Data assimilation

Sketch of the data assimilation principle: The general problem is to determine, among all solutions of a model, the one that minimizes a certain norm of the difference with respect to the observations (depending on their accuracy). The model can also be assumed imperfect, by looking for an approximate solution of the model equations (that become a weak constraint, instead of a strong constraint). Furthermore, if the observations are insufficient to determine the solution, it is necessary to introduce information about the model initial condition (as an additional weak contraint). The relative importance of these sources of information (observations, model, initial condition) can be ruled by statistical assumptions on the amplitude and shape of their respective errors.