Analysis of Stability and Convergence in Incremental Schemes for Nonlinear Satellite Cloud Radiance Assimilation

The widely adopted multi-incremental variational data assimilation (DA) framework faces convergence challenges when assimilating observations with nonlinear forward operators, even within the three-dimensional variational analysis. Despite discussions on convergence issues in the context of four-dimensional variational analysis for high-resolution models, the framework’s limitations in highly nonlinear scenarios remain unaddressed, particularly due to the absence of theoretical convergence analysis for incremental schemes. To improve analysis quality and ensure stability in real-time operations, it is essential to address these limitations. This study examines the performance of the incremental method in assimilating satellite cloudy radiance data and analyzes the effects of non-convergence. Our findings indicate that the incremental method experiences significant difficulties in achieving convergence, particularly when dealing with nonlinear cloudy satellite data. Although increasing the number of outer loops slightly improves the quality of the analysis field, this approach remains insufficient. This investigation highlights the need for more robust methods with established convergence properties, such as the full state method, to effectively and stably assimilate cloud and rainfall data in future operational scenarios.