  In a global numerical weather prediction (NWP) modeling framework we study
the implementation of Gaussian uncertainty of individual particles into the
assimilation step of a localized adaptive particle filter (LAPF). We obtain a
local representation of the prior distribution as a mixture of basis functions.
In the assimilation step, the filter calculates the individual weight
coefficients and new particle locations. It can be viewed as a combination of
the LAPF and a localized version of a Gaussian mixture filter, i.e., a
Localized Mixture Coefficients Particle Filter (LMCPF).
  Here, we investigate the feasibility of the LMCPF within a global operational
framework and evaluate the relationship between prior and posterior
distributions and observations. Our simulations are carried out in a standard
pre-operational experimental set-up with the full global observing system, 52
km global resolution and $10^6$ model variables. Statistics of particle
movement in the assimilation step are calculated. The mixture approach is able
to deal with the discrepancy between prior distributions and observation
location in a real-world framework and to pull the particles towards the
observations in a much better way than the pure LAPF. This shows that using
Gaussian uncertainty can be an important tool to improve the analysis and
forecast quality in a particle filter framework.
