# Nelson Feyeux, Inria Grenoble

## Optimal transport for data assimilation

##### Coauthors

MaĆ«lle Nodet, Arthur Vidard#### Abstract:

A common problem in data assimilation comes from misplacement of structures, which is called position error. It stems for example from a bad estimation of the velocity field in the model causing structures to be misplaced. Under such position errors, distances used in classical data assimilation lead to a poor analyzed state.

Recently, optimal transport theory has become widely used in image processing, from image classification to colour transfer through image segmentation and movie reconstruction. This theory defines the Wasserstein distance which looks for the optimal map transporting a density onto another one. One of its characteristics is to consider a density more as a positioning of different structures than as a real-valued function. In particular, the Wasserstein distance handles well data subject to position errors.

For this reason we investigate the use of such a distance in variational data assimilation. In the cost function, the difference between the observations and their model counterparts is computed using the Wasserstein distance. In this talk, we present such a cost function. In simple examples containing position errors, it shows promising results.

Keyword : optimal transport, Wasserstein distance, data assimilation of images, position errors.