The aim of the analysis (User Guide to ECMWF Products, 1995) is to provide the general circulation
numerical model with the most realistic state of the atmosphere. For so doing
the ECMWF uses a finite number of observations and a **first guess**
provided by the same forecasting model (generally the last six hours
prevision) or by climatology. The analysis must modify this first guess
integrating in the best way the information coming from the observations
which, in general, do not describe perfectly the atmospheric state. Different
quality controls are performed on the observations in order to select a
realistic set of data. The assimilation of the first guess and the
observations are made using an algorithm named **optimal interpolation**.
If A is the analyzed parameter, for each grid point one defines:

(7) |

where

- is the value of A that we want to know in the
*k*grid point; - is the value of the parameter provided by the first guess
in the
*k*grid point; - is the averaged weight associated to the quality of the observation (kind of measurement and kind of observed parameter), the distance between the analysis grid point and the observations grid point and the quality of the first guess;
- is the observed value of the parameter
*Y*(*Y*can be A or, more generally, a parameter linearly correlated to A); - is the value of
*Y*provided by the first guess.

The optimal interpolation method defines in the following way:

(8) |

(9) |

This analysis, named **uninitialized analysis**, can sometimes generate,
fictitious gravity waves during the simulations. To avoid this, they
must be initialized in order to be adapted to the dynamics of the model. This
more elaborate analysis is named **initialized analysis**.

In an operational schedule, the ECMWF produces global analysis and
predictions using data collected during time. The predictions are
permanently corrected by the observations that are injected in the algorithm
of the optimal interpolation. This feed-back system of assimilation data is
named **Analysis Assimilation.**

This work is supported by contract (Technical Report UNI-17400-0004) from ESO. The authors are grateful to M.Sarazin for his constant and dedicated presence in this feasibility study. They wish to thank the GMME team of the Centre National de Recherche Meteorologique for their scientific collaboration and logistical help. In particular, they gratefully acknowledge the many helpful discussions with J. Stein, P. Jabouille, J.L. Redelsperger and J.P. Lafore. The authors thank C. Coulman for his helpful comments and revision of the draft.

Copyright The European Southern Observatory (ESO)