Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. Ii: Numerical Results

Abstract The adjoint variational approach to data assimilation described in the first part of this paper is used, with the same vorticity equation model, to assimilate northern hemisphere radiosonde observations of wind and geopotential distributed over a 24‐hour period. Except over the eastern Pacific Ocean, where no observations are available, the variational assimilation reconstructs all structures of the flow resolvable by the model to an accuracy of about 30 m for geopotential heights and 8 m s −1 for wind vectors. A particular structure, the Aleutian depression, is reconstructed even though it was not covered by the available observations. The assimilation produces unrealistic small‐scale noise which can be reduced by adding an appropriate smoothing term to the distance function minimized in the variational process. Detailed study of the minimization strongly suggests that the distance function varies quadratically with respect to the model's initial conditions. This implies that the tangent linear equation of the model suffices to describe the 24‐hour evolution of the forecast error.