  A challenge arising from the local Bayesian assimilation of data in an
atmospheric flow simulation is the imbalances it may introduce. 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. (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 ensures that
a single time-step in the pseudo-incompressible regime is sufficient to filter
imbalances. 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. Travelling vortex and bubble
convection experiments show that the imbalance arising from assimilation of the
momentum fields can be eliminated by using this blended model, thereby
achieving balanced analysis fields. The leftover imbalance in the
thermodynamics can be quantified by scale analysis.
