Introduction to the Mm D Var Data Assimilation System Theoretical Basis

Data assimilation has long being regarded primarily as a mean of providing initial conditions for Numerical Weather Prediction NWP in meteorological centers Increas ingly it is now being recognized that through the constant confrontation of theory under the form of a numerical model that discretized the physical laws governing the atmospheric ow with reality as depicted by meteorological observations the data assimilation pro cess has the potential to bring major advances in our scienti c understanding of the atmo sphere An ideal assimilation should be able to process all the available information i e the observations themselves the meteorological model and the known statistical proper ties of the ow together with the uncertainties of these various sources of information to produce a complete and consistent description of the ow with its associated uncertainty Data assimilation is an estimation problem and Estimation theory constitutes the natural mathematical foundation for understanding data assimilation problems It provides in ad dition a number of algorithms for approaching and addressing these problems However as it was pointed out by Cohn while engineering problems for which Estimation Theory has primilary been developped are generally small scale and sometimes linear atmospheric data assimilation problems are large scale and generally non linear Sensible computational approximations have therefore to be made to implement these algorithms in atmospheric and oceanic application Indeed most of the research work performed on data assimilation is intended at determining cost e ective simpli cations to implement