4D Variational Data Analysis with Imperfect Model

One of the main hypothese made in variational data assimilation is to consider that the model is a strong constraint of the minimization, i.e. that the model describes exactly the behavior of the system. Obviously the hypothesis is never respected. We propose here an alternative to the 4D-Var that takes into account model errors by adding a nonphysical term into the model equation and controlling this term. A practical application is proposed on a simple case and a reduction of the size of control using preferred directions is introduced to make the method affordable for realistic applications.