Introduction

Weather forecast is the first application which has motivated the development of data assimilation.

The growing number of real time meteorological measurements, combined to the growing complexity of atmosphere numerical models, has necessitated sophisticated method to combine all the available information.

Data assimilation enables to determine to best estimation of the present weather, which is then used as the initial condition to make forecasts.

Beyond weather forecast, numerous applications benefits from the progress of the data assimilation theory that mixes physical modelling, statistical analysis and algorithms.

A series a example of increasing complexity is presented here to introduce this theory.