  This paper contains the latest installment of the authors' project on
developing ensemble based data assimilation methodology for high dimensional
fluid dynamics models. The algorithm presented here is a particle filter that
combines model reduction, tempering, jittering, and nudging. The methodology is
tested on a two-layer quasi-geostrophic model for a $\beta$-plane channel flow
with $O(10^6)$ degrees of freedom out of which only a minute fraction are
noisily observed. The model is reduced by following the stochastic variational
approach for geophysical fluid dynamics introduced in Holm (Proc Roy Soc A,
2015) as a framework for deriving stochastic parametrisations for unresolved
scales. The reduction is substantial: the computations are done only for
$O(10^4)$ degrees of freedom. We introduce a stochastic time-stepping scheme
for the two-layer model and prove its consistency in time. Then, we analyze the
effect of the different procedures (tempering combined with jittering and
nudging) on the performance of the data assimilation procedure using the
reduced model, as well as how the dimension of the observational data (the
number of "weather stations") and the data assimilation step affect the
accuracy and uncertainty of the results.
