Balanced data assimilation with a blended numerical model

Physical imbalances introduced by local sequential Bayesian data assimilation pose a problem for numerical weather prediction. For example, fast-mode acoustic imbalances of the order of the relevant slower dynamics destroy solution quality. We introduce a novel dynamics-driven method that suppresses imbalances arising from data assimilation. Specifically, we employ a blended numerical model with seamless access to compressible, soundproof, and hydrostatic dynamics. After careful numerical and asymptotic analysis, we introduce a one-step blending strategy to switch between model regimes within a simulation run. Upon assimilation of data, the model configuration is switched for one timestep to the limit soundproof pseudo-incompressible or hydrostatic regime. After that, the model configuration is switched back to the compressible regime for the duration of the assimilation window. The switching between model regimes is repeated for each subsequent assimilation window. Idealised experiments involving the travelling vortex, buoyancy-driven rising thermals, and internal gravity wave pulses demonstrate that our method successfully eliminates imbalances from data assimilation, yielding up to two orders-of-magnitude improvements in the analysis fields. While our studies involved eliminating acoustic and hydrostatic imbalances, this novel dynamics-driven method of achieving balanced data assimilation can be extended to eliminate other undesired imbalances, with significant prospective applications in real-world weather prediction.