil on the surface of the ocean produced by some industrial accident. Predicting the evolution of oil spots is very important for the environment.

From the viewpoints of:

-Modeling: there are strong local interactions between oil, ocean and atmosphere. It has been included in a global model which will used dome parametrization of the diffusion with uncertain parameters.

- Information: the main source of information on the development of oil spots is satellite imagery. Very few in-situ measurements are available.Therefore the question is how to couple models and images in order to retrieve the state of the environment?

To remain in the framework of variational methods we will have to compare the solutions of models and observations i.e. images? To apply the rules of Calculus of Variations images have to be plugged in some linear space. It's of importance to point out that the information provided by the dynamics of images is carried by the evolution of their discontinuities: fronts, filament, vortex..... Consequently we have defined the images par functions defining their level sets.

The definition of the assimilation of images will be complete if we define operators between the space of the solution of the model and images. Then we will be able to carry out the "regular" procedure od optimal control by deriving the Euler-Lagrange equation and optimization methods.

In this talk we will present the theory with some preliminary numerical results and will discuss about future potential applications for example in biology and medicine such as the development of tumors.

简介：Le Dimet 教授于1982年提出变分数据同化方法，该论文已被引用一千余次，该方法已被很多机构（如欧洲气象中心，日本气象中心，加拿大气象中心等）应用到实际天气预报中。 Le Dimet教授近年致力于数据同化在海洋污染、洪水灾害等领域的应用。