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.
The direct use of TOVS (TIROS Operational Vertical Sounder) cloud-cleared radiances in a three/fourdimensional variational data assimilation scheme is described. This scheme uses a fast radiative transfer model and its adjoint. Radiances are used together with all the other observational data. Global spectral fields of mass, wind and humidity are analysed simultaneously under certain mass/wind balance constraints which control the degree to which gravity waves enter into the analysis. In this way the need for a subsequent initialization is avoided. The scheme thus combines retrieval, analysis and initialization in one step and makes it possible to achieve a more optimal combination of the information contained in the radiances, the conventional data and the background (a six-hour forecast).At spectral truncation T63, a global three-dimensional variational analysis (3D-Var) of TOVS radiances and conventional data is compared with the ECMWF operational Optimum Interpolation scheme, which uses TOVS radiance information in the form of profiles of temperature and humidity, retrieved using a onedimensional variational method. The results of 3D-Var are in good agreement with the operational analysis at the same resolution.In an application of the four-dimensional scheme (4D-Var), data covering a period of 24 hours were used simultaneously. In 4D-Var consistency in time is ensured through the evolution of the forecast model and its adjoint. Using the adiabatic version of the ECMWF forecast model (spectral resolution T42) we show that 4D-Var is able to extract additional information from the dynamics of the model. In particular we show an impact on the tropical wind field from the use of the humidity-sensitive TOVS channels.
This work evaluates the scalability of the impact of the GPS radio occultation (GPSRO) measurements on the reduction of Numerical Weather Prediction forecast errors. We first show that the GPSRO bending angles from the eight satellites FORMOSAT‐3/COSMIC, CHAMP, and GRACE‐A lead to a reduction in geopotential height and temperature forecast Root Mean Square errors in Météo‐France global data assimilation system of a few percents in the Northern troposphere and larger in the Southern troposphere. As we double the number of GPSRO data assimilated, the forecast mean square error reduction grows by a factor between 1.1–1.8 for humidity and 1.3–2.4 for geopotential height, temperature, and wind. We do not observe any evidence of forecast impact saturation, though hints of leveling are apparent.
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