SUMMARY ERA-40 is a re-analysis of meteorological observations from September 1957 to August 2002 produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) in collaboration with many institutions. The observing system changed considerably over this re-analysis period, with assimilable data provided by a succession of satellite-borne instruments from the 1970s onwards, supplemented by increasing numbers of observations from aircraft, ocean-buoys and other surface platforms, but with a declining number of radiosonde ascents since the late 1980s. The observations used in ERA-40 were accumulated from many sources. The first part of this paper describes the data acquisition and the principal changes in data type and coverage over the period. It also describes the data assimilation system used for ERA-40. This benefited from many of the changes introduced into operational forecasting since the mid-1990s, when the systems used for the 15-year ECMWF re-analysis (ERA-15) and the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) re-analysis were implemented. Several of the improvements are discussed. General aspects of the production of the analyses are also summarized.A number of results indicative of the overall performance of the data assimilation system, and implicitly of the observing system, are presented and discussed. The comparison of background (short-range) forecasts and analyses with observations, the consistency of the global mass budget, the magnitude of differences between analysis and background fields and the accuracy of medium-range forecasts run from the ERA-40 analyses are illustrated. Several results demonstrate the marked improvement that was made to the observing system for the * Corresponding author: European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, UK. e-mail: adrian.simmons@ecmwf. southern hemisphere in the 1970s, particularly towards the end of the decade. In contrast, the synoptic quality of the analysis for the northern hemisphere is sufficient to provide forecasts that remain skilful well into the medium range for all years. Two particular problems are also examined: excessive precipitation over tropical oceans and a too strong Brewer-Dobson circulation, both of which are pronounced in later years. Several other aspects of the quality of the re-analyses revealed by monitoring and validation studies are summarized. Expectations that the 'second-generation' ERA-40 re-analysis would provide products that are better than those from the firstgeneration ERA-15 and NCEP/NCAR re-analyses are found to have been met in most cases.

SUMMARYIn the first of this set of three papers, the formulation of the European Centre for Medium-Range Weather Forecasts (ECMWF) implementation of 3D-Var is described. In the second, the specification of the structure function is presented, and the last is devoted to the results of the extensive numerical experimentation programme which was conducted. The 3D-Var formulation uses a spherical-harmonic expansion, much as the ECMWF optimal interpolation (01) scheme used an expansion of Bessel functions. This formulation is introduced using a convolution algebra over the sphere expressed directly in spectral space. It is shown that all features of the 0 1 statistical model can be implemented within 3D-Var. Furthermore, a non-separable statistical model is described. In the present formulation, geostrophy is accounted for through a Hough-modes separation of the gravity and Rossby components of the analysis increments. As in 01, the tropical analysis remains essentially non-divergent and with a weak mass-wind coupling. The observations used, as well as their specified statistics of errors, are presented, together with some implementation details. In the light of the results, 3D-Var was implemented operationally at the end of January 1996.

The AD/VI-Aeo/us mission will provide global wind profile observationswith the aim to demonstrate improvement in atmospheric wind analyses for the benefit of numerical weather prediction and climate studies.

SUMMARYThe influence matrix is used in ordinary least-squares applications for monitoring statistical multipleregression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis-the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the selfsensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems.Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system.

ECMWF's preparations for cloud and rain assimilation encompass development of linearized physics, improved satellite data utilization, a new humidity analysis, and another look at the "spindown" problem. European, American, and Japanese satellite agencies have a number of Earth-observation missions with the objective of providing improved measurements of components of the global hydrological cycle-clouds, precipitation, soil moisture, and water vapor-from a range of operational platforms in both polar and geostationary orbits. Significant development of data assimilation methods will be necessary to make full use of both the existing and new types of observations of the water cycle. The small-scale

Several networks of Global Positioning System receiving stations over Europe send their data to several processing centers to generate atmospheric Zenith Total Delay (ZTD) observations. Thanks to the efforts of the Targeting Optimal Use of Global Positioning System Humidity measurements in meteorology project, these observations combining surface pressure and total precipitable water information in the atmosphere have been delivered to the operational meteorological centers in near real‐time since 2004. This paper presents forecast impact trials of such ZTD observations in a global Four‐Dimensional Variational (4DVAR) assimilation and forecasting system. The implementation of the ZTD assimilation in the 4DVAR system is described, including a preprocessing developed specifically for the ZTD data. The preprocessing involves a time averaging procedure of the observations in order to ensure consistency with the resolution of the 4DVAR, a bias correction, and a station selection based on χ2 tests of the normality of the observation minus first‐guess differences. Three forecast trials were conducted: winter, spring, and summer 2005. These trials cover various meteorological conditions and a total of about 10 weeks of assimilation. All three trials suggest a positive impact of the ZTD data in helping constrain the synoptic circulation in 1 to 4 day forecasts. In the spring and the summer trials, the impact of the ZTD data also shows positively on the prediction of precipitation patterns as indicated by improved Quantitative Precipitation Forecast scores for total precipitation forecasts over France between +12 and +36 hours. We also assess in this paper ZTD observation and background errors.

In recent years difficulties have been experienced in exploiting satellite sounding data in numerical weather prediction (NWP) in the form of independently retrieved temperature and humidity profiles. Attention has now focused on methods through which the information in the radiance measurements may be assimilated more directly into the NWP system%. A scheme known as ‘one‐dimensional variational analysis’ (1DVAR) has been developed at the European Centre for Medium‐range Weather Forecasts as a method for extracting information from TIROS Operational Vertical Sounder radiances for use in the operational data‐assimilation system. The 1DVAR scheme is based on variational principles applied to the analysis of the atmospheric profile at a single location, using a forecast profile and its error covariance as constraints. The details of the scheme are presented. Errors in 1DVAR products are correlated with those of the short‐range forecast which serves as a background for the subsequent three‐dimensional analysis. Methods for addressing this aspect of the assimilation problem are discussed. The characteristics of 1DVAR products and their impact on the analysis are described. A series of forecast impact experiments has been conducted and has demonstrated consistent positive impacts on forecast skill in the northern hemisphere.

SUMMARYStructure functions for the 3D-Var assimilation scheme of the European Centre for Medium-Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time. Results compare satisfactorily with those reported in the existing literature. Non-separability of the correlation functions is a pervasive feature. Accounting for non-separability in 3D-Var is necessary to reproduce geostrophic characteristics of the statistics, such as the increase of length-scale with height for the horizontal correlation of the mass variable, sharper vertical correlations for wind than for mass and shorter horizontal length-scales for temperature than for mass. In our non-separable 3D-Var, the vertical correlations vary with total wave-number and the horizontal correlation functions vary with vertical level.