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In 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 (OI) 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 OI 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 OI, 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.

Titre traduit en français : "Correction de biais des mesures d'humidité réalisées par radiosonde au-dessus de l'Afrique de l'Ouest en vue des réanalyses effectuées au CEPMMT spécialement pour la campagne AMMA"; International audience; During the African Monsoon Multidisciplinary Analysis (AMMA) field experiment in 2006 there was a large increase in the number of radiosonde data over West Africa. This has the potential of improving the numerical weather prediction (NWP) analysis/forecast and the water budget studies over that region. However, it is well known that the humidity from radiosondes can have some errors depending on sonde type, relative humidity (RH), temperature and the age of the sensor and can give rise to dry biases that are typically between 5% and 30% for RH. Three main sonde types were used in the AMMA field experiment: Vaisala RS80A, Vaisala RS92 and MODEM. In this article, a new empirical method is presented by using the operational European Centre for Medium-Range Weather Forecasts (ECMWF) short-range forecast as an intermediary dataset for computing biases. The validation of the correction method using global positioning system (GPS) total columnar water vapour (TCWV) confirms that the method is able to correct for a large part of the dry biases associated with the different sonde types. Results from analysis experiments show how the correction of humidity is particularly important in the West African region due to its impact on the development of convection in NWP models. The proposed radiosonde humidity bias correction has been applied to the special AMMA reanalysis experiment performed at ECMWF for the 2006 West African wet monsoon season. This is expected to benefit a wide number of AMMA-related studies that make use of the reanalysis, in particular those focusing on the water cycle. Copyright © 2009 Royal Meteorological Society

SUMMARY In this third and final paper of a series, we assess the performance of the three-dimensional variational data assimilation scheme, in the light of the results from the extensive pre-operational programme of numerical experimentation. Its performance is compared with that of the previous operational scheme at the European Centre for Medium-Range Weather Forecasts, which was based on Optimal Interpolation. The main features of the new scheme are illustrated, in particular the effects of non-separable structure functions and the improved data usage. TIROS-N Operational Vertical Sounder cloud-cleared radiances, for example, are used directly without a separate retrieval step. Scatterometer data are assimilated in the form of ambiguous winds with the ambiguity removal taking place within the analysis itself. Problems encountered during the tests are discussed and the solutions implemented are explained. The overall impact on forecast accuracy in the troposphere of the northern hemisphere extratropics is neutral for geopotential and positive for wind and temperature. The impact is neutral in the tropics, and significantly positive in the southern hemisphere. Analyses and forecasts for the stratosphere have improved in all regions. Other positive results include a clear improvement in analyses of near-surface winds over oceans, particularly in the vicinity of tropical storms. This is predominantly because of the assimilation of scatterometer wind-data.