A New Method for Data Assimilation: the Diffusive Back and Forth Nudging Algorithm

International audienceData assimilation consists in estimating the state of a system by combining via numerical methods two different sources of information: models and observations. Data assimilation makes it possible to answer a wide range of questions such as: optimal identification of the initial state of a system, perform reliable numerical forecasts, identify or extrapolate non observed variables by using a numerical model. In external geophysics (meteorology, oceanography, …), the model is chaotic and hence very dependent on the initial condition. The inverse problem consists then in identifying the initial condition for the data assimilation period.Nudging can be seen as a simplified Kalman filter. Also known as the Luenberger or asymptotic observer, it consists in applying a Newtonian recall of the state value towards its direct observation. A main disadvantage of such sequential data assimilation methods is that it only takes into account past observations at a given time, and not future ones. Auroux and Blum proposed an original approach of backward and forward nudging (or back and forth nudging, BFN), which consists in initially solving the forward equations with a nudging term, and then, using the final state as an initial condition, in solving the same equations in a backward direction with a feedback term (with the opposite sign compared to the feedback term of forward nudging). This process is then repeated iteratively until convergence. The implementation of the BFN algorithm has been shown to be very easy, compared to other data assimilation methods