  A challenge arising from the local Bayesian assimilation of data in an
atmospheric flow simulation is the imbalances it may introduce. Acoustic
fast-mode imbalances of the order of the slower dynamics can be negated by
employing a blended numerical model with seamless access to the compressible
and the soundproof pseudo-incompressible dynamics. Here, the blended modelling
strategy by Benacchio et al., MWR, vol. 142 (2014) is upgraded in an advanced
numerical framework and extended with a Bayesian local ensemble data
assimilation method. Upon assimilation of data, the model configuration is
switched to the pseudo-incompressible regime for one time-step. After that, the
model configuration is switched back to the compressible model for the duration
of the assimilation window. The switching between model regimes is repeated for
each subsequent assimilation window. An improved blending strategy for the
numerical model ensures that a single time-step in the pseudo-incompressible
regime is sufficient to suppress imbalances coming from the initialisation and
data assimilation. This improvement is based on three innovations: (i) the
association of pressure fields computed at different stages of the numerical
integration with actual time levels; (ii) a conversion of pressure-related
variables between the model regimes derived from low Mach number asymptotics;
and (iii) a judicious selection of the pressure variables used in converting
numerical model states when a switch of models occurs. Idealised
two-dimensional travelling vortex and buoyancy-driven bubble convection
experiments show that acoustic imbalances arising from data assimilation can be
eliminated by using this blended model, thereby achieving balanced analysis
fields.
