Variational assimilation of conventional meteorological observations with a multilevel primitive-equation model

The paper describes a four-dimensional variational assimilation using a multilevel global primitive-equation spectral model. The experiments consist in minimizing the distance between the model solution and conventional observations spread over 24 hours. A first set of experiments was performed at low resolution (spectral truncation T21). The model solution converges to fit the observations satisfactorily over the whole assimilation period. The meteorological quality of the analyses, in terms of the large-scale part of the flow, is comparable with the ECMWF operational analysis. Confirming early results, the control of gravity waves in the solution can be easily handled using a combination of a penalty term and a normal-mode initialization scheme within the forward-backward process of the variational assimilation. Experiments excluding data over an area with a strong baroclinic development show that the information contained in the dynamics of the model is used successfully in the analysis over this area. In addition, the dynamics are able to inter implicitly flow-dependent structure functions. Higher-resolution experiments (spectral truncation T42) were performed and compared with optimum interpolation (OI) analyses performed under the same conditions. Although the lack of a first-guess term in the cost function leads to small-scale noise generation if the minimization is pursued, the quality of the variational assimilation is comparable with OI, and the error growth of the following 24-hour forecast is smaller when performed from the variational analysis. Moreover, experiments excluding wind data from aircraft show a clear advantage for the variational approach against OI in using, in a consistent way, the information coming from the model and the observations.