Mathematical models are essential for understanding the dynamics of the atmosphere and ocean. But if they were our only source of information no forecast would be possible, mainly due to the lack of a consistent initial condition. On the other hand observation of these systems are available in a larger and larger quantity, thanks to the numerous observation satellites that now cruises around our planet. These observations are often indirect and incomplete, and therefore do not provide a thorough knowledge of the state of the observed systems. Finally statistics are available on the fields of atmospheric variables, their variability and consistency in time and space. This information is also part of the data that will be used. As we shall see later the use of these statistics is very important to improve the forecast. I therefore present, in this paper, methods for combining all or part of this information in order to improve forecasts and knowledge of the behaviour of such systems. These methods are based most often on a solid mathematical theory, but applying them in a realistic setting is not always easy. That is why I think important to accompany the developments we make until operational applications or quasi-operational, in order to demonstrate their feasibility.
