This book gives a comprehensive presentation of our present understanding of the Earth's Hydrological cycle and the problems, consequences and impacts that go with this topic. Water is a central component in the Earth's system. It is indispensable for life on Earth in its present formand influences virtually every aspect of our planet's life support system. On relatively short time scales, atmospheric water vapor interacts with the atmospheric circulation and is crucial in forming the Earth's climate zones. Water vapor is the most powerful of the greenhouse gases and serves to enhance the tropospheric temperature. The dominant part of available water on Earth resides in the oceans. Parts are locked up in the land ice on Greenland and Antarctica and a smaller part is estimated to exist as groundwater. If all the ice over the land and all the glaciers were to melt, the sea level would rise by some 80 m. In comparison, the total amount of water vapor in the atmosphere is small; it amounts to 25 kg/m2, or the equivalent of 25 mm water for each column of air. Yet atmospheric water vapor is crucial for the Earth s energy balance. The book gives an up to date presentation of the present knowledge.Previously published in Surveys in Geophysics, Volume 35, No. 3, 2014"

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."