Forecasting the weather for the long and medium range is a difficult and scientifically challenging problem. Since the first operational weather prediction by numerical methods was carried out (on the BESK computer in Stockholm, Sweden, 1954) . there has been an ever accelerating development in computer technology. Hand in hand has followed a tremendous increase in the complexity of the atmospheric models used for weather prediction. The ability of these models to predict future states of the atmosphere has also increased rapidly, both due to model development and due to more accurate and plentiful observations of the atmosphere to define the initial . state for model integrations. It may however be argued on theoretical grounds that even if we have an almost perfect model with almost perfect initial data, we will never be able to make an accurate weather prediction more than a few weeks ahead. This is due to the inherent instability of the atmosphere and work in this field was pioneered by E. Lorenz. It is generally referred to as atmospheric predict ability and in the opening chapter of this book Professor Lorenz gives us an overview of the problem of atmospheric predictability. The contributions to this book were originally presented at the 1981 ECMWF Seminar (ECMWF - European Centre for Medium Range Weather Forecasts) which was held at ECMWF in Reading, England, in September 1981."

One of the main reasons we cannot tell what the weather will be tomorrow is that we do not know accurately enough what the weather is today. Mathematically speaking, numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear partial differential equations in which the necessary initial values are known only incompletely and inaccurately. Data at the initial time of a numerical forecast can be supplemented, however, by observations of the atmos phere over a time interval preceding it. New observing systems, in particular polar-orbiting and geostationary satellites, which are providing observations continuously in time, make is absolutely necess ary to find new and more satisfactory methods of assimilating meteorological observations - for the dual purpose of defining atmospheric states and of issuing forecasts from the states thus defined. FUndamental progress in this area has been made in recent years and this book attempts to give a review and some suggestions for further improvements in the field of meteorological data assimila tion methods. The European Centre for Medium Range Weather Forecasts (ECMWF) every year organises seminars for the benefit of meteorologists and geophysicists of the ECMWF Member states. The 1980 Seminar was devoted to data assimilation methods, and this book contains selected lectures from that seminar. The purpose of the seminar was twofold: it was intended to give a basic introduction to the subject, as well as an overview of the latest developments in the field."

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